Complex Amplitude Information Research Articles

Lensless Imaging Based on Dual‐Input Physics‐Driven Neural Network

Lensless imaging, as a novel computational imaging technique, has attracted great attention due to its simplicity, compactness, and flexibility. This technique analyzes and processes the diffraction of an object to obtain complex amplitude information. However, traditional algorithms such as Gerchberg‐Saxton (G–S) algorithm tend to exhibit significant errors in complex amplitude retrieval, particularly for edge information. Additional constraints have to be incorporated on top of amplitude constraints to enhance the accuracy. Recently, deep learning has shown promising results in optical imaging. However, it requires a large amount of training data. To address these issues, a novel approach called dual‐input physics‐driven network (DPNN) is proposed for lensless imaging. DPNN utilizes two diffractions recorded at different distances as inputs and uses an unsupervised approach that combines physical imaging model to reconstruct object information. DPNN adopts a U‐Net 3+ architecture with a loss function of mean absolute error (MAE) to better capture diffraction features. DPNN achieves highly accurate reconstruction without requiring extensive data and being immune to background noise. Based on different diffraction intervals, noise levels, and imaging models, DPNN exhibits superior capabilities in peak signal‐to‐noise ratio and structural similarity compared with conventional methods, effectively achieving accurate phase or amplitude information reconstruction.

Recoding double-phase holograms with the full convolutional neural network

Herein, we proposed a method to recode double-phase holograms (DPHs) with a full convolutional neural network (FCN) for alleviating the fringes and spatial shifting noises in that. There are many fringes near the edge of the diffraction field due to the incomplete Fresnel zone plate, and the pixel-by-pixel encoding method of DPH will cause above fringes to appear in the reconstructed image of that as well. Besides, the spatial shifting noises generated during the conversion from complex-amplitude information to pure-phase information will also decrease the reconstruction quality and definition. Depending on the great nonlinear fitting ability of FCN, the proposed method can recode DPHs, alleviating the fringes and removing the spatial shifting noises effectively. Finally, the phase-only holograms with the resolution 2400 × 4096 have been generated in 0.06 s, which have a peak signal to noise ratio (PSNR) of 35.6 dB in the mean reconstruction quality. Optical results showed that compared with the conventional methods, the target images reconstructed by the proposed method have less noise and a higher display quality.

Terahertz metasurface for independent modulation of amplitude and phase in multi-channels

It is necessary to achieve simultaneous and independent modulation of the amplitude, polarization and phase of lights utilizing metasurface, which is also a great challenge. In this paper, an all-dielectric metasurface is proposed for simultaneously controlling the amplitude and phase of orthogonal linearly polarized lights in multi-channels. Three pairs of complex amplitude information are encoded in three independent channels by elaborately selecting and combining the meta-atoms. To verify the performance of proposed metasurface in the terahertz (THz) band, three examples are designed, including producing multiple vortex beams and arbitrary orbital angular momentum (OAM) superposition states, producing multiple foci with controllable intensity ratios, and producing multiple foci with controllable intensity ratios and focal lengths. The simulative results agree with experimental results. The proposed design based on single-layer structure has advantages of controllable focusing, compact structure, and simple fabrication, providing an alternative way for the preparation of integrated multifunctional and miniaturized optical devices.

Terahertz all-silicon metasurfaces with off-axis bifocal characteristics for polarization detection

Abstract Functional devices for terahertz (THz) polarization detection in transmission mode are highly desired in integrated applications, but traditional polarization measurement systems are bulky and highly cost. The combination between all-silicon metasurfaces and focused beams carrying polarization information has offered a new opportunity for miniaturized polarization detection behavior. Here, we investigate and experimentally demonstrate a new scheme for realizing efficiently miniaturized polarization detection behavior based on the polarization multiplexing encoding technique. The full-Stokes parameter matrix of the incident polarization state can be reconstructed in a single snapshot by using a microprobe to record, pixel by pixel, the complex amplitude information contained in a pre-designed plane. Subsequently, the polarization detection capability of the proposed design principle is evaluated using random polarization states defined on the surface of a standard Poincaré sphere (PS). Such a scheme offers potential applications for the development of compact photonic meta-platforms for polarization detection in transmission mode, being highly favored in polarization high-resolution imaging, remote sensing, and THz communications.

High-Purity Multi-Mode Vortex Beam Generation With Full Complex-Amplitude-Controllable Metasurface

Vortex beam with inherent orbital angular momentum (OAM) is promising in high-capacity communication. On multimode vortex beam generation, metasurface has shown exceptional advantages of integration and miniaturization. For the current widely used phase-only methods on multimode vortex beam generation by metasurface, the purity of the OAM-mode spectrum is severely affected. A new method for generation of multimode vortex beam with high mode purity is proposed in this article by reconstructing the complete complex amplitude information on the meta-device aperture. A 20 dB suppression of the crosstalk modes is experimentally observed for the co-directional multimode vortex beam generation, which is much improved compared to the traditional phase-only scheme. In addition, the proposed scheme also provides the capability of generating high-purity multimode vortex beams with arbitrary preset propagation directions and power allocations. This study provides a platform for high-performance vortex beam communication by increasing the signal-to-noise ratio and enabling the multicasting scenarios with customized capacity requirements.

Complete modal decomposition of a few-mode fiber based on ptychography technology.

An exact modal decomposition method plays an important role in revealing the modal characteristics of a few-mode fiber, and it is widely used in various applications ranging from imaging to telecommunications. Here, ptychography technology is successfully used to achieve modal decomposition of a few-mode fiber. In our method, the complex amplitude information of the test fiber can be recovered by ptychography, and then the amplitude weight of each eigenmode and the relative phase between different eigenmodes can be easily calculated by modal orthogonal projection operations. In addition, we also propose a simple and effective method to realize coordinate alignment. Numerical simulations and optical experiments validate the reliability and feasibility of the approach.

End-to-end design of metasurface-based complex-amplitude holograms by physics-driven deep neural networks

Abstract Holograms which reconstruct the transverse profile of light with complex-amplitude information have demonstrated more excellent performances with an improved signal-to-noise ratio compared with those containing amplitude-only and phase-only information. Metasurfaces have been widely utilized for complex-amplitude holograms owing to its capability of arbitrary light modulation at a subwavelength scale which conventional holographic devices cannot achieve. However, existing methods for metasurface-based complex-amplitude hologram design employ single back-diffraction propagation and rely on the artificial blocks which are able to independently and completely control both amplitude and phase. Here, we propose an unsupervised physics-driven deep neural network for the design of metasurface-based complex-amplitude holograms using artificial blocks with incomplete light modulation. This method integrates a neural network module with a forward physical propagation module and directly maps geometric parameters of the blocks to holographic images for end-to-end design. The perfect reconstruction of holographic images verified by numerical simulations has demonstrated that compared with the complete blocks, an efficient utilization, association and cooperation of the limited artificial blocks can achieve reconstruction performance as well. Furthermore, more restricted controls of the incident light are adopted for robustness test. The proposed method offers a real-time and robust way towards large-scale ideal holographic displays with subwavelength resolution.

Common-path off-axis single-pixel holographic imaging.

Common-path off-axis single-pixel holographic imaging (COSHI) is proposed to obtain complex amplitude information using an in-line interferometer and a single-pixel (point-like) detector. COSHI is more robust to disturbances such as vibration than the conventional single-pixel digital holography technique because of its common-path configuration. In addition, the number of measurements can be reduced due to COSHI's reconstruction process based on the Fourier fringe analysis. In COSHI, an off-axis digital hologram can be obtained using the structured patterns composed of Hadamard basis patterns and stationary tilted phase distribution. Interestingly, COSHI's space bandwidth is larger than of the conventional off-axis digital holography because COSHI does not reconstruct the self-correlation term of an object. The proposed method is theoretically confirmed and numerical and experimental results show its feasibility.

Compact polarization-resolved common-path digital holography based on the Pancharatnam-Berry phase.

We propose a compact polarization-resolved common-path digital holography for measuring the polarization distribution of a light field dynamically with high temporal stability. The designed experimental setup allows simultaneously recording, in a common-path manner, two holograms carrying the complex amplitude information of two orthogonal polarization components of the light field. Based on the theory of the Pancharatnam-Berry phase to retrieve the full Stokes parameters of the light field, we demonstrate the experiments with polarized optical elements, stressed glass plate, and micrometer-sized liquid crystal droplet. The measurement results verify the method's high accuracy and stability, and the capability of measuring light fields with sizes ranging from centimeters to micrometers. Owing to the stable and compact optical path structure, this method is conducive to instrumentation and is expected to find wide applications in many fields.

Neuroblastoma Cells Classification Through Learning Approaches by Direct Analysis of Digital Holograms

The label-free single cell analysis by machine and Deep Learning, in combination with digital holography in transmission microscope configuration, is becoming a powerful framework exploited for phenotyping biological samples. Usually, quantitative phase images of cells are retrieved from the reconstructed complex diffraction patterns and used as inputs of a deep neural network. However, the phase retrieval process can be very time consuming and prone to errors. Here we address the classification of cells by using learning strategies with images coming directly from the raw recorded digital holograms, i.e. without any data processing or refocusing involved. Indeed, in the raw digital hologram the entire complex amplitude information of the sample is intrinsically embedded in the form of modulated fringes. We develop a training strategy, based on deep and feature based machine learning models, in order extract such information by skipping the classical reconstruction process for classifying different neuroblastoma cells. We provided an experimental validation by using the proposed strategy to classify two neuroblastoma cell lines.

All-dielectric metasurfaces capable of dual-channel complex amplitude modulation

Abstract One compound metasurface with multiple functions and precise complex amplitude modulation is beneficial to photonic integration. Here, all-silicon bifunctional metasurfaces capable of independent amplitude and phase modulation in two circular polarized channels are proposed, which encode complex amplitude information by integrating propagation phase and Pancharatnam-Berry phase. A switchable power-controllable axial bifocal metalens directly illustrates the feasibility of the proposed modulation scheme. Another switchable power-controllable horizontal/vertical bifocal metalens characterizes the versatility and flexibility of this approach. The experimental results agree well with the simulations and theoretical expectations. In addition, we also discuss the broadband performance of the proposed metalens and the dynamic focusing behavior under optical pumping. The proposed approach can directly generate editable amplitude and phase profiles and can find applications in dynamic holography, dynamic display, and other fields.

Encoding complex amplitude information onto phase-only diffractive optical elements using binary phase Nyquist gratings

We reexamine a simple technique for encoding complex amplitude information onto a phase-only spatial light modulator (SLM). The basis for the approach is to spatially vary the diffraction efficiency of a two-dimensional checkerboard binary phase diffraction grating where the period for the Nyquist grating is two pixels. As the phase depth of this 2D grating changes spatially, the amount of light diffracted into the zero order can be controlled. Unwanted information is encoded onto the first diffraction orders and is directed away from the center. This process uses a very simple coding algorithm to generate a complex beam reconstruction on-axis and allows exploiting the full spatial resolution for encoding amplitude. However, its experimental realization with the current liquid-crystal on silicon (LCOS) technology is strongly affected by the limitations imposed by the fringing effect in these devices. We provide experimental evidence of how this effect impacts the efficiency of diffraction gratings displayed on the SLM. We then show how it affects the encoding technique, both in the near field and in the Fourier transform domain, where the limitations imposed by the fringing effect are clearly visible in the form of a focused peak. These results provide evidence of the usefulness of the technique but also about the limitations imposed by the current LCOS technology, which do not allow fully exploiting their high resolution. Finally, we discuss the performance of these newer LCOS devices compared to other SLMs.

Y4-Net: a deep learning solution to one-shot dual-wavelength digital holographic reconstruction.

In this Letter, a deep learning solution (Y4-Net, four output channels network) to one-shot dual-wavelength digital holography is proposed to simultaneously reconstruct the complex amplitude information of both wavelengths from a single digital hologram with high efficiency. In the meantime, by using single-wavelength results as network ground truth to train the Y4-Net, the challenging spectral overlapping problem in common-path situations is solved with high accuracy.

Measurement of full polarization states with hybrid holography based on geometric phase.

We propose a method for measuring the full polarization states of a light field by using hybrid polarization-angular multiplexing digital holography based on geometric phase. Through acquiring the geometric phase distribution of the whole light field by only recording a composite hologram, and according to quantitative relationship between the geometric phase and polarization state, the Stokes parameters of a light field can be calculated. Compared with other methods, this method can be used to obtain the complex amplitude information of the light field simultaneously without requiring other complex devices or elements to be adjusted, thus enabling dynamic polarization state measurement. The measurement results of the light fields generated by standard polarized optical elements, vortex half-wave retarder, and liquid crystal depolarizer verified this method's feasibility and validity.

An Early Study on Imaging 3D Objects Hidden Behind Highly Scattering Media: a Round-Trip Optical Transmission Matrix Method

Imaging an object hidden behind a highly scattering medium is difficult since the wave has gone through a round-trip distortion: On the way in for the illumination and on the way out for the detection. Although various approaches have recently been proposed to overcome this seemingly intractable problem, they are limited to two-dimensional (2D) intensity imaging because the phase information of the object is lost. In such a case, the morphological features of the object cannot be recovered. Here, based on the round-trip optical transmission matrix of the scattering medium, we propose an imaging method to recover the complex amplitude (both the amplitude and the phase) information of the object. In this way, it is possible to achieve the three-dimensional (3D) complex amplitude imaging. To preliminarily verify the effectiveness of our method, a simple virtual complex amplitude object has been tested. The experiment results show that not only the amplitude but also the phase information of the object can be recovered directly from the distorted output optical field. Our method is effective to the thick scattering medium and does not involve scanning during the imaging process. We believe it probably has potential applications in some new fields, for example, using the scattering medium itself as an imaging sensor, instead of a barrier.

Lensless complex amplitude image retrieval through a visually opaque scattering medium.

We propose and experimentally demonstrate lensless complex amplitude image retrieval through a visually opaque scattering medium from spatially fluctuating fields using intensity measurement and a phase-retrieval algorithm. The complex amplitude information of the hidden object is encoded in the form of a real and nonnegative amplitude function represented as an interference pattern. A single charge coupled device (CCD) image of the scattered light collected through a visually opaque optical diffuser contains enough information to digitally regenerate the interference pattern. Furthermore, a lensless configuration is implemented which eliminates any possible aberration effects associated with optical components, and this further has promising applications where the use of imaging optics is not feasible. Experimental results for the recovery of complex fields corresponding to optical vortices of two different topological charges are presented.

Asymetric multiple-image authentication based on complex amplitude information multiplexing and RSA algorithm

By combining the iterative phase retrieval algorithm in the Fresnel domain with the shift rotation permutation operations of row vectors and column vectors, a new kind of asymmetric multiple-image authentication based on complex amplitude information multiplexing and RSA algorithm is proposed, where multiple complex amplitude information in the input plane is retrieved and generated by the phase retrieval algorithm in the Fresnel domain. In original binary amplitude mask, the row vector and column vectors random numbers are randomly generated in advance, such that each sampling mask for each authenticator is obtained by the shift rotation permutation operations of corresponding row vector and column vectors random numbers for original binary amplitude mask. Thus, one synthesized complex amplitude is generated by the operations of sampling, overlap and multiplexing, and then sent to the certification center for authentication use. At the same time, the row vector and column vectors random numbers are encoded to ciphers by the public keys of RSA algorithm, and then delivered to the corresponding authenticators. During the authentication process, the row vector and column vectors random numbers are first decoded by the private keys possessed by the authenticator; second, the authenticator’s sampling mask is reconstructed by the shift rotation permutation operations of the above decoded random numbers for original binary amplitude mask. Finally, the authenticator with other additional authentication keys is prompted to place the synthesized complex amplitude information and its sampling mask at the corresponding positions, when the system is illuminated by a plane wave with the correct wavelength. A recovered image is then recorded in the output plane, by calculating and displaying the nonlinear correlation coefficient between the recovered image and the certification image, if there exists a remarkable peak in its nonlinear correlation coefficient distributions, indicating that the authentication is successful. On the contrary, if there is no remarkable peak but uniformly distributed white noise in the map, the authentication process is a failure attempt. Any intruder with randomly generated forged authentication keys will end up with a failure which enhances the security of the system to some extent.

Circular property of complex-valued correlation learning in CMRF-based filtering for synthetic aperture radar interferometry

To deal with satellite interferometric synthetic aperture radar (InSAR), we previously proposed a powerful filtering process, namely the complex-valued Markov random field (CMRF) -based filter. There we estimate and utilize the local correlation between pixel values in interferogram. From the viewpoint of neural networks, the estimation is regarded as correlation learning in its simplest form. The correlation learning is performed in the complex domain since the InSAR system yields complex-amplitude data corresponding to the wave/coherent nature of the electromagnetic-wave propagation. This fact leads to a useful dynamics specific to such coherent radar signal processing, which cannot be realized in real-valued neural networks. One of the properties of coherent wave is circularity. We compare the performance of filters based on complex- and real-valued networks. We also evaluate the performance of the filter based on phase–amplitude network to demonstrate the importance of treating the data as complex-amplitude information in filtering SAR interferogram.

Identification of Malaria-Infected Red Blood Cells Via Digital Shearing Interferometry and Statistical Inference

Malaria is one of the most widespread diseases, particularly in Asia and Africa. Correct diagnosis of malaria is necessary for its proper treatment. A compact automated tool for malaria identification will greatly benefit healthcare professionals in these regions. We propose a method that has the potential to automatically detect malaria-infected red blood cells (RBCs). This method combines the simplicity and robustness of lateral shearing interferometry with the flexibility of statistical methods to achieve the classification of diseased RBCs. Shearing interferograms generated using a glass plate in a common path setup were Fourier analyzed to retrieve the gradient phase and amplitude information of the cell. Then, multiple features based on the complex amplitude information of the cells are measured automatically and used to differentiate healthy and malaria-infected cells. Multivariate statistical inference algorithm of the experimental data shows that there is a difference between the populations of healthy and malaria-infected RBCs by using the measured RBC features.

Three random phase encryption technology in the Fresnel diffraction system based on computer-generated hologram

We propose a new method of image encryption using Fourier computer-generated hologram (CGH) in the encryption system of multiple Fresnel diffraction transforms with phase masks. The digital image to be encrypted is modulated by a series of three random-phase masks in Fresnel diffraction system and finally is transformed into a complex-amplitude image which is stationary white noise (in which the information is like stationary-white-noise). Because the complex-amplitude information is not easy to be directly saved, the binary real value Fourier CGH is applied to record it. Compared with the traditional double random-phase image encryption technology, this method adds new keys which enhance the image encryption security and the Fourier CGH greatly improves the antinoise performance.