Jose-Angel Conchello

Optical sectioning microscopy

Confocal scanning microscopy, a form of optical sectioning microscopy, has radically transformed optical imaging in biology. These devices provide a powerful means to eliminate from images the background caused by out-of-focus light and scatter. Confocal techniques can also improve the resolution of a light microscope image beyond what is achievable with widefield fluorescence microscopy. The quality of the images obtained, however, depends on the users familiarity with the optical and fluorescence concepts that underlie this approach. We describe the core concepts of confocal microscopes and important variables that adversely affect confocal images. We also discuss data-processing methods for confocal microscopy and computational optical sectioning techniques that can perform optical sectioning without a confocal microscope.

Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy

We derive an algorithm for maximum-likelihood image estimation on the basis of the expectation-maximization (EM) formalism by using a new approximate model for depth-varying image formation for optical sectioning microscopy. This new strata-based model incorporates spherical aberration that worsens as the microscope is focused deeper under the cover slip and is the result of the refractive-index mismatch between the immersion medium and the mounting medium of the specimen. Images of a specimen with known geometry and refractive index show that the model captures the main features of the image. We analyze the performance of the depth-variant EM algorithm with simulations, which show that the algorithm can compensate for image degradation changing with depth.

Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images

Computational optical-sectioning microscopy with a nonconfocal microscope is fundamentally limited because the optical transfer function, the Fourier transform of the point-spread function, is exactly zero over a conic region of the spatial-frequency domain. Because of this missing cone of optical information, images are potentially artifactual. To overcome this limitation, superresolution, in the sense of band extrapolation, is necessary. I present a frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation. This analysis gives the theoretical absolute bandwidth of the restored image; however, this absolute value may not be realistic in many cases. Then a second analysis is presented that assumes a Gaussian point-spread function and a specimen function and shows more realistic behavior of the algorithm and demonstrates some of its properties. Experimental results on the superresolving capability of the algorithm are also presented.

Artifacts in computational optical-sectioning microscopy.

We tested the most complete optical model available for computational optical-sectioning microscopy and obtained four main results. First, we observed good agreement between experimental and theoretical point-spread functions (PSFs) under a variety of imaging conditions. Second, using these PSFs, we found that a linear restoration method yielded reconstructed images of a well-defined phantom object (a 10-microns-diameter fluorescent bead) that closely resembled the theoretically determined, best-possible linear reconstruction of the object. Third, this best linear reconstruction suffered from a (to our knowledge) previously undescribed artifactual axial elongation whose principal cause was not increased axial blur but rather the conical shape of the null space intrinsic to nonconfocal three-dimensional (3D) microscopy. Fourth, when 10-microns phantom beads were embedded at different depths in a transparent medium, reconstructed bead images were progressively degraded with depth unless they were reconstructed with use of a PSF determined at the beads depth. We conclude that (1) the optical model for optical sectioning is reasonably accurate; (2) if PSF shift variance cannot be avoided by adjustment of the optics, then reconstruction methods must be modified to account for this effect; and (3) alternative microscopical or nonlinear algorithmic approaches are required for overcoming artifacts imposed by the missing cone of frequencies that is intrinsic to nonconfocal 3D microscopy.

Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy

Imaging models for differential-interference-contrast (DIC) microscopy are presented. Two- and three-dimensional models for DIC imaging under partially coherent illumination were derived and tested by using phantom specimens viewed with several conventional DIC microscopes and quasi-monochromatic light. DIC images recorded with a CCD camera were compared with model predictions that were generated by using theoretical point-spread functions, computer-generated phantoms, and estimated imaging parameters such as bias and shear. Results show quantitative and qualitative agreement between model and data for several imaging conditions.

Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur

Blind-deconvolution microscopy, the simultaneous estimation of the specimen function and the point-spread function (PSF) of the microscope, is an underdetermined problem with nonunique solutions that are usually avoided by enforcing constraints on the specimen function and the PSF. We derived a maximum-likelihood-based method for blind deconvolution in which we assume a mathematical model for the PSF that depends on a small number of parameters (e.g., less than 20). The algorithm then estimates the unknown parameters together with the specimen function. The mathematical model ensures that all the constraints of the PSF are satisfied, and the maximum-likelihood approach ensures that the specimen is nonnegative. The method successfully estimates the PSF and removes out-of-focus blur. The PSF estimation is robust to aberrations in the PSF and to noise in the image.

Fast maximum-likelihood image-restoration algorithms for three- dimensional fluorescence microscopy

We have evaluated three constrained, iterative restoration algorithms to find a fast, reliable algorithm for maximum-likelihood estimation of fluorescence microscopic images. Two algorithms used a Gaussian approximation to Poisson statistics, with variances computed assuming Poisson noise for the images. The third method used Csiszars information-divergence (I-divergence) discrepancy measure. Each method included a nonnegativity constraint and a penalty term for regularization; optimization was performed with a conjugate gradient method. Performance of the methods was analyzed with simulated as well as biological images and the results compared with those obtained with the expectation-maximization-maximum-likelihood (EM-ML) algorithm. The I-divergence-based algorithm converged fastest and produced images similar to those restored by EM-ML as measured by several metrics. For a noiseless simulated specimen, the number of iterations required for the EM-ML method to reach a given log-likelihood value was approximately the square of the number required for the I-divergence-based method to reach the same value.

Enhanced three-dimensional reconstruction from confocal scanning microscope images. II. Depth discrimination versus signal-to-noise ratio in partially confocal images

The enhanced depth discrimination of a confocal scanning optical microscope is produced by a pinhole aperture placed in front of the detector to reject out-of-focus light. Strictly confocal behavior is impractical because an infinitesimally small aperture would collect very little light and would result in images with a poor signal-to-noise ratio (SNR), while a finite-sized partially confocal aperture provides a better SNR but reduced depth discrimination. Reconstruction algorithms, such as the expectationmaximization algorithm for maximum likelihood, can be applied to partially confocal images in order to achieve better resolution, but because they are sensitive to noise in the data, there is a practical trade-off involved. With a small aperture, fewer iterations of the reconstruction algorithm are necessary to achieve the desired resolution, but the low a priori SNR will result in a noisy reconstruction, at least when no regularization is used. With a larger aperture the a priori SNR is larger but the resolution is lower, and more iterations of the algorithm are necessary to reach the desired resolution; at some point the a posteriori SNR is lower than the a priori value. We present a theoretical analysis of the SNR-toresolution trade-off partially confocal imaging, and we present two studies that use the expectationmaximization algorithm as a postprocessor; these studies show that a for a given task there is an optimum aperture size, departures from which result in a lower a posteriori SNR.

Super-Resolution Laser Scanning Microscopy through Spatiotemporal Modulation

Super-resolution optical microscopy has attracted great interest among researchers in many fields, especially in biology where the scale of physical structures and molecular processes fall below the diffraction limit of resolution for light. As one of the emerging techniques, structured illumination microscopy can double the resolution by shifting unresolvable spatial frequencies into the pass-band of the microscope through spatial frequency mixing with a wide-field structured illumination pattern. However, such a wide-field scheme typically can only image optically thin samples and is incompatible with multiphoton processes such as two-photon fluorescence, which require point scanning with a focused laser beam. Here, we propose two new super-resolution schemes for laser scanning microscopy by generalizing the concept of a spatially nonuniform imaging system. One scheme, scanning patterned illumination (SPIN) microscopy, employs modulation of the excitation combined with temporally cumulative imaging by a nondescanned array detector. The other scheme, scanning patterned detection (SPADE) microscopy, utilizes detection modulation together with spatially cumulative imaging, in this case by a nondescanned single-element detector. When combined with multiphoton excitation, both schemes can image thick samples with three-dimensional optical sectioning and much improved resolution.

Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy

Maximum likelihood image restoration is a powerful method for 3D computational optical sectioning microscopy of extended objects. With punctate specimens, however, this method produces a few very bright isolated spots and dim detail around them is lost. The commonly used regularization methods (sieves and roughness penalty) decrease the amplitude of the bright spots, but do not avoid loosing dim detail. We derived an intensity regularization that decreases the amplitude of bright spots without loosing dim detail. In contrast with other regularization methods, this method does not increase significantly the computational complexity of the estimation algorithm.