Complex Amplitude Reconstruction Research Articles

Complex amplitude field recovery of a scattering media obstructed object with multi-captured images.

An iterative-based method for recovering the complex amplitude field behind scattering media is presented in this Letter. This method compensates the random phase modulation of scattering media by using multiple captured scattered light fields. Complex amplitude reconstruction with local iterative averaging of scattered light fields, and double weighted feedback is efficiently applied. Two feasible types of system setups, with varying detector positions and wavelength, are proposed. Simulations and proof-of-concept experiments are employed to demonstrate the effectiveness of the proposed method in reconstructing complex amplitude of a hidden target.

Dual-plane coupled phase retrieval for non-prior holographic imaging

Accurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves. Digital holography (DH) can perform quantitative analysis of wave–matter interactions. Full detector-bandwidth reconstruction can be realized based on in-line DH. But the overlapping of twin images strongly prevents quantitative analysis. For off-axis DH, the object wave and the detector bandwidth need to satisfy certain conditions to perform reconstruction accurately. Here, we present a reliable approach involving a coupled configuration for combining two in-line holograms and one off-axis hologram, using a rapidly converging iterative procedure based on two-plane coupled phase retrieval (TwPCPR) method. It realizes a fast-convergence holographic calculation method. High-resolution and full-field reconstruction by exploiting the full bandwidth are demonstrated for complex-amplitude reconstruction. Off-axis optimization phase provides an effective initial guess to avoid stagnation and minimize the required measurements of multi-plane phase retrieval. The proposed strategy works well for more extended samples without any prior assumptions of the objects including support, non-negative, sparse constraints, etc. It helps to enhance and empower applications in wavefront sensing, computational microscopy and biological tissue analysis.

Multi-depth hologram generation using stochastic gradient descent algorithm with complex loss function

The stochastic gradient descent (SGD) method is useful in the phase-only hologram optimization process and can achieve a high-quality holographic display. However, for the current SGD solution in multi-depth hologram generation, the optimization time increases dramatically as the number of depth layers of object increases, leading to the SGD method nearly impractical in hologram generation of the complicated three-dimensional object. In this paper, the proposed method uses a complex loss function instead of an amplitude-only loss function in the SGD optimization process. This substitution ensures that the total loss function can be obtained through only one calculation, and the optimization time can be reduced hugely. Moreover, since both the amplitude and phase parts of the object are optimized, the proposed method can obtain a relatively accurate complex amplitude distribution. The defocus blur effect is therefore matched with the result from the complex amplitude reconstruction. Numerical simulations and optical experiments have validated the effectiveness of the proposed method.

Iterative algorithm for beam complex amplitude reconstruction by radial shearing interferometry

An iterative algorithm for precisely reconstructing the complex amplitude of a laser beam based on a radial shearing interferometer is proposed. First, the complex amplitude of the modulation function that includes the test beam’s information is obtained from a cyclic radial shearing interferogram by the Fourier filtering method. Then the complex amplitude of the modulation function is used to estimate the complex amplitude of the laser output with a successive iterative process. The simulations and real experimental results show the performance of the proposed iteration method of beam complex amplitude reconstruction.

Complex amplitude reconstruction by iterative amplitude-phase retrieval algorithm with reference

Multi-image iterative phase retrieval methods have been successfully applied in plenty of research fields due to their simple but efficient implementation. However, there is a mismatch between the measurement of the first long imaging distance and the sequential interval. In this paper, an amplitude-phase retrieval algorithm with reference is put forward without additional measurements or priori knowledge. It gets rid of measuring the first imaging distance. With a designed update formula, it significantly raises the convergence speed and the reconstruction fidelity, especially in phase retrieval. Its superiority over the original amplitude-phase retrieval (APR) method is validated by numerical analysis and experiments. Furthermore, it provides a conceptual design of a compact holographic image sensor, which can achieve numerical refocusing easily.

An iterative algorithm for beam complex amplitude reconstruction by radial shearing interferometry

An iterative algorithm for beam complex amplitude reconstruction by radial shearing interferometry

Determination of the laser beam quality factor (M2) by stitching quadriwave lateral shearing interferograms with different exposures.

A complete complex amplitude reconstruction method for the determination of the laser beam quality factor M2 based on the multiple exposure of a quadriwave lateral shearing interferometer (QWLSI) is presented. The theoretical analysis and simulation of the influence of the information in the small signal area on the calculation of the M2 factor is provided. The experimental results demonstrate that the new method can be an accurate means to measure the M2 factor. The proposed method can avoid the influence of phase inaccuracy in the small signal area of the interferogram, during the measurement of the M2 factor.

Real-time complex amplitude reconstruction method for beam quality M2 factor measurement.

We present a real-time complex amplitude reconstruction method for determining the beam propagation ratio M2 of laser beams based on the transport of intensity equation (TIE). In this work, a synchronous acquisition system consisting of two identical CCDs is established. Once two beam intensity images at different cross-section positions along the optical axis are captured simultaneously by the system, the complex amplitude of the laser beam can be rapidly reconstructed using TIE algorithm. Then the beam intensity distribution at any section position along its propagation direction can be obtained by using angular spectrum (AS) theory. The beam quality M2 factor is therefore calculated utilizing the second-order moments and hyperbola fitting methods, which conform to the ISO standard. The suitability of this method is verified by the numerical analysis and experiments with the He-Ne and high-power fiber laser sources, respectively. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor.

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M2 factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M2 factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Super-resolution complex amplitude reconstruction of nanostructured binary data using an interference microscope with pattern matching

We propose a new method of optically reconstructing binary data formed by nanostructures with an elemental size several tens of nanometers smaller than the diffraction limit, implemented with an interference microscope and a complex-amplitude image pattern matching method. We examine the size dependency of the data reconstruction capacity using a light propagation simulation based on the finite-difference time-domain (FDTD) method and the Fourier spatial frequency filtering method. We demonstrated that the readable size of the binary nanostructure depends on the magnitude of noise.

Complex amplitude reconstruction and phase aberrations compensation in phase-shifting in-line image digital holographic microscopy

When an image digital holographic microscopy (DHM) layout is employed, the Fresnel integral cannot be used in separating the reconstructed image from its conjugate image and background. However, combining image plane DHM with the phase-shifting in-line technique, the complex amplitude of reconstructed image can be obtained without using Fresnel integral, moreover the approximate error of reconstruction calculation is easily eliminated and the signal-to-noise ratio of reconstructed image is significantly improved. Since a normal incidence plane wave is used as the reference wave, the difficulty and complexity of phase aberration and phase unwrapping of DHM are remarkably decreased.

Iterative generation of holograms on spatial light modulators

Iterative learning procedures on a hybrid electro-optic system can be employed to generate holograms on inexpensive liquid-crystal-television spatial light modulators. The algorithm takes into account random electronic noise in the system and compensates for spatial-light-modulator distortions. Experimental results are given for the reconstruction of intensity distribution, and computer complex amplitude reconstruction.