Phase Aberration Compensation Research Articles

Simultaneous phase aberration compensation and denoising for quantitative phase imaging in digital holographic microscopy with deep learning

In digital holographic microscopy, the quantitative phase image suffers from phase aberrations and coherent noises. To solve these problems, two independent steps are applied sequentially in the reconstruction procedure to compensate for the phase aberrations and denoising. Here we demonstrate for the first time, to the best of our knowledge, that the reconstruction process can be simplified by replacing the two step methods with a deep learning-based algorithm. A convolutional neural network is trained simultaneously for phase aberration correction and denoising from an only wrapped phase map. In order to train the network, a database consists of massive wrapped phase maps as input, and noise-free sample phase maps as labels are constructed. The generated wrapped phase maps include a variety of phase aberrations and faithful coherent noises that are reconstructed from a practical apparatus. The trained network is applied to correct phase aberrations and denoise of both simulated and experimental data for the quantitative phase image. It exhibits excellent performance with output comparable to that reconstructed from the double exposure method for phase aberration correction followed with block-matching and 3D filtering for denoising, while outperforming other conventional two step methods.

Efficient phase aberration compensation for digital holographic microscopy based on aberration-oriented phase unwrapping

In digital holographic microscopy, the phase map of the sample can be severely distorted by phase aberration, which is caused by the introduction of the microscopy imaging system and the misalignment of its elements. In this study, we propose an automatic compensation method based on noncontinuous-path phase unwrapping and least-squares fitting. The method preferentially and integrally unwraps the large-area aberration term with low dynamic range. Accurate fitting is achieved without the need for background segmentation or complex optimization. To the best of our knowledge, this is the first study to focus on the sequence of unwrapping in phase aberration compensation. Numerical simulations demonstrate that the proposed method can compensate not only for tilt and spherical aberration but also for high-order and cross-term aberration. Experiment results show that the method has significant advantages in terms of speed and robustness.

Automatic and accurate compensation for phase aberrations in digital holographic microscopy based on iteratively reweighted least squares fitting

Phase aberrations must be precisely compensated for phase-contrast imaging in digital holographic microscopy. In this paper, an automatic and accurate phase aberration compensation method is proposed based on iteratively reweighted least squares fitting. Instead of selecting the known-to-be-flat region with manual operation or image segmentation, this method starts from conventional least squares fitting in the whole image and attributes lower weights to the pixels with higher fitting residuals in an iterative reweighting procedure, during which the influence of specimen and noise is automatically reduced. Both phase curvature and high-order aberrations could be corrected without extra operation. Numerical simulation demonstrates that the proposed method is more accurate than the state-of-the-art numerical methods. Experimental result proves that this method is robust and fast enough for dynamic imaging of living cells.

Automatic aberration compensation for digital holographic microscopy based on bicubic downsampling and improved minimization of global phase gradients.

In digital holographic microscopy, aberrations caused by imperfect optical system settings can greatly affect the quantitative measurement of the target phase, so the compensation of aberrations in the distorted phase has become a key point of research in digital holographic microscopy. Here, we propose a fully automatic numerical phase aberration compensation method with fast computational speed and high robustness. The method uses bicubic downsampling to smooth the sample phase for reducing its disturbance to the background aberration fit, while reducing the computational effort of aberration compensation. Polynomial coefficients of the aberration fitting are iteratively optimized in the process of minimizing the global phase gradient by improving the phase gradient operator and constructing the loss function to achieve accurate fitting of the phase aberration. Simulation and experimental results show that the proposed method can achieve high aberration compensation accuracy without prior knowledge of the hologram recording settings or manual selection of the background area free of samples, and it is suitable for samples with moderate and relatively flat background area, which can be widely used in the quantitative analysis of biological tissues and micro and nano structures.

Dimensionality reduction technique based phase aberration compensation and spurious fringe removal in off-axis digital holographic microscopy

A dimensionality reduction technique based on singular value decomposition (SVD) is proposed for the aberration and spurious fringe removal from the phase measurement in off-axis digital holographic microscopy. The SVD of complex-valued virtual image obtained from numerically reconstructed hologram is computed. The phase aberration and spurious fringe compensated phase estimate is obtained by appropriate selection of singular values to reconstruct the denoised phase image. In order to remove the artifacts created along the x and y axis due to the SVD, the filtering procedure is implemented by rotating the phase image a fixed number of times. The effective denoised image is obtained by the weighted combination of denoised image evaluated for each rotation. Simulation and experimental studies are conducted to demonstrate the practical applicability of the proposed method.

Wrapped phase aberration compensation using deep learning in digital holographic microscopy

In digital holographic microscopy (DHM), phase aberration compensation is a general problem for improving the accuracy of quantitative phase measurement. Current phase aberration compensation methods mainly focus on the continuous phase map after performing the phase filtering and unwrapping to the wrapped phase map. However, for the wrapped phase map, when larger phase aberrations make the fringes too dense or make the noise frequency features indistinct, either spatial-domain or frequency-domain based filtering methods might be less effective, resulting in phase unwrapping anomalies and inaccurate aberration compensation. In order to solve this problem, we propose and design a strategy to advance the phase aberration compensation to the wrapped phase map with deep learning. As the phase aberration in DHM can be characterized by the Zernike coefficients, CNN (Convolutional Neural Network) is trained by using massive simulated wrapped phase maps as network inputs and their corresponding Zernike coefficients as labels. Then the trained CNN is used to directly extract the Zernike coefficients and compensate the phase aberration of the wrapped phase before phase filtering and unwrapping. The simulation results of different phase aberrations and noise levels and measurement results of MEMS chip and biological tissue samples show that, compared with current algorithms that perform phase aberration compensation after phase unwrapping, the proposed method can extract the Zernike coefficients more accurately, improve the phase data quality of the consequent phase filtering greatly, and achieve more accurate and reliable sample profile reconstruction. This phase aberration compensation strategy for the wrapped phase will have great potential in the applications of DHM quantitative phase imaging.

Accurate phase aberration compensation with convolutional neural network PACUnet3+ in digital holographic microscopy

To remove the effects of aberrations on quantitative phase image in digital holographic microscopy, a precise method that based on a data-driven phase aberrations compensations Unet3+ network (PACUnet3+) is presented. Unlike the existing methods that background segmentation should be implemented either in a phase image or in a sample hologram, the presented method doesn't need any preprocessing techniques. The PACUnet3+, which learning mappings between sample holograms and sample free holograms, produces a sample free hologram directly that contains all the background phase aberrations. Similar with double-exposure method, the phase aberrations can be removed by subtracting the background phase encoded in the generated sample-free hologram without any assumptions on the phase aberrations. The high fidelity of the method is demonstrated by measurement of engineered binary phase patterns. In phase aberrations correction, both numerical and experimental results confirmed the accuracy of the proposed method is benchmarking against the traditional double-exposure method.

Phase aberration adaptive compensation in digital holography based on phase imitation and metric optimization.

We proposed a numerical and accurate quadratic phase aberration compensation method in digital holography. A phase imitation method based on Gaussian 1σ-criterion is used to obtain the morphological features of the object phase using partial differential, filtering and integration successively. We also propose an adaptive compensation method based on a maximum-minimum-average- α-standard deviation (MMAαSD) evaluation metric to obtain optimal compensated coefficients by minimizing the above metric of the compensation function. The effectiveness and robustness of our method are demonstrated by simulation and experiments.

Phase aberration compensation via a self-supervised sparse constraint network in digital holographic microscopy

Phase aberration compensation is of great significance for the quantitative phase imaging in digital holographic microscopy. Least-square-based fitting algorithms are the most common options except for the double exposure method. However, they either require perturbation hypothesis, image segmentation, or an extra object-free hologram, leading to additional efforts for aberration elimination. In addition, supervised learning-based networks are mostly applied to create object-free masks automatically, but suffer from laborious label preparation and limited generalization capability. In this study, we propose a self-supervised sparse constraint network (SSCNet) for aberration compensation without the perturbation hypothesis, as well as an additional label or mask. Zernike model enhancement and sparse constraints are introduced for fitting aberration with only a single measured hologram. Simulation and experiment demonstrate that our proposed SSCNet can accurately compensate the phase aberration without object-free masks, and is more stable than other algorithms. It can be generalized to other samples with high accuracy and little time requirement. Moreover, SSCNet has advantage in the adaptive compensation of dynamic aberration in continuous measurement. Finally, it is an effective and practical fitting algorithm for phase aberration compensation.

Data-driven modeling and control of an X-ray bimorph adaptive mirror.

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

Quantitative phase imaging in digital holographic microscopy based on image inpainting using a two-stage generative adversarial network

Based on the hologram inpainting via a two-stage Generative Adversarial Network (GAN), we present a precise phase aberration compensation method in digital holographic microscopy (DHM). In the proposed methodology, the interference fringes of the sample area in the hologram are firstly removed by the background segmentation via edge detection and morphological image processing. The vacancy area is then inpainted with the fringes generated by a deep learning algorithm. The image inpainting finally results in a sample-free reference hologram containing the total aberration of the system. The phase aberrations could be deleted by subtracting the unwrapped phase of the sample-free hologram from our inpainting network results, in no need of any complex spectrum centering procedure, prior knowledge of the system, or manual intervention. With a full and proper training of the two-stage GAN, our approach can robustly realize a distinct phase mapping, which overcomes the drawbacks of multiple iterations, noise interference or limited field of view in the recent methods using self-extension, Zernike polynomials fitting (ZPF) or geometrical transformations. The validity of the proposed procedure is confirmed by measuring the surface of preprocessed silicon wafer with a Michelson interferometer digital holographic inspection platform. The results of our experiment indicate the viability and accuracy of the presented method. Additionally, this work can pave the way for the evaluation of new applications of GAN in DHM.

Phase-aberration compensation via deep learning in digital holographic microscopy

Digital holographic microscopy (DHM), a quantitative phase-imaging technology, has been widely used in various applications. Phase-aberration compensation in off-axis DHM is vital to reconstruct topographical images with high precision, especially for microstructures with a small background or a dense phase distribution. We propose a numerical method based on deep learning combined with DHM. First, a convolutional neural network (CNN) recognizes and segments the sample and the background area of the hologram. Zernike polynomial fitting is then executed on the extracted background area. Finally, the whole process of phase-aberration compensation is automatically performed. To obtain a robust and accurate deep-learning model for hologram segmentation, we collected many holograms corresponding to several samples that had different morphological characteristics. The experimental results confirm that the trained CNN can accurately segment the sample from the background area of the hologram, and that this method is applicable and effective in off-axis DHM.

Simulation of digital holographic recording and reconstruction using a generalized matrix method.

In recent years, research efforts in the field of digital holography have expanded significantly, due to the ability to obtain high-resolution intensity and phase images. The information contained in these images have become of great interest to the machine learning community, with applications spanning a wide portfolio of research areas, including bioengineering. In this work, we seek to demonstrate a high-fidelity simulation of holographic recording. By accurately and numerically simulating the propagation of a coherent light source through a series of optical elements and the object itself, we accurately predict the optical interference of the object and reference wave at the recording plane, including diffraction effects, aberrations, and speckle. We show that the optical transformation that predicts the complex field at the recording plane can be generalized for arbitrary holographic recording configurations using a matrix method. In addition, we provide a detailed description of digital phase reconstruction and aberration compensation for a variety of off-axis holographic configurations. Reconstruction errors are presented for the various holographic recording geometries and complex field objects. While the primary objective of this work is not to evaluate phase reconstruction approaches, the reconstruction of simulated holograms provides validation of the generalized simulation method. The long-term goal of this work is that the generalized holographic simulation motivates the use of phase reconstruction of the simulated holograms to populate databases for training machine-learning algorithms aimed at classifying relevant objects recorded through a variety of holographic setups.

Performance of the 1D standard polynomials fitting method for total phase aberration compensation in digital holographic microscopy

Digital holographic microscopy is widely used for quantitative phase information detection. However, in this technique, phase information is usually concealed by aberrations such as tilt, quadratic aberration, and other high-order aberrations. There are few methods that truly capable of total phase aberration compensation. The method based on 1D standard polynomials fitting is one of them. Here, we will study its performance, including the ability of compensating large amount of high-order aberrations, the influence of sample locations and noise. The results are compared with that of the classical 2D Zernike polynomials fitting method. We also give some guidance on sample locations so that the samples are properly located to guarantee the good compensation. Additionally, we thoroughly analyze the similarity and difference between the two methods that both based on the 1D standard polynomials fitting. The results will facilitate the understanding and implement of this type of methods.

Single-shot common-path off-axis dual-wavelength digital holographic microscopy

A single-shot common-path off-axis self-interference dual-wavelength digital holographic microscopic (DHM) system based on a cube beam splitter is demonstrated to expand the phase range in a stepped microstructure and for simultaneous measurement of the refractive index and physical thickness of a specimen. In the system, two laser beams with wavelengths of 532 nm and 632.8 nm are used. These laser beams are combined to transilluminate the object under study, then the object beam is divided into two beams by using a beam splitter oriented in such a way that both the beams propagate in almost the same direction, with an appropriate lateral separation between them. One of the object beams is spatially filtered at its Fourier plane, using a pinhole to generate a reference spherical beam free from the object information. The reference beam interferes with the object beam to form a digital hologram at the faceplate of the image sensor. The phase information is extracted from a single recorded digital hologram using the phase aberration compensation method that is based on principal component analysis (PCA). Owing to the common-path configuration, the system shows high temporal phase stability and it is less vibration-sensitive compared to counterparts such as a Mach-Zehnder type DHM. The performance of the dual-wavelength DHM system is verified in two different application fields by conducting the experiments using microsphere beads and living plant cells.

Automatic removal of phase aberration in holographic microscopy for drug sensitivity detection of ovarian cancer cells

Real-time and long-term monitoring of the morphological changes of cells in biomedical science is highly desired. Quantitative phase imaging (QPI) obtained by various interferometric methods is the ideal tool for monitoring such processes as it allows to get quantitative information and thus assessing the right response on cell behaviors. Among QPI, digital holography (DH) in microscope configuration is a powerful tool as it is tolerant versus defocusing and for this reason is able to compensate for eventual defocusing effect during long time-lapse recording. Moreover, DH dynamic phase imaging for biological specimens has several advantages, namely non-invasive, label-free, and high-resolution. However, in DH, one of the main limitations is due to the need compensate aberrations due to the optical components in the object beam. In fact, the image of the object is inevitably embedded in aberrations due to the microscope objective (MO) and other optical components in the optical setup. Here, we propose an automatic and robust phase aberration compensation method based on a synthetic difference (SD) image process. The method is able to detect automatically object-free regions. From such regions, hologram’s aberrations can be accurately evaluated and cleaned up in the final QPI maps. Thanks to our method, temporal evolutions of cell morphological parameters were quantitatively analyzed, hence helping in studying the drug sensitivity of ovarian cancer cells. The experimental results demonstrated that the proposed method could robustly separate the object-free region from the distorted phase image and automatically compensate the total aberrations without any manual interventions, extra components, prior knowledge of the object, and optical setup.

Automatic and robust phase aberration compensation for digital holographic microscopy based on minimizing total standard deviation

A totally automatic and robust phase aberration compensation method is proposed for digital holographic microscopy. The correction needs no manual operation or prior knowledge of the recording setup. As the phase aberrations are modeled with orthogonal polynomials, not only phase curvature but also high order aberrations could be corrected with a single hologram. The polynomial coefficients are obtained in an optimization procedure by minimizing the total standard deviation, i.e., the sum of local standard deviation of the compensated phase map. Since both the global and the local phase variations are considered, the proposed method is more accurate and robust than the state-of-the-art numerical methods with the existence of abrupt edges and phase noise. The effectiveness of the proposed method is validated with numerical simulation and the experimental results of mouse osteoblastic MC3T3-E1 living cells and USAF 1951 resolution target.

Numerical Evaluation of the Influence of Skull Heterogeneity on Transcranial Ultrasonic Focusing.

In transcranial penetration, ultrasound undergoes refraction, diffraction, multi-reflection, and mode conversion. These factors lead to phase aberration and waveform distortion, which impede the realization of transcranial ultrasonic imaging and therapy. Ray tracing has been used to correct the phase aberration and is computationally more efficient than traditional full-wave simulation. However, when ray tracing has been used for transcranial investigation, it has generally been on the premise that the skull medium is homogeneous. To find suitable homogeneity that balances computational speed and accuracy, the present work investigates how the focus deviates after phase-aberration compensation with ray tracing using time-reversal theory. The waveforms are synthetized with ray tracing for phase aberration, by which the properties of the skull bone are simplified for refraction calculation as those of either (i) the cortical bone or (ii) the mean of the entire skull bone, and the focusing accuracy is evaluated for each hypothesis. The propagation of ultrasound for transcranial focusing is simulated with the elastic model using the k-space pseudospectral method. Unlike the fluid model, the elastic model does not omit shear waves in the skull bones, and the influence of that omission is investigated, with the fluid model resulting in a focal deflection of 0.5 mm. The focusing deviations are huge when the properties of the skull bone are idealized with ray tracing as those of the mean of the entire skull bone. The focusing accuracy improves when the properties of the skull bone are idealized as those of the cortical bone. The results reveal minimal deviation (8.6, 3.9, and 3.2% in the three Cartesian coordinates) in the focal region and suggest that transcranial focusing deflections are caused mostly by ultrasonic refraction on the surface of the skull bone. A heterogeneous skull bone causes wave bending but minimal focusing deflection. The proposed simplification of a homogeneous skull bone is more accurate for transcranial ultrasonic path estimation and offers promising applications in transcranial ultrasonic focusing and imaging.

Phase aberration compensation of digital holographic microscopy with curve fitting preprocessing and automatic background segmentation for microstructure testing

In the digital holographic microscopy, the phase aberration is a key problem limiting the quantitative phase measurement, especially for the microstructure whose phase distribution is dense with few and discontinuous background region. A numerical phase aberration compensation method with global curve fitting preprocessing and automatic extraction of the background region for microstructure testing is proposed. The global curve fitting is implemented to compensate most of the tilt, quadratic and partial high order aberrations and make the profile of the measured object significantly distinguishable. Then the background region is automatically extracted by directly segmenting the converted grayscale phase image. At last, the Zernike polynomial fitting is performed on the extracted background region, and the obtained coefficients are used to calculate the phase aberration of the whole phase image. Simulation and experimental results demonstrated that the proposed method is able to accurately extract background region and compensate the phase aberration for the complicated dense microstructure.

Automatic compensation of phase aberrations in digital holographic microscopy based on sparse optimization

In digital holographic microscopy, phase aberrations, which are usually caused by the imperfections of components and nontelecentric configuration of the optical system, severely affect the visualization and quantitative measurement for phase-contrast imaging. Here, we propose a purely numerical and automatic method to compensate for phase aberrations. Without any manual involvement of selecting a sample-free background, the compensation is cast as a surface fitting problem, in which the aberration surface is approximated by formulating an inverse problem. By adopting the ℓ1-norm as the loss function and by minimizing an objective function, aberrations can be accurately fitted and thus removed numerically. Synthetic and experimental results are demonstrated to verify the efficacy of this method over the least squares method.