Coded Aperture Imaging with Helico-Conical Beams

Coded Aperture Imaging with Helico-Conical Beams | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Coded Aperture Imaging with Helico-Conical Beams Harsh Vardhan, Shivasubramanian Gopinath, Vipin Tiwari, Aswathi K Sivarajan, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6847611/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Nov, 2025 Read the published version in Applied Physics B → Version 1 posted 12 You are reading this latest preprint version Abstract Interferenceless Coded Aperture Correlation Holography (I-COACH) has emerged as a powerful computational imaging technique for retrieving three-dimensional information from an object without requiring two-beam interference. In this study, we propose and experimentally demonstrate an I-COACH system employing a Helico-Conical Vortex (HCV) mask. The HCV mask carries orbital angular momentum and features a phase profile with non-separable dependence on both azimuthal and radial coordinates. It is generated by combining helical and conical phase functions, resulting in a spiral-shaped intensity distribution at the focal plane. We compare the performance of I-COACH with the HCV mask against other coded masks (CMs), including random lens, ring lens, higher-order Bessel beam generator, axicon, and spiral phase plate. Additionally, we evaluate image reconstruction using four widely adopted algorithms: non-linear reconstruction (NLR), Lucy-Richardson algorithm (LRA), Lucy-Richardson-Rosen algorithm (LRRA), and non-linear LRA (NL-LRA). Quantitative analysis is conducted using figures of merit such as entropy, root mean squared error (RMSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR). The proposed approach holds promise for advancing incoherent holography and computational imaging applications. helico-conical beams incoherent imaging computational imaging coded aperture imaging deconvolution diffractive optics digital holography Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Computational imaging (CI) is an emerging research domain with vast potential and wide-ranging applications [ 1 ]. A prominent sub-field of CI is coded aperture imaging (CAI), initially developed to overcome the challenges of fabricating lenses for non-visible electromagnetic regions such as gamma rays and X-rays [ 2 – 5 ]. CAI replaces traditional lens-based imaging with a two-step process: the object is first encoded using an optical system, followed by digital reconstruction of the image through computational algorithms [ 6 ]. Although this procedure resembles digital holography, the requirements and objectives differ significantly [ 7 ]. In digital holography, this two-step process captures three-dimensional spatial or phase information, depending on whether the source is incoherent or coherent, using a recorded hologram. Image reconstruction is then carried out via numerical backpropagation techniques [ 2 , 7 , 8 ]. CAI, on the other hand, achieves lensless imaging by first recording the point spread function (PSF) using a point source. This PSF is then used to computationally reconstruct the image of an object recorded under similar conditions. Research in CAI has primarily focused on two aspects: (1) improving the design and fabrication of coded masks (CMs), and (2) developing advanced reconstruction algorithms to enhance the signal-to-noise ratio (SNR) [ 9 ]. A variety of CMs including Fresnel zone apertures (FZA) [ 9 ], uniformly redundant arrays (URA) [ 4 ], modified URAs (MURA) [ 10 , 11 ], and scattering masks [ 12 ] have been explored to reach the performance of direct imaging systems. Early reconstruction relied on matched filtering, but this later evolved to include more robust methods such as phase-only filters [ 13 ], inverse filters [ 14 ], Wiener deconvolution [ 15 ], and the Lucy–Richardson algorithm [ 16 , 17 ]. These innovations aimed to push CAI performance closer to that of direct imaging, making CAI a viable alternative. The technology has also been extended to applications in spectral imaging and sensing [ 18 , 19 ]. A major breakthrough in CAI occurred with the development of interferenceless coded aperture correlation holography (I-COACH) in 2017, enabling three-dimensional imaging across spatial dimensions without the need for two-beam interference [ 20 ]. Since then, I-COACH has been applied in diverse contexts, including field-of-view expansion [ 21 ], depth-of-field engineering [ 22 ], partial aperture imaging [ 23 ], and imaging through scattering media [ 24 ]. However, conventional reconstruction methods are often inadequate when reconstructing complex objects composed of multiple depth planes. To address this, multi-shot approaches were proposed using complex PSFs processed via matched or phase-only filters—though these reduce temporal resolution. To enable high-speed imaging with improved SNR, advanced algorithms were introduced. The non-linear reconstruction (NLR) method enabled single-shot imaging but suffered from reduced SNR compared to direct imaging methods [ 25 ]. To overcome these limitations, the Lucy–Richardson–Rosen algorithm (LRRA) was introduced by integrating NLR into the classical Lucy–Richardson algorithm (LRA) [ 26 – 28 ]. This was further enhanced by the development of INDIA (Incoherent Nonlinear Deconvolution using an Iterative Algorithm) [ 29 ], which can improve the output of various reconstruction algorithms, although its performance depends on the quality of the initial reconstruction. Recently, two more non-linear LRA-based methods: NL-LRA1 and NL-LRA2, were proposed for reconstructing limited support images (LSI) and full-view images (FVI), respectively [ 30 ]. More recently, a recursive LRRA called interlooped LRRA (I-LRRA) and LR-Wiener deconvolution with reconstruction performances similar to that of LRRA were developed [ 31 ]. Meanwhile, optical vortices and structured light beams, particularly those carrying orbital angular momentum (OAM), have drawn increasing interest due to their unique phase singularities and azimuthal phase profiles [ 32 ]. Among these, helico-conical vortex (HCV) beams have recently shown promise in structured light applications. HCV beams feature a non-separable phase structure dependent on both radial and azimuthal coordinates and can be synthesized by combining helical and conical phase profiles, producing a spiral-shaped intensity distribution at the focal plane [ 33 , 34 ]. Motivated by these characteristics, we propose and experimentally demonstrate, for the first time to our knowledge, an I-COACH system using HCV beams. The resulting PSF exhibits a conically varying spiral vortex profile, offering new capabilities for image reconstruction in incoherent holography. The remainder of the manuscript is structured as follows: Section 2 presents the methodology and design of the phase masks; Section 3 details the experimental validation; and Section 4 provides concluding remarks and discusses future directions. 2. Methodology The imaging process of I-COACH system is depicted in Fig. 1 The light emitted or reflected from an object is collimated by a refractive lens and the collimated light is further modulated by a CM and the modulated light is then recorded by an image sensor. The PSF is recorded in advance and serve as a reconstruction function to retrieve information about the object. Various methods such as the matched filter, NLR, LRA, LRRA, and others are available for processing the PSF along with the object intensity distribution. The proposed analysis considers spatially incoherent illumination conditions. A point object with an amplitude of \(\:\sqrt{{I}_{s}}\) is positioned at \(\:\left({\stackrel{-}{r}}_{s};{z}_{s}\right)\) . The complex amplitude before the refractive lens with a phase of \(\:exp\left[i\pi\:{\left({z}_{s}\lambda\:\right)}^{-1}{R}^{2}\right]\) where \(\:R=\sqrt{\left({x}^{2}+{y}^{2}\right)}\) located at a distance of z s can be expressed as \(\:\sqrt{{I}_{\varvec{s}}}{C}_{1}L\left(\frac{\stackrel{-}{{r}_{s}}}{{z}_{s}}\right)Q\left(\frac{1}{{z}_{s}}\right)\) , where Q represents quadratic phase function which can be expressed as \(\:Q\left(b\right)=exp\left[i\pi\:b{\lambda\:}^{-1}{R}^{2}\right]\) , L represents the linear phase function and can be expressed as \(\:L\left(\frac{\stackrel{-}{s}}{z}\right)=exp\left[i2\pi\:{\left(\lambda\:z\right)}^{-1}\left({s}_{x}x+{s}_{y}y\right)\right]\) , C 1 is a complex constant. The complex amplitude after the refractive lens is \(\:\sqrt{{I}_{\varvec{s}}}{C}_{1}L\left(\frac{\stackrel{-}{{r}_{s}}}{{z}_{s}}\right)Q\left(\frac{1}{{z}_{s}}\right)exp\left[i\pi\:{\left({z}_{s}\lambda\:\right)}^{-1}{R}^{2}\right]\) . For simplicity, it is assumed that the refractive lens and the SLM are in tandem. The CM with a complex amplitude ψ PM is displayed on the SLM to generate the optical field of interest. The complex amplitude after the SLM can be expressed as \(\:\sqrt{{I}_{s}}{C}_{1}L\left(\frac{\stackrel{-}{{r}_{s}}}{{z}_{s}}\right){\psi\:}_{PM}\) , which propagates over a distance z h and captured by image sensor, with resulting intensity distribution given as: $$\:{I}_{PSF}\left({\stackrel{-}{r}}_{0};{\stackrel{-}{r}}_{s},\:{z}_{s}\right)={\left|\sqrt{{I}_{\varvec{s}}}{C}_{1}L\left(\frac{\stackrel{-}{{r}_{s}}}{{z}_{s}}\right){\psi\:}_{PM}\otimes\:Q\left(\frac{1}{{z}_{h}}\right)\right|}^{2}$$ 1 , where, \(\:{\stackrel{-}{r}}_{0}=\:\left(u,v\right)\) represents location vector in sensor plane, \(\:\otimes\:\) denotes the 2D convolution operator. In a system that is linear and shift-invariant, the \(\:{I}_{PSF}\) can be described as: $$\:{I}_{PSF}\left({\stackrel{-}{r}}_{0};{z}_{s}\right)={I}_{PSF}\left({\stackrel{-}{r}}_{0}-\frac{{z}_{h}}{{z}_{s}}{\stackrel{-}{r}}_{s};0,{z}_{s}\right)$$ 2 . Equation ( 2 ) represents shift invariance, indicating that the sensor plane intensity pattern is a shifted replica of the response generated when a point object is placed on the optical axis at \(\:{\stackrel{-}{r}}_{s}=0.\) The shift distance is \(\:\frac{{z}_{h}}{{z}_{s}}{\stackrel{-}{r}}_{s}\) . A two-dimensional object O composed of N point sources can be expressed mathematically as a sum of N Kronecker delta functions, as shown below: $$\:O\left({\stackrel{-}{r}}_{s}\right)={\sum\:}_{j}^{N}{a}_{j}\delta\:\left(\stackrel{-}{r}-{\stackrel{-}{r}}_{s,j}\right)$$ 3 , where, the amplitude of the corresponding point object with the label j is represented by the a j . Due to absence of spatial coherence, light diffracted from different points does not interfere, instead there is only a simple intensity addition which can be expressed as: $$\:{I}_{O}\left({\stackrel{-}{r}}_{0};{z}_{s}\right)={\sum\:}_{j}^{N}{a}_{j}{I}_{PSF}\left({\stackrel{-}{r}}_{0}-\frac{{z}_{h}}{{z}_{s}}{\stackrel{-}{r}}_{s,j};{z}_{s}\right)$$ 4 . The object O can be reconstructed by applying the deconvolution techniques to the recorded intensity I O and I PSF . Recently, two additional reconstruction algorithms, NL-LRA1 and NL-LRA2, have been introduced. NL-LRA1 target images with limited support, while NL-LRA2 is designed for full-view images by minimizing entropy [ 30 ]. The ( n + 1) th reconstructed image can be expressed as $$\:{I}_{R}^{n+1}={I}_{R}^{n}\left\{\frac{{I}_{O}}{{I}_{R}^{n}\otimes\:{I}_{PSF}}{⊚}_{\beta\:}^{\alpha\:}{I}_{PSF}\right\}$$ 5 , where ‘ \(\:A{⊚}_{\beta\:}^{\alpha\:}B\) ’ refers to \(\:{\mathcal{F}}^{-1}\left\{{\left|\stackrel{\sim}{A}\right|}^{\alpha\:}\text{e}\text{x}\text{p}\left[j\bullet\:\text{a}\text{r}\text{g}\left(\stackrel{\sim}{A}\right)\right]{\left|\stackrel{\sim}{B}\right|}^{\beta\:}\text{e}\text{x}\text{p}\left[-j\bullet\:\text{a}\text{r}\text{g}\left(\stackrel{\sim}{B}\right)\right]\right\}\) in which \(\:{\mathcal{F}}^{-1}\) is inverse Fourier transform operator and \(\:\stackrel{\sim}{I}\) is the Fourier transform of I . The parameters α and β are tuned between − 1 and + 1 and iterated m times until minimum entropy is obtained. 2.1 Design of coded masks The HCV beam represents a compelling advancement in the field of singular optics, offering new insights into the behavior of structured light fields with complex phase profiles. HCV beams carry OAM and exhibit a distinctive phase structure, resulting from the superposition of helical and conical phase components. This combination produces a spiral-shaped intensity distribution at the focal plane after undergoing a Fourier transform [ 33 ], [ 35 ]. Unlike traditional vortex beams such as Laguerre–Gaussian [ 32 ] and Bessel–Gaussian beams [ 36 ], HCV beams possess a non-separable dependence on both radial and angular coordinates. This non-separability imparts chiral characteristics and unique propagation dynamics, making HCV beams particularly suitable for applications in particle manipulation [ 37 ], [ 38 ], nanostructure fabrication [ 39 ], and optical metrology [ 40 ], [ 41 ]. In the far field, HCV beams display twisted phase and intensity distributions while maintaining a high photon density even at large values of topological charge [ 42 ]. The three-dimensional intensity distribution of HCV beams was first demonstrated in 2007 by Alonzo, and their self-healing properties were later investigated in 2013 [ 43 ]. Although HCV beams have found applications across various optical domains, to the best of our knowledge, this is the first time they have been applied in the context of CAI. The HCV mask and other CMs that have been used in the study can be generated by using the following mathematical equations: The phase of HCV mask is given as \(\:\psi\:\left(R,\:\theta\:\right)=l\theta\:\left(K-\frac{R}{{R}_{n}}\right)\) , where l denotes the topological charge, θ is the azimuth angle, K takes values 0 or 1, R is radial coordinate and R n is the constant used for normalization and the parameters were set to l = 15 and 20, K = 1, R = ( x 2 + y 2 ) 1/2 , R n = 1; random lens with a phase of \(\:\text{e}\text{x}\text{p}\left[-i\pi\:{\left(\lambda\:f\right)}^{-1}{R}^{2}\right]\times\:\text{e}\text{x}\text{p}\left[i{\varphi\:}_{\sigma\:}\left(x,y\right)\right]\) , where ϕ is random phase function and σ is scattering degree set at 0.05 and f = z h ; ring lens with a phase of \(\:\text{e}\text{x}\text{p}\left(-i2\pi\:{{\Lambda\:}}^{-1}R\right)\times\:\text{e}\text{x}\text{p}\left[-i\pi\:{\left(\lambda\:f\right)}^{-1}{R}^{2}\right]\) with Λ = 320 µm; spiral axicon with a phase of \(\:\text{e}\text{x}\text{p}\left(-i2\pi\:{{\Lambda\:}}^{-1}r\right)\times\:\text{e}\text{x}\text{p}\left(il\theta\:\right)\) with l = 5; axicon with a phase of \(\:exp\left(-i2\pi\:{{\Lambda\:}}^{-1}R\right)\) ; spiral lens with a phase of \(\:\text{e}\text{x}\text{p}\left[-i\pi\:{\left(\lambda\:f\right)}^{-1}{R}^{2}\right]\times\:exp\left(il\theta\:\right)\) . 3. Experimental analysis A photograph and schematic of the optical experimental setup employed for the experiments are displayed in Figs. 2 (a) and 2(b), respectively. The illumination in the set up is provided by a high-power red LED (Element 1) from Thorlabs (940 mW, λ = 660 nm, Δλ = 20 nm). An iris (Element 3) is used to control the illumination of light. The grating lines are eliminated and the background image of the electrodes from the LED is scattered using a diffuser (Element 4) made by Thorlabs (Ø1″ Ground Glass Diffuser-220 GRIT). A refractive lens (Element 5) with a 7.5 cm focal length collimates the light from the diffuser. The collimated light passes through a polarizer (Element 6), which is aligned with the active axis of the SLM (Element 11) from Thorlabs (Exulus HD2, 1920 × 1200 pixels, pixel size: 8 µm). A refractive lens (Element 7) with a 5 cm focal length accumulates the light from the polarizer and critically illuminates the pinhole or object (R1DS1N − Negative 1951 USAF Test Target, Ø1″) (Element 7). For this demonstration, a 50 µm pinhole and the numeric object digits ‘2’ and ‘1’ from Group (5) of the test target were utilized. A refractive lens (Element 9) with a 5 cm focal length is used to collimate the light from the pinhole or object. Next, the iris limits the luminance of the light. The collimated light is directed to the beam splitter (Element 10), where it is incident on the SLM. The coded masks shown in Fig. 3 (a) (row 1) were sequentially displayed on the SLM, and the corresponding I PSF and I O were captured by an image sensor (Element 13) from Thorlabs (Zelux CS165MU/M, 1.6 MP monochrome CMOS camera, 1440 × 1080 pixels, pixel size ~ 3.5 µm), positioned 18 cm away from the SLM. Figure 3 illustrates the experimental outcomes for a single numeric ‘digit 2’object. This study made use of a variety of phase-only CMs, including a HCV mask of topological charge ( l = 15; 20), random lens, ring lens, spiral axicon ( l = 5), diffractive axicon, and spiral lens ( l = 5). Figure 3 (row1) depicts the CMs sequentially. Rows 2 and 3 of Fig. 3 illustrates the recorded I PSF and I O at z s = 5 cm. The reconstructed results corresponding to the NLR, LRA, LRRA and NL-LRA1 are presented in rows 4–7 of Fig. 3 . Figure 3 at the bottom depicts the direct image of object. Research in CAI primarily aims to enhance image quality, striving to match or exceed the performance of conventional direct imaging systems. These improvements are generally pursued via two main strategies: (1) optimizing the design of coded masks (CMs) or (2) developing advanced reconstruction algorithms to better retrieve the original image. In this study, we focus on the former by exploring an unconventional CM design namely, the HCV mask with two different topological charges as part of a preliminary investigation. The HCV mask introduces a unique phase encoding structure that distinguishes it from traditional CMs and, to our knowledge, is applied for the first time in the context of CAI. Our reconstruction results indicate that the HCV mask with dual topological charges yields comparable or superior performance relative to existing CMs. To quantitatively evaluate the reconstruction quality, we computed several metrics: entropy, root mean square error (RMSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR). The corresponding results are summarized in Tables 1 – 4 , and visualized in Figs. 4 (a)–4(d). The bar plots illustrate that the HCV mask performs on par with, or better than, conventional masks, thereby validating its effectiveness in image reconstruction within CAI frameworks. Table 1 Entropy analysis of the DOEs under different reconstruction techniques. Entropy NLR LRA LRRA NL-LRA1 HCV ( l = 15) 3.7865 0.426 0.7647 0.2872 HCV ( l = 20) 4.2269 0.4804 0.8455 0.2947 Random Lens 4.9069 0.8206 1.2018 0.3229 Ring Lens 5.0645 0.6598 0.9213 0.3063 Spiral Axicon ( l = 5) 4.5157 0.6339 1.8645 0.3029 Axicon 4.4135 0.6024 1.5588 0.306 Spiral Lens ( l = 5) 4.2901 0.4573 0.7424 0.3151 Table 2 RMSE analysis of the DOEs under different reconstruction techniques. RMSE NLR LRA LRRA NL-LRA1 HCV ( l = 15) 0.049 0.0613 0.0457 0.0555 HCV ( l = 20) 0.0559 0.057 0.0401 0.0514 Random Lens 0.0986 0.0307 0.0316 0.0312 Ring Lens 0.0769 0.0476 0.0409 0.0512 Spiral Axicon ( l = 5) 0.0668 0.0622 0.0476 0.0484 Axicon 0.0608 0.0604 0.0413 0.0436 Spiral Lens ( l = 5) 0.0687 0.0506 0.0383 0.0402 Table 3 SSIM analysis of the DOEs under different reconstruction techniques. SSIM NLR LRA LRRA NL-LRA1 HCV ( l = 15) 0.5171 0.9497 0.952 0.9603 HCV ( l = 20) 0.4317 0.9502 0.9535 0.9619 Random Lens 0.2806 0.9791 0.9572 0.9638 Ring Lens 0.2619 0.9482 0.9618 0.9613 Spiral Axicon ( l = 5) 0.151 0.9569 0.9052 0.9619 Axicon 0.158 0.9506 0.9341 0.9636 Spiral Lens ( l = 5) 0.4033 0.9545 0.9664 0.9625 Table 4 PSNR analysis of the DOEs under different reconstruction techniques. PSNR NLR LRA LRRA NL-LRA1 HCV ( l = 15) 26.2019 24.2475 26.7934 25.1108 HCV ( l = 20) 25.0587 24.8834 27.9338 25.7771 Random Lens 20.1188 30.2434 30.0073 30.1185 Ring Lens 22.2791 26.4547 27.7633 25.8134 Spiral Axicon ( l = 5) 23.5011 24.1175 26.4403 26.3076 Axicon 24.3223 24.3763 27.6894 27.2179 Spiral Lens ( l = 5) 23.2553 25.9156 28.3399 27.9242 The experimental results for the other number ‘1’ at a different plane at z s = 5.2 cm are displayed in the Fig. 5 . The object and PSF are recorded at two different planes to demonstrate 3D imaging through summation. Figure 5 (row 2 & 3) illustrates the I PSF and I O for the HCV ( l = 15; l = 20), random lens, ring lens, spiral axicon ( l = 5), axicon, and spiral lens ( l = 5). The reconstruction outcomes for NLR, LRA, LRRA, and NL-LRA1 are shown in rows 4, 5, 6, and 7, respectively. A direct image of the object is shown at the bottom of Fig. 5 . To evaluate the results of all the reconstruction techniques discussed, Entropy, RMSE, SSIM and PSNR were computed for each case, as given in Table 5 to Table 8 . The entropy, RMSE, SSIM and PSNR graphs that correspond to Tables 5 and 8 are displayed in Figs. 6 (a) and 6(d). Table 5 Entropy analysis of the DOEs under different reconstruction techniques. Entropy NLR LRA LRRA NL-LRA1 HCV ( l = 15) 5.2303 0.2572 0.6938 0.1927 HCV ( l = 20) 5.1309 0.2439 0.6836 0.1937 Random Lens 4.9286 0.5325 1.4844 0.196 Ring Lens 2.7482 0.2817 0.4782 0 Spiral Axicon ( l = 5) 4.5962 0.4042 1.0262 0.1891 Axicon 4.6083 0.359 0.4821 0.182 Spiral Lens ( l = 5) 5.5412 0.417 1.0519 0.1959 Table 6 RMSE analysis of the DOEs under different reconstruction techniques. RMSE NLR LRA LRRA NL-LRA1 HCV ( l = 15) 0.0849 0.0371 0.0366 0.0379 HCV ( l = 20) 0.0793 0.0371 0.0322 0.0358 Random Lens 0.1094 0.0172 0.036 0.027 Ring Lens 0.0257 0.0366 0.0267 NaN Spiral Axicon ( l = 5) 0.0562 0.0386 0.0334 0.0294 Axicon 0.0524 0.0371 0.0331 0.0311 Spiral Lens ( l = 5) 0.0909 0.0246 0.0214 0.02 Table 7 SSIM analysis of the DOEs under different reconstruction techniques. SSIM NLR LRA LRRA NL-LRA1 HCV( l = 15) 0.226 0.9817 0.971 0.9778 HCV( l = 20) 0.2409 0.9811 0.9734 0.9786 Random Lens 0.304 0.9817 0.9051 0.9793 Ring Lens 0.7328 0.9773 0.9861 NaN Spiral Axicon ( l = 5) 0.1075 0.9749 0.9559 0.9794 Axicon 0.0905 0.9745 0.9799 0.978 Spiral Lens ( l = 5) 0.173 0.9874 0.9542 0.9803 Table 8 PSNR analysis of the DOEs under different reconstruction techniques. PSNR NLR LRA LRRA NL-LRA1 HCV ( l = 15) 21.4259 28.6238 28.734 28.433 HCV ( l = 20) 22.0095 28.6023 29.8467 28.9211 Random Lens 19.2201 35.2739 28.875 31.3874 Ring Lens 31.7945 28.7254 31.4679 NaN Spiral Axicon ( l = 5) 25.0024 28.2695 29.5184 30.6218 Axicon 25.6162 28.6231 29.5975 30.1405 Spiral Lens ( l = 5) 20.8299 32.192 33.3819 33.9977 4. Conclusion In conclusion, we have implemented the Helico-conical vortex CM in the framework of I-COACH system for the first time and compared its performance with the existing phase masks. The object hologram and point spread function were recorded at two different planes to verify the three-dimensional capabilities. The experimental demonstration confirms the effectiveness of the proposed phase mask in I-COACH system. The reconstruction efficacy of the proposed mask is either better or comparable to the other phase masks. Furthermore, the effect of TC of the HCV is also discussed with two values, l = 15 and 20 by keeping other parameters unchanged. The results were slightly better with l = 20 in case of LRA and LRRA reconstruction whereas the reconstruction was better with l = 15 in the case of NLR and NL-LRA1. The results indicate that one should choose the phase mask and reconstruction algorithm consciously depending on their application. In future, the non-separable dependence on both azimuthal and radial coordinates property of HCV can be further explored for improving the resolution and contrast in OAM holography. We strongly believe that the HCV coded mask holds great potential for applications in incoherent digital holography, coded aperture imaging (CAI), quantum optics and communication, etc. Declarations Funding: RK would like to acknowledge the support from the Science and Engineering Research Board (SERB), the Government of India, under the SERB SURE research grant (File No. SUR/2022/000910) and SRM University – AP for seed grant SRMAP/URG/SEED/2024-25/041. SG, VT and VA acknowledge the European Union’s Horizon 2020 research and innovation programme grant agreement No. 857627 (CIPHR). Author Contribution H.V. and A.K.S.: Methodology, Software, Investigation, Writing – original draft, Visualization; S.G. and V.T.: Experiments, Investigations, analysis; S.C.: Investigations, Writing – review & editing, Visualization. S.G.R.: Conceptualization, Writing – review & editing, Supervision, Resources. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6847611","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471639309,"identity":"1842a7ea-9eee-4433-a160-2136798d50aa","order_by":0,"name":"Harsh Vardhan","email":"","orcid":"","institution":"SRM University-AP","correspondingAuthor":false,"prefix":"","firstName":"Harsh","middleName":"","lastName":"Vardhan","suffix":""},{"id":471639310,"identity":"93d12037-9106-4869-8be5-d8618f63afe1","order_by":1,"name":"Shivasubramanian Gopinath","email":"","orcid":"","institution":"University of Tartu","correspondingAuthor":false,"prefix":"","firstName":"Shivasubramanian","middleName":"","lastName":"Gopinath","suffix":""},{"id":471639311,"identity":"7ee4bf79-6a70-4ca7-9cab-eb1b0a65744f","order_by":2,"name":"Vipin Tiwari","email":"","orcid":"","institution":"University of Tartu","correspondingAuthor":false,"prefix":"","firstName":"Vipin","middleName":"","lastName":"Tiwari","suffix":""},{"id":471639312,"identity":"fe09f9ef-6e07-4cf9-91b7-9108dbc03ada","order_by":3,"name":"Aswathi K Sivarajan","email":"","orcid":"","institution":"SRM University-AP","correspondingAuthor":false,"prefix":"","firstName":"Aswathi","middleName":"K","lastName":"Sivarajan","suffix":""},{"id":471639313,"identity":"5f60f045-755d-417f-b226-288cc55973b6","order_by":4,"name":"Sakshi Choudhary","email":"","orcid":"","institution":"SRM University-AP","correspondingAuthor":false,"prefix":"","firstName":"Sakshi","middleName":"","lastName":"Choudhary","suffix":""},{"id":471639314,"identity":"a6c938ac-7e9f-4136-8581-80ec152abac4","order_by":5,"name":"Salla Gangi Reddy","email":"","orcid":"","institution":"SRM University-AP","correspondingAuthor":false,"prefix":"","firstName":"Salla","middleName":"Gangi","lastName":"Reddy","suffix":""},{"id":471639315,"identity":"e0c6c067-030d-4727-8e89-69778d92b695","order_by":6,"name":"Vijayakumar Anand","email":"","orcid":"","institution":"University of Tartu","correspondingAuthor":false,"prefix":"","firstName":"Vijayakumar","middleName":"","lastName":"Anand","suffix":""},{"id":471639316,"identity":"c61280c6-6f18-4234-83a9-5a3e25c1cfc9","order_by":7,"name":"Ravi Kumar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYFAC5gOH/1SwyYGYBx4Qp4Ut8QHPGT5jsJYE4rTwGBvwtsklNoDYRGkxn5FgJiHBZpY+P+zwQ6AtdnK6DQS0yNxISJMw4EnL3Xg7zQCoJdnY7AABLRISCcckEiSO5W6cnQDSciBxG2EtiW0SBwz+pxvOTv9ArJZkZsOGBLYEeekcYm3hecb4mOEAm+EG6ZyCAwkGxPiFPf/DYcZ/bPLys9M3f/hQYSdHUAuDQAKENgCrNCCkHAT4oYbKNxCjehSMglEwCkYkAAAeD0U3K8JuTAAAAABJRU5ErkJggg==","orcid":"","institution":"SRM University-AP","correspondingAuthor":true,"prefix":"","firstName":"Ravi","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2025-06-08 13:08:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6847611/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6847611/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00340-025-08585-x","type":"published","date":"2025-11-10T15:56:49+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":85361831,"identity":"7a50a157-f980-4849-88cd-61e23ca9ab91","added_by":"auto","created_at":"2025-06-25 06:12:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":293820,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the optical recording setup and computational reconstruction.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/0069f0ac72726db009663f9f.png"},{"id":85360688,"identity":"cd5982b9-0678-4d2b-baa7-44e3db8f1557","added_by":"auto","created_at":"2025-06-25 06:04:13","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":970183,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic and (b) photograph illustrating the experimental components used in I-COACH system. (1) Red LED source; (2) LED Power controller; (3) iris; (4) diffuser; (5) refractive lens (\u003cem\u003ef\u003c/em\u003e=7.5cm); (6) polarizer; (7) refractive lens (\u003cem\u003ef\u003c/em\u003e =5cm); (8) pinhole/object; (9) refractive lens \u003cem\u003e(f\u003c/em\u003e=5cm); (10) beam splitter; (11) spatial light modulator (SLM); (13) image sensor.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/9030e0c637797f23197426bf.jpeg"},{"id":85360689,"identity":"695be673-5f34-49dc-8238-f31fbf39b5ed","added_by":"auto","created_at":"2025-06-25 06:04:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":361623,"visible":true,"origin":"","legend":"\u003cp\u003eRow1: Coded masks; Row2: Intensity of point spread function (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e); Row 3 Object hologram (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e); Row4 – Row7 Reconstruction of image by NLR, LRA, LRRA, NL-LRA1; At the bottom, the direct image of the object is given.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/67eac52f36397bb193e576d7.png"},{"id":85360687,"identity":"1b82620f-1d63-48a9-8c63-c182bafb62aa","added_by":"auto","created_at":"2025-06-25 06:04:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":193690,"visible":true,"origin":"","legend":"\u003cp\u003ePlots of Entropy, RMSE, SSIM and PSNR for HCV (\u003cem\u003el\u003c/em\u003e=15; 20), random lens, ring lens, spiral axicon(\u003cem\u003el\u003c/em\u003e=5), axicon, spiral lens (\u003cem\u003el\u003c/em\u003e=5) are illustrated in (a - d) and for quantitative analysis the corresponding values are depicted in Table 1 to Table 4 presented below.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/f5b436ebb197fa90f34f6bee.png"},{"id":85361832,"identity":"786cd33b-f4c0-4cae-951e-7345b3c99682","added_by":"auto","created_at":"2025-06-25 06:12:13","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":360926,"visible":true,"origin":"","legend":"\u003cp\u003eRow1: Coded masks; Row2: Intensity of point spread function (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e); Row 3 Object hologram (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e); Row4 – Row7 Reconstruction of image by NLR, LRA, LRRA, NL-LRA1; At the bottom, the direct image of the object is given.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/ef96ad1fd36cb33b343da054.png"},{"id":85362319,"identity":"7ec958f0-3c50-4089-a75e-21d76196f362","added_by":"auto","created_at":"2025-06-25 06:20:13","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":218125,"visible":true,"origin":"","legend":"\u003cp\u003ePlots of Entropy, RMSE, SSIM and PSNR for HCV (\u003cem\u003el\u003c/em\u003e=15; 20), random lens, ring lens, spiral axicon(\u003cem\u003el\u003c/em\u003e=5), axicon, spiral lens (\u003cem\u003el\u003c/em\u003e=5) are illustrated in (a - d) and for quantitative analysis the corresponding values are depicted in Table 5 to Table 8 presented below.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/ebf66f30770bf3541a496492.png"},{"id":96104913,"identity":"b2491a52-3c24-415a-9183-ae40f6478713","added_by":"auto","created_at":"2025-11-17 15:59:22","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3300346,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6847611/v1/0f35b660-312c-44cf-82f2-4056c70a07f9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Coded Aperture Imaging with Helico-Conical Beams","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eComputational imaging (CI) is an emerging research domain with vast potential and wide-ranging applications [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A prominent sub-field of CI is coded aperture imaging (CAI), initially developed to overcome the challenges of fabricating lenses for non-visible electromagnetic regions such as gamma rays and X-rays [\u003cspan additionalcitationids=\"CR3 CR4\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. CAI replaces traditional lens-based imaging with a two-step process: the object is first encoded using an optical system, followed by digital reconstruction of the image through computational algorithms [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Although this procedure resembles digital holography, the requirements and objectives differ significantly [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn digital holography, this two-step process captures three-dimensional spatial or phase information, depending on whether the source is incoherent or coherent, using a recorded hologram. Image reconstruction is then carried out via numerical backpropagation techniques [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. CAI, on the other hand, achieves lensless imaging by first recording the point spread function (PSF) using a point source. This PSF is then used to computationally reconstruct the image of an object recorded under similar conditions.\u003c/p\u003e \u003cp\u003eResearch in CAI has primarily focused on two aspects: (1) improving the design and fabrication of coded masks (CMs), and (2) developing advanced reconstruction algorithms to enhance the signal-to-noise ratio (SNR) [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. A variety of CMs including Fresnel zone apertures (FZA) [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], uniformly redundant arrays (URA) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], modified URAs (MURA) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and scattering masks [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] have been explored to reach the performance of direct imaging systems. Early reconstruction relied on matched filtering, but this later evolved to include more robust methods such as phase-only filters [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], inverse filters [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], Wiener deconvolution [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], and the Lucy\u0026ndash;Richardson algorithm [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThese innovations aimed to push CAI performance closer to that of direct imaging, making CAI a viable alternative. The technology has also been extended to applications in spectral imaging and sensing [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eA major breakthrough in CAI occurred with the development of interferenceless coded aperture correlation holography (I-COACH) in 2017, enabling three-dimensional imaging across spatial dimensions without the need for two-beam interference [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Since then, I-COACH has been applied in diverse contexts, including field-of-view expansion [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], depth-of-field engineering [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], partial aperture imaging [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], and imaging through scattering media [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eHowever, conventional reconstruction methods are often inadequate when reconstructing complex objects composed of multiple depth planes. To address this, multi-shot approaches were proposed using complex PSFs processed via matched or phase-only filters\u0026mdash;though these reduce temporal resolution. To enable high-speed imaging with improved SNR, advanced algorithms were introduced. The non-linear reconstruction (NLR) method enabled single-shot imaging but suffered from reduced SNR compared to direct imaging methods [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo overcome these limitations, the Lucy\u0026ndash;Richardson\u0026ndash;Rosen algorithm (LRRA) was introduced by integrating NLR into the classical Lucy\u0026ndash;Richardson algorithm (LRA) [\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This was further enhanced by the development of INDIA (Incoherent Nonlinear Deconvolution using an Iterative Algorithm) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], which can improve the output of various reconstruction algorithms, although its performance depends on the quality of the initial reconstruction. Recently, two more non-linear LRA-based methods: NL-LRA1 and NL-LRA2, were proposed for reconstructing limited support images (LSI) and full-view images (FVI), respectively [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. More recently, a recursive LRRA called interlooped LRRA (I-LRRA) and LR-Wiener deconvolution with reconstruction performances similar to that of LRRA were developed [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMeanwhile, optical vortices and structured light beams, particularly those carrying orbital angular momentum (OAM), have drawn increasing interest due to their unique phase singularities and azimuthal phase profiles [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Among these, helico-conical vortex (HCV) beams have recently shown promise in structured light applications. HCV beams feature a non-separable phase structure dependent on both radial and azimuthal coordinates and can be synthesized by combining helical and conical phase profiles, producing a spiral-shaped intensity distribution at the focal plane [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMotivated by these characteristics, we propose and experimentally demonstrate, for the first time to our knowledge, an I-COACH system using HCV beams. The resulting PSF exhibits a conically varying spiral vortex profile, offering new capabilities for image reconstruction in incoherent holography.\u003c/p\u003e \u003cp\u003eThe remainder of the manuscript is structured as follows: Section 2 presents the methodology and design of the phase masks; Section 3 details the experimental validation; and Section 4 provides concluding remarks and discusses future directions.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eThe imaging process of I-COACH system is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e The light emitted or reflected from an object is collimated by a refractive lens and the collimated light is further modulated by a CM and the modulated light is then recorded by an image sensor. The PSF is recorded in advance and serve as a reconstruction function to retrieve information about the object. Various methods such as the matched filter, NLR, LRA, LRRA, and others are available for processing the PSF along with the object intensity distribution. The proposed analysis considers spatially incoherent illumination conditions. A point object with an amplitude of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{{I}_{s}}\\)\u003c/span\u003e\u003c/span\u003e is positioned at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\stackrel{-}{r}}_{s};{z}_{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e. The complex amplitude before the refractive lens with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:exp\\left[i\\pi\\:{\\left({z}_{s}\\lambda\\:\\right)}^{-1}{R}^{2}\\right]\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R=\\sqrt{\\left({x}^{2}+{y}^{2}\\right)}\\)\u003c/span\u003e\u003c/span\u003e located at a distance of \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e can be expressed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{{I}_{\\varvec{s}}}{C}_{1}L\\left(\\frac{\\stackrel{-}{{r}_{s}}}{{z}_{s}}\\right)Q\\left(\\frac{1}{{z}_{s}}\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eQ\u003c/em\u003e represents quadratic phase function which can be expressed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\left(b\\right)=exp\\left[i\\pi\\:b{\\lambda\\:}^{-1}{R}^{2}\\right]\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003eL\u003c/em\u003e represents the linear phase function and can be expressed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\left(\\frac{\\stackrel{-}{s}}{z}\\right)=exp\\left[i2\\pi\\:{\\left(\\lambda\\:z\\right)}^{-1}\\left({s}_{x}x+{s}_{y}y\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e is a complex constant. The complex amplitude after the refractive lens is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{{I}_{\\varvec{s}}}{C}_{1}L\\left(\\frac{\\stackrel{-}{{r}_{s}}}{{z}_{s}}\\right)Q\\left(\\frac{1}{{z}_{s}}\\right)exp\\left[i\\pi\\:{\\left({z}_{s}\\lambda\\:\\right)}^{-1}{R}^{2}\\right]\\)\u003c/span\u003e\u003c/span\u003e. For simplicity, it is assumed that the refractive lens and the SLM are in tandem. The CM with a complex amplitude \u003cem\u003eψ\u003c/em\u003e\u003csub\u003e\u003cem\u003ePM\u003c/em\u003e\u003c/sub\u003e is displayed on the SLM to generate the optical field of interest. The complex amplitude after the SLM can be expressed as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sqrt{{I}_{s}}{C}_{1}L\\left(\\frac{\\stackrel{-}{{r}_{s}}}{{z}_{s}}\\right){\\psi\\:}_{PM}\\)\u003c/span\u003e\u003c/span\u003e, which propagates over a distance \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e and captured by image sensor, with resulting intensity distribution given as:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{I}_{PSF}\\left({\\stackrel{-}{r}}_{0};{\\stackrel{-}{r}}_{s},\\:{z}_{s}\\right)={\\left|\\sqrt{{I}_{\\varvec{s}}}{C}_{1}L\\left(\\frac{\\stackrel{-}{{r}_{s}}}{{z}_{s}}\\right){\\psi\\:}_{PM}\\otimes\\:Q\\left(\\frac{1}{{z}_{h}}\\right)\\right|}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{r}}_{0}=\\:\\left(u,v\\right)\\)\u003c/span\u003e\u003c/span\u003e represents location vector in sensor plane, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\otimes\\:\\)\u003c/span\u003e\u003c/span\u003e denotes the 2D convolution operator.\u003c/p\u003e \u003cp\u003eIn a system that is linear and shift-invariant, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{I}_{PSF}\\)\u003c/span\u003e\u003c/span\u003e can be described as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{I}_{PSF}\\left({\\stackrel{-}{r}}_{0};{z}_{s}\\right)={I}_{PSF}\\left({\\stackrel{-}{r}}_{0}-\\frac{{z}_{h}}{{z}_{s}}{\\stackrel{-}{r}}_{s};0,{z}_{s}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eEquation (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) represents shift invariance, indicating that the sensor plane intensity pattern is a shifted replica of the response generated when a point object is placed on the optical axis at \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{r}}_{s}=0.\\)\u003c/span\u003e\u003c/span\u003e The shift distance is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{z}_{h}}{{z}_{s}}{\\stackrel{-}{r}}_{s}\\)\u003c/span\u003e\u003c/span\u003e. A two-dimensional object \u003cem\u003eO\u003c/em\u003e composed of \u003cem\u003eN\u003c/em\u003e point sources can be expressed mathematically as a sum of \u003cem\u003eN\u003c/em\u003e Kronecker delta functions, as shown below:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:O\\left({\\stackrel{-}{r}}_{s}\\right)={\\sum\\:}_{j}^{N}{a}_{j}\\delta\\:\\left(\\stackrel{-}{r}-{\\stackrel{-}{r}}_{s,j}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere, the amplitude of the corresponding point object with the label \u003cem\u003ej\u003c/em\u003e is represented by the \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e. Due to absence of spatial coherence, light diffracted from different points does not interfere, instead there is only a simple intensity addition which can be expressed as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{I}_{O}\\left({\\stackrel{-}{r}}_{0};{z}_{s}\\right)={\\sum\\:}_{j}^{N}{a}_{j}{I}_{PSF}\\left({\\stackrel{-}{r}}_{0}-\\frac{{z}_{h}}{{z}_{s}}{\\stackrel{-}{r}}_{s,j};{z}_{s}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eThe object \u003cem\u003eO\u003c/em\u003e can be reconstructed by applying the deconvolution techniques to the recorded intensity \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e. Recently, two additional reconstruction algorithms, NL-LRA1 and NL-LRA2, have been introduced. NL-LRA1 target images with limited support, while NL-LRA2 is designed for full-view images by minimizing entropy [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe (\u003cem\u003en\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1)\u003csup\u003eth\u003c/sup\u003e reconstructed image can be expressed as\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{I}_{R}^{n+1}={I}_{R}^{n}\\left\\{\\frac{{I}_{O}}{{I}_{R}^{n}\\otimes\\:{I}_{PSF}}{⊚}_{\\beta\\:}^{\\alpha\\:}{I}_{PSF}\\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u0026lsquo;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A{⊚}_{\\beta\\:}^{\\alpha\\:}B\\)\u003c/span\u003e\u003c/span\u003e\u0026rsquo; refers to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathcal{F}}^{-1}\\left\\{{\\left|\\stackrel{\\sim}{A}\\right|}^{\\alpha\\:}\\text{e}\\text{x}\\text{p}\\left[j\\bullet\\:\\text{a}\\text{r}\\text{g}\\left(\\stackrel{\\sim}{A}\\right)\\right]{\\left|\\stackrel{\\sim}{B}\\right|}^{\\beta\\:}\\text{e}\\text{x}\\text{p}\\left[-j\\bullet\\:\\text{a}\\text{r}\\text{g}\\left(\\stackrel{\\sim}{B}\\right)\\right]\\right\\}\\)\u003c/span\u003e\u003c/span\u003e in which \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathcal{F}}^{-1}\\)\u003c/span\u003e\u003c/span\u003e is inverse Fourier transform operator and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{\\sim}{I}\\)\u003c/span\u003e\u003c/span\u003e is the Fourier transform of \u003cem\u003eI\u003c/em\u003e. The parameters \u003cem\u003eα\u003c/em\u003e and \u003cem\u003eβ\u003c/em\u003e are tuned between \u0026minus;\u0026thinsp;1 and +\u0026thinsp;1 and iterated \u003cem\u003em\u003c/em\u003e times until minimum entropy is obtained.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Design of coded masks\u003c/h2\u003e \u003cp\u003eThe HCV beam represents a compelling advancement in the field of singular optics, offering new insights into the behavior of structured light fields with complex phase profiles. HCV beams carry OAM and exhibit a distinctive phase structure, resulting from the superposition of helical and conical phase components. This combination produces a spiral-shaped intensity distribution at the focal plane after undergoing a Fourier transform [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Unlike traditional vortex beams such as Laguerre\u0026ndash;Gaussian [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and Bessel\u0026ndash;Gaussian beams [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], HCV beams possess a non-separable dependence on both radial and angular coordinates. This non-separability imparts chiral characteristics and unique propagation dynamics, making HCV beams particularly suitable for applications in particle manipulation [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], nanostructure fabrication [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], and optical metrology [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the far field, HCV beams display twisted phase and intensity distributions while maintaining a high photon density even at large values of topological charge [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. The three-dimensional intensity distribution of HCV beams was first demonstrated in 2007 by Alonzo, and their self-healing properties were later investigated in 2013 [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. Although HCV beams have found applications across various optical domains, to the best of our knowledge, this is the first time they have been applied in the context of CAI.\u003c/p\u003e \u003cp\u003eThe HCV mask and other CMs that have been used in the study can be generated by using the following mathematical equations: The phase of HCV mask is given as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\psi\\:\\left(R,\\:\\theta\\:\\right)=l\\theta\\:\\left(K-\\frac{R}{{R}_{n}}\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003el\u003c/em\u003e denotes the topological charge, \u003cem\u003eθ\u003c/em\u003e is the azimuth angle, \u003cem\u003eK\u003c/em\u003e takes values 0 or 1, \u003cem\u003eR\u003c/em\u003e is radial coordinate and \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e is the constant used for normalization and the parameters were set to \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15 and 20, \u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, \u003cem\u003eR\u003c/em\u003e = (\u003cem\u003ex\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003ey\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e)\u003csup\u003e1/2\u003c/sup\u003e, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e = 1; random lens with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{e}\\text{x}\\text{p}\\left[-i\\pi\\:{\\left(\\lambda\\:f\\right)}^{-1}{R}^{2}\\right]\\times\\:\\text{e}\\text{x}\\text{p}\\left[i{\\varphi\\:}_{\\sigma\\:}\\left(x,y\\right)\\right]\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eϕ\u003c/em\u003e is random phase function and \u003cem\u003eσ\u003c/em\u003e is scattering degree set at 0.05 and \u003cem\u003ef\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e; ring lens with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{e}\\text{x}\\text{p}\\left(-i2\\pi\\:{{\\Lambda\\:}}^{-1}R\\right)\\times\\:\\text{e}\\text{x}\\text{p}\\left[-i\\pi\\:{\\left(\\lambda\\:f\\right)}^{-1}{R}^{2}\\right]\\)\u003c/span\u003e\u003c/span\u003e with \u003cem\u003eΛ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;320 \u0026micro;m; spiral axicon with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{e}\\text{x}\\text{p}\\left(-i2\\pi\\:{{\\Lambda\\:}}^{-1}r\\right)\\times\\:\\text{e}\\text{x}\\text{p}\\left(il\\theta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e with \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5; axicon with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:exp\\left(-i2\\pi\\:{{\\Lambda\\:}}^{-1}R\\right)\\)\u003c/span\u003e\u003c/span\u003e; spiral lens with a phase of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{e}\\text{x}\\text{p}\\left[-i\\pi\\:{\\left(\\lambda\\:f\\right)}^{-1}{R}^{2}\\right]\\times\\:exp\\left(il\\theta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Experimental analysis","content":"\u003cp\u003eA photograph and schematic of the optical experimental setup employed for the experiments are displayed in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) and 2(b), respectively. The illumination in the set up is provided by a high-power red LED (Element 1) from Thorlabs (940 mW, λ\u0026thinsp;=\u0026thinsp;660 nm, Δλ\u0026thinsp;=\u0026thinsp;20 nm). An iris (Element 3) is used to control the illumination of light. The grating lines are eliminated and the background image of the electrodes from the LED is scattered using a diffuser (Element 4) made by Thorlabs (\u0026Oslash;1\u0026Prime; Ground Glass Diffuser-220 GRIT). A refractive lens (Element 5) with a 7.5 cm focal length collimates the light from the diffuser. The collimated light passes through a polarizer (Element 6), which is aligned with the active axis of the SLM (Element 11) from Thorlabs (Exulus HD2, 1920 \u0026times; 1200 pixels, pixel size: 8 \u0026micro;m). A refractive lens (Element 7) with a 5 cm focal length accumulates the light from the polarizer and critically illuminates the pinhole or object (R1DS1N\u0026thinsp;\u0026minus;\u0026thinsp;Negative 1951 USAF Test Target, \u0026Oslash;1\u0026Prime;) (Element 7). For this demonstration, a 50 \u0026micro;m pinhole and the numeric object digits \u0026lsquo;2\u0026rsquo; and \u0026lsquo;1\u0026rsquo; from Group (5) of the test target were utilized. A refractive lens (Element 9) with a 5 cm focal length is used to collimate the light from the pinhole or object. Next, the iris limits the luminance of the light. The collimated light is directed to the beam splitter (Element 10), where it is incident on the SLM. The coded masks shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) (row 1) were sequentially displayed on the SLM, and the corresponding \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e were captured by an image sensor (Element 13) from Thorlabs (Zelux CS165MU/M, 1.6 MP monochrome CMOS camera, 1440 \u0026times; 1080 pixels, pixel size\u0026thinsp;~\u0026thinsp;3.5 \u0026micro;m), positioned 18 cm away from the SLM.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the experimental outcomes for a single numeric \u0026lsquo;digit 2\u0026rsquo;object. This study made use of a variety of phase-only CMs, including a HCV mask of topological charge (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15; 20), random lens, ring lens, spiral axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5), diffractive axicon, and spiral lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (row1) depicts the CMs sequentially.\u003c/p\u003e \u003cp\u003eRows 2 and 3 of Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the recorded \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e at \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e = 5 cm. The reconstructed results corresponding to the NLR, LRA, LRRA and NL-LRA1 are presented in rows 4\u0026ndash;7 of Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e at the bottom depicts the direct image of object. Research in CAI primarily aims to enhance image quality, striving to match or exceed the performance of conventional direct imaging systems. These improvements are generally pursued via two main strategies: (1) optimizing the design of coded masks (CMs) or (2) developing advanced reconstruction algorithms to better retrieve the original image. In this study, we focus on the former by exploring an unconventional CM design namely, the HCV mask with two different topological charges as part of a preliminary investigation.\u003c/p\u003e \u003cp\u003eThe HCV mask introduces a unique phase encoding structure that distinguishes it from traditional CMs and, to our knowledge, is applied for the first time in the context of CAI. Our reconstruction results indicate that the HCV mask with dual topological charges yields comparable or superior performance relative to existing CMs. To quantitatively evaluate the reconstruction quality, we computed several metrics: entropy, root mean square error (RMSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR). The corresponding results are summarized in Tables\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and visualized in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a)\u0026ndash;4(d). The bar plots illustrate that the HCV mask performs on par with, or better than, conventional masks, thereby validating its effectiveness in image reconstruction within CAI frameworks.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEntropy analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEntropy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.7865\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.426\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7647\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.2872\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.2269\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4804\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.8455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.2947\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.9069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.2018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3229\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.0645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3063\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.5157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.8645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.4135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.5588\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.306\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.2901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3151\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRMSE analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0613\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0555\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0559\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0514\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0312\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0512\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0668\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0622\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0484\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0604\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0413\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0436\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0687\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.0402\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSSIM analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSIM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.5171\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9603\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4317\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9535\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9619\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9572\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9638\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9618\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9613\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.151\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9569\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9619\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.158\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9636\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9545\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9625\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePSNR analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePSNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e26.2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.2475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26.7934\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.1108\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.0587\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.8834\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.9338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.7771\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.1188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30.2434\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30.0073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e30.1185\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22.2791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.4547\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.7633\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25.8134\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.5011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.1175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26.4403\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e26.3076\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.3223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.3763\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.6894\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e27.2179\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.2553\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.9156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.3399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e27.9242\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe experimental results for the other number \u0026lsquo;1\u0026rsquo; at a different plane at \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e = 5.2 cm are displayed in the Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The object and PSF are recorded at two different planes to demonstrate 3D imaging through summation. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (row 2 \u0026amp; 3) illustrates the \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ePSF\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eO\u003c/em\u003e\u003c/sub\u003e for the HCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15; \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20), random lens, ring lens, spiral axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5), axicon, and spiral lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5). The reconstruction outcomes for NLR, LRA, LRRA, and NL-LRA1 are shown in rows 4, 5, 6, and 7, respectively. A direct image of the object is shown at the bottom of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. To evaluate the results of all the reconstruction techniques discussed, Entropy, RMSE, SSIM and PSNR were computed for each case, as given in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e to Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The entropy, RMSE, SSIM and PSNR graphs that correspond to Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e are displayed in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) and 6(d).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEntropy analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEntropy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.2303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2572\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1927\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.1309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2439\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1937\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.4844\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.196\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.7482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2817\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.5962\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.0262\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1891\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.6083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.182\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.5412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.0519\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1959\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRMSE analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0379\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0793\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0322\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0358\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0172\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0257\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNaN\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0386\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0294\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0524\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0311\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0909\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.0214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSSIM analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSSIM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV(\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9817\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9778\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV(\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9786\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9817\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9793\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.7328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNaN\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9749\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9559\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9794\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9745\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9799\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.978\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9803\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePSNR analysis of the DOEs under different reconstruction techniques.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePSNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNLR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLRRA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNL-LRA1\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21.4259\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.6238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.433\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHCV (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22.0095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.6023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.8467\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.9211\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.2201\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e35.2739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31.3874\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRing Lens\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31.7945\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.7254\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e31.4679\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNaN\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Axicon (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.2695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.5184\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30.6218\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxicon\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.6162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.6231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.5975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30.1405\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpiral Lens (\u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.8299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e32.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e33.3819\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e33.9977\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn conclusion, we have implemented the Helico-conical vortex CM in the framework of I-COACH system for the first time and compared its performance with the existing phase masks. The object hologram and point spread function were recorded at two different planes to verify the three-dimensional capabilities. The experimental demonstration confirms the effectiveness of the proposed phase mask in I-COACH system. The reconstruction efficacy of the proposed mask is either better or comparable to the other phase masks. Furthermore, the effect of TC of the HCV is also discussed with two values, \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15 and 20 by keeping other parameters unchanged. The results were slightly better with \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20 in case of LRA and LRRA reconstruction whereas the reconstruction was better with \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15 in the case of NLR and NL-LRA1. The results indicate that one should choose the phase mask and reconstruction algorithm consciously depending on their application. In future, the non-separable dependence on both azimuthal and radial coordinates property of HCV can be further explored for improving the resolution and contrast in OAM holography. We strongly believe that the HCV coded mask holds great potential for applications in incoherent digital holography, coded aperture imaging (CAI), quantum optics and communication, etc.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eRK would like to acknowledge the support from the Science and Engineering Research Board (SERB), the Government of India, under the SERB SURE research grant (File No. SUR/2022/000910) and SRM University \u0026ndash; AP for seed grant SRMAP/URG/SEED/2024-25/041. SG, VT and VA acknowledge the European Union\u0026rsquo;s Horizon 2020 research and innovation programme grant agreement No. 857627 (CIPHR).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eH.V. and A.K.S.: Methodology, Software, Investigation, Writing \u0026ndash; original draft, Visualization; S.G. and V.T.: Experiments, Investigations, analysis; S.C.: Investigations, Writing \u0026ndash; review \u0026amp; editing, Visualization. S.G.R.: Conceptualization, Writing \u0026ndash; review \u0026amp; editing, Supervision, Resources. V.A. and R.K.: Conceptualization, Methodology, Project administration, Funding acquisition, Supervision.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJ. N. Mait, G. W. Euliss, and R. A. Athale, \u0026ldquo;Computational imaging,\u0026rdquo; \u003cem\u003eAdv. Opt. Photon.\u003c/em\u003e, vol. 10, no. 2, pp. 409\u0026ndash;483, Jun. 2018, doi: 10.1364/AOP.10.000409.\u003c/li\u003e\n\u003cli\u003eJ. 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Lett.\u003c/em\u003e, vol. 38, no. 3, pp. 383\u0026ndash;385, Feb. 2013, doi: 10.1364/OL.38.000383.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"applied-physics-b","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aphb","sideBox":"Learn more about [Applied Physics B](http://link.springer.com/journal/340)","snPcode":"340","submissionUrl":"https://submission.nature.com/new-submission/340/3","title":"Applied Physics B","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"helico-conical beams, incoherent imaging, computational imaging, coded aperture imaging, deconvolution, diffractive optics, digital holography","lastPublishedDoi":"10.21203/rs.3.rs-6847611/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6847611/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInterferenceless Coded Aperture Correlation Holography (I-COACH) has emerged as a powerful computational imaging technique for retrieving three-dimensional information from an object without requiring two-beam interference. In this study, we propose and experimentally demonstrate an I-COACH system employing a Helico-Conical Vortex (HCV) mask. The HCV mask carries orbital angular momentum and features a phase profile with non-separable dependence on both azimuthal and radial coordinates. It is generated by combining helical and conical phase functions, resulting in a spiral-shaped intensity distribution at the focal plane. We compare the performance of I-COACH with the HCV mask against other coded masks (CMs), including random lens, ring lens, higher-order Bessel beam generator, axicon, and spiral phase plate. Additionally, we evaluate image reconstruction using four widely adopted algorithms: non-linear reconstruction (NLR), Lucy-Richardson algorithm (LRA), Lucy-Richardson-Rosen algorithm (LRRA), and non-linear LRA (NL-LRA). Quantitative analysis is conducted using figures of merit such as entropy, root mean squared error (RMSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR). The proposed approach holds promise for advancing incoherent holography and computational imaging applications.\u003c/p\u003e","manuscriptTitle":"Coded Aperture Imaging with Helico-Conical Beams","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-25 06:04:08","doi":"10.21203/rs.3.rs-6847611/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-25T11:35:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-24T16:21:06+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-14T15:23:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"264213463259187114084036466091199711709","date":"2025-07-14T15:20:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-28T08:33:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"128061852802078537751463741453405945225","date":"2025-06-25T17:34:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"269225144557377047835708175205716267571","date":"2025-06-23T15:28:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"299076560017627699446683004563964867665","date":"2025-06-16T00:51:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-15T10:14:43+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-09T10:06:13+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-09T07:52:51+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Physics B","date":"2025-06-08T13:02:34+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-physics-b","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"aphb","sideBox":"Learn more about [Applied Physics B](http://link.springer.com/journal/340)","snPcode":"340","submissionUrl":"https://submission.nature.com/new-submission/340/3","title":"Applied Physics B","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"276da597-4db9-4e0e-b85d-8daaa569107b","owner":[],"postedDate":"June 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-17T15:58:55+00:00","versionOfRecord":{"articleIdentity":"rs-6847611","link":"https://doi.org/10.1007/s00340-025-08585-x","journal":{"identity":"applied-physics-b","isVorOnly":false,"title":"Applied Physics B"},"publishedOn":"2025-11-10 15:56:49","publishedOnDateReadable":"November 10th, 2025"},"versionCreatedAt":"2025-06-25 06:04:08","video":"","vorDoi":"10.1007/s00340-025-08585-x","vorDoiUrl":"https://doi.org/10.1007/s00340-025-08585-x","workflowStages":[]},"version":"v1","identity":"rs-6847611","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6847611","identity":"rs-6847611","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}