Axial multi-image phase retrieval under tilt illumination

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.

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.

Phase retrieval using axial diffraction patterns and a ptychographic iterative engine

We propose a phase retrieval method using axial diffraction patterns under planar and spherical wave illuminations. The proposed method uses a ptychographic iterative engine (PIE) for the phase retrieval algorithm. The proposed approach uses multiple diffraction patterns. Thus, adjusting the alignment of each diffraction pattern is mandatory, and we propose a method to adjust the alignment. In addition, a random selection of the measured diffraction patterns is used to further accelerate the convergence of the PIE-based optimization. To confirm the effectiveness of the proposed method, we compare the conventional and proposed methods using a simulation and optical experiments.

Robust autofocusing method for multi-wavelength lensless imaging

Lensless imaging based on multi-wavelength phase retrieval becomes a promising technology widely used as it has simple acquisition, miniaturized size and low-cost setup. However, measuring the sample-to-sensor distance with high accuracy, which is the key for high-resolution reconstruction, is still a challenge. In this work, we propose a multi-wavelength criterion to realize autofocusing modulation, i.e., achieving much higher accuracy in determining the sample-to-sensor distance, compared to the conventional methods. Three beams in different spectrums are adopted to illuminate the sample, and the resulting holograms are recorded by a CCD camera. The patterns calculated by performing back propagation of the recorded holograms, with exhaustively searched sample-to-sensor distance value, are adopted to access the criterion. Image sharpness can be accessed and the optimal sample-to-sensor distance can be finely determined by targeting the valley of the curve given by the criterion. Through our novel multi-wavelength based autofocusing strategy and executing further phase retrieval process, high-resolution images can be finally retrieved. The applicability and robustness of our method is validated both in simulations and experiments. Our technique provides a useful tool for multi-wavelength lensless imaging under limited experimental conditions.

Computational coherent imaging by rotating a cylindrical lens

To overcome longitudinal sampling rate fluctuation in axial multi-image computational imaging, an effortless and high-efficient optical scanning imaging system via the rotation of single cylindrical lens (RSCL) is proposed for reconstructing the amplitude and phase information of sample. Here the cylinder is a non-axial-symmetry phase modulator for generating diffracted intensity patterns. To determine the explicit rotation angle as a core parameter in the perfect reconstruction of the light field, two-step Radon transform (TsRT) is designed to obtain accurate rotation status of the cylindrical lens with diffraction patterns at the focal plane. All rotation operations are at a lateral plane for keeping the same scale in this multiple parameter computational imaging system. As a kind of scanning imaging approach, the experiment of RSCL is greatly simplified.

Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination

Multi-distance phase retrieval (MDPR) based lensfree imaging is promising for an aberration free and compact biological imaging system. In the MDPR processing, the measurement uncertainty of the sample-to-sensor distance undermines its imaging quality and imposes a heavy workload to achieve a perfect reconstruction. The optimal distance can be searched by using an image sharpness quantification function with a refocused data set, however, the scanning is sensitive to noise and aliasing artifact for MDPR. In this work, we propose an adaptive imaging scheme with the help of a diffuser inserted in the lensfree system. The optimal sample-to-sensor distance is searched by combing speckle imaging with sharpness quantification function. With this speckle-based auxiliary, intensity patterns under a coherent illumination are directly used to achieve an in-focusing image reconstruction. Experiments are given to demonstrate the stability, imaging resolution and optical sectioning for our scheme. This method provides a simple, stable and robust tool for the auto-focusing imaging.

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.

Wavefront reconstruction of a non-coaxial diffraction model in a lens system

To reconstruct a wavefront in a non-coaxial lens system, we propose a diffraction model using the Fresnel integral. Inclination angle is the newly included parameter in the mathematical formula describing beam propagation. It is determined through two ways in this paper, which are correlation operation and optical flow method. Furthermore, the multi-image phase retrieval is incorporated to reconstruct the complex optical field of sample from an overdetermined dataset. The combination is much closer to the actual situation and thus more practical. The proposed diffraction model is validated by numerical analysis and experiment. The work will further benefit the application of multi-image phase retrieval, such as in biomedical imaging and optical metrology.

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.