Hybrid Input-output Algorithm Research Articles

Robust 3D phase retrieval via compressed support detection from snapshot diffraction pattern

Traditional multislice iterative phase retrieval (MIPR) from snapshot two-dimensional measurements suffers from the two limitations of pre-defined support and iterative stagnation. To eliminate the requirements for priori knowledge of support masks, this paper proposes a multislice iterative phase retrieval algorithm based on compressed support detection and hybrid input-output algorithm (CSD-MIPR-HIO). The CSD-MIPR-HIO algorithm firstly uses compressed support detection to adaptively detect the support masks of each plane from single 2D diffraction intensity, and then uses a hybrid input-output (HIO) iterative algorithm for MIPR. The proposed method breaks the limitations of traditional MIPR algorithms on priori knowledge of support masks and achieve high-quality reconstruction in noisy environments. Numerical and optical experiments confirm the feasibility, superiority, and robustness of our proposed CSD-MIPR-HIO method.

Dual-domain mean-reverting diffusion model-enhanced temporal compressive coherent diffraction imaging

Temporal compressive coherent diffraction imaging is a lensless imaging technique with the capability to capture fast-moving small objects. However, the accuracy of imaging reconstruction is often hindered by the loss of frequency domain information, a critical factor limiting the quality of the reconstructed images. To improve the quality of these reconstructed images, a method dual-domain mean-reverting diffusion model-enhanced temporal compressive coherent diffraction imaging (DMDTC) has been introduced. DMDTC leverages the mean-reverting diffusion model to acquire prior information in both frequency and spatial domain through sample learning. The frequency domain mean-reverting diffusion model is employed to recover missing information, while hybrid input-output algorithm is carried out to reconstruct the spatial domain image. The spatial domain mean-reverting diffusion model is utilized for denoising and image restoration. DMDTC has demonstrated a significant enhancement in the quality of the reconstructed images. The results indicate that the structural similarity and peak signal-to-noise ratio of images reconstructed by DMDTC surpass those obtained through conventional methods. DMDTC enables high temporal frame rates and high spatial resolution in coherent diffraction imaging.

2D shape reconstruction of submillimetric irregular rough particles from speckle pattern in interferometric particle imaging measurement

Particle shape is a significant feature of irregular particles. The interferometric particle imaging (IPI) technique has been introduced to retrieve submillimetric irregular rough particle shapes, while inevitable experimental noises hinder the convergence of two-dimensional (2D) particle shapes from single speckle patterns. In this work, a hybrid input–output algorithm with shrink-wrap support and oversampling smoothness constraints is utilized to suppress the Poisson noise in IPI measurement and recover accurate 2D shapes of particles. Our method is tested in numerical simulations on ice crystal shapes and actual IPI measurements on four different types of irregular, rough particles. The shape similarity of the reconstructed 2D shape has reached an average Jaccard Index score of 0.927, and the relative deviation of the reconstructed size is within 7% for all 60 tested irregular particles at the maximum shot noise level of 7.4%. Furthermore, our method has obviously reduced the uncertainty in the 3D shape reconstruction of irregular, rough particles.

Extension of nonnegative constraints to difference-map algorithm on both real and imaginary parts of real space in phase retrieval

The difference-map (DM) algorithm is an iterative method to retrieve the image of an object from its diffraction pattern. Our study proposes the use of nonnegative constraints, reducing the number of unknown variables by half, on both the real and imaginary parts of the object space to reconstruct the image of a complex-valued object in the iterative process of the DM algorithm. The feasibility of the algorithm in biological cell applications was demonstrated using both simulations and optical laser coherent diffraction experiments. The results show that a more accurate image of the object can be retrieved using a loose support by nonnegative constraints than by the same support alone. The comparison indicates that the DM algorithm is superior to the hybrid input–output algorithm in the presence of nonnegative constraints. Therefore, during the execution of a DM algorithm, a loose support allows for more accurate reconstruction than a tight support, which can hardly be found in most cases because of the noise blurring of the retrieved image, and considerable reduction in the reconstruction errors.

Polarization multiplexing scattering imaging

Imaging through scattering media, such as clouds, biological tissues, and seawater, has broad application prospects in transportation, medical diagnosis, and information technology. Researchers have proposed various techniques to obtain images from scattered light passing through the scattering media, among which speckle correlation imaging has developed rapidly. Speckle correlation imaging requires non-coherent light sources due to the requirement of memory effect. This requirement makes the imaging device complex, and the light source utilization rate low. Additionally, this method is limited in its application under the illumination of spatially coherent light sources. This paper proposes a new method of speckle correlation imaging based on the illumination of spatially coherent light, which is achieved by multiplexing different polarization direction speckle patterns, called polarization multiplexing scattering imaging. To achieve the decoherence of the light source, previous approaches have used a rotating scattering medium to generate time-varying speckle patterns that are integrated over the shutter time of the camera to eliminate coherent noise, or multiplexed wavelength-dependent speckle multiplexing to achieve this. This paper uses spatially incoherent light sources to obtain different polarization direction speckle patterns by rotating polarizers placed in the illumination path. These patterns are superimposed and averaged, and phase recovery algorithm is used to reconstruct the object image. This experiment uses Ping-Pang (PP) algorithm with fusion error reduction and hybrid input-output algorithm to reconstruct targets quickly and with high quality. The comparison of the reconstruction results of different numbers of reused speckle patterns demonstrates that using more speckle patterns can achieve better image quality. Compared with conventional speckle correlation imaging technology, the proposed method reduces the requirements of light sources, improves the utilization rate of light sources, and makes the device simpler and more compact. Experimental results show that this method is feasible and has strong environmental adaptability, which can expand the application scope of speckle correlation imaging methods.

Phase-retrieval algorithm based on Kramers–Kronig relations in coherent diffraction imaging

Coherent diffraction imaging (CDI) is a high-resolution technique that does not require x-ray lenses. With advances in scientific technology, such as synchrotron radiation, x-ray free-electron lasers, and coherent electron sources, CDI has been applied to diverse fields, such as biology, medicine, and semiconductors, as a high-resolution, nondestructive measure. With the rapid increase in demand for these applications, enhancing the efficiency of processing high-volume data has become a significant challenge for promotion. In this study, we proposed an algorithm that combines Kramers–Kronig (KK) relations with oversampling smoothness (OSS). The results were evaluated by introducing an error coefficient. We found that the error of the KK-OSS algorithm is always reduced by approximately 50% compared with the error reduction (ER) algorithm, hybrid input–output (HIO) algorithm, and OSS in real space. In the diffraction space, the error in the KK-OSS can be decreased to 0.11. With 100 iterations, KK-OSS spent 218.3 s on reconstructing most of the sample information, while ER was 258.1 s, HIO algorithm took 296.7 s and the reconstruction was still a random value. In Fraunhofer diffraction, it cost KK-OSS 58.8 s to reconstruct, while OSS took 61.9 s. Therefore, this method can reduce the reconstruction error, shorten the reconstruction time, and improve the efficiency compared with the ER, HIO, and OSS algorithms using a random phase as the initial value.

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.

Continually reactivating iterative-projection method for instantiating microstructure from two-point statistics

Processing-structure (PS) linkages play a significant role in materials development. Nevertheless, currently there is a fascinating but of bottleneck task in terms of instantiating microstructure to understand and validate PS linkages. Its challenge lies on the lack of a robust method in computation efficiency and accuracy. Inspired from several advanced techniques such as hybrid input-output (HIO) algorithm, image processing operations and different-phase neighbors-based pixel swapping rule, we proposed a continually reactivating iterative-projection process (CRIP) method to address the challenge above. The output at each iteration in CRIP is continuously improved by eliminating and moving isolated or noise pixels towards an error-reduction direction to activate the iterative-projection process of the next iteration. The performance of the method was examined on two microstructure examples. It shows at least 99.86% improvement in convergence time compared with the classical simulated annealing algorithm and around 6.14 ×10−4 reduction in error compared with the traditional HIO algorithm. More importantly, CRIP is suitable for the task of instantiating microstructure from periodic two-point statistics predicted by PS linkage, which has been demonstrated by applying it to two experimental datasets of Ni-based superalloys and dual-phase steels. Our proposed method has the advantages of high efficiency, easy operation, reliable accuracy and remarkable generalization ability.

Simulated Annealing Applied to HIO Method for Phase Retrieval

Phase retrieval utilizing Fourier amplitudes plays a significant role in image recovery. Iterative phase retrieval algorithms have been developed to retrieve phase information that cannot be recorded by detectors directly. However, iterative algorithms face the problem of being trapped in local minima due to the nonconvexity of phase retrieval, and most existing works addressed this by optimizing in multiple runs parallelly to improve the possibility that one of these could reach the global minimum. Alternatively, we propose in this work to increase the probability of reaching the global minimum with one arbitrary initial distribution by adapting simulated annealing in the standard hybrid input-output (HIO) algorithm. Numerical and experimental results demonstrate that the proposed method reconstructs images with mean square errors 50.12% smaller than those reconstructed by HIO. More importantly, the proposed method can be applied to any HIO-based algorithm with multiple runs to further improve the performance.

Phase retrieval algorithms for lensless imaging using diffractive shearing interferometry.

Diffractive shearing interferometry (DSI) is a method that has recently been developed to perform lensless imaging using extreme ultraviolet radiation generated by high-harmonic generation. In this paper, we investigate the uniqueness of the DSI solution and the requirements for the support constraint size. We find that there can be multiple solutions to the DSI problem that consist of displaced copies of the actual object. These alternative solutions can be eliminated by enforcing a sufficiently tight support constraint, or by introducing additional synthetic constraints. We furthermore propose a new DSI algorithm inspired by the analogy with coherent diffractive imaging (CDI) algorithms: the original DSI algorithm is in a way analogous to the hybrid input-output algorithm as used in CDI, and we propose a new algorithm that is more analogous to the error reduction algorithm as used in CDI. We find that the newly proposed algorithm is suitable for final refinement of the reconstruction.

Investigation of the tolerance of the phase retrieval algorithm to missing information at the center of a detector in the case of coherent scattering from an ordered structure

The hybrid input-output algorithm is a phase retrieval method that provides solution for the phase problem of coherent X-ray diffraction imaging of micro- and nano-objects from the diffraction pattern alone without using any focusing optics. In this paper, we have studied a tolerance of this algorithm to missing information at the center of the diffraction pattern, which is a frequent problem in problems of small-angle scattering. We considered the particular problem of the stability of the algorithm in the case of scattering from an ordered structure and provided a qualitative and quantitative description of the degradation of image reconstruction with an increase in the amount of missing information.

Ciphertext-only attack on optical scanning cryptography

The optical scanning cryptography (OSC) is one of the most utilized optical encryption systems. Our research is inspired from the observation that there is a linear system property within the ciphertext expression equation of OSC. Given the linear system property, it is feasible to recover the plaintext with cipher-only attack (COA). Our proposed COA method converts the problem of COA into a phase retrieval problem with a single intensity measurement. With the frequency domain constraint and the object domain support obtained from the ciphertext of OSC, the hybrid input-output (HIO) algorithm can be used to recover plaintext. Simulation results demonstrate the feasibility and robustness of the attack. This shows for the first time that the OSC scheme is vulnerable to COA attack.

Performance analysis of adaptive optics with a phase retrieval algorithm in orbital-angular-momentum-based oceanic turbulence links

Recently, orbital angular momentum (OAM) beams have been applied in underwater optical communication (UWOC) to build a high-capacity communication link. However, a wave-front-sensitive OAM beam suffers significant distortion due to oceanic turbulence (OT), resulting in considerable intermodal crosstalk that degrades the UWOC performance. Herein, we propose and demonstrate an adaptive optics (AO)-based correction approach with a phase retrieval algorithm (PRA) to compensate for the distorted OAM beams induced by OT. In a simulation, an OT model with the random phase screen method is utilized. Two PRAs, the Gerchberg-Saxton algorithm (GSA) and the hybrid input-output algorithm (HIOA), are utilized to reconstruct the distorted phase-front of the OAM beam. The simulation results illustrate that the PRA-based AO approach can effectively compensate for the distorted OAM beam and improve the bit error rate performance in an oceanic channel. Additionally, the compensation performance of HIOA-based AO is superior to that of GSA-based AO in terms of convergence performance. This work verifies the feasibility and validity of a PRA-based AO approach in underwater turbulence optical communication and provides new insights into the OAM underwater communication system.

Position correction in ptychography using hybrid input–output (HIO) and cross-correlation

Ptychography is a form of coherent diffractive imaging; it employs far-field intensity patterns of the object to reconstruct the object. In ptychography, an important limiting factor for the reconstructed image quality is the uncertainty in the probe positions. Here, we propose a new approach which uses the hybrid input–output algorithm and cross-correlation in a way that can correct our estimates of the probe positions. The performance and limitations of the method in the presence of noise, varying overlap, and maximum recoverable error are studied using simulations. A brief comparison with other existing methods is also discussed here.

Non-locally coded Fourier-transform ghost imaging.

A non-locally coded Fourier-transform ghost imaging (FGI) scheme and relevant coded phase retrieval method have been proposed to improve the image quality in ghost imaging. By inserting masks in the reference beam, the sample in the test beam is non-locally modulated, and coded Fourier-transform diffraction patterns of the sample are obtained via intensity correlation calculations between the two beams. Encoding and decoding procedures are incorporated in the phase retrieval process based on traditional hybrid input-output algorithm. Simulation and experiment results show that the spatial information of samples is successfully recovered from the coded diffraction patterns obtained using three masks, and the image quality is improved remarkably. If promoting this approach to x-ray FGI systems, it may realize high-resolution x-ray microscopy without increasing the sample's radiation damage.

Cyphertext-only attack on the joint-transform-correlator-based optical encryption: experimental demonstration.

A cyphertext-only attack (COA) on a joint transform correlator encryption system is proposed. Under the proposed COA scheme, the energy spectral density of plaintext can be calculated with cyphertext, and then plaintext information can be recovered by using a phase retrieval algorithm such as the hybrid input-output algorithm. We also numerically and experimentally demonstrate the COA to verify feasibility of the proposed technique.

Adaptive turbulence compensation with a hybrid input-output algorithm in orbital angular momentum-based free-space optical communication.

Atmospheric turbulence is a major challenge for practical orbital angular momentum (OAM)-based free-space optical (FSO) communication systems that causes intermodal crosstalk and degrades the performance of the system. Herein, we propose a hybrid input-output algorithm (HIOA)-based adaptive optics (AO) system to compensate for distorted OAM beams. The principle and parameters of the HIOA-based AO system in an OAM-based FSO system are analyzed, and the performance is discussed. The simulation results indicate that the HIOA-based AO system can effectively correct distorted OAM beams and that the HIOA improves the compensation performance and convergence speed compared to the traditional Gerchberg-Saxton algorithm. Moreover, we analyze the compensation performance based on different probe beams. Using an OAM beam with state l=1 as a probe beam can yield better correction effects than a Gaussian beam. This work verifies the feasibility of using an HIOA for adaptive turbulence compensation and provides new insights into OAM communication systems.

Two-dimensional shape retrieval from the interferometric out-of-focus image of a nonspherical particle-Part I: theory.

Shape is one of the important characteristics of nonspherical particles. Herein, the two-dimensional shapes of several micrometer/millimeter-sized particles with a variety of geometrical forms are retrieved from simulated interferometric out-of-focus images using the Hybrid Input-Output algorithm. The particle concerned can be either a single particle or a complex particle with separate parts. The impact of the axial size of the three-dimensional particle on the retrieval of the two-dimensional shape (i.e., the projection of the particle on the image sensor) is analyzed, showing that an increase of the axial size increases the deviation of low frequencies in the interferometric out-of-focus image and eventually degrades the quality of the reconstructed shape. This study demonstrates the capability of the interferometric out-of-focus imaging technique on shape information retrieval for micrometer/millimeter-sized nonspherical particles.

Experimental determination of pore shapes using phase retrieval from q-space NMR diffraction.

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical q-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

Iterative pixelwise approach applied to computer-generated holograms and diffractive optical elements.

This paper presents a novel approach to optimizing the design of phase-only computer-generated holograms (CGH) for the creation of binary images in an optical Fourier transform system. Optimization begins by selecting an image pixel with a temporal change in amplitude. The modulated image function undergoes an inverse Fourier transform followed by the imposition of a CGH constraint and the Fourier transform to yield an image function associated with the change in amplitude of the selected pixel. In iterations where the quality of the image is improved, that image function is adopted as the input for the next iteration. In cases where the image quality is not improved, the image function before the pixel changed is used as the input. Thus, the proposed approach is referred to as the pixelwise hybrid input-output (PHIO) algorithm. The PHIO algorithm was shown to achieve image quality far exceeding that of the Gerchberg-Saxton (GS) algorithm. The benefits were particularly evident when the PHIO algorithm was equipped with a dynamic range of image intensities equivalent to the amplitude freedom of the image signal. The signal variation of images reconstructed from the GS algorithm was 1.0223, but only 0.2537 when using PHIO, i.e., a 75% improvement. Nonetheless, the proposed scheme resulted in a 10% degradation in diffraction efficiency and signal-to-noise ratio.