Linear space-variant optical cryptosystem via Fourier ptychography

Redundant information model for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a computational optical imaging technique that overcomes the traditional trade-off between resolution and field of view (FOV) by exploiting abundant redundant information in both spatial and frequency domains for high-quality image reconstruction. However, the redundant information in FPM remains ambiguous or abstract, which presents challenges to further enhance imaging capabilities and deepen our understanding of the FPM technique. Inspired by Shannon's information theory and extensive experimental experience in FPM, we defined the specimen complexity and reconstruction algorithm utilization rate and reported a model of redundant information for FPM to predict reconstruction results and guide the optimization of imaging parameters. The model has been validated through extensive simulations and experiments. In addition, it provides a useful tool to evaluate different algorithms, revealing a utilization rate of 24%±1% for the Gauss-Newton algorithm, LED Multiplexing, Wavelength Multiplexing, EPRY-FPM, and GS. In contrast, mPIE exhibits a lower utilization rate of 19%±1%.

Design of Fourier ptychographic illuminator for single full-FOV reconstruction

Fourier ptychographic microscopy (FPM) is a spatial-temporal-modulation high-throughput imaging technique via a sequential angle-varied LED illumination. Therefore, the illuminator is one of the key components and the design of this illuminator is significant. However, because of the property of spherical wave, partial coherence, and aperture-induced vignetting, the acquired images must be processed in blocks first, and rely on parallel reconstruction via a graphics processing unit (GPU). The high cost makes it unappealing compared with commercial whole slide imaging system via a low-cost central processing unit (CPU). Especially, the vignetting severely destroys the space-invariant model and induces obvious artifacts in FPM, which is the most difficult problem. The conventional method is to divide the field of view (FOV) into many tiles and omit those imperfect images, which is crude and may discards low frequency information. In this paper, we reevaluated the conditions of vignetting in FPM. Through our analysis, the maximum side length of FOV is 0.759 mm for a single full-FOV reconstruction via a 4×/0.1 NA objective and a 4 mm spacing LED array in theory, while almost 1.0 mm can be achieved in practice due to the tolerance of algorithm. We found that FPM system can treat the vignetting coefficient Vf below 0.1 as brightfield images and Vf lager than 0.9 as darkfield images, respectively. We reported an optimized distribution for designing an illuminator without vignetting effect according to the off-the-shelf commercial products, which can reconstruct full FOV in one time via a CPU. By adjusting the distribution of LED units, the system could retrieve the object with the side length of FOV up to 3.8 mm for a single full-FOV reconstruction, which achieves the largest FOV that a typical 4×/0.1 NA objective with the field number of 22 mm can afford.

Optical asymmetric JTC cryptosystem based on binary phase modulation and image superposition-subtraction operation

The joint transform correlator (JTC) cryptosystem is a simple and practical optical cryptosystem. But its identical key in both encryption and decryption brings security risks in the key distribution and management. To overcome these drawbacks, we first create a trapdoor one-way function based on image superposition and subtraction operation. Then combined with the one-way binary phase modulation, an optical asymmetric JTC cryptosystem is proposed in this paper. These two kinds of trapdoor one-way functions are not only effective and implementable, but also can greatly enhance the ability of our proposal to resist various attacks. In addition, we select the structured spiral phase mask (SSPM) controlled by its structural parameters as the key mask of the JTC cryptosystem to facilitate the key transmission. When the structural parameters of the SSPM are protected by the RSA algorithm during encryption and decryption, not only the security of the proposed cryptosystem can be enhanced, but also the key distribution and management will be improved. This also makes our proposal conform more closely to the basic agreement of the public key cryptosystem. Simulation analysis and initial experimental results verified the correctness and feasibility of our proposal.

Asymmetric double-image encryption based on chaotic random phase encoding

An asymmetric double-image encryption scheme based on chaotic random phase encoding (CRPE) is proposed. In this proposed encryption scheme, two grayscale images to be encrypted are first Fresnel transformed and combined into a complex image. Then, the amplitude and phase components are obtained by conducting phase-amplitude truncation on the complex image. Finally, the amplitude component is again Fresnel transformed and encrypted into a noise-like pattern by the CRPE in the Fresnel domain. Since the initial values and control parameters of the chaotic map can replace the random phase masks to serve as secret keys, the management and transmission of secret keys will become more convenient in the proposed encryption scheme. Furthermore, the Fresnel transform parameters and phase keys derived from the complex image's phase component can also act as secret keys during the decryption process. Numerical simulations have demonstrated the feasibility, security, and robustness of the proposed encryption scheme.

Multi-Image Encryption Method via Computational Integral Imaging Algorithm

Under the framework of computational integral imaging, a multi-image encryption scheme based on the DNA-chaos algorithm is proposed. In this scheme, multiple images are merged to one image by a computational integral imaging algorithm, which significantly improves the efficiency of image encryption. Meanwhile, the computational integral imaging algorithm can merge images at different depth distances, thereby the different depth distances of multiple images can also be used as keys to increase the security of the encryption method. In addition, the high randomness of the chaos algorithm is combined to address the outline effect caused by the DNA encryption algorithm. We have experimentally verified the proposed multi-image encryption scheme. The entropy value of the encrypted image is 7.6227, whereas the entropy value of the merge image with two input images is 3.2886, which greatly reduces the relevance of the image. The simulation results also confirm that the proposed encryption scheme has high key security and can protect against various attacks.

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

Fourier ptychographic microscopy (FPM) has risen as a promising computational imaging technique that breaks the trade-off between high resolution and large field of view (FOV). Its reconstruction is normally formulated as a blind phase retrieval problem, where both the object and probe have to be recovered from phaseless measured data. However, the stability and reconstruction quality may dramatically deteriorate in the presence of noise interference. Herein, we utilized the concept of alternating direction method of multipliers (ADMM) to solve this problem (termed ADMM-FPM) by breaking it into multiple subproblems, each of which may be easier to deal with. We compared its performance against existing algorithms in both simulated and practical FPM platform. It is found that ADMM-FPM method belongs to a global optimization algorithm with a high degree of parallelism and thus results in a more stable and robust phase recovery under noisy conditions. We anticipate that ADMM will rekindle interest in FPM as more modifications and innovations are implemented in the future.

Cross-iteration multi-step optimization strategy for three-dimensional intensity position correction in phase diverse phase retrieval

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

Optical scanning Fourier ptychographic microscopy

We propose a lower-cost and practical active scanning optical scanning Fourier ptychographic microscopy (OSFPM). Featured is a simple setup of Galvo mirrors capable of scanning large-sized objects. The active scanning laser beam is projected onto the sample in a circular pattern to form multiple lower-resolution images. With multiple lower-resolution images, a higher-resolution image is subsequently reconstructed. The OSFPM is able to more precisely control the overlap of the incident light illumination as compared to that in conventional LED-based or other laser-based scanning FPM systems. The proposed microscope is also suitable for applications where a larger size of the object needs to be imaged with efficient illumination.

Coherent synthetic aperture imaging for visible remote sensing via reflective Fourier ptychography

Synthetic aperture radar can measure the phase of a microwave with an antenna, which cannot be directly extended to visible light imaging due to phase lost. In this Letter, we report an active remote sensing with visible light via reflective Fourier ptychography, termed coherent synthetic aperture imaging (CSAI), achieving high resolution, a wide field-of-view (FOV), and phase recovery. A proof-of-concept experiment is reported with laser scanning and a collimator for the infinite object. Both smooth and rough objects are tested, and the spatial resolution increased from 15.6 to 3.48 µm with a factor of 4.5. The speckle noise can be suppressed obviously, which is important for coherent imaging. Meanwhile, the CSAI method can tackle the aberration induced from the optical system by one-step deconvolution and shows the potential to replace the adaptive optics for aberration removal of atmospheric turbulence.

High-resolution and large field-of-view Fourier ptychographic microscopy and its applications in biomedicine

Fourier ptychographic microscopy (FPM) is a promising and fast-growing computational imaging technique with high resolution, wide field-of-view (FOV) and quantitative phase recovery, which effectively tackles the problems of phase loss, aberration-introduced artifacts, narrow depth-of-field and the trade-off between resolution and FOV in conventional microscopy simultaneously. In this review, we provide a comprehensive roadmap of microscopy, the fundamental principles, advantages, and drawbacks of existing imaging techniques, and the significant roles that FPM plays in the development of science. Since FPM is an optimization problem in nature, we discuss the framework and related work. We also reveal the connection of Euler's formula between FPM and structured illumination microscopy. We review recent advances in FPM, including the implementation of high-precision quantitative phase imaging, high-throughput imaging, high-speed imaging, three-dimensional imaging, mixed-state decoupling, and introduce the prosperous biomedical applications. We conclude by discussing the challenging problems and future applications. FPM can be extended to a kind of framework to tackle the phase loss and system limits in the imaging system. This insight can be used easily in speckle imaging, incoherent imaging for retina imaging, large-FOV fluorescence imaging, etc.

Single-shot sequential projection phase retrieval and 3D localization from chromatic aberration

A phase retrieval method based on sequential projection and chromatic aberration is reported. Construction of this method includes a red, green and blue (RGB) LED, an objective and a color camera. Owing to the chromatic aberration characteristics of the objective, three color images obtained by the color camera correspond to three equivalent propagation planes. Equivalent relative distances among these planes can be obtained by defining and iteratively minimizing the convergence index. Then, sequential projection strategy is used for phase retrieval in each image plane. Based on the recovered phase information and angular spectrum propagation principle, digital refocusing and 3D localization can be achieved for each subregion of the sample. Finally, the feasibility of our method is demonstrated by simulations and experiments.

Known-plaintext attack to optical encryption systems with space and polarization encoding

Space-based optical encryption (SBOE) and double random polarization encoding (DRPO) are previously considered to be more secure than common random-phase-encoding-based optical cryptosystems. The known-plaintext attack (KPA) to SBOE and DRPO was seldomly investigated in the past. A matrix regression approach based on training samples is proposed in this paper to crack these two optical cryptosystems. The relationship between plaintexts and ciphertexts is directly modeled by a complex-amplitude weighting matrix, which is optimized by a gradient descent algorithm. This approach has a simple model compared with deep learning and the KPA can be implemented without recovering the exact key. Our proposed KPA schemes reveal the security flaws of SBOE and DRPO, as well as other linear optical cryptosystems.