It is well known that the coherence vortices are robust against atmospheric turbulence and can be effectively utilized for communication and imaging applications. In this paper, we study, both theoretically and experimentally, the generation of coherence vortices by the cross-correlation between two scattered optical vortices with different topological orders and how the orders of the input fields affect the size of the generated coherence vortices. We have analyzed the size by considering the coherence vortex at a given plane as a ring with inner and outer radii. The inner and outer radii vary linearly with order and the propagation distance. The slope of radius vs. propagation distance is considered as the divergence by which one will be able to find the order. All the theoretical predictions have been validated with the experimental results. It is also observed that the propagation characteristics are similar to the coherent optical vortices

The topological charge (TC) of optical vortex beams can be measured using various interferometric and non-interferometric techniques in both coherent and partially coherent domains. However, these methods are not suitable for obstructed vortex beams, also known as open optical vortex (OOV) beams. Recently, several methods for studying open optical vortex (OOV) beams, have recently been proposed and demonstrated based on interferometry, phase retrieval, spatial coherence analysis, which limit their applicability in the presence of significant perturbations or long-distance propagation. In this study, we propose and experimentally demonstrate an efficient method for measuring both the magnitude and sign of the topological charge (TC) of OOV beams using the auto-correlation distribution after scattering through a rough surface. We generated the OOV beams using partially blocked computer-generated holograms. Although the rings or zero points present in the auto-correlation are broken, the number of rings is equal to the TC. Further, we have utilized the radius of the first ring and its divergence with propagation distance, which can be easily observed for all orders, for finding the TC of higher orders. We can measure the sign of the topological charge solely through intensity measurements using the rotation of the autocorrelation profile with the help of blocking parameter. Furthermore, we demonstrate that the characteristics of OOV beams derived from our proposed method align well with the propagation characteristics of unobstructed OV beams. The results confirm the efficacy of optical vortex beams for free-space optical communication

Dendrites are beautifully designed branched structures found everywhere in nature, for example, in neurons, snowflakes, and trees. These unique properties of dendritic structures contribute to their applications in tissue integration, light manipulation, energy storage, charge transport, sensing, and other fields. In recent years, plasmonic nanodendrites have been extensively employed for surface-enhanced Raman scattering (SERS) applications, incorporating the highly dense electromagnetic field hot spots at the dendritic tips in addition to the increased surface area. These structures have shown their potential for sensing a wide range of analytes, including explosives, pesticides, bacteria, and viruses. This review provides in-depth information about the fundamentals of the SERS mechanism, fabrication techniques to manipulate dendrite structures for improved SERS performance, and the role of nanodendrite structures in SERS applications. Through an extensive survey, this review compiles the current state-of-the-art technologies for developing plasmonic dendrites and applying them for SERS-based sensing applications. Finally, we present the current challenges and future perspectives of developing such sensors

The study introduces a novel asymmetric optical cryptosystem that utilizes bright C-point polarization singularity speckle (BCPSS) patterns as security keys while offering multiuser capabilities. The C-point singular beams, with spatially varying polarization distributions, are created by superposing optical vortex modes of different magnitudes into an orthogonal polarization basis. This complex light beam is then scattered through a rough surface to generate the BCPSS patterns. These generated speckle patterns inherit some unique properties due to the vectorial light field and the randomness of the rough surface, which make them nearly impossible to duplicate. To generate a complex image, the BCPSS phase mask is used to further modify the original image after it has been phase encoded. The final encrypted image is then obtained by processing the intermediate complex image using two-dimensional non-separable linear canonical transform (2D-NS-LCT) and polar decomposition. The 2D-NS-LCT has ten independent parameters which expends the key space, improving its resistance to various attacks. The implementation of polar decomposition in the proposed cryptosystem enables us to have two private keys, helping in multiuser functionality. The proposed method is also validated by testing it against various potential attacks, including contamination and plaintext attacks. Numerical simulations confirm the authenticity and reliability of the proposed cryptosystem

Authentication techniques can be used to overcome the hologram counterfeiting problems. Here, we demonstrate an authentication scheme for digital holograms in a raw-complex form that is stored either in the cloud or on the metasurface using a CNN

A new nonlinear optical multi-image authentication scheme is proposed based on Kramers-Kronig digital holography and orthogonal triangular decomposition or QR decomposition. Here, the complex light field carrying the information of multiple images is modulated by random phase masks and propagated at certain distance. Afterwards, the QR decomposition is applied to the complex wavefront to generate the private keys and to add the non-linearity in the scheme. Next, the product of orthogonal matrix and upper triangular matrix is processed further. The obtained output is modulated by different phase masks and interfered with reference beam to record the encrypted image. For decryption, the Kramer-Kronig relation is utilized to extract the plaintext images directly with only the positive frequency part. A series of numerical simulations are conducted to validate the efficacy and robustness of proposed image authentication scheme.

We propose an optical asymmetric phase image encryption method in which the vectorial light field is used to encode the data. In transverse plane, the vectorial light field has spatially varying polarization distributions where we are allowed to have a greater number of degrees of freedom. In this scheme, the input image is first phase encoded and then modulated by a phase encrypting key, synthesized from the speckles obtained by the scattering of Hermite–Gaussian beams. The modulated image is further processed using fractional Fourier transform with a specific order (?). A pixel scrambling operator is utilized to increase the randomness to further enhance the security and singular value decomposition approach is employed to add the nonlinearity in the encryption process. Now, the stokes parameters, i.e. S1 and S2 are calculated using the light intensities correspond to different polarizations. S1 is used as the encrypted image for transmission and S2 is reserved as one of the private decryption keys. The robustness of the proposed technique is tested against various existing attacks, such as known plaintext attack, chosen plaintext attack, and contamination attacks. Numerically simulated results validate the effectiveness and efficiency of the proposed method

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography. © The Author(s) 2024.

We propose a new asymmetric optical cryptosystem for phase image encoding with the utilization of speckles generated by scattering the Hermite Gaussian beams (HGBs) through a rough surface. These speckle patterns are unique and almost impossible to clone as one cannot mimic the physical process. The generalized Schur decomposition, named as, QZ decomposition, approach is used to generate unique private keys for decrypting the encoded data. The plaintext image is first phase-encoded and then modulated with the pattern obtained by the convolution of HGBs and random phase masks. The modulated image is then Fresnel propagated for a distance of z, and the QZ decomposition operation is performed on the complex wavefront to generate the private keys. Afterward, the gyrator transforms with a rotational angle (?), and the phase truncation is used to further process the information. The phase truncation and phase reservation (PT/PR) will result in another phase private key, which will be utilized for decryption. A non-linear power function is introduced to modify the amplitude part after PT/PR operation and the resultant is modulated using an HGB amplitude mask to get an intermediate wavefront. Finally, the encrypted image is obtained by Fresnel propagating the intermediate wavefront with a distance of z. The effectiveness and validity of the proposed method are tested and verified through numerical simulations. A series of potential attacks such as contamination and plaintext attacks have been tried and tested to further check the robustness of the proposed method. The results confirm the efficacy of the proposed method.

In the modern era, the secure transmission and storage of information are among the utmost priorities. Optical security protocols have demonstrated significant advantages over digital counterparts, i.e., a high speed, a complex degree of freedom, physical parameters as keys (i.e., phase, wavelength, polarization, quantum properties of photons, multiplexing, etc.) and multi-dimension processing capabilities. This paper provides a comprehensive overview of optical cryptosystems developed over the years. We have also analyzed the trend in the growth of optical image encryption methods since their inception in 1995 based on the data collected from various literature libraries such as Google Scholar, IEEE Library and Science Direct Database. The security algorithms developed in the literature are focused on two major aspects, i.e., symmetric and asymmetric cryptosystems. A summary of state-of-the-art works is described based on these two aspects. Current challenges and future perspectives of the field are also discussed.

We propose a new multiuser nonlinear optical cryptosystem using fractional-order vortex speckle (FOVS) patterns as security keys. In conventional optical cryptosystems, mostly random phase masks are used as the security keys which are prone to various attacks such as brute force attack. In the current study, the FOVSs are generated optically by the scattering of the fractional-order vortex beam, known for azimuthal phase and helical wavefronts, through a ground glass diffuser. FOVSs have a remarkable property that makes them almost impossible to replicate. In the input plane, the amplitude image is first phase encoded and then modulated with the FOVS phase mask to obtain the complex image. This complex image is further processed to obtain the encrypted image using the proposed method. Two private security keys are obtained through polar decomposition which enables the multi-user capability in the cryptosystem. The robustness of the proposed method is tested against existing attacks such as the contamination attack and known-plaintext attack. Numerical simulations confirm the validity and feasibility of the proposed method.

The security strength of a double-image cryptosystem using spatial encoding and phase-truncation Fourier transforms (PTFTs) is evaluated. Unlike the conventional PTFT-based cryptosystem, where two random phase masks (RPMs) are used as public keys to provide enough phase constrains in the estimation, in the improved cryptosystem, the RPM generated by a random amplitude mask (RAM) is treated as an unknown parameter. Due to this fixed RAM, the number of constraints in the estimation decreases to achieve high robustness against potential iterative attacks. Moreover, instead of two phase-only masks (POMs), here the two POMs and the RAM are utilized as the private keys in the improved cryptosystem; thus, the key space of the double-image cryptosystem has been enlarged. However, we noticed that the RAM used to encode plaintexts spatially and to generate the phase encryption key is independent of the plaintexts. This could be recovered by a known pair of plaintexts and the ciphertext. Once the information of the RAM is retrieved, the phase key RPM can also be produced making the cryptosystem vulnerable. Based on this finding, new hybrid algorithms, including a known-plaintext attack and a known key attack are proposed to crack the enhanced PTFT-based cryptosystem. The information of the plaintexts can be retrieved from one POM using the proposed algorithms without any knowledge of another POM and the corresponding ciphertext. Numerical simulations have been carried out to validate the information disclosure problem still exists in the double-image cryptosystem based on spatial encoding and PTFTs.

We propose a new asymmetric cryptosystem for phase image encryption, using the physically unclonable functions (PUFs) as security keys. For encryption, the original amplitude image is first converted into a phase image and modulated with a PUF to obtain a complex image. This complex image is then illuminated with a plane wave, and the complex wavefront at a distance d is recorded. The real part of the complex wavefront is further processed to obtain the encrypted image and the imaginary part is kept as the private key. The polar decomposition approach is utilized to generate two more private security keys and to enable the multi-user capability in the cryptosystem. Numerical simulations confirm the feasibility of the proposed method.

Designing a pure phase multifunctional diffractive optical element (M-DOE) is a challenging task, as the regular summation of multiple pure phase functions results in a complex function. One of the widely used multiplexing methods to design a pure phase M-DOE is the random multiplexing method. In this method, different pure phase functions are multiplied to mutually exclusive binary random functions before summation. However, M-DOEs designed using the random multiplexing method are prone to scattering noise. In this study, a novel approach based on a modified Gerchberg-Saxton algorithm (GSA) has been proposed and demonstrated for the design of pure-phase multifunctional DOEs. In this approach, the complex M-DOE obtained by regular summation is used as a reference, and with suitable constraints, the amplitude component of the complex M-DOE is transported into the phase component, resulting in a pure phase MDOE. This modified algorithm is called Transport of Amplitude into Phase based on GSA (TAP-GSA). This method has been demonstrated on a well-established incoherent digital holography technique called Fresnel incoherent correlation holography (FINCH). In FINCH, it is necessary to multiplex two-phase masks, which can be achieved using random multiplexing or polarization multiplexing, resulting in reconstruction noise and low light throughput, respectively. Under low-light conditions, random multiplexing is a better choice than the polarization multiplexing method. The M-DOE designed using TAP-GSA for FINCH improved the light throughput and exhibited a higher SNR in comparison to the random multiplexing method.

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Interferenceless coded aperture correlation holography (I-COACH) is one of the simplest incoherent holography techniques. In I-COACH, the light from an object is modulated by a coded mask, and the resulting intensity distribution is recorded. The 3D image of the object is reconstructed by processing the object intensity distribution with the pre-recorded 3D point spread intensity distributions. The first version of I-COACH was implemented using a scattering phase mask, which makes its implementation challenging in light-sensitive experiments. The I-COACH technique gradually evolved with the advancement in the engineering of coded phase masks that retain randomness but improve the concentration of light in smaller areas in the image sensor. In this direction, I-COACH was demonstrated using weakly scattered intensity patterns, dot patterns and recently using accelerating Airy patterns, and the case with accelerating Airy patterns exhibited the highest SNR. In this study, we propose and demonstrate I-COACH with an ensemble of self-rotating beams. Unlike accelerating Airy beams, self-rotating beams exhibit a better energy concentration. In the case of self-rotating beams, the uniqueness of the intensity distributions with depth is attributed to the rotation of the intensity pattern as opposed to the shifts of the Airy patterns, making the intensity distribution stable along depths. A significant improvement in SNR was observed in optical experiments.

This study demonstrates a new multi-wavelength imaging technique with an extended depth of field. The spatial and spectral information of the objects is encoded into a single bipolar function of sparse dots using coded phase masks (CPMs) and a radial quartic phase function (RQPF). Each wavelength produces an intensity response of sparse dots with a unique set of distances between the dots, enabling the decoding of multispectral information. The RQPF is introduced to extend the depth of focus for different wavelengths. A library of point spread holograms (PSHs) is prerecorded with uniquely designed CPMs by placing the point objects of multiple wavelengths at the system input. For reconstruction, the object hologram is cross-correlated with a PSH corresponding to the wavelength of the object. The results are compared with direct imaging and with the conventional technique of interferenceless coded aperture correlation holography. The method is unique because the number of camera shots required for multi-wavelength imaging is the same as for monochromatic imaging.

The security strength of an enhanced cryptosystem based on interference and the phase-retrieval technique is evaluated. The security strength of the optical cryptosystem was improved through the phase-retrieval technique used to generate a phase-only mask (POM) as the ciphertext. Due to the complex mathematical model of the phase-retrieval technique, it seems that a silhouette problem existing in the conventional interference-based scheme was removed. However, we noted that the random phase mask (RPM) regarded as the only private key was fixed in the encryption path, which is not related to the plaintext and makes it possible to be recovered using a known-plaintext attack (KPA). Moreover, we also found that the RPM has high key sensitivity, and it should be recovered precisely to retrieve information of plaintexts during the attack. Thus, a hybrid KPA where three pairs of known plaintexts and their ciphertexts are regarded as the amplitude and phase constraints to obtain the precise estimation of the RPM is proposed. Then, with the help of the estimated private key, information of the original plaintexts encoded using the cryptosystem under study could be retrieved from an arbitrarily given ciphertext without any knowledge of the private key. Our cryptoanalysis shows that the cryptosystem based on interference and the phase-retrieval technique is vulnerable to the proposed attack, and there is a security leak in it. Numerical simulations have been carried out to demonstrate the performance of our proposed attack.

The security strength of a phase-only asymmetric cryptosystem based on interference and phase-truncated Fourier transforms (PTFTs) has been evaluated. Compared to the conventional PTFTs-based scheme where the plaintext is directly encoded into two phase masks (PMs) and the ciphertext, here the plaintext is firstly converted to the phase-only distribution by PTFTs-based encryption process I, and then modulated by the encryption process II with the aid of two masks generated by a carrier image. The security strength of this cryptosystem has been enhanced by an additional secure layer for the output of PTFTs-based structure. Moreover, the four masks generated in the encryption processes I and II are required for the decryption also, it enlarges the key space which further ensures the security strength of the improved cryptosystem. However, we noticed that the carrier image used to generate one of private keys is same as the ciphertext when the input of the encryption is the zero matrix. Thus, the amplitude mask (AM) as the private key could be recovered by the designed chosen-plaintext attack, and then it can be used as the known parameter in the iterative attacks. Employing the recovered mask, two specific attacks with different constraints are designed to break the cryptosystem based on interference and PTFTs successfully. Based on our cryptoanalysis, it is found that most information of the plaintexts were encoded into the AM and the PM in the encryption process I, and silhouette problem would be caused when one of these keys is known. Numerical simulations have been carried out to validate the feasibility and effectiveness of proposed hybrid attacks.

Fresnel incoherent correlation holography (FINCH) is a well-established incoherent digital holography technique. In FINCH, light from an object point splits into two, differently modulated using two diffractive lenses with different focal distances and interfered to form a self-interference hologram. The hologram numerically back propagates to reconstruct the image of the object at different depths. FINCH, in the inline configuration, requires at least three camera shots with different phase shifts between the two interfering beams followed by superposition to obtain a complex hologram that can be used to reconstruct an object’s image without the twin image and bias terms. In general, FINCH is implemented using an active device, such as a spatial light modulator, to display the diffractive lenses. The first version of FINCH used a phase mask generated by random multiplexing of two diffractive lenses, which resulted in high reconstruction noise. Therefore, a polarization multiplexing method was later developed to suppress the reconstruction noise at the expense of some power loss. In this study, a novel computational algorithm based on the Gerchberg-Saxton algorithm (GSA) called transport of amplitude into phase (TAP-GSA) was developed for FINCH to design multiplexed phase masks with high light throughput and low reconstruction noise. The simulation and optical experiments demonstrate a power efficiency improvement of ~ 150 and ~ 200% in the new method in comparison to random multiplexing and polarization multiplexing, respectively. The SNR of the proposed method is better than that of random multiplexing in all tested cases but lower than that of the polarization multiplexing method.

Interferenceless coded aperture correlation holography (I-COACH) techniques have revolutionized the field of incoherent imaging, offering multidimensional imaging capabilities with a high temporal resolution in a simple optical configuration and at a low cost. The I-COACH method uses phase modulators (PMs) between the object and the image sensor, which encode the 3D location information of a point into a unique spatial intensity distribution. The system usually requires a one-time calibration procedure in which the point spread functions (PSFs) at different depths and/or wavelengths are recorded. When an object is recorded under identical conditions as the PSF, the multidimensional image of the object is reconstructed by processing the object intensity with the PSFs. In the previous versions of I-COACH, the PM mapped every object point to a scattered intensity distribution or random dot array pattern. The scattered intensity distribution results in a low SNR compared to a direct imaging system due to optical power dilution. Due to the limited focal depth, the dot pattern reduces the imaging resolution beyond the depth of focus if further multiplexing of phase masks is not performed. In this study, I-COACH has been realized using a PM that maps every object point into a sparse random array of Airy beams. Airy beams during propagation exhibit a relatively high focal depth with sharp intensity maxima that shift laterally following a curved path in 3D space. Therefore, sparse, randomly distributed diverse Airy beams exhibit random shifts with respect to one another during propagation, generating unique intensity distributions at different distances while retaining optical power concentrations in small areas on the detector. The phase-only mask displayed on the modulator was designed by random phase multiplexing of Airy beam generators. The simulation and experimental results obtained for the proposed method are significantly better in SNR than in the previous versions of I-COACH.

A 4D computational incoherent imaging technique using accelerating Airy beams (A-beams) and nonlinear reconstruction (NLR) has been developed. The phase mask was designed as a binary version for the generation of a sparse random array of A-beams. The imaging process consist of three steps. In the first step a 4D point spread function (PSF) was recorded at different wavelengths and depths. In the next step, a multicolor, multiplane object was loaded and a single camera shot was recorded. Finally, the 4D information of the object was reconstructed by processing the object intensity distribution and 4D PSFs. The simulation results for the imaging concept are presented.

Optical information security techniques have several advantages over digital counterparts such as ability to process information parallelly, use of physical parameters as security keys, efficient storage capability etc. In last few years, several optical cryptosystems have been designed based on different optical aspects. In this chapter, we discuss optical cryptosystems based on spiral/vortex phase modulation in details. The orbital angular momentum (OAM) associated with a spatially helical phase or vortex beam can be utilized to design enhanced security protocols. Moreover, since the OAM has theoretically unlimited values of topological charges (TCs) and have the orthogonality of OAM modes with different integer TCs, it is an excellent candidate for designing high-capacity secure optical cryptosystems. Here, the spiral phase functions have been first introduced with different TCs and then the 2D spiral phase transform (SPT) and several optical cryptosystems based on it are discussed in detail with possible optical configurations for practice applications. Numerical simulation results for three cryptosystems are discussed showing their feasibility. The security analysis in terms of keys sensitivity and robustness against existing attacks is also performed and discussed for these cryptosystems.

The security strength of the improved optical cryptosystem based on interference has been evaluated. Compared to the previous interference-based cryptosystems in which the plaintext is encoded into two phase-only masks (POMs), here the plaintext is encoded into a POM and an amplitude mask (AM). Since the information of the plaintext cannot be recovered directly when one of the masks is released in the decryption process of the improved cryptosystem, it seems that it is free from the silhouette problem. However, we found that the random phase mask (RPM) serving as the encryption key is not related to the plaintext. Thus, it is possible to recover the RPM first by using the known-plaintext attack (KPA). Moreover, the POM and the AM generated in the encryption path only contains the phase and amplitude information, respectively. Thus, these can be utilized as additional constraints in the proposed iterative process. Based on these findings, two kinds of hybrid attacks, including a KPA and the iterative processes with different constraints, are proposed to crack the improved cryptosystem. In the designed KPA with a pair of the known plaintext and its corresponding masks, the RPM is recovered first. With the aid of the recovered RPM, two iterative processes with different released masks are proposed to recover the information of the plaintext without any knowledge of another mask. To the best of our knowledge, this is the first time that the existence of the silhouette problem in the cryptosystem under study has been reported. Numerical simulation has been carried out to validate the feasibility and effectiveness of the proposed hybrid attacks.

A new multiuser optical image encryption and authentication technique is proposed. Sparse multiplexing and polar decomposition are used in the Fresnel domain to obtain the ciphertext of an input image. To enable the multiuser platform, multiple private keys are obtained through polar decomposition during the encryption process. It will allow multiple authorized users to access the secure information simultaneously without having a key distribution problem among them. The proposed method has a large key space and is robust against several attacks, such as contamination attacks (noise and occlusion), brute force attack, plaintext attacks, and special iterative attack. A comparative analysis of the presented technique is also performed with the similar existing techniques. The numerical simulation results demonstrate the robustness and feasibility of the proposed algorithm.

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