A pixel‐based likelihood framework for analysis of fluorescence recovery after photobleaching data

A new framework for the estimation of diffusion coefficients from data on fluorescence recovery after photobleaching (FRAP) with confocal laser scanning microscopy (CLSM) is presented. It is a pixel‐based statistical methodology that efficiently utilizes all information about the diffusion process in the available set of images. The likelihood function for a series of images is maximized which gives both an estimate of the diffusion coefficient and a corresponding error. This framework opens up possibilities (1) to obtain localized diffusion coefficient estimates in both homogeneous and heterogeneous materials, (2) to account for time differences between the registrations at the pixels within each image, and (3) to plan experiments optimized with respect to the number of replications, the number of bleached regions for each replicate, pixel size, the number of pixels, the number of images in each series etc. To demonstrate the use of the new framework, we have applied it to a simple system with polyethylene glycol (PEG) and water where we find good agreement with diffusion coefficient estimates from NMR diffusometry. In this experiment, it is also shown that the effect of the point spread function is negligible, and we find fluorochrome‐concentration levels that give a linear response function for the fluorescence intensity.     

On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

The point spread function is widely used to characterize the three‐dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is most often neglected because the phase information is not retrieved in noninterferometric imaging systems. However, phase point spread functions are needed to evaluate phase‐sensitive imaging systems and we believe that phase data can play an essential role in the full aberrations' characterization. In this paper, standard diffraction models have been used for the computation of the complex amplitude point spread function. In particular, the Debye vectorial model has been used to compute the amplitude point spread function of ×63/0.85 and ×100/1.3 microscope objectives, exemplifying the phase point spread function specific for each polarization component of the electromagnetic field. The effect of aberrations on the phase point spread function is then analyzed for a microscope objective used under nondesigned conditions, by developing the Gibson model ( Gibson & Lanni, 1991 ), modified to compute the three‐dimensional amplitude point spread function in amplitude and phase. The results have revealed a novel anomalous phase behaviour in the presence of spherical aberration, providing access to the quantification of the aberrations. This work mainly proposes a method to measure the complex three‐dimensional amplitude point spread function of an optical imaging system. The approach consists in measuring and interpreting the amplitude point spread function by evaluating in amplitude and phase the image of a single emitting point, a 60‐nm‐diameter tip of a Near Field Scanning Optical Microscopy fibre, with an original digital holographic experimental setup. A single hologram gives access to the transverse amplitude point spread function. The three‐dimensional amplitude point spread function is obtained by performing an axial scan of the Near Field Scanning Optical Microscopy fibre. The phase measurements accuracy is equivalent to λ/60 when the measurement is performed in air. The method capability is demonstrated on an Achroplan ×20 microscope objective with 0.4 numerical aperture. A more complete study on a ×100 microscope objective with 1.3 numerical aperture is also presented, in which measurements performed with our setup are compared with the prediction of an analytical aberrations model.     

Out‐of‐focus background subtraction for fast structured illumination super‐resolution microscopy of optically thick samples

We propose a structured illumination microscopy method to combine super resolution and optical sectioning in three‐dimensional (3D) samples that allows the use of two‐dimensional (2D) data processing. Indeed, obtaining super‐resolution images of thick samples is a difficult task if low spatial frequencies are present in the in‐focus section of the sample, as these frequencies have to be distinguished from the out‐of‐focus background. A rigorous treatment would require a 3D reconstruction of the whole sample using a 3D point spread function and a 3D stack of structured illumination data. The number of raw images required, 15 per optical section in this case, limits the rate at which high‐resolution images can be obtained. We show that by a succession of two different treatments of structured illumination data we can estimate the contrast of the illumination pattern and remove the out‐of‐focus content from the raw images. After this cleaning step, we can obtain super‐resolution images of optical sections in thick samples using a two‐beam harmonic illumination pattern and a limited number of raw images. This two‐step processing makes it possible to obtain super resolved optical sections in thick samples as fast as if the sample was two‐dimensional.     

编码孔径和解码孔径的设计

基于光学外差扫描全息术 3D成像的基本原理和编码孔径成像技术 ,设计了用于正在研制的“近红外扫描全息光学层析成像系统”中的编码孔径和解码孔径。当编码函数非负时 ,设计能取正负值的解码函数可以改善系统的点扩散函数 ,使其更接近于理想的二维 δ函数。在点扩散函数分布中的均匀或起伏较小的背景将降低重建图像的对比度。计算机模拟结果表明 ,采用对比度增强技术可以减少菲涅耳波带板和非冗余小孔阵列编码孔径重建图像的背景噪音 ,提高图像的对比度     

Localizing and extracting filament distributions from microscopy images

Detailed quantitative measurements of biological filament networks represent a crucial step in understanding architecture and structure of cells and tissues, which in turn explain important biological events such as wound healing and cancer metastases. Microscopic images of biological specimens marked for different structural proteins constitute an important source for observing and measuring meaningful parameters of biological networks. Unfortunately, current efforts at quantitative estimation of architecture and orientation of biological filament networks from microscopy images are predominantly limited to visual estimation and indirect experimental inference. Here, we describe a new method for localizing and extracting filament distributions from 2D microscopy images of different modalities. The method combines a filter‐based detection of pixels likely to contain a filament with a constrained reverse diffusion‐based approach for localizing the filaments centrelines. We show with qualitative and quantitative experiments, using both simulated and real data, that the new method can provide more accurate centreline estimates of filament in comparison to other approaches currently available. In addition, we show the algorithm is more robust with respect to variations in the initial filter‐based filament detection step often used. We demonstrate the application of the method in extracting quantitative parameters from confocal microscopy images of actin filaments and atomic force microscopy images of DNA fragments.     

基于图像反卷积的平板探测器信号串扰校正

平板探测器是锥束CT的关键组成部件，像元间的信号串扰是造成平板探测器投影图像空间分辨率低于极限值的主要因素，校正平板探测器信号串扰对提高锥束CT检测精度具有重要意义。本文基于点扩散函数矩阵反卷积投影图像去串扰校正思路，研究了点扩散函数矩阵的准确性对投影图像串扰校正的影响、点扩散函数和线扩散函数的关系及其与X射线成像的相似性，提出一种结合刀口法测量线扩散函数与平行束CT扫描重建的平板探测器点扩散函数矩阵测算方法。DR/CT扫描成像实验中，应用本文方法校正信号串扰后，DR成像空间分辨率由约10 lp/mm提升至优于25 lp/mm,高能CT成像空间分辨率由不到4 lp/mm提升至优于5 lp/mm,实验证明，应用本文方法能有效校正平板探测器信号串扰，提升锥束CT图像的空间分辨率和对比度。     

Retracted: Localizing and extracting filament distributions from microscopy images

Detailed quantitative measurements of biological filament networks represent a crucial step in understanding architecture and structure of cells and tissues, which in turn explain important biological events such as wound healing and cancer metastases. Confocal microscope images of biological specimens marked for different structural proteins constitute an important source for observing and measuring meaningful parameters of biological networks. Unfortunately, current efforts at quantitative estimation of architecture and orientation of biological filament networks from microscopy images are predominantly limited to visual estimation and indirect experimental inference. Here we describe a new method for localizing and extracting filament distributions from 2D confocal microscopy images. The method combines a filter‐based detection of pixels likely to contain a filament with a constrained reverse diffusion‐based approach for localizing the filaments centrelines. We show with qualitative and quantitative experiments, using both simulated and real data, that the new method can provide more accurate centreline estimates of filament in comparison to other approaches currently available. In addition, we show the algorithm is more robust with respect to variations in the initial filter‐based filament detection step often used. We demonstrate the application of the method in extracting quantitative parameters from an experiment that seeks to quantify the effects of carbon nanotubes on actin cytoskeleton in live HeLa cells. We show that their presence can disrupt the overall actin cytoskeletal organization in such cells.     

Image enhancement and post-processing for low resolution compressed video

This research paper recommends the point spread function(PSF)forecasting technique based on the projection onto convex set(POCS)and regularization to acquire low resolution images.As the environment for the production of user created contents(UCC)videos(one of the contents on the Internet)becomes widespread,resolution reduction and image distortion occurs,failing to satisfy users who desire high quality images.Accordingly,this research neutralizes the coding artifact through POCS and regularization processes by:1)factoring the local characteristics of the image when it comes to the noise that results during the discrete cosine transform(DCT)and quantization process;and 2)removing the blocking and ring phenomena which are problems with the existing video compression.Moreover,this research forecasts the point spread function to obtain low resolution images using the above-mentioned methods.Thus,a method is suggested for minimizing the errors found among the forecasting interpolation pixels.Low-resolution image quality obtained through the experiment demonstrates that significant enhancement was made on the visual level compared to the original image.     

Shack-Hartmann wave front measurements in cortical tissue for deconvolution of large three-dimensional mosaic transmitted light brightfield micrographs

We present a novel approach for deconvolution of 3D image stacks of cortical tissue taken by mosaic/optical‐sectioning technology, using a transmitted light brightfield microscope. Mosaic/optical‐sectioning offers the possibility of imaging large volumes (e.g. from cortical sections) on a millimetre scale at sub‐micrometre resolution. However, a blurred contribution from out‐of‐focus light results in an image quality that usually prohibits 3D quantitative analysis. Such quantitative analysis is only possible after deblurring by deconvolution. The resulting image quality is strongly dependent on how accurate the point spread function used for deconvolution resembles the properties of the imaging system. Since direct measurement of the true point spread function is laborious and modelled point spread functions usually deviate from measured ones, we present a method of optimizing the microscope until it meets almost ideal imaging conditions. These conditions are validated by measuring the aberration function of the microscope and tissue using a Shack‐Hartmann sensor. The analysis shows that cortical tissue from rat brains embedded in Mowiol and imaged by an oil‐immersion objective can be regarded as having a homogeneous index of refraction. In addition, the amount of spherical aberration that is caused by the optics or the specimen is relatively low. Consequently the image formation is simplified to refraction between the embedding and immersion medium and to 3D diffraction at the finite entrance pupil of the objective. The resulting model point spread function is applied to the image stacks by linear or iterative deconvolution algorithms. For the presented dataset of large 3D images the linear approach proves to be superior. The linear deconvolution yields a significant improvement in signal‐to‐noise ratio and resolution. This novel approach allows a quantitative analysis of the cortical image stacks such as the reconstruction of biocytin‐stained neuronal dendrites and axons.     

Precise 3D image alignment in micro-axial tomography

Micro (µ‐) axial tomography is a challenging technique in microscopy which improves quantitative imaging especially in cytogenetic applications by means of defined sample rotation under the microscope objective. The advantage of µ‐axial tomography is an effective improvement of the precision of distance measurements between point‐like objects. Under certain circumstances, the effective (3D) resolution can be improved by optimized acquisition depending on subsequent, multi‐perspective image recording of the same objects followed by reconstruction methods. This requires, however, a very precise alignment of the tilted views. We present a novel feature‐based image alignment method with a precision better than the full width at half maximum of the point spread function. The features are the positions (centres of gravity) of all fluorescent objects observed in the images (e.g. cell nuclei, fluorescent signals inside cell nuclei, fluorescent beads, etc.). Thus, real alignment precision depends on the localization precision of these objects. The method automatically determines the corresponding objects in subsequently tilted perspectives using a weighted bipartite graph. The optimum transformation function is computed in a least squares manner based on the coordinates of the centres of gravity of the matched objects. The theoretically feasible precision of the method was calculated using computer‐generated data and confirmed by tests on real image series obtained from data sets of 200 nm fluorescent nano‐particles. The advantages of the proposed algorithm are its speed and accuracy, which means that if enough objects are included, the real alignment precision is better than the axial localization precision of a single object. The alignment precision can be assessed directly from the algorithm's output. Thus, the method can be applied not only for image alignment and object matching in tilted view series in order to reconstruct (3D) images, but also to validate the experimental performance (e.g. mechanical precision of the tilting). In practice, the key application of the method is an improvement of the effective spatial (3D) resolution, because the well‐known spatial anisotropy in light microscopy can be overcome. This allows more precise distance measurements between point‐like objects.     

Capturing and displaying microscopic images used in medical diagnostics and forensic science using 4K video resolution – an application in higher education

To analyze, interpret and evaluate microscopic images, used in medical diagnostics and forensic science, video images for educational purposes were made with a very high resolution of 4096 × 2160 pixels (4K), which is four times as many pixels as High‐Definition Video (1920 × 1080 pixels). The unprecedented high resolution makes it possible to see details that remain invisible to any other video format. The images of the specimens (blood cells, tissue sections, hair, fibre, etc.) are recorded using a 4K video camera which is attached to a light microscope. After processing, this resulted in very sharp and highly detailed images. This material was then used in education for classroom discussion. Spoken explanation by experts in the field of medical diagnostics and forensic science was also added to the high‐resolution video images to make it suitable for self‐study.     

A method for estimating spatial resolution of real image in the Fourier domain

Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high‐angle diffraction in reciprocal space. In electron microscopy, correlation in the Fourier domain is used for estimating the resolution. In this paper, we report a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain. The logarithmic intensity plots of test images indicated that the full width at half maximum of a Gaussian point spread function can be estimated from the images. The spatial resolution of imaging X‐ray microtomography using Fresnel zone‐plate optics was also estimated with this method. A cross section of a test object visualized with the imaging microtomography indicated that square‐wave patterns up to 120‐nm pitch were resolved. The logarithmic intensity plot was calculated from a tomographic cross section of brain tissue. The full width at half maximum of the point spread function estimated from the plot coincided with the resolution determined from the test object. These results indicated that the logarithmic intensity plot in the Fourier domain provides an alternative measure of the spatial resolution without explicitly defining a noise criterion.     

Non-optical bimorph-based tapping-mode force sensing method for scanning near-field optical microscopy

A non‐optical bimorph‐based tapping‐mode force sensing method for tip–sample distance control in scanning near‐field optical microscopy is developed. Tapping‐mode force sensing is accomplished by use of a suitable piezoelectric bimorph cantilever, attaching an optical fibre tip to the extremity of the cantilever free end and fixing the guiding portion of the fibre to a stationary part near the tip to decouple it from the cantilever. This method is mainly characterized by the use of a bimorph, which carries out simultaneous excitation and detection of mechanical vibration at its resonance frequency owing to piezoelectric and anti‐piezoelectric effects, resulting in simplicity, compactness, ease of implementation and lack of parasitic optical background. In conjugation with a commercially available SPM controller, tapping‐mode images of various samples, such as gratings, human breast adenocarcinoma cells, red blood cells and a close‐packed layer of 220‐nm polystyrene spheres, have been obtained. Furthermore, topographic and near‐field optical images of a layer of polystyrene spheres have also been taken simultaneously. The results suggest that the tapping‐mode set‐up described here is reliable and sensitive, and shows promise for biological applications.     

Comparison of two automatic cell‐counting solutions for fluorescent microscopic images

Cell counting in microscopic images is one of the fundamental analysis tools in life sciences, but is usually tedious, time consuming and prone to human error. Several programs for automatic cell counting have been developed so far, but most of them demand additional training or data input from the user. Most of them do not allow the users to online monitor the counting results, either. Therefore, we designed two straightforward, simple‐to‐use cell‐counting programs that also allow users to correct the detection results. In this paper, we present the Cellcounter and Learn 123 programs for automatic and semiautomatic counting of objects in fluorescent microscopic images (cells or cell nuclei) with a user‐friendly interface. Although Cellcounter is based on predefined and fine‐tuned set of filters optimized on sets of chosen experiments, Learn 123 uses an evolutionary algorithm to determine the adapt filter parameters based on a learning set of images. Cellcounter also includes an extension for analysis of overlaying images. The efficiency of both programs was assessed on images of cells stained with different fluorescent dyes by comparing automatically obtained results with results that were manually annotated by an expert. With both programs, the correlation between automatic and manual counting was very high (R² < 0.9), although Cellcounter had some difficulties processing images with no cells or weakly stained cells, where sometimes the background noise was recognized as an object of interest. Nevertheless, the differences between manual and automatic counting were small compared to variations between experimental repeats. Both programs significantly reduced the time required to process the acquired images from hours to minutes. The programs enable consistent, robust, fast and accurate detection of fluorescent objects and can therefore be applied to a range of different applications in different fields of life sciences where fluorescent labelling is used for quantification of various phenomena. Moreover, Cellcounter overlay extension also enables fast analysis of related images that would otherwise require image merging for accurate analysis, whereas Learn 123's evolutionary algorithm can adapt counting parameters to specific sets of images of different experimental settings.     

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.     

Signal‐to‐noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky–Golay filters and weighted least squares error

A new technique based on cubic spline interpolation with Savitzky–Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real‐time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky–Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal‐to‐noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation‐based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real‐time SEM images, without generating corruption or increasing scanning time.     

Quasi-spherical focal spot in two-photon scanning microscopy by three-ring apodization

We present a beam-shaping technique for two-photon excitation (TPE) fluorescence microscopy. We show that by inserting a properly designed three-ring pupil filter in the illumination beam of the microscope, the effective optical sectioning capacity of such a system improves so that the point spread function gets a quasi-spherical shape. Such an improvement, which allows the acquisition of 3D images with isotropic quality, is obtained at the expense of only a small increase of the overall energy in the axial sidelobes. The performance of this technique is illustrated with a scanning TPE microscopy experiment in which the image of small beads is obtained. We demonstrate an effective narrowing of 12.5% in the axial extent of the point spread function, while keeping the 82% of the spot-fluorescence efficiency.     

Analysis of spatial cross‐correlations in multi‐constituent volume data

We investigate spatial cross‐correlations between two constituents, both belonging to the same microstructure. These investigations are based on two approaches: one via the measurement of the cross‐correlation function and the other uses the spatial distances between the constituents. The cross‐correlation function can be measured using the fast Fourier transform, whereas the distances are determined via the Euclidean distance transform. The characteristics are derived from volume images obtained by synchrotron microtomography. As an example we consider pore formation in metallic foams, knowledge of which is important to control the foam production process. For this example, we discuss the spatial cross‐correlation between the pore space and the blowing agent particles in detail.     

Rapid microscope auto‐focus method for uneven surfaces based on image fusion

Microscopic imaging of uneven surfaces is difficult because of the limited depth of field. In this study, we developed a rapid auto‐focus method for uneven surfaces based on image fusion. The Prewitt operator was used to detect the vertical edges of the images. Then, the focus position was theoretically calculated using a Gaussian function, and image fusion was applied to obtain the final in‐focus image. An experiment was designed to verify the developed method. The results revealed that this method is effective for printed circuit boards.