Single-plane multiple speckle pattern phase retrieval using a deformable mirror

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.

High-resolution multi-wavelength lensless diffraction imaging with adaptive dispersion correction

Multi-wavelength imaging diffraction system is a promising phase imaging technology due to its advantages of no mechanical movement and low complexity. In a multi-wavelength focused system, spectral bandwidth and dispersion correction are critical for high resolution reconstruction. Here, an optical setup for the multi-wavelength lensless diffraction imaging system with adaptive dispersion correction is proposed. Three beams with different wavelengths are adopted to illuminate the test object, and then the diffraction patterns are recorded by a image sensor. The chromatic correction is successfully realized by a robust refocusing technique. High-resolution images can be finally retrieved through phase retrieval algorithm. The effectiveness and reliability of our method is demonstrated in numerical simulation and experiments. The proposed method has the potential to be an alternative technology for quantitative biological 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.

Optimization of random phase diversity for adaptive optics using an LCoS spatial light modulator

Phase retrieval is an attractive approach for sensor-less adaptive optics (AO) because of its relatively simple implementation. Recently, random phase diversity has shown fast convergence for phase retrieval algorithms. In this study, design optimization using random phase diversity is discussed with respect to a sensor-less AO system using a liquid-crystal-on-silicon (LCoS) spatial light modulator. The extrinsic phase disturbances studied are due to Kolmogorov turbulence. Simulation analysis shows that the size of super-pixel segments of the random phase patterns on the LCoS and the cropped image area of the phasorgrams are determined by Fried's parameter for high-Strehl-ratio and low-iteration-number reconstruction. AO experiments with an LCoS spatial light modulator confirm the simulation results.

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.

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.

Phase and amplitude beam shaping with two deformable mirrors implementing input plane and Fourier plane phase modifications

We find that ideas in optical image encryption can be very useful for adaptive optics in achieving simultaneous phase and amplitude shaping of a laser beam. An adaptive optics system with simultaneous phase and amplitude shaping ability is very desirable for atmospheric turbulence compensation. Atmospheric turbulence-induced beam distortions can jeopardize the effectiveness of optical power delivery for directed-energy systems and optical information delivery for free-space optical communication systems. In this paper, a prototype adaptive optics system is proposed based on a famous image encryption structure. The major change is to replace the two random phase plates at the input plane and Fourier plane of the encryption system, respectively, with two deformable mirrors that perform on-demand phase modulations. A Gaussian beam is used as an input to replace the conventional image input. We show through theory, simulation, and experiments that the slightly modified image encryption system can be used to achieve arbitrary phase and amplitude beam shaping within the limits of stroke range and influence function of the deformable mirrors. In application, the proposed technique can be used to perform mode conversion between optical beams, generate structured light signals for imaging and scanning, and compensate atmospheric turbulence-induced phase and amplitude beam distortions.

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.

Coherent laser phase retrieval in the presence of measurement imperfections and incoherent light

Phase retrieval is a powerful numerical method that can be used to determine the wavefront of laser beams based only on intensity measurements, without the use of expensive, low-resolution specialized wavefront sensors such as Shack-Hartmann sensors. However, phase retrieval techniques generally suffer from poor convergence and fidelity when the input measurements contain electronic or optical noise and/or an incoherent intensity contribution overlapped with the otherwise spatially coherent laser beam. Here, we present an implementation of a modified version of the standard multiple-plane Gerchberg-Saxton algorithm and demonstrate that it is highly successful at extracting the intensity profile and wavefront of the spatially coherent part of the light from various lasers, including tapered laser diodes, at a very high fidelity despite the presence of incoherent light and noise.

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.

Complex wavefront reconstruction from multiple-image planes produced by a focus tunable lens

We propose, through simulations and experiments, a wavefront reconstruction technique using a focus-tunable lens and a phase-retrieval technique. A collimated beam illuminates a complex object (amplitude and phase), and a diffuser then modulates the outgoing wavefront. Finally the diffracted complex field reaches the focus-tunable lens, and a CMOS camera positioned at a fixed plane registers the subjective speckle distribution produced by the lens (one pattern for each focal length). We have demonstrated that a tunable lens can replace the translation stage used in the conventional single-beam, multiple-intensity reconstruction algorithm. In other words, through iterations with a modified version of this algorithm, the speckle images produced by different focal lengths can be successfully employed to recover the initial complex object. With no movable elements, (speckle) image sampling can be performed at high frame rates, which is suitable for dynamical reconstruction applications.

Optical encryption using multiple intensity samplings in the axial domain

Image encryption with optical means has attracted attention due to its inherent multidimensionality and degrees of freedom, including phase, amplitude, polarization, and wavelength. In this paper, we propose an optical encoding system based on multiple intensity samplings of the complex-amplitude wavefront with axial translation of the image sensor. The optical encoding system is developed based on a single optical path, where multiple diffraction patterns, i.e., ciphertexts, are sequentially recorded through the axial translation of a CCD camera. During image decryption, an iterative phase retrieval algorithm is proposed for extracting the plaintext from ciphertexts. The results demonstrate that the proposed phase retrieval algorithm possesses a rapid convergence rate during image decryption, and high security can be achieved in the proposed optical cryptosystem. In addition, other advantages of the proposed method, such as high robustness against ciphertext contaminations, are also analyzed.

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.

Correction for spatial averaging in laser speckle contrast analysis

Practical laser speckle contrast analysis systems face a problem of spatial averaging of speckles, due to the pixel size in the cameras used. Existing practice is to use a system factor in speckle contrast analysis to account for spatial averaging. The linearity of the system factor correction has not previously been confirmed. The problem of spatial averaging is illustrated using computer simulation of time-integrated dynamic speckle, and the linearity of the correction confirmed using both computer simulation and experimental results. The valid linear correction allows various useful compromises in the system design.