Wavefront sensing with random amplitude mask and phase retrieval

Maximizing atmospheric-disturbed fiber coupling efficiency with speckle-based phase retrieval and a single-pixel camera

An approach to adaptive optics utilizing a single-pixel camera (SPC) is proposed to maximize fiber coupling efficiency at the receiver side of an optical satellite-to-ground link perturbed by atmospheric turbulence. Using a single-pixel wavefront sensor enables operation at longer optical wavelengths, such as near and far infrared, which have advantageous propagation characteristics for free space optical communication. In this approach, a focal plane intensity image of the atmospheric-disturbed wavefront is taken via an SPC using a compressed sensing technique. An iterative speckle-based phase retrieval algorithm is then applied to infer the phase distortion corrected by a deformable mirror in a feedback loop. This computational approach to inferring the phase of the wavefront overcomes the limitations of traditional Shack-Hartman-based approaches, which are difficult to implement at high speed and at the long infrared wavelengths proposed for future optical satellite communication downlinks. It has been shown that fiber coupling efficiency is increased from less than 5% to 40%-50% in medium-to-strong turbulence scenarios with the phase retrieval algorithm proposed in this work.

Phase retrieval for arbitrary complex-valued objects using structured illumination

A method to solve of the phase retrieval problem in a non-convex formulation for complex-valued objects with a support constraint is proposed. It is shown that two coded diffraction patterns (CDPs) obtained in the same Fresnel or Fraunhofer diffraction plane by masking an object with two, direct and inverse, random binary amplitude masks, are sufficient to reconstruct an arbitrary complex-valued object up to the global phase. The general solution of the problem was found as the sum of two mutually phase-consistent partial solutions obtained by applying the modified error-reduction or hybrid input-output algorithm to each of two "mask+CDP" pairs. The results of model experiments confirmed the possibility of noise-resistant and high-accuracy retrieval of complex-valued objects of various types with the oversampling ratio σ ≥ 2 making use of a small number of iterations. The method is applicable to coherent radiation of any kind.

Tailoring 3D Speckle Statistics

We experimentally generate three-dimensional speckles with customized intensity statistics. By appropriately modulating the phase front of a laser beam, the far-field speckles can maintain a desired intensity probability density function upon axial propagation: while evolving into different spatial patterns. We also demonstrate how to design speckle patterns that obtain distinct tailored intensity statistics on multiple designated axial planes. The ability to design 3D speckle statistics opens many possibilities: three-dimensional imaging and sensing, optical trapping, and manipulation.

Adaptive optics compensation of orbital angular momentum beams using a hybrid input-output algorithm with complementary binary masks

For orbital angular momentum (OAM) beams, we show that the twin-image problem in the single-intensity-measurement hybrid input-output algorithm (HIOA) severely impairs the phase retrieval performance and propose a very simple method to overcome this problem. First, we introduce the principle of the single-intensity-measurement HIOA together with the underlying reason for the twin-image problem and propose a new scheme of the HIOA using a pair of complementary binary masks (CBMs) to overcome the twin-image problem. To verify the usefulness of the proposed CBM-HIOA in the OAM free-space optical system, a wave-optics simulation is used to produce relatively realistic atmospheric turbulence, and the turbulence-induced distorted phase of the probe Gaussian beam is retrieved to compensate for the phase distortion of OAM beams. The suppression of the bidirectional and stagnant convergence caused by the twin-image problem, the compensation of the turbulence-induced distorted phase of the OAM beams, and the influence of different CBM shapes are studied in detail by numerical simulations. The corresponding numerical results show the feasibility and efficacy of the CBM-HIOA used for the adaptive optics compensation of OAM beams.

SiSPRNet: end-to-end learning for single-shot phase retrieval

With the success of deep learning methods in many image processing tasks, deep learning approaches have also been introduced to the phase retrieval problem recently. These approaches are different from the traditional iterative optimization methods in that they usually require only one intensity measurement and can reconstruct phase images in real-time. However, because of tremendous domain discrepancy, the quality of the reconstructed images given by these approaches still has much room to improve to meet the general application requirements. In this paper, we design a novel deep neural network structure named SiSPRNet for phase retrieval based on a single Fourier intensity measurement. To effectively utilize the spectral information of the measurements, we propose a new feature extraction unit using the Multi-Layer Perceptron (MLP) as the front end. It allows all pixels of the input intensity image to be considered together for exploring their global representation. The size of the MLP is carefully designed to facilitate the extraction of the representative features while reducing noises and outliers. A dropout layer is also equipped to mitigate the possible overfitting problem in training the MLP. To promote the global correlation in the reconstructed images, a self-attention mechanism is introduced to the Up-sampling and Reconstruction (UR) blocks of the proposed SiSPRNet. These UR blocks are inserted into a residual learning structure to prevent the weak information flow and vanishing gradient problems due to their complex layer structure. Extensive evaluations of the proposed model are performed using different testing datasets of phase-only images and images with linearly related magnitude and phase. Experiments were conducted on an optical experimentation platform (with defocusing to reduce the saturation problem) to understand the performance of different deep learning methods when working in a practical environment. The results demonstrate that the proposed approach consistently outperforms other deep learning methods in single-shot maskless phase retrieval. The source codes of the proposed method have been released in Github [see references].

Phase retrieval by random binary amplitude modulation and ptychography principle

An improved binary amplitude modulation-based phase retrieval method studied by means of simulations and experiments is presented in this paper. The idea of ptychography is introduced for the purpose of designing random binary amplitude masks. The masks have the features that part of the light transmission regions is overlapped with each other and the overlapping positions are randomly distributed. The requirement for the consistency of light field in overlapping regions forms a strong constraint which is similar to the overlap constraint in ptychography. The constraint makes the iterative algorithm have high convergence accuracy in comparison to that of the original binary amplitude modulation method. Influences of amounts and overlap ratio of the modulation mask on reconstruction accuracy and speed of imaging process are analyzed. The comparison between our method and the original binary amplitude modulation method is performed in order to verify the feasibility of the proposed method.

Enhancing Multi-Distance Phase Retrieval via Unequal Interval Measurements

In the conventional methods of multi-distance phase retrieval, the diffraction intensity patterns are recorded at equal intervals, which can induce slow convergence or stagnation in the subsequent reconstruction process. To solve this problem, a measurement method with unequal intervals is proposed in this paper. The interval spacings between adjacent measurement planes are decreased gradually. A large gap accelerates retrieval progress, and a short span helps to recover detailed information. The proposed approach makes full use of the available measured dataset and simultaneously generates variations in diversity amplitude, which is a crucial issue for the techniques of multi-image phase retrieval. Both computational simulations and experiments are performed. The results demonstrate that this method can improve the convergence speed by 2 to 3 times and enhance the quality of reconstruction results in comparison to that of the conventional methods.

Fourier single-pixel reconstruction of a complex amplitude optical field

Based on a Fourier single-pixel imaging (SPI) technique and interference between an unknown field and a reference beam, we implement amplitude and phase reconstruction of the unknown complex field. In this Letter, we use a chessboard pattern to divide the unknown field into the signal and reference parts. A high-speed digital micro-mirror device is used to modulate the relative phase between the reference and signal fields, and the SPI method is used to acquire the Fourier spectrum of the signal field. We experimentally reconstruct a 103×103-pixel complex amplitude field with a resolution of 68.4 μm. The single-pixel real-time wavefront detection is also implemented in the rate of four frames per second.

Super-resolution microscopy for biological specimens: lensless phase retrieval in noisy conditions

The paper is devoted to a computational super-resolution microscopy. A complex-valued wavefront of a transparent biological cellular specimen is restored from multiple intensity diffraction patterns registered with noise. For this problem, the recently developed lensless super-resolution phase retrieval algorithm [Optica, 4(7), 786 (2017)] is modified and tuned. This algorithm is based on a random phase coding of the wavefront and on a sparse complex-domain approximation of the specimen. It is demonstrated in experiments, that the reliable phase and amplitude imaging of the specimen is achieved for the low signal-to-noise ratio provided a low dynamic range of observations. The filterings in the observation domain and specimen variables are specific features of the applied algorithm. If these filterings are omitted the algorithm becomes a super-resolution version of the standard iterative phase retrieval algorithms. In comparison with this simplified algorithm with no filterings, our algorithm shows a valuable improvement in imaging with much smaller number of observations and shorter exposure time. In this way, presented algorithm demonstrates ability to work in a low radiation photon-limited mode.

3D Imaging Based on Depth Measurement Technologies

Three-dimensional (3D) imaging has attracted more and more interest because of its widespread applications, especially in information and life science. These techniques can be broadly divided into two types: ray-based and wavefront-based 3D imaging. Issues such as imaging quality and system complexity of these techniques limit the applications significantly, and therefore many investigations have focused on 3D imaging from depth measurements. This paper presents an overview of 3D imaging from depth measurements, and provides a summary of the connection between the ray-based and wavefront-based 3D imaging techniques.

Coherent amplitude modulation imaging based on partially saturated diffraction pattern

A single-shot phase retrieval algorithm based on a random aperture and partially saturated diffraction pattern is proposed. The diffraction pattern in the saturated area could be retrieved during the iterative process, which circumvents the problem of limited dynamic range of the detector. Besides, the random aperture is easier to be manufactured and if the accuracy of the random aperture is high enough, the design value could be used directly for iterations. It has the potential to be adapted for different wavelengths without additional transmission measurement of the wave modulator. The validity has been demonstrated by simulations and experiment.

A fast-converging iterative method based on weighted feedback for multi-distance phase retrieval

Multiple distance phase retrieval methods hold great promise for imaging and measurement due to their less expensive and compact setup. As one of their implementations, the amplitude-phase retrieval algorithm (APR) can achieve stable and high-accuracy reconstruction. However, it suffers from the slow convergence and the stagnant issue. Here we propose an iterative modality named as weighted feedback to solve this problem. With the plug-ins of single and double feedback, two augmented approaches, i.e. the APRSF and APRDF algorithms, are demonstrated to increase the convergence speed with a factor of two and three in experiments. Furthermore, the APRDF algorithm can extend the multiple distance phase retrieval to the partially coherent illumination and enhance the imaging contrast of both amplitude and phase, which actually relaxes the light source requirement. Thus the weighted feedback enables a fast-converging and high-contrast imaging scheme for the iterative phase retrieval.

Enhancing imaging contrast via weighted feedback for iterative multi-image phase retrieval

Iterative phase retrieval (IPR) has developed into a feasible and simple computational method to retrieve a complex-valued sample. Due to coherent illumination, the reconstructed image quality is degraded by speckle noise arising from a laser. Accordingly, partially coherent illumination has been introduced to alleviate this restriction. We apply weighted feedback modality into multidistance and multiwavelength phase retrieval to realize high-contrast and fast imaging. In simulation, it is proved that IPR based on weighted feedback accelerates the convergence in partially coherent illumination and speckle illumination. In experiment, the resolution chart and biological specimen are reconstructed in lensless and lens-based systems, which also demonstrate the performance of weighted feedback. This work provides a simple and high-contrast imaging modality for IPR. Also, it facilitates compact and flexible experimental implementation for label-free imaging.

Real-time acquisition of complex optical fields by binary amplitude modulation

We describe, through simulations and experiments, a real-time wavefront acquisition technique using random binary amplitude masks and an iterative phase retrieval algorithm based on the Fresnel propagator. By using a digital micromirror device, it is possible to recover an unknown complex object by illuminating with this set of masks and simultaneously recording the resulting intensity patterns with a high-speed camera, making this technique suitable for dynamic applications.

Wavefront sensing based on a spatial light modulator and incremental binary random sampling

A wavefront sensing method based on a spatial light modulator (SLM) and an incremental binary random sampling (IBRS) algorithm is proposed. In this method, the recording setup is built just by a transmittance SLM and an image sensor. The tested wavefront incident to the SLM plane can be quantitatively retrieved from the diffraction intensities of the wavefront passed through the SLM displaying a IBRS pattern. Because only two modulation states (opaque and transparent) of the SLM are used, the method does not need to know the concrete modulation function of the SLM in advance. In addition by introducing the concept of the incremental random sampling into wavefront sensing, the adaptability of phase retrieving based on the diffraction intensities is significantly improved. To the best of our knowledge, no previous study has used this concept for the same purpose. Some experimental results are given for demonstrating the feasibility of our method.

Spatial-light-modulator-based adaptive optical system for the use of multiple phase retrieval methods

We propose an adaptive optical setup using a spatial light modulator (SLM), which is suitable to perform different phase retrieval methods with varying optical features and without mechanical movement. By this approach, it is possible to test many different phase retrieval methods and their parameters (optical and algorithmic) using one stable setup and without hardware adaption. We show exemplary results for the well-known transport of intensity equation (TIE) method and a new iterative adaptive phase retrieval method, where the object phase is canceled by an inverse phase written into part of the SLM. The measurement results are compared to white light interferometric measurements.

Application of the speckle-based phase retrieval method in reconstructing two unknown interfering wavefronts

We numerically demonstrate a novel method to simultaneously reconstruct two unknown interfering wavefronts. The speckle-based phase retrieval technique is applied to derive the interference field. The derived interference field along with the phase-shifting concept is used for calculating the interfering wavefronts. Our results show the success of this method even under noisy conditions.

Phase retrieval and diffractive imaging based on Babinet's principle and complementary random sampling

We proposed an iterative method for phase retrieval and diffractive imaging based on Babinet's principle and complementary random sampling (CRS). We demonstrated that the whole complex amplitude (not sieved) of an object wave can be accurately retrieved from the diffraction intensities of the object wave sampled by a group of binary CRS masks and the diffractive imaging for the object can be realized through a single digital inverse diffraction. Some experimental results are given for the demonstration. Our experimental results reveal that, using CRS, the influence of a binary random sampling mask on the retrieved field can be well eliminated, and the accuracy and efficiency of the phase retrieval can be greatly improved.

Quantitative cell imaging using single beam phase retrieval method

Quantitative three-dimensional imaging of cells can provide important information about their morphology as well as their dynamics, which will be useful in studying their behavior under various conditions. There are several microscopic techniques to image unstained, semi-transparent specimens, by converting the phase information into intensity information. But most of the quantitative phase contrast imaging techniques is realized either by using interference of the object wavefront with a known reference beam or using phase shifting interferometry. A two-beam interferometric method is challenging to implement especially with low coherent sources and it also requires a fine adjustment of beams to achieve high contrast fringes. In this letter, the development of a single beam phase retrieval microscopy technique for quantitative phase contrast imaging of cells using multiple intensity samplings of a volume speckle field in the axial direction is described. Single beam illumination with multiple intensity samplings provides fast convergence and a unique solution of the object wavefront. Three-dimensional thickness profiles of different cells such as red blood cells and onion skin cells were reconstructed using this technique with an axial resolution of the order of several nanometers.

Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging

In recent years, the interferometric imaging method has been applied to analyze the structure of various specimens, such as crystals and biological tissues. However, the interferometric imaging method may require a relatively complex optical recording system, such as a reference wave and temporal coherence. In this paper, we propose a method based on noninterferometric imaging for quantitative phase retrieval of complex-valued specimens. A strategy using different focal lengths in the lens function is developed, and a series of diffraction intensity maps is recorded. Numerical simulation results are presented to demonstrate the feasibility and effectiveness of the proposed method.

Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging

In recent years, coherent diffractive imaging has been considered as a promising alternative for information retrieval instead of conventional interference methods. Coherent diffractive imaging using the X-ray light source has opened up a new research perspective for the measurement of non-crystalline and biological specimens, and can achieve unprecedentedly high resolutions. In this paper, we show how a three-dimensional (3D) particle-like distribution and coherent diffractive imaging can be applied for a study of optical cryptography. An optical multiple-random-phase-mask encoding approach is used, and the plaintext is considered as a series of particles distributed in a 3D space. A topology concept is also introduced into the proposed optical cryptosystem. During image decryption, a retrieval algorithm is developed to extract the plaintext from the ciphertexts. In addition, security and advantages of the proposed optical cryptography topology are also analyzed.

Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields

Generally, 3D digital holographic microscopy requires the interference of the object wave with a known reference beam under coherent illumination to perform numerical focusing. This configuration may be challenging for some applications, including the use of exotic wavelengths such as x rays, miniaturized instrumentation, etc. Single-beam intensity measurement followed by phase retrieval techniques is attractive for wavefront sensing and reconstruction, including applications with low coherence. We use this method to construct a 3D microscope using volume speckle fields. Transparent phase objects are investigated using this principle. To the best of our knowledge, this is the first report on the application of this principle applied to microscopy.

Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval

Shape and deformation measurement of diffusely reflecting 3D objects are very important in many application areas, including quality control, nondestructive testing, and design. When rough objects are exposed to coherent beams, the scattered light produces speckle fields. A method to measure the shape and deformation of 3D objects from the sequential intensity measurements of volume speckle field and phase retrieval based on angular-spectrum propagation technique is described here. The shape of a convex spherical surface was measured directly from the calculated phase map, and micrometer-sized deformation induced on a metal sheet was obtained upon subtraction of the phase, corresponding to unloaded and loaded states. Results from computer simulations confirm the experiments.

Angular displacement and deformation analyses using a speckle-based wavefront sensor

Wavefronts incident on a random phase plate are reconstructed via phase retrieval utilizing axially displaced speckle intensity measurements and the wave propagation equation. Retrieved phases and phase subtraction facilitate the investigations of wavefronts from test objects before and after undergoing a small rotation or deformation without sign ambiguity. Angular displacement (Deltatheta) between incident planar wavefronts is determined from the light source vacuum wavelength (lambda) divided by the fringe spacing (Lambda). Fourier analysis of the wavefront phase difference yields a peak frequency that is inversely proportional to Lambda, and the sign gives the direction of rotation. Numerical simulations confirm the experimental results. In the experiments, the smallest Deltatheta measured is 0.031 degrees . The technique also permits deformation analysis of a reflecting test object under thermal loading. The technique offers simple, high resolution, noncontact, and whole field evaluation of three-dimensional objects before and after undergoing rotation or deformation.

Generation of hollow Gaussian beam by phase-only filtering

We propose a novel phase retrieval algorithm in Hankel (or called Fourier-Bessel) transform domains by using Monte-Carlo method. Based on the proposed algorithm, we investigate the generation of Gaussian-like beams, such as hollow Gaussian beam, Bessel-Gaussian beam and Laguerre-Gaussian beam, with double phase filtering operations. The phase distributions of filters are determined by employing the proposed phase retrieval algorithm. The advantage of the method is that the total energy of the beam is conservative. Numerical simulations are shown to demonstrate the validity of the scheme.

Interferometric evaluation of angular displacements using phase retrieval

Phase retrieval is carried out using sequential intensity measurements of a volume speckle field and a wave propagation equation. Retrieved phases and phase subtraction facilitate the analysis of wavefronts before and after undergoing a small rotation. Angular displacement between incident planar wavefronts is determined from the unwrapped phase difference, phase diffuser aperture diameter, and the light source wavelength. Numerical simulations confirm the experimental results.

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.

Wavefront sensing using speckles with fringe compensation

Wavefront sensing with numerical phase-error correction system is carried out using a random phase plate and phase retrieval using multiple intensity measurements of axially-displaced speckle patterns and the wave propagation equation. Various wavefronts with smooth curvatures incident on the developed phase plate (DPP) are examined: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious fringe pattern in the wavefront reconstructions due to a small tilt (Delta theta=0.212 degrees) in the plane illumination wave is detected and numerically corrected for. Fringe pattern of the illumination wave obtained for the setup without the phase object being investigated is used as reference fringe pattern. Fringe compensation yields wavefronts with the correct shape and numerical value based on the specifications of the setup. The numerical phase-error correction system described in this study can be extended to other types of phase errors such as those due to aberrations if optical elements are present in the setup or due to perturbations in the environment.