Coded Aperture Imaging with Helico-Conical Beams

doi:10.21203/rs.3.rs-6847611/v1

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Coded Aperture Imaging with Helico-Conical Beams

https://doi.org/10.21203/rs.3.rs-6847611/v1

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published 10 Nov, 2025

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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

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.

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 $\:L\left(\frac{\stackrel{-}{s}}{z}\right)=exp\left[i2\pi\:{\left(\lambda\:z\right)}^{-1}\left({s}_{x}x+{s}_{y}y\right)\right]$, C₁ 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:

$$\:{I}_{PSF}\left({\stackrel{-}{r}}_{0};{\stackrel{-}{r}}_{s},\:{z}_{s}\right)={\left|\sqrt{{I}_{\varvec{s}}}{C}_{1}L\left(\frac{\stackrel{-}{{r}_{s}}}{{z}_{s}}\right){\psi\:}_{PM}\otimes\:Q\left(\frac{1}{{z}_{h}}\right)\right|}^{2}$$

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:

$$\:{I}_{PSF}\left({\stackrel{-}{r}}_{0};{z}_{s}\right)={I}_{PSF}\left({\stackrel{-}{r}}_{0}-\frac{{z}_{h}}{{z}_{s}}{\stackrel{-}{r}}_{s};0,{z}_{s}\right)$$

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:

$$\:O\left({\stackrel{-}{r}}_{s}\right)={\sum\:}_{j}^{N}{a}_{j}\delta\:\left(\stackrel{-}{r}-{\stackrel{-}{r}}_{s,j}\right)$$

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:

$$\:{I}_{O}\left({\stackrel{-}{r}}_{0};{z}_{s}\right)={\sum\:}_{j}^{N}{a}_{j}{I}_{PSF}\left({\stackrel{-}{r}}_{0}-\frac{{z}_{h}}{{z}_{s}}{\stackrel{-}{r}}_{s,j};{z}_{s}\right)$$

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

$$\:{I}_{R}^{n+1}={I}_{R}^{n}\left\{\frac{{I}_{O}}{{I}_{R}^{n}\otimes\:{I}_{PSF}}{⊚}_{\beta\:}^{\alpha\:}{I}_{PSF}\right\}$$

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 = (x² + y²)^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 $\:\text{e}\text{x}\text{p}\left[-i\pi\:{\left(\lambda\:f\right)}^{-1}{R}^{2}\right]\times\:exp\left(il\theta\:\right)$.

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

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.

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. V.A. and R.K.: Conceptualization, Methodology, Project administration, Funding acquisition, Supervision.

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Coded Aperture Imaging with Helico-Conical Beams

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2.1 Design of coded masks

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