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.     

Improved correction of axial geometrical distortion in index-mismatched fluorescent confocal microscopic images using high-aperture objective lenses

Extracting quantitative data from microscopic volume images is straightforward when the refractive indices of the immersion medium and the mounting medium are equal. The readings of the position of the specimen stage can be directly used to measure depth and width. Imperfectly matched immersion and mounting media result in axial geometrical distortion. Linear correction of the axial distortion using the paraxial estimate of the axial scaling factor yields results that may differ as much as 4% from the actual values. From calculations based on a theoretical expression of the 3‐D point‐spread function in the focal region of a high‐aperture microscope focussing into a mismatched mounting medium, we derived axial scaling factors that result in quantitative results accurate to better than 1%. From a non‐linear correction procedure, an improved formula for the paraxial estimate of the axial scaling factor is derived.     

Utilizing confocal microscopy to measure refractive index of articular cartilage

This study proposes a method for measuring the refractive index of articular cartilage within a thin and small specimen slice. The cartilage specimen, with a thickness of about 50 μm, was put next to a thin film of immersion oil of similar thickness. Both the articular cartilage and immersion oil were scanned along the depth direction using a confocal microscope. The refractive index mismatch between the cartilage and the immersion oil induced a slight axial deformation in the confocal images of the cartilage specimen that was accurately measured by a subpixel edge‐detection‐based technique. A theoretical model was built to quantify the focal shift of confocal microscopy caused by the refractive index mismatch. With the quantitative deformations of cartilage images and the quantified function of focal shift, the refractive index of articular cartilage was accurately interpolated. At 561 nm, 0.1 MPa and 20 °C, the overall refractive index of the six cartilage plugs was 1.3975 ± 0.0156. The overall coefficient of variation of all cartilage specimens was 0.68%, which indicated the high repeatability of our method. The verification experiments using distilled water showed a minimal relative error of 0.02%.     

A procedure to determine the correct thickness of an object with confocal microscopy in case of refractive index mismatch

A difference in refractive index (n) between immersion medium and specimen results in increasing loss of intensity and resolution with increasing focal depth and in an incorrect axial scaling in images of a confocal microscope. Axial thickness measurements of an object on such images are therefore not exact. The present paper describes a simple procedure to determine the correct axial thickness of an object with confocal fluorescence microscopy. We study this procedure for a specimen that has a higher refractive index than the immersion medium and with a thickness up to 100 µm. The measuring method was experimentally tested by comparing the thickness of polymer layers measured on axial images of a confocal microscope in case of a water–polymer mismatch to reference values obtained from an independent technique, i.e. scanning electron microscopy. The case when the specimen has a lower refractive index than the immersion medium is also shown by way of illustration. Measured thickness data of a water layer and an oil layer with the same actual thickness were obtained using an oil-immersion objective lens with confocal microscopy. Good agreement between theory and experiment was found in both cases, consolidating our method.     

A new high-aperture glycerol immersion objective lens and its application to 3D-fluorescence microscopy

High‐resolution light microscopy of glycerol‐mounted biological specimens is performed almost exclusively with oil immersion lenses. The reason is that the index of refraction of the oil and the cover slip of ~1.51 is close to that of ~1.45 of the glycerol mountant, so that refractive index mismatch‐induced spherical aberrations are tolerable to some extent. Here we report the application of novel cover glass‐corrected glycerol immersion lenses of high numerical aperture (NA) and the avoidance of these aberrations. The new lenses feature a semi‐aperture angle of 68.5°, which is slightly larger than that of the diffraction‐limited 1.4 NA oil immersion lenses. The glycerol lenses are corrected for a quartz cover glass of 220 µm thickness and for a 80% glycerol‐water immersion solution. Featuring an aberration correction collar, the lens can adapt to glycerol concentrations ranging between 72% and 88%, to slight variations of the temperature, and to the cover glass thickness. As the refractive index mismatch‐induced aberrations are particularly important to quantitative confocal fluorescence microscopy, we investigated the axial sectioning ability and the axial chromatic aberrations in such a microscope as well as the image brightness as a function of the penetration depth. Whereas there is a significant decrease in image brightness associated with oil immersion, this decrease is absent with the glycerol immersion system. In addition, we show directly the compression of the optic axis in the case of oil immersion and its absence in the glycerol system. The unique advantages of these new lenses in high‐resolution microscopy with two coherently used opposing lenses, such as 4 Pi‐microscopy, are discussed.     

Digital differential confocal microscopy based on spatial shift transformation

Differential confocal microscopy is a particularly powerful surface profilometry technique in industrial metrology due to its high axial sensitivity and insensitivity to noise. However, the practical implementation of the technique requires the accurate positioning of point detectors in three‐dimensions. We describe a simple alternative based on spatial transformation of a through‐focus series of images obtained from a homemade beam scanning confocal microscope. This digital differential confocal microscopy approach is described and compared with the traditional Differential confocal microscopy approach. The ease of use of the digital differential confocal microscopy system is illustrated by performing measurements on a 3D standard specimen.     

Adaptive optics in spinning disk microscopy: improved contrast and brightness by a simple and fast method

Multiconfocal microscopy gives a good compromise between fast imaging and reasonable resolution. However, the low intensity of live fluorescent emitters is a major limitation to this technique. Aberrations induced by the optical setup, especially the mismatch of the refractive index and the biological sample itself, distort the point spread function and further reduce the amount of detected photons. Altogether, this leads to impaired image quality, preventing accurate analysis of molecular processes in biological samples and imaging deep in the sample. The amount of detected fluorescence can be improved with adaptive optics. Here, we used a compact adaptive optics module (adaptive optics box for sectioning optical microscopy), which was specifically designed for spinning disk confocal microscopy. The module overcomes undesired anomalies by correcting for most of the aberrations in confocal imaging. Existing aberration detection methods require prior illumination, which bleaches the sample. To avoid multiple exposures of the sample, we established an experimental model describing the depth dependence of major aberrations. This model allows us to correct for those aberrations when performing a z‐stack, gradually increasing the amplitude of the correction with depth. It does not require illumination of the sample for aberration detection, thus minimizing photobleaching and phototoxicity. With this model, we improved both signal‐to‐background ratio and image contrast. Here, we present comparative studies on a variety of biological samples.     

3D deconvolution of spherically aberrated images using commercial software

Refractive index mismatch between the specimen and the objective immersion oil results in spherical aberration, which causes distortion and spreading of the point spread function, as well as incorrect readings of the axial coordinates. These effects have to be taken into account when performing three-dimensional restoration of wide-field fluorescence images. By using objects with well-defined geometry (fluorescently stained Escherichia coli or actin filaments) separated from a cover slip by a layer of oil with known refractive index, we investigated the accuracy of three-dimensional shape restoration by the commercial programs Huygens and Autoquant. Aberration correction available in the software dramatically reduced the axial blur compared to deconvolution that ignored the refractive index mismatch. At the same time, it failed to completely recover the cylindrical symmetry of bacteria or of actin fibres, which showed up to a three to five times larger width along the optical axis compared to the lateral plane. The quality of restoration was only moderately sensitive to the exact values of the specimen refractive index but in some cases improved significantly by assuming a reduced NA of the objective. Because image restoration depends on the knowledge of the vertical scale, we also performed detailed measurements of the axial scaling factor and concluded (in agreement with some previous authors) that scaling is adequately described by the simple paraxial formula, even when high-NA oil-immersion objectives are used.     

Volume measurements in three-dimensional microscopy

A refractive index mismatch between the oil immersion and the microscopic object can lead to a severe over-estimation of the object's size. The cause of this effect is explained and a simple calibration method to compensate for its occurrence is presented. A practical example is discussed. The analysis applies to both conventional three-dimensional, and confocal microscopy.     

Axial tomographic confocal fluorescence microscopy

By physical rotation of the sample, axial tomography enables the acquisition of otherwise inaccessible spatial information from an object. In combination with confocal microscopy, the method can fundamentally improve the effective three‐dimensional (3D) resolution. In this report we present a novel method for high resolution reconstruction of confocal axial tomographic data. The method automatically determines the relative angles of rotation, aligns the data from different rotational views and reconstructs a single high resolution 3D dataset. The reconstruction makes use of a known point spread function and is based on an unconstrained maximum likelihood deconvolution performed simultaneously from multiple (in our case three) angular views. It was applied to simulated as well as to experimental confocal datasets. The gain in resolution was quantified and the effect of choice of overrelaxation factors on the speed of convergence was investigated. A clearly improved 3D resolution was obtained by axial tomography together with reconstruction as compared with reconstruction of confocal data from only a single angular view.     

Effects of specimen refractive index on confocal imaging

The aberrations introduced when focusing within a specimen with a refractive index equal to that of water using an oil-immersion objective are investigated theoretically. The peak intensity in the confocal point spread function drops by a factor of two for focusing less than 10 μm into the specimen. The effects on scaling of dimensions in the resulting images are discussed. The image exhibits an axial stretching by a factor of about 1.12.     

Multipoint scanning dual‐detection confocal microscopy for fast 3D volumetric measurement

We propose a multipoint scanning dual‐detection confocal microscopy (MS‐DDCM) system for fast 3D volumetric measurements. Unlike conventional confocal microscopy, MS‐DDCM can accomplish surface profiling without axial scanning. Also, to rapidly obtain 2D images, the MS‐DDCM employs a multipoint scanning technique, with a digital micromirror device used to produce arrays of effective pinholes, which are then scanned. The MS‐DDCM is composed of two CCDs: one collects the conjugate images and the other collects nonconjugate images. The ratio of the axial response curves, measured by the two detectors, provides a linear relationship between the height of the sample surface and the ratio of the intensity signals. Furthermore, the difference between the two images results in enhanced contrast. The normalising effect of the MS‐DDCM provides accurate sample heights, even when the reflectance distribution of the surface varies. Experimental results confirmed that the MS‐DDCM achieved high‐speed surface profiling with improved image contrast capability.     

An application of spatial deconvolution to a capillary-based high-pressure chamber for fluorescence microscopy imaging

Capillary‐based high‐pressure chambers for which the wall serves as both the optical window and mechanical support have been reported for fluorescence microscopy imaging. Although capillary chambers are straightforward and economical to construct, the curved capillary wall introduces image aberrations. The significance of these aberrations in imaging sub‐cellular‐dimension objects has yet to be assessed. Using a capillary chamber that is routinely pressurized to between 20 and 30 MPa, a pressure range suitable for studying a wide variety of cellular processes, we demonstrate sub‐cellular‐dimension spatial resolution in the imaging of fluorescent micro‐spheres. Objectives with a range of numerical apertures (0.5–1.3) and working distances (0.1–7.4 mm) are considered. We show that spatial (or point‐spread function, PSF) deconvolution improves image contrast in capillary‐based images by comparing deconvolution results with those obtained from slide‐mounted controls. Furthermore, similar deconvolution results between a measured PSF and a calculated, flat‐geometry PSF indicate that the capillary wall is optically flat on cellular length scales. Results here facilitate the application of contemporary techniques in fluorescence microscopy to high‐pressure imaging fields.     

Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index

The effect of refractive-index mismatch, as encountered in the observation of biological specimens, on the image acquisition process in confocal fluorescence microscopy is investigated theoretically. The analysis takes the vectorial properties of light into account and is valid for high numerical apertures. Quantitative predictions on the decrease of resolution, intensity drop and shift of focus are given for practical situations. When observing with a numerical aperture of 1·3 (oil immersion) and an excitation wavelength of 514 nm the centre of the focus shifts 1·7 μm per 10 μm of axial displacement in an aqueous medium, thus yielding an image that is scaled by a factor of 1·2 in the axial direction. Furthermore, it can be expected that for a fluorescent plane 20 μm deep inside an aqueous medium the peak intensity is 40% less than for a plane which is 10 μm deep. In addition, the axial resolution is decreased by a factor of 1·4. The theory was experimentally verified for test samples with different refractive indices.     

Three-dimensional point spread function model for line-scanning confocal microscope with high-aperture objective

Point Spread Function (PSF) modelling is an important task in image formation analysis. In confocal microscopy, the exact PSF is rarely known, thus one has to rely on its approximation. An initial estimation is usually performed experimentally by measuring fluorescent beads or analytically by studying properties of the optical system. Yet, fluorescent line‐scanning confocal microscopes are not widespread; therefore, very few adapted models are available in the literature. In this paper, we propose an analytical PSF model for line‐scanning confocal microscopes. Validation is performed by measuring the error between our model and an experimental PSF measured with fluorescent beads, assumed to represent the real PSF. Comparison with existing models is also presented.     

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.     

基于并行共聚焦显微系统的物方差动轴向测量

差动共聚焦显微成像技术可以获得很高的轴向测量精度,然而已有的差动共聚焦测量技术主要适用于激光扫描共聚焦,还不能满足微纳加工过程中对工件进行非接触式的在线、在位测量的要求。本文在分析差动共聚焦显微成像系统能够实现轴向测量原理的基础上,提出了适用于并行共聚焦技术的轴向测量方法。该方法利用均匀白光照明,在像方只需要使用一台相机做探测器,在物方通过移动载物台分别对样品在焦前和焦后两次成像,根据预先刻度好的差动曲线就可以得出物体表面的高度。理论模拟与实验结果均表明,该方法可以实现高精度的轴向测量,对500nm的台阶样品测量的平均误差为2.9nm,相对误差为0.58%。该方法简单、廉价、测量精度高,可以用于普通显微镜,易于实现样品的三维快速形貌还原与测量。     

High-precision distance measurements and volume-conserving segmentation of objects near and below the resolution limit in three-dimensional confocal fluorescence microscopy

This study presents a method for high-precision distance measurements and for the volume-conserving segmentation of fluorescent objects with a size of the order of the microscopic observation volume. The segmentation was performed via a model-based approach, using an algorithm that was calibrated by the microscopic point spread function. Its performance was evaluated for three different fluorochromes using model images and fluorescent microspheres as test targets. The fundamental limits which the microscopic imaging process imposes on the accuracy of volume and distance measurements were evaluated in detail. A method for the calibration of the axial stepwidth of a confocal microscope is presented. The results suggest that in biological applications, 3D distances and radii of objects in cell nuclei can be determined with an accuracy of ≤ 60 nm. Using objects of different spectral signature, 3D distance measurements substantially below the lateral half width of the confocal point spread function are feasible. This is shown both theoretically and experimentally.     

Algorithms for accurate 3D registration of neuronal images acquired by confocal scanning laser microscopy

This paper presents automated and accurate algorithms based on high‐order transformation models for registering three‐dimensional (3D) confocal images of dye‐injected neurons. The algorithms improve upon prior methods in several ways, and meet the more stringent image registration needs of applications such as two‐view attenuation correction recently developed by us. First, they achieve high accuracy (≈ 1.2 voxels, equivalent to 0.4 µm) by using landmarks, rather than intensity correlations, and by using a high‐dimensional affine and quadratic transformation model that accounts for 3D translation, rotation, non‐isotropic scaling, modest curvature of field, distortions and mechanical inconsistencies introduced by the imaging system. Second, they use a hierarchy of models and iterative algorithms to eliminate potential instabilities. Third, they incorporate robust statistical methods to achieve accurate registration in the face of inaccurate and missing landmarks. Fourth, they are fully automated, even estimating the initial registration from the extracted landmarks. Finally, they are computationally efficient, taking less than a minute on a 900‐MHz Pentium III computer for registering two images roughly 70 MB in size. The registration errors represent a combination of modelling, estimation, discretization and neuron tracing errors. Accurate 3D montaging is described; the algorithms have broader applicability to images of vasculature, and other structures with distinctive point, line and surface landmarks.     

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.