Automatic deconvolution in 4Pi-microscopy with variable phase (original) (raw)

Automatic deconvolution of 4Pi-microscopy data with arbitrary phase

Optics Letters, 2009

We propose a maximum a posteriori-based method that solves an important practical problem in the deconvolution of 4Pi images by simultaneously delivering an estimate of both the object and the unknown phase. The method was tested in simulations and on data from both test samples and biological specimen. It generates object estimates that are free from interference artifacts and reliably recovers arbitrary relative phases. Based on vectorial focusing theory, our theoretical analysis allowed for a simple and efficient implementation of the algorithm. Taking several 4Pi images at different relative phases of the interfering beams is shown to improve the robustness of the approach.

4Pi microscopy deconvolution with a variable point-spread function

Applied Optics, 2006

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.

Parametric Blind Deconvolution for Confocal Laser Scanning Microscopy (CLSM)Proof of Concept

We propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscope (CLSM) images with parametric estimation of the acquisition system's Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the image suffers from two primary physical limitations. The first is due to the diffraction-limited nature of the optical system and the second is due to the reduced amount of light detected by the photomultiplier tube (PMT). These limitations cause blur and photon counting noise respectively. The images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observation data. We also introduce a priori knowledge of the specimen that permits stabilization of the estimation process and favorizes the convergence. Experiments on simulated data show that the PSF could be estimated with a higher degree of accuracy and those done on real data show very good deconvolution results in comparison to the theoretical microscope PSF model.

Lensless phase microscopy using phase retrieval with multiple illumination wavelengths

2012

A phase retrieval method for microscopy using multiple illumination wavelengths is proposed. A fast algorithm suitable for calculations with high numerical aperture is used for the iterative retrieval of the object wavefront. The advantages and limitations of the technique are systematically analyzed and demonstrated by both simulation and experimental results.

Blind deconvolution for thin-layered confocal imaging

Applied Optics, 2009

In this paper, we have proposed an Alternate Minimization (AM) algorithm for estimating the Point-Spread Function (PSF) of a Confocal Laser Scanning Microscope (CLSM) and the specimen fluorescence distribution. A 3-D separable Gaussian model is used to restrict the PSF solution space and a constraint on the specimen is used so as to favor the stabilization and convergence of the algorithm. The results obtained from the simulation show that the PSF can be estimated to a high degree of accuracy, and those on real data show better deconvolution as compared to a full theoretical PSF model. Most of the fluorescence microscopes that image a uniformly illuminated threedimensional (3-D) object by the optical sectioning technique, are affected by some out-of-focus fluorescence contributions. Secondary fluorescence from the sections away from the region of interest often interferes with the contrast and resolution of those features that are in focus. Let us take the case of a single-photon (1-p) fluorescence microscope like the Widefield Microscope (WFM) and the Confocal Laser Scanning Microscope (CLSM) [1]. For the sake of simplicity, if we assume that the detectors are the same, then a WFM could be seen as a CLSM but with a fully-open pinhole.

Fast phase reconstruction in white light diffraction phase microscopy

Applied Optics, 2012

In off-axis interferometry, we usually have to deal with the unwrapping process, which is very computationally intensive and prevents us from real time phase reconstruction. The wrapping problem usually occurs when imaging thick objects, which introduce phase shifts of more than 2π radians. However, in off-axis interferometry, the nonzero angle of interference of the two beams creates a ramp in the phase across the image that can produce phase wrapping errors. In this paper, we propose a simple technique that avoids the need for the unwrapping step in reconstructing quantitative phase images in white light diffraction phase microscopy of thin samples. We show that this approach can improve significantly the phase reconstruction speed and allow high impact applications, such as real-time blood testing.

Blind Depth-variant Deconvolution of 3D Data in Wide-field Fluorescence Microscopy

Scientific Reports, 2015

This paper proposes a new deconvolution method for 3D fluorescence wide-field microscopy. Most previous methods are insufficient in terms of restoring a 3D cell structure, since a point spread function (PSF) is simply assumed as depth-invariant, whereas a PSF of microscopy changes significantly along the optical axis. A few methods that consider a depth-variant PSF have been proposed; however, they are impractical, since they are non-blind approaches that use a known PSF in a pre-measuring condition, whereas an imaging condition of a target image is different from that of the pre-measuring. To solve these problems, this paper proposes a blind approach to estimate depth-variant specimen-dependent PSF and restore 3D cell structure. It is shown by experiments on that the proposed method outperforms the previous ones in terms of suppressing axial blur. The proposed method is composed of the following three steps: First, a non-parametric averaged PSF is estimated by the Richardson Lucy algorithm, whose initial parameter is given by the central depth prediction from intensity analysis. Second, the estimated PSF is fitted to Gibson's parametric PSF model via optimization, and depth-variant PSFs are generated. Third, a 3D cell structure is restored by using a depth-variant version of a generalized expectation-maximization. 3D wide-field fluorescence microscopy (WFM) is an essential tool in many disciplines, particularly biological and medical sciences. WFM provides molecular specificity by visualizing only biomolecules where fluorescence dyes can be selectively responded under a dark background. This property makes it possible to obtain micrographs with high contrast. Applying 3D WFM to observe 3D cellular structures refers to optical sectioning, that is, generating a series of discrete 2D image planes (x-y plane) 1. 3D WFM, however, has several issues, such as out-of-focus blur obscuring the entire in-focus detail and thereby reducing the contrast of the in-focus object. Two major approaches to overcome these problems have been devised 1. The first approach is to apply new microscopy optics. Confocal microscopy, the most widely used approach, suppresses out-of-focus blur by means of a pinhole. On the other hand, it causes limitations of slow image acquisition and photobleaching. The second approach is to apply image restoration by a deconvolution algorithm. It enhances the resolution and contrast of blurred WFM images that do not have any limitation mentioned above in the first approach. In this study, the second approach was focused on, and a method for deconvolution of 3D WFM images is proposed. To implement the proposed image deconvolution algorithm, it is most important to obtain an accurate point spread function (PSF) of a 3D WFM imaging system. One of the main characteristics of a PSF of 3D WFM is depth variance along the optical axis (z axis), while general camera model ignores this variance 2. This characteristic is because an aberration of WFM is caused by mismatch between the refractive indices of the immersion medium and the specimen. As the optical system focuses on a deeper specimen, the aberration increases. This aberration phenomenon is the mechanism of the depth-variant characteristics for 3D WFM. Aiming to improve the resolution and contrast of 3D WFM through image deconvolution, numerous studies have been carried out 3. Most of them have conducted depth-invariant image restoration owing to a simplicity of PSF modelling 4-7. If the specimen is thin enough, the depth variance of PSF can be ignored, and their methods suppress the blur effectively, thereby increasing the resolution of 3D WFM up to that of confocal microscopy 8. However, in case of an average size of common specimen (10-20mm), the axial blur along the z axis still remains 9. For instance, the diameter of the blurred image of a 2500nm bead was measured as 4760nm (with axial blur) and 2867nm (with transverse blur), and after deconvolution of these values under the assumption that the specimen is thin enough, these results were respectively 4000nm and 2664nm 10. These deconvoluted values indicate that the restored image is lengthened along the optical axis. This phenomenon, called elongation, occurs when the image

Towards real-time image deconvolution: Application to confocal and STED microscopy

Scientific Reports, 2013

Although deconvolution can improve the quality of any type of microscope, the high computational time required has so far limited its massive spreading. Here we demonstrate the ability of the scaled-gradient-projection (SGP) method to provide accelerated versions of the most used algorithms in microscopy. To achieve further increases in efficiency, we also consider implementations on graphic processing units (GPUs). We test the proposed algorithms both on synthetic and real data of confocal and STED microscopy. Combining the SGP method with the GPU implementation we achieve a speed-up factor from about a factor 25 to 690 (with respect the conventional algorithm). The excellent results obtained on STED microscopy images demonstrate the synergy between super-resolution techniques and image-deconvolution. Further, the real-time processing allows conserving one of the most important property of STED microscopy, i.e the ability to provide fast sub-diffraction resolution recordings. I mage deconvolution is a computational technique that mitigates the distortions created by an optical system. Agard first applied image deconvolution to fluorescence microscopy in the early 1980s 1 . In this seminal paper Agard proposed different algorithms for deconvolving images acquired as three-dimensional (3D) stacks using wide-field microscopy (WFM). In a nutshell, the focal plane of the objective lens moves along the thickness of the specimen and for each position the microscope generates a bi-dimensional (2D) image. Due to the diffraction phenomena, each 2D image, also called optical section, includes considerable out-of-focus light originating from regions of the specimen above and below the focal plane. Image deconvolution uses information describing how the microscope produces the image (forward model) as the basis of a mathematical transformation that reassigns the out-of-focus light to the points of origin.