Anisoplanatic deconvolution of adaptive optics images

A modified method for maximum-likelihood deconvolution of astronomical adaptive optics images is presented. By parametrizing the anisoplanatic character of the point-spread function (PSF), a simultaneous optimization of the spatially variant PSF and the deconvolved image can be performed. In the ideal case of perfect information, it is shown that the algorithm is able to perfectly cancel the adverse effects of anisoplanatism down to the level of numerical precision. Exploring two different modes of deconvolution (using object bases of pixel values or stellar field parameters), we then quantify the performance of the algorithm in the presence of Poissonian noise for crowded and noncrowded stellar fields.     

Blind deconvolution of fluorescence micrographs by maximum-likelihood estimation

We report some recent algorithmic refinements and the resulting simulated and real image reconstructions of fluorescence micrographs by using a blind-deconvolution algorithm based on maximum likelihood estimation. Blind-deconvolution methods encompass those that do not require either calibrated or theoretical predetermination of the point-spread function (PSF). Instead, a blind deconvolution reconstructs the PSF concurrently with deblurring of the image data. Two-dimensional computer simulations give some definitive evidence of the integrity of the reconstructions of both the fluorescence concentration and the PSF. A reconstructed image and a reconstructed PSF from a two-dimensional fluorescent data set show that the blind version of the algorithm produces images that are comparable with those previously produced by a precursory nonblind version of the algorithm. They furthermore show a remarkable similarity, albeit not perfectly identical, with a PSF measurement taken for the same data set, provided by Agard and colleagues. A reconstructed image of a three-dimensional confocal data set shows a substantial axial smear removal. There is currently an existing trade-off in using the blind deconvolution in that it converges at a slightly slower rate than the nonblind approach. Future research, of course, will address this present limitation.     

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.     

Restoration of medical ultrasound images using two-dimensionalhomomorphic deconvolution

Describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro     

On- and off-axis statistical behavior of adaptive-optics-corrected short-exposure Strehl ratio

Statistical behavior of the adaptive-optics- (AO-) corrected short-exposure point-spread function (PSF) is derived assuming a perfect correction of the phase's low spatial frequencies. Analytical expressions of the Strehl ratio (SR) fluctuations of on- and off-axis short-exposure PSFs are obtained. A theoretical expression of the short SR angular correlation is proposed and used to derive a definition of an anisoplanatic angle for AO-corrected images. Several applications of the analytical expressions are proposed: AO performance characterization, postprocessing imaging, light coupling into fiber, and exoplanet detection from a ground-based telescope.     

基于APEX方法的湍流退化图像复原算法

在目标探测过程中,为了消除大气湍流带来的影响,提出了一种基于APEX方法的盲去卷积图像复原算法.该算法是一种非迭代的盲图像复原算法,以湍流退化系统具有G类点扩展函数为假设前提,通过模糊图像的频谱信息直接估计点扩展函数,并采用SECB方法实现目标图像的重建.本文对该算法的原理及其对湍流退化图像复原的可行性进行了深入研究,进行了真实的湍流退化图像的复原实验,其结果表明,该算法能够快速实现对湍流退化图像的重建,并具有一定的稳定性,能满足目标探测过程中的实时性要求.     

4Pi microscopy deconvolution with a variable point-spread function

To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.     

Ultrasonic imaging using a computed point spread function

An explicit point spread function (PSF) evaluator in the frequency domain is described for an ultrasonic transducer operating in the pulse-echo mode. The PSF evaluator employs the patch element model for transducer field determination and scattered field assessment from a small but finite "point" reflector. The PSF for a planar transducer in a medium has been evaluated in the near and the far field. The computed PSFs were used to deconvolve and restore surface images, obtained experimentally, of a single hole and a five-hole cluster in an Al calibration block. A calibration plot is arrived at for estimating, without the need for deconvolution, the actual diameters of circular reflectors from apparent diameters obtained experimentally for a single-medium imaging configuration. The PSF, when the transducer and the point reflector are in two media separated by a planar interface, was evaluated in the near and far field. The computed PSFs were used to deconvolve and restore subsurface images, obtained experimentally, of flat bottom holes (FBHs) in an Al calibration block. We show that the PSF, in the presence of a planar interface, can be obtained from a single-medium PSF model using an effective single-medium path length concept. The PSFs and modulation transfer functions (MTFs) are evaluated for spherical focused and annular transducers and compared with those for the planar transducer. We identify imaging distances to get better-resolved images when using planar, spherical focused, and annular transducers.     

MLEM deconvolution of protein X-ray diffraction images based on a multiple-PSF model

In this paper we analyze the degradation of protein X-ray diffraction images by diffuse light distortion (DLD). In order to correct the degradation, a new multiple point spread function (PSF) model is introduced and used to restore X-ray diffraction image data (XRD). Raw PSFs are collected from isolated spots in high-resolution areas on the diffraction patterns which represent the orientation of DLDs. An adaptive ridge regression (ARR) technique is used to remove noise from the raw PSF data. A target Gaussian function is used to model the raw PSFs. A maximum likelihood expectation maximization (MLEM) algorithm combined with a multi-PSF model is employed to restore high intensity, asymmetrical protein X-ray diffraction data. Experimental results using a single and multiple PSFs are presented and discussed. We show that using a multiple PSF model in the deconvolution algorithm improved the quality of the XRD and as a result the spot integration error (/spl chi//sup 2/) and corresponding electron density map are improved.     

Automatic threshold technique for holographic particle field characterization

The 3D distribution of a particle field by digital holography is obtained by 3D numerical reconstruction of a 2D hologram. The proper identification of particles from the background during numerical reconstruction influences the overall effectiveness of the technique. The selection of a suitable threshold value to segment particles from the background of reconstructed images during 3D holographic reconstruction process is a critical issue, which influences the accuracy of particle size and number density of reconstructed particles. The object particle field parameters, such as depth of sample volume and density of object particles, influence the optimal threshold value. The present study proposes a novel technique for the determination of the optimal threshold value of a reconstructed image. The effectiveness of the proposed technique is demonstrated using both simulated and experimental data. The proposed technique is robust to variation in optical properties of particle and background, depth of sample volume, and number density of object particle field. The particle diameter obtained from the proposed threshold technique is within 5% of that obtained from the particle size analyzer. There is a maximum ten times increase in reconstruction effectiveness by using the proposed automatic threshold technique in comparison with the fixed manual threshold technique.     

Resolution enhancement in standing-wave total internal reflection microscopy: a point-spread-function engineering approach.

The theoretical basis for resolution enhancement in standing-wave total internal reflection microscopy (SW-TIRM) is examined. This technique relies on the formation of an excitation field containing super-diffraction-limited spatial-frequency components. Although the fluorescence generated at the object planes contains high-frequency information of the object distribution, this information is lost at the image plane, where the detection optics acts as a low-pass filter. From the perspective of point-spread-function (PSF) engineering, one can show that if this excitation field is translatable experimentally, the high-frequency information can be extracted from a set of images where the excitation fields have different displacement vectors. We have developed algorithms to combine this image set to generate a composite image with an effective PSF that is equal to the product of the excitation field and the Fraunhofer PSF. This approach can easily be extended to incorporate nonlinear excitation modalities into SW-TIRM for further resolution improvement. We theoretically examine high-resolution imaging based on the addition of two-photon, pump-probe, and stimulated-emission depletion methods to SW-TIRM and show that resolution better than 1/20 of the emission wavelength may be achievable.     

基于反卷积的手机屏下成像图像恢复

随着全面屏手机的发展,手机屏下成像的研究应运而生。但由于手机屏幕存在电路走线和其他不透明部分,光通过屏幕会产生衍射,降低成像结果的图像质量,本文从图像复原的角度,对屏下相机拍摄的图像进行恢复。通过测量得到手机成像系统的点扩散函数(PSF),利用测得的PSF,对图像进行反卷积处理。本文改进了传统的反卷积方法,对原始图像进行颜色空间转换,然后对不同的通道分别处理。相较于传统反卷积方法,改进后的反卷积方法得到的处理结果在结构相似度(SSIM)、峰值信噪比(PSNR)等指标上都有提高,运行时间更短。在分通道反卷积之后,使用非局部平均算法进行去噪处理,进一步提高了屏下图像的质量。     

Angular motion point spread function model considering aberrations and defocus effects

When motion blur is considered, the optics point spread function (PSF) is conventionally assumed to be fixed, and therefore cascading of the motion optical transfer function (OTF) with the optics OTF is allowed. However, in angular motion conditions, the image is distorted by space-variant effects of wavefront aberrations, defocus, and motion blur. The proposed model considers these effects and formulates a combined space-variant PSF obtained from the angle-dependent optics PSF and the motion PSF that acts as a weighting function. Results of comparison of the new angular-motion-dependent PSF and the traditional PSF show significant differences. To simplify the proposed model, an efficient approximation is suggested and evaluated.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging

3D deconvolution is an established technique in microscopy that may be useful for low-cost high-resolution imaging of the retina. We report on a myopic 3D deconvolution method developed in a Bayesian framework. This method uses a 3D imaging model, a noise model that accounts for both photon and detector noises, a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas, a positivity constraint, and a smart parameterization of the point-spread function (PSF) by the pupil phase. It estimates the object and the PSF jointly. The PSF parameterization through the pupil phase constrains the inversion by dramatically reducing the number of unknowns. The joint deconvolution is further constrained by an additional longitudinal support constraint derived from a 3D interpretation of the phase-diversity technique. This method is validated by simulated retinal images.     

Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction

It is well known that atmospheric turbulence severely degrades the performance of ground-based imaging systems. Techniques to overcome the effects of the atmosphere have been developing at a rapid pace over the past 10 years. These techniques can be grouped into two broad categories: predetection and postdetection techniques. A recent newcomer to the postdetection scene is deconvolution from wave-front sensing (DWFS). DWFS is a postdetection image-reconstruction technique that makes use of one feature of predetection techniques. A wave-front sensor (WFS) is used to record the wave-front phase distortion in the pupil of the telescope for each short-exposure image. The additional information provided by the WFS is used to estimate the system's point-spread function (PSF). The PSF is then used in conjunction with the ensemble of short-exposure images to obtain an estimate of the object intensity distribution through deconvolution. With the addition of DWFS to the suite of possible postdetection image-reconstruction techniques, it is natural to ask "How does DWFS compare with both traditional linear and speckle image-reconstruction techniques?" In the results we make a direct comparison based on a frequency-domain signal-to-noise-ratio performance metric. This metric is applied to each technique's image-reconstruction estimator. We find that DWFS nearly always results in improved performance over the estimators of traditional linear image reconstruction such as Wiener filtering. On the other hand, DWFS does not always outperform speckle-imaging techniques, and in cases that it does the improvement is small.     

Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwell's electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwell's equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.     

Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images

A wide-field-of-view white-light imaging experiment with artificially generated turbulence layers located between the extended object and the imaging system is described. Relocation of the turbulence sources along the imaging path allowed the creation of controllable anisoplanatic effects. We demonstrate that the recently proposed synthetic imaging technique [J. Opt. Soc. Am. A 16, 1623 (1999)] may result in substantial improvement in image quality for highly anisoplanatic conditions. It is shown that for multisource objects located at different distances the processing of turbulence-degraded short-exposure images may lead to a synthetic image that has an image quality superior to that of the undistorted image obtained in the absence of turbulence (turbulence-induced image quality enhancement).     

Upscaling image resolution of compact imaging systems using wavefront coding and a property of the point-spread function

We propose an image-resolution upscaling method for compact imaging systems. The image resolution is calculated using the resolving power of the optics and the pixel size of a digital image sensor. The resolution limit of the compact imaging system comes from its size and the number of allowed lenses. To upscale the image resolution but maintain the small size, we apply wavefront coding and image restoration. Conventional image restoration could not enhance the image resolution of the sensor. Here, we use the upscaled image of a wavefront-coded optical system and apply an image-restoration algorithm using a more precisely calculated point-spread function (PSF) as the deconvolution filter. An example of a wavefront-coded optical system with a 5-megapixel image sensor is given. The final image had a resolution equivalent to that of a 10-megapixel image using only four plastic lenses. Moreover, image degradation caused by hand motion could also be reduced using the proposed method.     

Comparative study on basis functions for projection matrix of three-dimensional tomographic reconstruction for analysis of dropletbehavior from electrohydrodynamic jet

Three-dimensional optical tomography techniques were developed to reconstruct three-dimensional objects using a set of two-dimensional projection images. Five basis functions, such as cubic B-spline, o-Moms, keys, and cosine functions and Gaussian basis functions, were used to calculate the weighting coefficients for a projection matrix. Two different forms of a multiplicative algebraic reconstruction technique were also used to solve inverse problems. The reconstruction algorithm was examined by using several phantoms, which included droplet behaviors and random distributions of particles in a volume. The three-dimensional volume comprised of particles was reconstructed from four projection angles, which were positioned at an offset angle of 45° between each other. Then, three-dimensional velocity fields were obtained from the reconstructed particle volume by three-dimensional cross correlation. The velocity field of the synthetic vortex flow was reconstructed to analyze the three-dimensional tomography algorithm.