Image processing with the radial Hilbert transform: theory and experiments

Isotropic and anisotropic edge enhancement using a lemon-star polarization dipole

A spiral phase filter can perform a radial Hilbert transform (RHT) and is useful in isotropic edge enhancement. For selective edge enhancement, the inclusion of anisotropy warrants the filter to be replaced. In this Letter, we introduce for the first time, to our knowledge, a novel and versatile filter that can be tuned between isotropic/anisotropic edge detection and contrast enhancement protocols. To achieve this, we use a lemon-star polarization dipole: a special kind of spin-orbit beam that is a superposition of spin and orbital angular momentum states of light. We devised a 4f imaging setup in microscope configuration to encode the object Fourier spectrum into inhomogeneous polarization distribution. The novelty and advantages of the proposed method lie in selecting the spatial frequency content through polarization transformations in the image reconstruction path, just before the detector, without altering the Fourier plane parameters. Considering a scalar-to-vector diffraction approach and invoking the polarization degree of freedom of light, the edge enhancement capabilities of a lemon-star polarization dipole and a monopole (star or lemon) are shown through experiment results.

Mid-infrared edge-enhanced imaging via angle-selective nonlinear filtering

We propose a novel, to the best of our knowledge, scheme for mid-infrared upconversion imaging with high tunability between bright-field and edge-enhanced modalities. The involved engineering of the nonlinear process favors shaping the optical transfer function of the imaging system. Consequently, a nonlinear angle-selective filter can be configured to perform an all-optical Fourier processing of the image, which highly depends on phase-matching parameters. We numerically demonstrate the ability to switch modalities between the bright-field and edge-enhanced imaging by tuning the crystal temperature and simultaneously acquiring both information by dichromatic illumination. Notably, the achieved reconfigurability is realized without changing the imaging settings, which contrasts with previous instantiations based on pump adaptation. Therefore, the proposed architecture of upconversion imagers would pave a novel way to implement layout-compact and all-optical processing for infrared images.

Fast selective edge-enhanced imaging with topological chiral lamellar superstructures

Edge detection is a fundamental operation for feature extraction in image processing. The all-optical method has aroused growing interest owing to its ultra-fast speed, low energy consumption and parallel computation. However, current optical edge detection methods are generally limited to static devices and fixed functionality. Herein, we propose a fast-switchable scheme based on a ferroelectric liquid crystal topological structure. The self-assembled chiral lamellar superstructure, directed by the azimuthally variant photo-alignment agent, can be dynamically controlled by the polarity of the external electric field and respectively generates the vector beams with nearly orthogonal polarization distribution. Even after thousands of cycles, the horizontal and vertical edges of the object are selectively enhanced with an ultra-fast switching time of ∼57 μs. Broadband edge-enhanced imaging is efficiently demonstrated. This work extends the ingenious building of topological heliconical superstructures and offers an important glimpse into their potential in the emerging frontiers of optical computing for artificial intelligence.

Self-healing spiral phase contrast imaging

Spiral phase contrast imaging alleviates the information load by extracting the geometric features of objects and is one of the most representative branches of instant imaging processing. The self-healing capacity of edge detectors can enhance their robustness to obstacles in practical applications. Here, a self-healing spiral phase contrast imaging scheme is proposed and experimentally demonstrated by a liquid crystal edge detector combining a spiral phase, an axicon phase, and a lens phase. The spiral phase is encoded into a liquid crystal by photopatterning. Self-healing contrast imaging is characterized by a series of edge images of both high-contrast amplitude-type and low-contrast phase-type objects. This work extends the self-healing capacity of these detectors to instant imaging processing and paves the way for optical applications with self-healing features.

Two-dimensional optical multiple-order differentiations based on spatial spectrum modulation

Optical differential operations have recently attracted considerable attention owing to the capabilities of ultrafast speed and low power consumption. The transfer function, which embodies the frequency-domain characteristics of differential systems, plays an important role in differentiator design. Here, we report a super-Gaussian aperture differential filter, and we reveal unique characteristics of odd- and even-order transfer functions and corresponding differential effects via spatial spectrum modulation. We show that the feature of the transfer function is well maintained, and more precise differentiation can be achieved using the designed filter. Two-dimensional first- to fifth-order full and partial differentiations are implemented both theoretically and experimentally. Our work provides an approach for engineering customized multiple-order differentiators and promotes the advancements of related areas such as optical analog computing and image processing.

Short-wavelength-infrared upconversion edge enhancement imaging based on a Laguerre-Gaussian composite vortex filter

Edge-enhanced imaging by spiral phase contrast has proven instrumental in revealing phase or amplitude gradients of an object, with notable applications spanning feature extraction, target recognition, and biomedical fields. However, systems deploying spiral phase plates encounter limitations in phase mask modulation, hindering the characterization of the modulation function during image reconstruction. To address this need, we propose and demonstrate an innovative nonlinear reconstruction method using a Laguerre-Gaussian composite vortex filter, which modulates the spectrum of the target. The involved nonlinear process spectrally transforms the incident short-wavelength-infrared (SWIR) signal from 1550 to 864 nm, subsequently captured by a silicon charge-coupled device. Compared with conventional schemes, our novel filtering method effectively suppresses the diffraction noise, significantly enhancing image contrast and resolution. By loading specific phase holograms on the spatial light modulator, bright-field imaging, isotropic, amplitude-controlled anisotropic, and directional second-order edge-enhanced imaging are realized. Anticipated applications for the proposed SWIR edge-enhanced imaging system encompass domains such as artificial intelligence recognition, deep tissue medical diagnostics, and non-destructive defect inspection. These applications underscore the valuable potential of our cutting-edge methodology in furthering both scientific exploration and practical implementations.

Fractional topological charge measurement through optical correlation

The emerging field of optical vortex beams having fractional topological charges (TCs) is of high interest due to its usefulness in various applications. The efficiency of the result depends on the precise measurement of the orbital angular momentum information tied to the fractional TC. This Letter demonstrates, to our knowledge, a novel and simple technique to measure the fractional TC of optical vortex beams through a hybrid digital-optical correlator with the help of auto-correlation between fork-shaped interference patterns corresponding to integer and fractional TCs. Unlike machine learning-based approaches, the proposed method does not require a complex architecture, which lowers computational cost and enables real-time implementation.

Nonlinear edge enhancement imaging based on Laguerre-Gaussian superimposed vortex filters

Nonlinear reconstruction, which is based on the principle of cross correlation, is a commonly employed reconstruction technique in incoherent correlated digital holography systems. However, the modulation of phase masks in these systems is suppressed during the reconstruction process, resulting in an inability to express the characteristics of the phase masks. Consequently, achieving edge enhancement within these systems is constrained. We propose a nonlinear reconstruction method utilizing Laguerre-Gaussian superimposed vortex filters, which modulates the spectrum of the target during the reconstruction process. Experimental results demonstrate that this method performs well in reconstructing image edges for various phase-masked incoherent imaging systems and effectively suppresses noise. Additionally, this method enables directional edge enhancement.

Edge enhancement in three-dimensional vortex imaging based on FINCH by Bessel-like spiral phase modulation

Edge enhancement, as an important part of image processing, has played an essential role in amplitude-contrast and phase-contrast object imaging. The edge enhancement of three-dimensional (3D) vortex imaging has been successfully implemented by Fresnel incoherent correlation holography (FINCH), but the background noise and image contrast effects are still not satisfactory. To solve these issues, the edge enhancement of FINCH by employing Bessel-like spiral phase modulation is proposed and demonstrated. Compared with the conventional spiral phase modulated FINCH, the proposed technique can achieve high-quality edge enhancement 3D vortex imaging with lower background noise, higher contrast and resolution. The significantly improved imaging quality is mainly attributed to the effective sidelobes' suppression in the generated optical vortices with the Bessel-like modulation technique. Experimental results of the small circular aperture, resolution target, and the Drosophila melanogaster verify its excellent imaging performance. Moreover, we also proposed a new method for selective edge enhancement of 3D vortex imaging by breaking the symmetry of the spiral phase in the algorithmic model of isotropic edge enhancement. The reconstructed images of the circular aperture show that the proposed method is able to enhance the edges of the given objects selectively in any desired direction.

Polychromatic Dual-Mode Imaging with Structured Chiral Photonic Crystals

Optical spatial differentiation is a typical operation of optical analog computing and can single out the edge to accelerate the subsequent image processing, but in some cases, overall information about the object needs to be presented synchronously. Here, we propose a multifunctional optical device based on structured chiral photonic crystals for the simultaneous realization of real-time dual-mode imaging. This optical differentiator is realized by self-organized large-birefringence cholesteric liquid crystals, which are photopatterned to encode with a special integrated geometric phase. Two highly spin-selective modes of second-order spatial differentiation and bright-field imaging are exhibited in the reflected and transmitted directions, respectively. Two-dimensional edges of both amplitude and phase objects have been efficiently enhanced in high contrast and the broadband spectrum. This work extends the ingenious building of hierarchical chiral nanostructures, enriches their applications in the emerging frontiers of optical computing, and boasts considerable potential in machine vision and microscopy.

Intelligent Phase Contrast Meta-Microscope System

Phase contrast imaging techniques enable the visualization of disparities in the refractive index among various materials. However, these techniques usually come with a cost: the need for bulky, inflexible, and complicated configurations. Here, we propose and experimentally demonstrate an ultracompact meta-microscope, a novel imaging platform designed to accomplish both optical and digital phase contrast imaging. The optical phase contrast imaging system is composed of a pair of metalenses and an intermediate spiral phase metasurface located at the Fourier plane. The performance of the system in generating edge-enhanced images is validated by imaging a variety of human cells, including lung cell lines BEAS-2B, CLY1, and H1299 and other types. Additionally, we integrate the ResNet deep learning model into the meta-microscope to transform bright-field images into edge-enhanced images with high contrast accuracy. This technology promises to aid in the development of innovative miniature optical systems for biomedical and clinical applications.

Edge-enhanced microscopy of complex objects using scalar and vectorial vortex filtering

Recently, a 4f system containing a q-plate has been used to perform edge detection and enhancement of amplitude or phase objects. However, only a few studies have concentrated on edge enhancement of complex phase-amplitude objects. Here we experimentally verified the functional difference between scalar and vectorial vortex filtering with the q-plate using an onion cell as a complex object and the vectorial vortex filtering successfully enhanced the edges of phase and amplitude objects in the phase-amplitude object. One problem, however, is indistinguishability of the equally-enhanced edges of the phase and amplitude objects. To address this issue, we propose a method to isolate the edge of the phase object from the edge of the amplitude object using off-axis beam illumination. We theoretically calculated the isolation of the edge of the phase object from the amplitude object, and verified via numerical simulations.

Simultaneous chiral polarization and edge enhancement imaging enabled by a single geometric-phase-based element

In this Letter, we propose a multifunctional imaging system enabled by a single geometric-phase-based liquid crystal (LC) element, which integrates chiral polarization and edge enhancement imaging. The element is located at the frequency domain plane in a 4F imaging system, and the phase profile of the element consists of a fork grating in the x direction and a grating in the y direction, which provide edge enhancement and chiral polarization imaging capabilities. Benefiting from the tunable property of the LC, the system can be switched from a polarization and edge imaging mode to the normal conventional imaging mode which is capable of conveniently acquiring the needed image information. Experiments demonstrate that the system can easily achieve multifunctional and switchable imaging, which agrees well with our design, and our LC element can work in the broadband spectrum because of the geometric phase modulation. The multifunctional strategy used here can effectively avoid the need to increase the size of the original microscopic system and the need for additional mechanical rotation of components. We believe that the proposed system with the additional advantages of electric control and tunability can find applications in biological imaging, medical detection, and optical computing.

Amp-vortex edge-camera: a lensless multi-modality imaging system with edge enhancement

We demonstrate a lensless imaging system with edge-enhanced imaging constructed with a Fresnel zone aperture (FZA) mask placed 3 mm away from a CMOS sensor. We propose vortex back-propagation (vortex-BP) and amplitude vortex-BP algorithms for the FZA-based lensless imaging system to remove the noise and achieve the fast reconstruction of high contrast edge enhancement. Directionally controlled anisotropic edge enhancement can be achieved with our proposed superimposed vortex-BP algorithm. With different reconstruction algorithms, the proposed amp-vortex edge-camera in this paper can achieve 2D bright filed imaging, isotropic, and directional controllable anisotropic edge-enhanced imaging with incoherent light illumination, by a single-shot captured hologram. The effect of edge detection is the same as optical edge detection, which is the re-distribution of light energy. Noise-free in-focus edge detection can be achieved by using back-propagation, without a de-noise algorithm, which is an advantage over other lensless imaging technologies. This is expected to be widely used in autonomous driving, artificial intelligence recognition in consumer electronics, etc.

Topological spatial differentiation via complex amplitude filtering in Fourier space

Various approaches to implementing optical analog differentiation have been studied extensively and applied in edge-based image processing. Here, we report a topological optical differentiation scheme based on complex amplitude filtering, i.e., amplitude and spiral phase modulation in Fourier space. The isotropic and anisotropic multiple-order differentiation operations are demonstrated both theoretically and experimentally. Meanwhile, we also achieve multiline edge detection corresponding to the differential order for the amplitude and phase objects. This proof-of-principle work could open up new avenues for engineering a nanophotonic differentiator and realizing a more compact image-processing system.

Dielectric Metasurface for Synchronously Spiral Phase Contrast and Bright-Field Imaging

Spiral phase contrast imaging and bright-field imaging are two widely used modes in microscopy, providing distinct morphological information about objects. However, conventional microscopes are always unable to operate with these two modes at the same time and need additional optical elements to switch between them. Here, we present a microscopy setup that incorporates a dielectric metasurface capable of achieving spiral phase contrast imaging and bright-field imaging synchronously. The metasurface not only can focus the light for diffraction-limited imaging but also can perform a two-dimensional spatial differentiation operation by imparting an orbital angular momentum to the incident light field. This allows two spatially separated images to be simultaneously obtained, one containing high-frequency edge information and the other showing the entirety of the object. Combined with the advantages of planar architecture and ultrathin thickness of the metasurface, this approach is expected to provide support in the fields of microscopy, biomedicine, and materials science.

Measurement of the fractional topological charge of an optical vortex beam through interference fringe dislocation

An optical vortex beam carrying fractional topological charge (TC) has become an immerging field of interest due to its unique intensity distribution and fractional phase front in a transverse plane. Potential applications include micro-particle manipulation, optical communication, quantum information processing, optical encryption, and optical imaging. In these applications, it is necessary to know the correct information of the orbital angular momentum, which is related to the fractional TC of the beam. Therefore, the accurate measurement of fractional TC is an important issue. In this study, we demonstrate a simple technique to measure the fractional TC of an optical vortex with a resolution of 0.05 using a spiral interferometer and fork-shaped interference patterns. We further show that the proposed technique provides satisfactory results in cases of low to moderate atmospheric turbulences, which has relevance in free-space optical communications.

Optical Computing: Status and Perspectives

For many years, optics has been employed in computing, although the major focus has been and remains to be on connecting parts of computers, for communications, or more fundamentally in systems that have some optical function or element (optical pattern recognition, etc.). Optical digital computers are still evolving; however, a variety of components that can eventually lead to true optical computers, such as optical logic gates, optical switches, neural networks, and spatial light modulators have previously been developed and are discussed in this paper. High-performance off-the-shelf computers can accurately simulate and construct more complicated photonic devices and systems. These advancements have developed under unusual circumstances: photonics is an emerging tool for the next generation of computing hardware, while recent advances in digital computers have empowered the design, modeling, and creation of a new class of photonic devices and systems with unparalleled challenges. Thus, the review of the status and perspectives shows that optical technology offers incredible developments in computational efficiency; however, only separately implemented optical operations are known so far, and the launch of the world's first commercial optical processing system was only recently announced. Most likely, the optical computer has not been put into mass production because there are still no good solutions for optical transistors, optical memory, and much more that acceptance to break the huge inertia of many proven technologies in electronics.

Advances on Solid-State Vortex Laser

Vortex beams (VBs) are structured beams with helical wavefronts carrying orbital angular momentum (OAM) and they have been widely used in lots of domains, such as optical data-transmission, optical tweezer, quantum entanglement, and super-resolution imaging. The ability to generate vortex beams with favorable performance is of great significance for these advanced applications. Compared with extra-cavity schemes, such as spatial light modulation, mode conversion, and others which transform other modes into vortex modes, solid-state vortex lasers can output vortex beams directly and show advantages including a compact structure, high robustness, easy to integrate, and low cost. In this review, we summarize intra-cavity generation approaches to vortex beams in solid-state lasers. Our work on 1.6μm eye-safe vector vortex lasers is also introduced.

Ultracompact meta-imagers for arbitrary all-optical convolution

Electronic digital convolutions could extract key features of objects for data processing and information identification in artificial intelligence, but they are time-cost and energy consumption due to the low response of electrons. Although massless photons enable high-speed and low-loss analog convolutions, two existing all-optical approaches including Fourier filtering and Green's function have either limited functionality or bulky volume, thus restricting their applications in smart systems. Here, we report all-optical convolutional computing with a metasurface-singlet or -doublet imager, considered as the third approach, where its point spread function is modified arbitrarily via a complex-amplitude meta-modulator that enables functionality-unlimited kernels. Beyond one- and two-dimensional spatial differentiation, we demonstrate real-time, parallel, and analog convolutional processing of optical and biological specimens with challenging pepper-salt denoising and edge enhancement, which significantly enrich the toolkit of all-optical computing. Such meta-imager approach bridges multi-functionality and high-integration in all-optical convolutions, meanwhile possessing good architecture compatibility with digital convolutional neural networks.

Computing metasurfaces for all-optical image processing: a brief review

Computing metasurfaces are two-dimensional artificial nanostructures capable of performing mathematical operations on the input electromagnetic field, including its amplitude, phase, polarization, and frequency distributions. Rapid progress in the development of computing metasurfaces provide exceptional abilities for all-optical image processing, including the edge-enhanced imaging, which opens a broad range of novel and superior applications for real-time pattern recognition. In this paper, we review recent progress in the emerging field of computing metasurfaces for all-optical image processing, focusing on innovative and promising applications in optical analog operations, image processing, microscopy imaging, and quantum imaging.

Review on fractional vortex beam

As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro-particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano-optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.

Customizing structured light beams with a differential operator

We show that structured light beams can be customized with a differential operator in Fourier space. This operator is represented as an algebraic function that acts on a seed beam for adjusting its shape. If the seed beams are perfect Laguerre-Gauss beams (PLGBs) and Bessel beams (BBs) without orbital angular momentum, we demonstrate that the custom beams generated on the seed-PLG preserve their distribution a longer distance than the propagation-invariant custom-caustic light fields obtained with the seed-Bessel, where both beams have similar initial conditions. In this sense, the custom-PLGBs can be a better option for many applications where the propagation-invariant light fields are used. We show some beam distributions-astroid, deltoid, and parabolic-generated with both seeds.

Isotropic and anisotropic edge enhancement with a superposed-spiral phase filter

In this paper, we present edge detection schemes with specially designed superposed spiral phase plate (SSPP) filters in the Fourier domain both for intensity or phase objects. A special SSPP whose function is equivalent to Sobel operator in space domain is firstly designed by weighting different topological charge spiral phase plate (SPP) filters. Later, a SSPP with controllable direction parameters is then discussed to enhance the anisotropic edges by controlling the direction parameter. Numerical simulation and experimental results show that either isotropic or anisotropic edge information can be enhanced by using our proposed schemes. The signal-to-noise ratio and the root-mean-square-error performance are improved in comparison with those using traditional SPP filter. Importantly, it is the first time to present the special ways of superposing and the SSPP can be designed before the experiment so that a clear edge can be achieved at real time without the convolutional operation.

Characterization of Collagen I Fiber Thickness, Density, and Orientation in the Human Skin In Vivo Using Second-Harmonic Generation Imaging

The assessment of dermal alterations is necessary to monitor skin aging, cancer, and other skin diseases and alterations. The gold standard of morphologic diagnostics is still histopathology. Here, we proposed parameters to distinguish morphologically different collagen I structures in the extracellular matrix and to characterize varying collagen I structures in the skin with similar SAAID (SHG-to-AF Aging Index of Dermis, SHG—second-harmonic generation; AF—autofluorescence) values. Test datasets for the papillary and reticular extracellular matrix from images in 24 female subjects, 36 to 50 years of age, were generated. Parameters for SAAID, edge detection, and fast Fourier transformation directionality were determined. Additionally, textural analyses based on the grey level co-occurrence matrix (GLCM) were conducted. At first, changes in the GLCM parameters were determined in the native greyscale images and, furthermore, in the Hilbert-transformed images. Our results demonstrate a robust set of parameters for noninvasive in vivo classification for morphologically different collagen I structures in the skin, with similar and different SAAID values. We anticipate our method to enable an automated prevention and monitoring system with an age- and gender-specific algorithm.

Terahertz Spiral Spatial Filtering Imaging

In this paper, we propose a terahertz (THz) spiral spatial filtering (SSF) imaging method that can enable image contrast enhancement. The related theory includes three main steps: (1) the THz image of the target is Fourier transformed to the spatial spectrum distribution; (2) the spatial spectrum is modulated by a spiral phase at the Fourier plane; (3) the filtered spatial spectrum is inverse Fourier transformed to the desired THz image. Meanwhile, analytic expression of the final THz image is derived. Due to the unique nature of the spiral phase, THz image contrast enhancement can be achieved and verified by various simulated target images with different contrasts. In our designed THz SSF imaging system, Fourier transform is carried out by the lens, and the spiral phase is acquired by the spiral phase plate (SPP). Proof-of-principle experiments with three different types of targets (carved metal letters, a high-density polyethylene (HDPE) piece with a scratch, and a leaf) were carried out, and the effectiveness of contrast enhancement and edge extraction on the THz reconstruction images was validated.

Real-time quantum edge enhanced imaging

With the development of optical information processing technology, image edge enhancement technology has rapidly received extensive attention, especially in the field of quantum imaging. However, quantum edge enhanced imaging faces challenges in terms of time-consuming acquisition processes and the complexity of the devices used, which limits practical applications in real-time usage scenarios. Here we introduce and experimentally demonstrate a real-time (0.5 Hz) quantum edge enhanced imaging method that combines the spiral phase contrast technique with heralded single-photon imaging. The edge enhancement results show high quality and background free from raw data. Compared with direct imaging, our configuration can improve the signal-to-noise ratio significantly using the tight time correlations between photon pairs. The method also offers competitive advantages over ghost imaging, including higher brightness and a compact optical fiber delay rather than a free space delay. Additionally, we explore curved edge enhancement for specific feature recognition and the oriented shadow effect. Overall, this efficient and versatile platform paves an alternative path toward real-time quantum edge detection in applications including nondestructive bio-imaging, night vision and covert monitoring.

Implementing selective edge enhancement in nonlinear optics

Recently, it has been demonstrated that a nonlinear spatial filter using second harmonic generation can implement a visible edge enhancement under invisible illumination, and it provides a promising application in biological imaging with light-sensitive specimens. But with this nonlinear spatial filter, all phase or intensity edges of a sample are highlighted isotropically, independent of their local directions. Here we propose a vectorial one to cover this shortage. Our vectorial nonlinear spatial filter uses two cascaded nonlinear crystals with orthogonal optical axes to produce superposed nonlinear vortex filtering. We show that with the control of the polarization of the invisible illumination, one can highlight the features of the samples in special directions visually. Moreover, we find the intensity of the sample arm can be weaker by two orders of magnitude than the filter arm. This striking feature may offer a practical application in biological imaging or microscopy, since the light field reflected from the sample is always weak. Our work offers an interesting way to see and emphasize the different directions of edges or contours of phase and intensity objects with the polarization control of the invisible illumination.

Mathematical Mirroring for Identification of Local Symmetry Centers in Microscopic Images Local Symmetry Detection in FIJI

Symmetry is omnipresent in nature and we encounter symmetry routinely in our everyday life. It is also common on the microscopic level, where symmetry is often key to the proper function of core biological processes. The human brain is exquisitely well suited to recognize such symmetrical features with ease. In contrast, computational recognition of such patterns in images is still surprisingly challenging. In this paper we describe a mathematical approach to identifying smaller local symmetrical structures within larger images. Our algorithm attributes a local symmetry score to each image pixel, which subsequently allows the identification of the symmetrical centers of an object. Though there are already many methods available to detect symmetry in images, to the best of our knowledge, our algorithm is the first that is easily applicable in ImageJ/FIJI. We have created an interactive plugin in FIJI that allows the detection and thresholding of local symmetry values. The plugin combines the different reflection symmetry axis of a square to get a good coverage of reflection symmetry in all directions. To demonstrate the plugins potential, we analyzed images of bacterial chemoreceptor arrays and intracellular vesicle trafficking events, which are two prominent examples of biological systems with symmetrical patterns.

X-ray microscope for imaging topological charge and orbital angular momentum distribution formed by chirality

The distribution of topological charges on X-ray vortices was measured by differential Fourier space filtering microscope, differential radial Hilbert transform microscope. It was experimentally verified for the first time using a Spiral Fresnel zone plate objective lens. This X-ray microscope is highly sensitive to X-ray topological defects, such as edges and vortices, at the exit-face wave field of objects. Its efficient use is also discussed.

Enhanced optical edge detection based on a Pancharatnam-Berry flat lens with a large focal length

In this Letter, we employ photo-aligned liquid crystals to record a flat lens pattern through a simple exposure method to produce a large focal length Pancharatnam-Berry (PB) lens with a film thickness of 2µm without using expensive equipment. This PB lens with a focal length of 240.6 m (at 532 nm) can transmit up to 97% across visible wavelengths and maintain high diffraction efficiency (>90%). An improved two-dimensional optical edge detection design based on this lens is proposed. We experimentally demonstrate the integrity and high efficiency of edge information that may play an important role in the application of image processing and high-contrast microscopy.

Image correlation by one-dimensional signatures invariant to rotation, position, and scale using the radial Hilbert transform optimized

This paper presents a new methodology for pattern recognition invariant to rotation, position, and scale. The method uses the correlation of signatures, where the signatures were created with a new equation called the radial Hilbert transform optimized (RHTO) for longer signatures. An analysis with eight non-homogeneous illumination patterns was performed with 2000 letter variants and 30 phytoplankton species. The higher confidence level was founded using the radial Hilbert optimized methodology. Also, it utilized a correlation called adaptive linear-nonlinear correlation, which gave a better discrimination performance than the nonlinear correlation function.

Inverse design of a spatial filter in edge enhanced imaging

A spatial filter, as a key element in edge enhanced imaging, determines the resolution and the contrast of imaging. However, the conventional spiral phase filter (SPF) results in background noise near the edges of objects in the formed images due to the fact that the point spread function (PSF) of the SPF has sub-oscillations that decrease the edge resolution. In this Letter, we propose a method for inversely designing the spatial filter, aiming to achieve high-resolution images. We show that the sub-oscillations in the PSF of the filter can be, in principle, completely suppressed. Further, we experimentally demonstrate the edge enhancement, with high resolution, for both amplitude and phase objects by using our own designed filter. Our method may find potential applications in fingerprint identification and image processing.

Photonic Spin-Multiplexing Metasurface for Switchable Spiral Phase Contrast Imaging

As the two most representative operation modes in an optical imaging system, bright-field imaging and phase contrast imaging can extract different morphological information on an object. Developing a miniature and low-cost system capable of switching between these two imaging modes is thus very attractive for a number of applications, such as biomedical imaging. Here, we propose and demonstrate that a Fourier transform setup incorporating an all-dielectric metasurface can perform a two-dimensional spatial differentiation operation and thus achieve isotropic edge detection. In addition, the metasurface can provide two spin-dependent, uncorrelated phase profiles across the entire visible spectrum. Therefore, based on the spin-state of incident light, the system can be used for either diffraction-limited bright-field imaging or isotropic edge-enhanced phase contrast imaging. Combined with the advantages of planar architecture and ultrathin thickness of the metasurface, we envision this approach may open new vistas in the very interdisciplinary field of imaging and microscopy.

Effect of Airy Gaussian vortex beam array on reducing intermode crosstalk induced by atmospheric turbulence

Vortex beam carrying angular momentum (OAM) will be disturbed by the random fluctuation of the refraction index of turbulent atmosphere, resulting in intermodal crosstalk among the different OAM modes. Recent advances have demonstrated that the employment of the abruptly autofocusing vortex beams can potentially mitigate the crosstalk effect. In this paper, a new type of abruptly autofocusing vortex beams, called Airy Gaussian vortex beam array (AGVBA) is proposed. By means of multi-plane wave optics simulation, the degradation of signal mode for AGVBA propagating through isotropic atmospheric turbulence is studied. In a comparison with the conventional abruptly autofocusing vortex beams, such as the ring Airy vortex beam (RAVB) and the Airy vortex beam array (AVBA), it is shown that AGVBA achieves more centralized intensity as well as a larger spot at the focal plane, thus can effectively balance the beam spreading and beam wander effect, resulting in mitigation of intermodal crosstalk.

High-contrast anisotropic edge enhancement free of shadow effect

We propose a Bessel-like composite vortex filter to perform high-contrast and power-controlled anisotropic edge enhancement with shadow-effect-free and low background noise. The background noise, which is commonly found and strongly decreases the filtered image quality in previous anisotropic vortex filters, is effectively reduced by suppressing the side lobes of the system point spread function, thereby increasing the image edge contrast to 0.98. The shadow effect is totally eliminated by keeping the radial symmetry of the filtering process, which makes edges sharper and improves image resolution. By introducing a weighting factor between two opposite vortex filter components, the power of edge enhancement becomes controllable. Numerical simulations and experimental results prove that the proposed filter achieves higher-contrast edge enhancement for both phase-contrast and amplitude-contrast objects.

Reducing the cross-talk among different orbital angular momentum modes in turbulent atmosphere by using a focusing mirror

The cross-talk among different orbital angular momentum (OAM) modes induced by the turbulent atmosphere is a challenging effect commonly occurring in OAM-based free-space optical (FSO) communication. The aim of this study is to propose a simple method to reduce the crosstalk and demonstrate its effect by analytical derivation and numerical simulation. It is found that the crosstalk is largely reduced by using a focusing mirror. Our results will be useful in free-space optical communication.

Spiral-Phase Masked Optical Image Health Care Encryption System for Medical Images Based on Fast Walsh-Hadamard Transform for Security Enhancement

This article describes how a new digital spiral phase masked encryption scheme is proposed for health care system based on the Fast Walsh-Hadamard transform (FWHT) to enhance the security of the health-related information systems. The proposed encryption system uses the brain scan image to encrypt brain information from the unauthorized access. Spiral mask used here is a hybrid of Radial Hilbert Mask (RHM) and Toroidal Zone Plate (TZP) Mask which makes the key strong and enhances the security. Proposed schemes not only increase the key space but also increases the number of parameters which makes it difficult for an attacker to find exact key to recover original image. Another advantage of this proposed scheme is FWHT which reduces the quantization error that helps in reconstructing the brain image and information perfectly. The robustness of the proposed cryptosystem has been analysed by simulating on MATLAB 8.1.0(R2012b). The experimental results are provided to highlight the effectiveness, robustness and suitability of the proposed cryptosystem that prove the system can be used in healthcare data encryption.

Edge enhancement by negative Poincare-Hopf index filters

Phase and polarization are interrelated quantities, and hence polarization elements that perform like phase elements can be designed. In this Letter, we show that a polarizing element producing a negative Poincare-Hopf (PH) index beam can be used as a spatial filter to perform edge enhancement. Either isotropic or anisotropic edge enhancement can be achieved by polarization selection of the light that illuminates the sample. A conventional microscope imaging system is modified into a polarization-selective optical Fourier processor. Experimental results are presented to show that negative PH index filters, producing a set of orthogonal polarization distribution and their superpositions, can also be used for edge enhancement in optical signal processing.

Polarization singularity index sign inversion by a half-wave plate

Inhomogeneous polarization distributions can host polarization singularities such as lemons, monstars, stars, flowers, spider webs, and higher-order C-points in optical beams. Singularities in ellipse fields are characterized by a C-point index and singularities in vector fields by the Poincare-Hopf index. These singularities can be generated by diffractive or interference methods. In this paper, we show that a half-wave plate (HWP) can be used for polarization singularity index sign inversion. The result presented here is powerful, and it shows the importance of a HWP in the study of polarization singularities. The HWP affects the entire state of polarization (SOP) distribution in the index sign inversion process. The concomitant global change of the SOP distribution happens in an orderly fashion to change the polarity of the polarization singularity index. This method of changing the polarity of the polarization singularity index by a HWP holds good both for ellipse fields as well as for vector fields.

Polarization-based spatial filtering for directional and nondirectional edge enhancement using an S-waveplate

Using polarization as an additional parameter apart from amplitude and phase in spatial filtering experiments offers additional advantages and possibilities. An S-waveplate that can convert a linearly polarized light into radially or azimuthally polarized light can also be used for isotropic edge enhancement. For anisotropic edge enhancement, introduction of a polarizer at the output was recommended and edge selection was done by orientation of the polarizer. But the full potential of the S-waveplate as a spatial filter has not been exploited so far. Unlike the standard amplitude and phase-based Fourier filters, which are independent to the state of polarization of the illuminating beam, the S-waveplate acts in a different way depending on the state of polarization. The edge selection does not need to be carried out by changing the orientation of the polarizer. With a fixed polarizer at the output, we show that either isotropic or anisotropic edge enhancement in any desired orientation can be performed by operating the same spatial filter setup in different illuminating polarization states.

Anisotropic edge enhancement with spiral zone plate under femtosecond laser illumination

Fractional and de-centered phase spiral zone plates (SZPs) are proposed for anisotropic edge enhancement using a femtosecond laser. The transmission functions of the two types of phase SZPs are deduced and the diffraction distributions are theoretically analyzed and simulated as well. By setting the fractional topological charge p and the orientation angle ϑ of a fractional SZP (FSZP), the intensity and the direction of the anisotropic edge enhancement can be controlled. A de-centered SZP (DSZP) can be obtained by shifting the coordinates of the traditional phase SZP while the topological charge equals to 1. The intensity and direction of the anisotropic edge enhancement can be controlled by setting the displacement distance r₀ and the azimuthal angle φ₀ of a DSZP. The anisotropic edge enhancement of the two phase SZPs was experimentally demonstrated with a phase pattern and living biological cells under femtosecond laser illumination.

Orbital angular momentum light in microscopy

Light with a helical phase has had an impact on optical imaging, pushing the limits of resolution or sensitivity. Here, special emphasis will be given to classical light microscopy of phase samples and to Fourier filtering techniques with a helical phase profile, such as the spiral phase contrast technique in its many variants and areas of application.This article is part of the themed issue 'Optical orbital angular momentum'.

Beam wander relieved orbital angular momentum communication in turbulent atmosphere using Bessel beams

Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.

Near-core structure of a propagating optical vortex

We study the propagation of a charge-1 vortex beam using the angular spectrum method. While vortex beams are commonly assumed to have a helical wavefront, it is well known that the phase of the vortex in the near-core region varies arbitrarily quickly. In order to explain the wavefront behavior in the near-core region, ideas such as evanescent fields or superoscillatory functions have been used before. Our study using the angular spectrum method can inherently take into account the propagating as well as evanescent spatial frequencies and is able to provide the detailed wavefront structure as the vortex wavefront evolves. We report that the vortex wavefront shows a significant phase dip in the near-core region for all propagation distances, and the phase contour lines in this region are seen to spiral around the core. While the radial extent of this phase dip is seen to expand on propagation, the magnitude of the dip remains constant. Both propagating as well as evanescent components are seen to contribute to this phase dip, which we attribute to the presence of the radial component in the propagation vector near the core. The angular spectrum method as used here can be a valuable tool for probing the near-core structure of optical vortices.

Image edge enhancement using Airy spiral phase filter

The isotropic and anisotropic image edge enhancements by employing Airy spiral phase filters are proposed and demonstrated. The coherent spread functions of the image systems are derived from transmittance functions of their corresponding filters. In the isotropic method, the distributions of the coherent spread function with the radius of the main ring ρ₀ and the scaled parameter w₀ are numerically analyzed. It is found that the width of the main lobe determining the resolution decreases with the increased ρ₀, and the amplitudes of the side lobes connecting with the contrast fluctuate with w₀. Compared with the existing spiral phase filters, higher contrast and resolution can be achieved by adjusting the two parameters in the Airy spiral phase filter. Moreover, an off-axis Airy spiral phase filter by controlling the center position (ρ₀,ϕ₁) is designed and employed to implement anisotropic edge enhancement. In the experiments, two methods of image edge enhancement have been verified by using the amplitude-contrast and phase-contrast objects.

Revealing the radial modes in vortex beams

Light beams that carry orbital angular momentum are often approximated by modulating an initial beam, usually Gaussian, with an azimuthal phase variation to create a vortex beam. Such vortex beams are well defined azimuthally, but the radial profile is neglected in this generation approach. Here, we show that a consequence of this is that vortex beams carry very little energy in the desired zeroth radial order, as little as only a few percent of the incident power. We demonstrate this experimentally and illustrate how to overcome the problem by complex amplitude modulation of the incident field.

Gradual edge enhancement in spiral phase contrast imaging with fractional vortex filters

In the spiral phase contrast imaging, the integer spiral phase plate (SPP) are generally employed to perform the radial Hilbert transform on the object. Here we introduce fractional SPP filters, instead of the integer ones, to investigate the gradual formation of edge enhancement for pure phase objects. Two spatial light modulators are used in our experimental configuration. One is addressed to display the pure phase object of a five-pointed star, while the other serves as a dynamic filter of fractional topological charge Q. Of interest is the observation of the complete reversal of the edge and background brightness by gradually changing the fractional vortices from Q = 0 to 1. The experimental results were well interpreted based on the OAM spectra of fractional SPP, which indicates that the filtered output image can be considered as a coherent superposition of all possible images that are individually resulted from the integer OAM filtering. Besides, we show that the spiral phase contrast effect can still be observed in real time for a rotating three-leaf clover. Our results may find potential applications in the optical microscopic imaging.

Generation of optical vortices by using binary vortex producing lenses

Experimental high-quality optical vortices of different topological charges are generated by using a vortex producing lens with two phase levels. In our setup, the lens is displayed on a liquid-crystal spatial light modulator that only attains phase modulation of around 1.2π. This achievement opens the real possibility of creating high-quality optical vortices with devices of very low phase modulation capacity. The experimental setup is fully described, and the considerations to set the optimal parameters to obtain high-quality optical vortices are discussed and experimentally established. The phase and intensity of the optical vortices are recovered. The phase is obtained through a phase-shifting method that is directly programmed onto the modulator avoiding any class of mechanical displacement.