The effects of spherical aberration on multiphoton fluorescence excitation microscopy

Multiphoton fluorescence excitation microscopy is almost invariably conducted with samples whose refractive index differ from that of the objective immersion medium, conditions that cause spherical aberration. Due to the quadratic nature of multiphoton fluorescence excitation, spherical aberration is expected to profoundly affect the depth dependence of fluorescence excitation. In order to determine the effect of refractive index mismatch in multiphoton fluorescence excitation microscopy, we measured signal attenuation, photobleaching rates and resolution degradation with depth in homogeneous samples with minimal light scattering and absorption over a range of refractive indices. These studies demonstrate that signal levels and resolution both rapidly decline with depth into refractive index mismatched samples. Analyses of photobleaching rates indicate that the preponderance of signal attenuation with depth results from decreased rates of fluorescence excitation, even in a system with a descanned emission collection pathway. Similar results were obtained in analyses of fluorescence microspheres embedded in rat kidney tissue, demonstrating that spherical aberration is an important limiting factor in multiphoton fluorescence excitation microscopy of biological samples.     

Digital scanned laser light-sheet fluorescence lifetime microscopy with wide-field time-gated imaging

We develop a multidimensional fluorescence imaging technique by implementing a wide-field time-gated fluorescence lifetime imaging into digital scanned laser light-sheet microscopy (FLIM-DSLM) to measure 3D fluorescence lifetime distribution in mesoscopic specimens with high resolution. This is achieved by acquiring a series of time-gated images at different relative time delays with respect of excitation pulses at different depths. The lifetime is determined for each voxel by iteratively fitting to single exponential decay. The performance of the developed system is evaluated with the measurements of a lifetime reference Rhodamine 6G solution and a subresolution fluorescent bead phantom. We also demonstrate the application performances of this system to ex vivo and in vivo imaging of Tg(kdrl:EGFP) transgenic zebrafish embryos, illustrating the lifetime differences between the GFP signal and the autofluorescence signal. The results show that FLIM-DSLM can be used for sample size up to a few millimetres and can be utilised as a powerful and robust method for biomedical research, for example as a readout of protein–protein interactions via Förster resonance energy transfer.     

The effects of refractive index heterogeneity within kidney tissue on multiphoton fluorescence excitation microscopy

Although multiphoton fluorescence excitation microscopy has improved the depth at which useful fluorescence images can be collected in biological tissues, the reach of multiphoton fluorescence excitation microscopy is nonetheless limited by tissue scattering and spherical aberration. Scattering can be reduced in fixed samples by mounting in a medium whose refractive index closely matches that of the fixed material. Using optical 'clearing', the effects of refractive index heterogeneity on signal attenuation with depth are investigated. Quantitative measurements show that by mounting kidney tissue in a high refractive index medium, less than 50% of signal attenuates in 100 μm of depth.     

Phase‐retrieved pupil function and coherent transfer function in confocal microscopy

This work reports on the retrieval of the pupil function and coherent transfer function of a coherent reflection type confocal microscope from simulated measurements of the intensity point spread function. Two phase retrieval algorithms are presented in this vein, which incorporate the multiple pupil dependence of image formation in confocal microscopy. Verification of the algorithms follows by numerical simulations.     

Dispersion, aberration and deconvolution in multi-wavelength fluorescence images

The wavelength dependence of the incoherent point spread function in a wide-field microscope was investigated experimentally. Dispersion in the sample and optics can lead to significant changes in the point spread function as wavelength is varied over the range commonly used in fluorescence microscopy. For a given sample, optical conditions can generally be optimized to produce a point spread function largely free of spherical aberration at a given wavelength. Unfortunately, deviations in wavelength from this value will result in spherically aberrated point spread functions. Therefore, when multiple fluorophores are used to localize different components in the same sample, the image of the distribution of at least one of the fluorophores will be spherically aberrated. This aberration causes a loss of intensity and resolution, thereby complicating the localization and analysis of multiple components in a multi-wavelength image. We show that optimal resolution can be restored to a spherically aberrated image by constrained, iterative deconvolution, as long as the spherical aberration in the point spread function used for deconvolution matches the aberration in the image reasonably well. The success of this method is essentially independent of the initial degree of spherical aberration in the image. Deconvolution of many biological images can be achieved by collecting a small library of spherically aberrated and unaberrated point spread functions, and then choosing a point spread function appropriate for deconvolving each image. The co-localization and relative intensities of multiple components can then be accurately studied in a multi-wavelength image.     

Application of the split-gradient method to 3D image deconvolution in fluorescence microscopy

The methods of image deconvolution are important for improving the quality of the detected images in the different modalities of fluorescence microscopy such as wide‐field, confocal, two‐photon excitation and 4Pi. Because deconvolution is an ill‐posed problem, it is, in general, reformulated in a statistical framework such as maximum likelihood or Bayes and reduced to the minimization of a suitable functional, more precisely, to a constrained minimization, because non‐negativity of the solution is an important requirement. Next, iterative methods are designed for approximating such a solution. In this paper, we consider the Bayesian approach based on the assumption that the noise is dominated by photon counting, so the likelihood is of the Poisson‐type, and that the prior is edge‐preserving, as derived from a simple Markov random field model. By considering the negative logarithm of the a posteriori probability distribution, the computation of the maximum a posteriori (MAP) estimate is reduced to the constrained minimization of a functional that is the sum of the Csiszár I‐divergence and a regularization term. For the solution of this problem, we propose an iterative algorithm derived from a general approach known as split‐gradient method (SGM) and based on a suitable decomposition of the gradient of the functional into a negative and positive part. The result is a simple modification of the standard Richardson–Lucy algorithm, very easily implementable and assuring automatically the non‐negativity of the iterates. Next, we apply this method to the particular case of confocal microscopy for investigating the effect of several edge‐preserving priors proposed in the literature using both synthetic and real confocal images. The quality of the restoration is estimated both by computation of the Kullback–Leibler divergence of the restored image from the detected one and by visual inspection. It is observed that the noise artefacts are considerably reduced and desired characteristics (edges and minute features as islets) are retained in the restored images. The algorithm is stable, robust and tolerant at various noise (Poisson) levels. Finally, by remarking that the proposed method is essentially a scaled gradient method, a possible modification of the algorithm is briefly discussed in view of obtaining fast convergence and reduction in computational time.     

An efficient algorithm for measurement and correction of chromatic aberrations in fluorescence microscopy

Even the best optical microscopes available on the market exhibit chromatic aberrations to some extent. In some types of study, chromatic aberrations of current optics cannot be neglected and a software correction is highly desirable. This paper describes a novel method of chromatic aberration measurement and software correction using sub-resolution bead imaging and computer image analysis. The method is quick, precise and enables the determination of both longitudinal and lateral chromatic aberrations. Correction function can be computed in about half an hour, including image acquisition. Using this approach, chromatic aberrations can be reduced to 10–20 nm laterally and 10–60 nm axially depending on the type of optical set-up. The method is especially suitable for fluorescence microscopy, where a limited number of wavelengths are observed.     

Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror

We demonstrate adaptive aberration correction for depth‐induced spherical aberration in a multiphoton scanning microscope with a micromachined deformable mirror. Correction was made using a genetic learning algorithm with two‐photon fluorescence intensity feedback to determine the desired shape for an adaptive mirror. For a 40×/0.6 NA long working distance objective, the axial scanning range was increased from 150 mm to 600 mm.     

Image calibration in fluorescence microscopy

A fluorescence image calibration method is presented based on the use of standardized uniformly fluorescing reference layers. It is demonstrated to be effective for the correction of non‐uniform imaging characteristics across the image (shading correction) as well as for relating fluorescence intensities between images taken with different microscopes or imaging conditions. The variation of the illumination intensity over the image can be determined on the basis of the uniform bleaching characteristics of the layers. This permits correction for the latter and makes bleach‐rate‐related imaging practical. The significant potential of these layers for calibration in quantitative fluorescence microscopy is illustrated with a series of applications. As the illumination and imaging properties of a microscope can be evaluated separately, the methods presented are also valuable for general microscope testing and characterization.     

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.     

An open‐source deconvolution software package for 3‐D quantitative fluorescence microscopy imaging

Deconvolution techniques have been widely used for restoring the 3‐D quantitative information of an unknown specimen observed using a wide‐field fluorescence microscope. Deconv , an open‐source deconvolution software package, was developed for 3‐D quantitative fluorescence microscopy imaging and was released under the GNU Public License. Deconv provides numerical routines for simulation of a 3‐D point spread function and deconvolution routines implemented three constrained iterative deconvolution algorithms: one based on a Poisson noise model and two others based on a Gaussian noise model. These algorithms are presented and evaluated using synthetic images and experimentally obtained microscope images, and the use of the library is explained. Deconv allows users to assess the utility of these deconvolution algorithms and to determine which are suited for a particular imaging application. The design of Deconv makes it easy for deconvolution capabilities to be incorporated into existing imaging applications.     

Noise suppression of point spread functions and its influence on deconvolution of three-dimensional fluorescence microscopy image sets

The point spread function (PSF) is of central importance in the image restoration of three-dimensional image sets acquired by an epifluorescent microscope. Even though it is well known that an experimental PSF is typically more accurate than a theoretical one, the noise content of the experimental PSF is often an obstacle to its use in deconvolution algorithms. In this paper we apply a recently introduced noise suppression method to achieve an effective noise reduction in experimental PSFs. We show with both simulated and experimental three-dimensional image sets that a PSF that is smoothed with this method leads to a significant improvement in the performance of deconvolution algorithms, such as the regularized least-squares algorithm and the accelerated Richardson–Lucy algorithm.     

A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy

We have compared different image restoration approaches for fluorescence microscopy. The most widely used algorithms were classified with a Bayesian theory according to the assumed noise model and the type of regularization imposed. We considered both Gaussian and Poisson models for the noise in combination with Tikhonov regularization, entropy regularization, Good's roughness and without regularization (maximum likelihood estimation). Simulations of fluorescence confocal imaging were used to examine the different noise models and regularization approaches using the mean squared error criterion. The assumption of a Gaussian noise model yielded only slightly higher errors than the Poisson model. Good's roughness was the best choice for the regularization. Furthermore, we compared simulated confocal and wide-field data. In general, restored confocal data are superior to restored wide-field data, but given sufficient higher signal level for the wide-field data the restoration result may rival confocal data in quality. Finally, a visual comparison of experimental confocal and wide-field data is presented.     

Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images

Although confocal microscopes have considerably smaller contribution of out-of-focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum-likelihood algorithms with regularization have been used. However, the choice of regularization parameters is often unknown although it has considerable effect on the result of deconvolution process. The aims of this work were: to find good estimates of deconvolution parameters; and to develop an open source software package that would allow testing different deconvolution algorithms and that would be easy to use in practice. Here, Richardson-Lucy algorithm has been implemented together with the total variation regularization in an open source software package IOCBio Microscope. The influence of total variation regularization on deconvolution process is determined by one parameter. We derived a formula to estimate this regularization parameter automatically from the images as the algorithm progresses. To assess the effectiveness of this algorithm, synthetic images were composed on the basis of confocal images of rat cardiomyocytes. From the analysis of deconvolved results, we have determined under which conditions our estimation of total variation regularization parameter gives good results. The estimated total variation regularization parameter can be monitored during deconvolution process and used as a stopping criterion. An inverse relation between the optimal regularization parameter and the peak signal-to-noise ratio of an image is shown. Finally, we demonstrate the use of the developed software by deconvolving images of rat cardiomyocytes with stained mitochondria and sarcolemma obtained by confocal and widefield microscopes.     

Fluorescence photobleaching-based shading correction for fluorescence microscopy

A thin fluorescent test layer, which is used in a practically mono-exponential bleaching regime, is employed to determine separately the excitation intensity and the fluorescence detection efficiency distributions in the field of view of a confocal fluorescence microscope. We demonstrate that once these distributions are known, it is possible to correct an image of a specimen for intensity variations which are caused by spatial nonuniformities of the illumination and the detection efficiency of the microscope. It is indicated that, provided a photophysically well-characterized fluorescent test layer is available, the method is potentially capable of quantifying the fluorescence intensities in an image of a specimen in terms of the fluorescence quantum yield, the absorption cross-section and the concentration of the fluorophore in the specimen.     

Effects of objective numerical apertures on achievable imaging depths in multiphoton microscopy

Multiphoton microscopy is a powerful technique for achieving three-dimensional submicron imaging in biological specimens. However, specimen optical parameters such as refractive indices and scattering coefficients can result in the loss of image resolution and decreased signal in depth. These factors are coupled to the focusing objective's numerical aperture (NA) in limiting the achievable imaging depths. In this work, we performed multiphoton imaging on aqueous fluorescent solution, human skin, and rat tail tendon to show that, under the same immersion condition, lower NA objectives can examine more deeply into biological specimens and should be used when optimal imaging depths is desired.     

Correlative fluorescence and electron microscopy in tissues: immunocytochemistry

Correlative microscopy is a collection of procedures that rely upon two or more imaging modalities to examine the same specimen. The imaging modalities employed should each provide unique information and the combined correlative data should be more information rich than that obtained by any of the imaging methods alone. Currently the most common form of correlative microscopy combines fluorescence and electron microscopy. While much of the correlative microscopy in the literature is derived from studies of model cell culture systems we have focused, primarily, on correlative microscopy in tissue samples. The use of tissue, particularly human tissue, may add constraints not encountered in cell culture systems. Ultrathin cryosections, typically used for immunoelectron microscopy, have served as the substrate for correlative fluorescence and electron microscopic immunolocalization in our studies. In this work, we have employed the bifunctional reporter FluoroNanogold. This labeling reagent contains both a fluorochrome and a gold-cluster compound and can be imaged by sequential fluorescence and electron microscopy. This approach permits the examination of exactly the same sub-cellular structures in both fluorescence and electron microscopy with a high level of spatial resolution.     

Scanning optical fluorescence microscopy

A scanning optical fluorescence microscope is described which possesses several advantages over a conventional fluorescence microscope. These include improved resolution, a reduction in background- and auto-fluorescence, an increase in the available fluorescence spectrum and simple modification for automated fluorescence studies. Experimental results are included.     

X-ray omni microscopy

The science of wave‐field phase retrieval and phase measurement is sufficiently mature to permit the routine reconstruction, over a given plane, of the complex wave‐function associated with certain coherent forward‐propagating scalar wave‐fields. This reconstruction gives total knowledge of the information that has been encoded in the complex wave‐field by passage through a sample of interest. Such total knowledge is powerful, because it permits the emulation in software of the subsequent action of an infinite variety of coherent imaging systems. Such ‘virtual optics’, in which software forms a natural extension of the ‘hardware optics’ in an imaging system, may be useful in contexts such as quantitative atom and X‐ray imaging, in which optical elements such as beam‐splitters and lenses can be realized in software rather than optical hardware. Here, we develop the requisite theory to describe such hybrid virtual‐physical imaging systems, which we term ‘omni optics’ because of their infinite flexibility. We then give an experimental demonstration of these ideas by showing that a lensless X‐ray point projection microscope can, when equipped with the appropriate software, emulate an infinite variety of optical imaging systems including those which yield interferograms, Zernike phase contrast, Schlieren imaging and diffraction‐enhanced imaging.