Coherent diffraction imaging by moving a lens

Fractional Fourier-transform off-axis digital holographic imaging

A fractional Fourier-transform digital holographic imaging method with resolution enhancement features is presented. In an optical configuration, an extended fractional Fourier-transform optical setup is set in the object arm of an off-axis digital holographic recording system to record a fractional Fourier-transform hologram via the optical interference of the fractional Fourier-transform wavefront of an object wave with a reference wave. For reconstruction imaging, the reconstruction approach for fractional Fourier-transform holograms is given. In the experiment, the fractional Fourier-transform digital holograms are recorded under the different recording parameters, and their amplitude images are effectively reconstructed. The imaging results demonstrate that the reconstruction-imaging resolution of fractional-order Fourier-transform holograms is obviously enhanced compared to that of conventional image-plane holograms. The presented fractional Fourier-transform digital holographic imaging with resolution enhancement and optical configuration flexibility provides, to our knowledge, a novel way for off-axis digital holographic imaging.

Fractional Fourier-transform filtering and reconstruction in off-axis digital holographic imaging

An off-axis digital holographic reconstruction method with fractional Fourier transform domain filtering is proposed. The theoretical expression and analysis of the characteristics of fractional-transform-domain filtering are given. It is proven that the filtering in a lower fractional-order transform domain can utilize more high-frequency components than that in a conventional Fourier transform domain under the same size of filtering regions. In simulation and experiment, the results demonstrate that the reconstruction imaging resolution can be improved by filtering in the fractional Fourier transform domain. The presented fractional Fourier transform filtering reconstruction provides a novel (to our knowlede) optional way for off-axis holographic imaging.

Enhanced Single-Beam Multiple-Intensity Phase Retrieval Using Holographic Illumination

Single-beam multiple-intensity iterative phase retrieval is a high-precision and lens-free computational imaging method, which reconstructs the complex-valued distribution of the object from a volume of axially captured diffraction intensities using the post-processing algorithm. However, for the object with slowly-varying waves, the method may encounter the problem of convergence stagnation since the lack of diversity between the captured intensity patterns. In this paper, a novel technique to enhance phase retrieval using holographic illumination is proposed. One special computer-generated hologram is designed, which can generate multiple significantly different images at the required distances. The incident plane wave is firstly modulated by the hologram, and then the exit wave is used to illuminate the object. Benefitting from this holographic illumination, remarkable intensity changes in the given detector planes can be produced, which is conducive to fast and high-accuracy reconstruction. Simulation and optical experiments are performed to verify the feasibility of the proposed method.

Image Reconstruction Using Autofocus in Single-Lens System

To reconstruct the wavefront in a single-lens coherent diffraction imaging (CDI) system, we propose a closed-loop cascaded iterative engine (CIE) algorithm based on the known information of the imaging planes. The precision of diffraction distance is an important prerequisite for a perfect reconstruction of samples. For coherent diffraction imaging with a lens, autofocus is investigated to accurately determine the object distance and image distance. For the case of only the object distance being unknown, a diffuser is used to scatter the coherent beam for speckle illumination to improve the performance of autofocus. The optimal object distance is obtained stably and robustly by combing speckle imaging with clarity evaluation functions. SSIM and MSE, using the average pixel value of the reconstructed data set as a reference, are applied on two-unknown-distance autofocus. Simulation and experiment results are presented to prove the feasibility of the CIE and proposed auto-focusing method.

Simple phase retrieval method based on two intensity measurements on a single plane

In this work, a simple phase retrieval method is proposed by observing two intensity patterns on a single plane, which are generated with and without a lens. Rigorous theoretical derivations show that the two fields constitute the Fourier transform pairs, and a modified Gerchberg-Saxton algorithm is proposed to recover the phase patterns from the Fourier pairs. The proposed method does not require the intensity patterns to be measured on two different planes along the propagation distance, and this is quite beneficial in a system with a phase tuning element like a spatial light modulator, which can form a virtual lens by creating a parabola-like phase distribution. Experiments are conducted to demonstrate the effectiveness of the proposed phase retrieval method.

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.

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.

Computational aberration correction of VIS-NIR multispectral imaging microscopy based on Fourier ptychography

Due to the chromatic dispersion properties inherent in all optical materials, even the best-designed multispectral objective will exhibit residual chromatic aberration. Here, we demonstrate a multispectral microscope with a computational scheme based on the Fourier ptychographic microscopy (FPM) to correct these effects in order to render undistorted, in-focus images. The microscope consists of 4 spectral channels ranging from 405 nm to 1552 nm. After the computational aberration correction, it can achieve isotropic resolution enhancement as verified with the Siemens star sample. We image a flip-chip to show the promise of our system to conduct fault detection on silicon chips. This computational approach provides a cost-efficient strategy for high quality multispectral imaging over a broad spectral range.

Parameter estimation of linear frequency modulation signals based on sampling theorem and fractional broadening

Linear frequency modulation (LFM) signals are a class of important radar signals, but it is difficult to estimate their parameters in electronic warfare. Fractional Fourier transform (FRFT) is one of the most important methods for estimating the parameters of LFM signals, but the computational efficiency is strongly influenced by the search range and evaluation of the optimum FRFT order. To improve the estimation speed, we present a novel method for the parameter estimation of LFM signals using sampling theorem and fractional broadening. First, sampling theorem is used to calculate the search range of the optimum FRFT transform order. Then, the LFM signals are transformed by FRFT in the search range. Finally, the fractional broadening of the LFM signals is calculated, and the optimum FRFT order is obtained according to the relationship between the fractional broadening and the FRFT order. Experiments are performed to compare the proposed method and the traditional FRFT method. The results show that the proposed method is six times faster than the traditional FRFT method while preserving the accuracy. Moreover, it can quickly and accurately achieve the parameter estimation of multi-component LFM signals in the case of white Gaussian noise with a low signal-to-noise ratio.

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.

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.

Amplitude and phase retrieval with simultaneous diversity estimation using expectation maximization

Iterative amplitude and phase retrieval algorithms have been proven to accurately reconstruct arbitrary wavefronts from multiple intensity measurements when system parameters are known exactly, given the ability to induce phase diversity between images. Such sets of intensity images with phase diversity can be generated by moving a lens in the optical system, but any position error on the lens will degenerate the reconstruction result. We demonstrate the use of an expectation-maximization algorithm with Kalman smoothing for recovering both the complex field and the lens position from a stack of intensity images. Our method successfully reduces the mean-squared-error of the estimated wavefront in comparison to an approach without position error estimation. We present and discuss the results of using a Kalman smoother and nonlinear least-squares optimization for the estimation of the moving lens position.

New design model for high efficiency cylindrical diffractive microlenses

A new model, i.e., the decreasing thickness model (DTM) is proposed and employed for designing the cylindrical diffractive microlenses (CDMs). Focal performances of the designed CDMs are theoretically investigated by solving Maxwell’s equations with the boundary element method. For comparison, the CDMs designed by the traditional equal thickness model (ETM) are also studied. Theoretical simulations demonstrate that focal performances of the designed CDMs are improved a lot via replacing the traditional ETM with the proposed DTM. Concretely, the focal efficiency is heightened and the focal spot size is shrunk. Experimental measurements verify the theoretical simulations well. Especially, the above-mentioned improvements become more prominent for the CDM with a higher numerical aperture.

Axial multi-image phase retrieval under tilt illumination

As a coherent diffractive imaging technique, axial multi-image phase retrieval utilizes a series of diffraction patterns on the basis of axial movement diversity to reconstruct full object wave field. Theoretically, fast convergence and high-accuracy of axial multi-image phase retrieval are demonstrated. In experiment, its retrieval suffers from the tilt illumination, in which diffraction patterns will shift in the lateral direction as the receiver traverses along the axis. In this case, the reconstructed result will be blurry or even mistaken. To solve this problem, we introduce cross-correlation calibration to derive the oblique angle and employ tilt diffraction into axial phase retrieval to recover a target, which is successfully demonstrated in simulation and experiment. Also, our method could provide a useful guidance for measuring how obliquely the incident light illuminates in an optical system.

Two noise-robust axial scanning multi-image phase retrieval algorithms based on Pauta criterion and smoothness constraint

We proposed two noise-robust iterative methods for phase retrieval and diffractive imaging based on the Pauta criterion and the smoothness constraint. The work is to address the noise issue plaguing the application of iterative phase retrieval algorithms in coherent diffraction imaging. It is demonstrated by numerical analysis and experimental results that our proposed algorithms have higher retrieval accuracy and faster convergence speed at a high shot noise level. Moreover, they are proved to hold the superiority to cope with other kinds of noises. Due to the inconvenience of conventional iteration indicators in experiments, a more reliable retrieval metric is put forward and verified its effectiveness. It should be noted that the proposed methods focus on exploiting the longitudinal diversity. It is anticipated that our work can further expand the application of iterative multi-image phase retrieval methods.