A Model‐based approach for microvasculature structure distortion correction in two‐photon fluorescence microscopy images

This paper investigates a postprocessing approach to correct spatial distortion in two‐photon fluorescence microscopy images for vascular network reconstruction. It is aimed at in vivo imaging of large field‐of‐view, deep‐tissue studies of vascular structures. Based on simple geometric modelling of the object‐of‐interest, a distortion function is directly estimated from the image volume by deconvolution analysis. Such distortion function is then applied to subvolumes of the image stack to adaptively adjust for spatially varying distortion and reduce the image blurring through blind deconvolution. The proposed technique was first evaluated in phantom imaging of fluorescent microspheres that are comparable in size to the underlying capillary vascular structures. The effectiveness of restoring three‐dimensional (3D) spherical geometry of the microspheres using the estimated distortion function was compared with empirically measured point‐spread function. Next, the proposed approach was applied to in vivo vascular imaging of mouse skeletal muscle to reduce the image distortion of the capillary structures. We show that the proposed method effectively improve the image quality and reduce spatially varying distortion that occurs in large field‐of‐view deep‐tissue vascular dataset. The proposed method will help in qualitative interpretation and quantitative analysis of vascular structures from fluorescence microscopy images.     

Blind deconvolution of 3D fluorescence microscopy using depth‐variant asymmetric PSF

The 3D wide‐field fluorescence microscopy suffers from depth‐variant asymmetric blur. The depth‐variance and axial asymmetry are due to refractive index mismatch between the immersion and the specimen layer. The radial asymmetry is due to lens imperfections and local refractive index inhomogeneities in the specimen. To obtain the PSF that has these characteristics, there were PSF premeasurement trials. However, they are useless since imaging conditions such as camera position and refractive index of the specimen are changed between the premeasurement and actual imaging. In this article, we focus on removing unknown depth‐variant asymmetric blur in such an optical system under the assumption of refractive index homogeneities in the specimen. We propose finding few parameters in the mathematical PSF model from observed images in which the PSF model has a depth‐variant asymmetric shape. After generating an initial PSF from the analysis of intensities in the observed image, the parameters are estimated based on a maximum likelihood estimator. Using the estimated PSF, we implement an accelerated GEM algorithm for image deconvolution. Deconvolution result shows the superiority of our algorithm in terms of accuracy, which quantitatively evaluated by FWHM, relative contrast, standard deviation values of intensity peaks and FWHM. Microsc. Res. Tech. 79:480–494, 2016. © 2016 Wiley Periodicals, Inc.     

Application of an advanced maximum likelihood estimation restoration method for enhanced‐resolution and contrast in second‐harmonic generation microscopy

Second‐harmonic generation (SHG) microscopy has gained popularity because of its ability to perform submicron, label‐free imaging of noncentrosymmetric biological structures, such as fibrillar collagen in the extracellular matrix environment of various organs with high contrast and specificity. Because SHG is a two‐photon coherent scattering process, it is difficult to define a point spread function (PSF) for this modality. Hence, compared to incoherent two‐photon processes like two‐photon fluorescence, it is challenging to apply the various PSF‐engineering methods to improve the spatial resolution to be close to the diffraction limit. Using a synthetic PSF and application of an advanced maximum likelihood estimation (AdvMLE) deconvolution algorithm, we demonstrate restoration of the spatial resolution in SHG images to that closer to the theoretical diffraction limit. The AdvMLE algorithm adaptively and iteratively develops a PSF for the supplied image and succeeds in improving the signal to noise ratio (SNR) for images where the SHG signals are derived from various sources such as collagen in tendon and myosin in heart sarcomere. Approximately 3.5 times improvement in SNR is observed for tissue images at depths of up to ～480 nm, which helps in revealing the underlying helical structures in collagen fibres with an ～26% improvement in the amplitude contrast in a fibre pitch. Our approach could be adapted to noisy and low resolution modalities such as micro‐nano CT and MRI, impacting precision of diagnosis and treatment of human diseases.     

High‐resolution wide‐field microscopy with adaptive optics for spherical aberration correction and motionless focusing

Live imaging in cell biology requires three‐dimensional data acquisition with the best resolution and signal‐to‐noise ratio possible. Depth aberrations are a major source of image degradation in three‐dimensional microscopy, causing a significant loss of resolution and intensity deep into the sample. These aberrations occur because of the mismatch between the sample refractive index and the immersion medium index. We have built a wide‐field fluorescence microscope that incorporates a large‐throw deformable mirror to simultaneously focus and correct for depth aberration in three‐dimensional imaging. Imaging fluorescent beads in water and glycerol with an oil immersion lens we demonstrate a corrected point spread function and a 2‐fold improvement in signal intensity. We apply this new microscope to imaging biological samples, and show sharper images and improved deconvolution.     

Specimen-induced distortions in light microscopy

Specimen‐induced aberrations affect the imaging properties in optical 3D microscopy, especially when high numerical aperture lenses are used. Studies on aberrations are often properly concerned with the degradation of image quality such as compromised resolution or reduced signal intensity. Apart from these, aberration effects can also introduce geometric image distortions. The effects, discussed here are particularly strong when thick biological specimens are investigated. Using a high numerical aperture interferometer, we measured wavefront aberrations in transmission mode and quantified geometric distortions associated with specimen‐induced aberrations. This assessment for a range of biological specimens allows estimation of the accuracy of spatial measurements. The results show that high‐resolution spatial measurements can be significantly compromised by specimen‐induced aberrations.     

A method of PSF generation for 3D brightfield deconvolution

This paper addresses the problem of 3D deconvolution of through focus widefield microscope datasets (Z‐stacks). One of the most difficult stages in brightfield deconvolution is finding the point spread function. A theoretically calculated point spread function (called a ‘synthetic PSF’ in this paper) requires foreknowledge of many system parameters and still gives only approximate results. A point spread function measured from a sub‐resolution bead suffers from low signal‐to‐noise ratio, compounded in the brightfield setting (by contrast to fluorescence) by absorptive, refractive and dispersal effects. This paper describes a method of point spread function estimation based on measurements of a Z‐stack through a thin sample. This Z‐stack is deconvolved by an idealized point spread function derived from the same Z‐stack to yield a point spread function of high signal‐to‐noise ratio that is also inherently tailored to the imaging system. The theory is validated by a practical experiment comparing the non‐blind 3D deconvolution of the yeast Saccharomyces cerevisiae with the point spread function generated using the method presented in this paper (called the ‘extracted PSF’) to a synthetic point spread function. Restoration of both high‐ and low‐contrast brightfield structures is achieved with fewer artefacts using the extracted point spread function obtained with this method. Furthermore the deconvolution progresses further (more iterations are allowed before the error function reaches its nadir) with the extracted point spread function compared to the synthetic point spread function indicating that the extracted point spread function is a better fit to the brightfield deconvolution model than the synthetic point spread function.     

Saturation modified point spread functions in two-photon microscopy

Excitation saturation can dramatically alter the effective imaging point spread function (PSF) in two-photon fluorescence microscopy. The saturation-modified PSF can have important implications for resolution in fluorescence imaging as saturation leads to both an increased fluorescence observation volume and an altered spatial profile for the PSF. We introduce here a computational approach to accurately quantify molecular excitation profiles that represent the modified imaging PSF in two-photon microscopy under the influence of excitation saturation. An analytical model that accounts for pulsed laser excitation is developed to calculate the influence of saturation at any location within the excitation laser profile. The overall saturation modified molecular excitation profiles are then evaluated numerically. Our results demonstrate that saturation can play an important role in two-photon fluorescence microscopy even with relatively modest excitation levels.     

Spatially varying regularization of deconvolution in 3D microscopy

Confocal microscopy has become an essential tool to explore biospecimens in 3D. Confocal microcopy images are still degraded by out‐of‐focus blur and Poisson noise. Many deconvolution methods including the Richardson–Lucy (RL) method, Tikhonov method and split‐gradient (SG) method have been well received. The RL deconvolution method results in enhanced image quality, especially for Poisson noise. Tikhonov deconvolution method improves the RL method by imposing a prior model of spatial regularization, which encourages adjacent voxels to appear similar. The SG method also contains spatial regularization and is capable of incorporating many edge‐preserving priors resulting in improved image quality. The strength of spatial regularization is fixed regardless of spatial location for the Tikhonov and SG method. The Tikhonov and the SG deconvolution methods are improved upon in this study by allowing the strength of spatial regularization to differ for different spatial locations in a given image. The novel method shows improved image quality. The method was tested on phantom data for which ground truth and the point spread function are known. A Kullback–Leibler (KL) divergence value of 0.097 is obtained with applying spatially variable regularization to the SG method, whereas KL value of 0.409 is obtained with the Tikhonov method. In tests on a real data, for which the ground truth is unknown, the reconstructed data show improved noise characteristics while maintaining the important image features such as edges.     

Increasing microscopy resolution with photobleaching and intensity cumulant analysis

Super‐resolution fluorescence microscopy and its applications for analysis of biological structures are evolving rapidly field. A number of approaches aimed at overcoming the fundamental limit imposed by diffraction have been proposed in recent years. Here we present a modification of super‐resolution optical fluctuation imaging (SOFI), a technique based on spatio‐temporal evaluation of the optical signal from independently fluctuating emitters. Instead of rapid, reversible photoswitching, photobleaching is used to produce irreversible transitions between emitting and nonemitting states of the fluorochrome molecules. Simulated images are used to demonstrate that, in the absence of noise, the proposed SOFI modification increases the efficiency of transfer of high spatial frequencies in a fluorescence microscope. Correspondingly, a decrease of the point spread function (PSF) width is obtained. Moreover, the modified SOFI algorithm is capable of resolving point emitters in the presence of simulated noise. Using real biological images we demonstrate that an increase of resolution is obtained in 2D optical sections through densely packed chromatin in cell nuclei and lamin layer at the nuclear envelope. Finally, the approach is extended to 3D wide‐field microscopy, allowing reduction of out‐of‐focus image blurring. Microsc. Res. Tech. 78:958–968, 2015. © 2015 Wiley Periodicals, Inc.