Chrysanthe Preza

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.

Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections

The inverse problem involving the determination of a three-dimensional biological structure from images obtained by means of optical-sectioning microscopy is ill posed. Although the linear least-squares solution can be obtained rapidly by inverse filtering, we show here that it is unstable because of the inversion of small eigenvalues of the microscopes point-spread-function operator. We have regularized the problem by application of the linear-precision-gauge formalism of Joyce and Root [J. Opt. Soc. Am. A 1, 149 (1984)]. In our method the solution is regularized by being constrained to lie in a subspace spanned by the eigenvectors corresponding to a selected number of large eigenvalues. The trade-off between the variance and the regularization error determines the number of eigenvalues inverted in the estimation. The resulting linear method is a one-step algorithm that yields, in a few seconds, solutions that are optimal in the mean-square sense when the correct number of eigenvalues are inverted. Results from sensitivity studies show that the proposed method is robust to noise and to underestimation of the width of the point-spread function. The method proposed here is particularly useful for applications in which processing speed is critical, such as studies of living specimens and time-lapse analyses. For these applications existing iterative methods are impractical without expensive and/or specially designed hardware.

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.

Rotational-diversity phase estimation from differential- interference-contrast microscopy images

An iterative phase-estimation method for the calculation of a specimens phase function or optical-path-length (OPL) distribution from differential-interference-contrast (DIC) microscopy images is presented. The method minimizes the least-squares discrepancy measure by use of the conjugate-gradient technique to estimate the phase function from multiple DIC images acquired at different specimen rotations. The estimate is regularized with a quadratic smoothness penalty. Results from testing the method with simulations and measured DIC images show improvement in the estimated phase when at least two rotationally diverse DIC images instead of a single DIC image are used for the estimation. The OPL of a cell that is estimated from two DIC images was found to be much more reliable than the OPL computed from single DIC images (which had a coefficient of variation equal to 15.8%).

Quantitative phase microscopy through differential interference imaging

An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform. We apply this method to simulated and experimentally acquired images of partially absorptive test objects. A direct comparison of the computationally determined phase to the true object phase demonstrates the capabilities of the method. Simulation results predict and confirm results obtained from experimentally acquired images.

Point-spread function engineering to reduce the impact of spherical aberration on 3D computational fluorescence microscopy imaging

Wavefront encoding (WFE) with different cubic phase mask designs was investigated in engineering 3D point-spread functions (PSF) to reduce their sensitivity to depth-induced spherical aberration (SA) which affects computational complexity in 3D microscopy imaging. The sensitivity of WFE-PSFs to defocus and to SA was evaluated as a function of phase mask parameters using mean-square-error metrics to facilitate the selection of mask designs for extended-depth-of-field (EDOF) microscopy and for computational optical sectioning microscopy (COSM). Further studies on pupil phase contribution and simulated WFE-microscope images evaluated the engineered PSFs and demonstrated SA insensitivity over sample depths of 30 μm. Despite its low sensitivity to SA, the successful WFE design for COSM maintains a high sensitivity to defocus as it is desired for optical sectioning.

3D fluorescence microscopy imaging accounting for depth-varying point-spread functions predicted by a strata interpolation method and a principal component analysis method

In three-dimensional (3D) computational imaging for wide-field microscopy, estimation methods that solve the inverse imaging problem play an important role. The accuracy of the forward model has a significant impact on the complexity of the estimation method and consequently on the accuracy of the estimated intensity. Previous studies have shown that a forward model based on a depth-varying point-spread function (DV-PSF) leads to a substantial improvement in the resulting images because it accounts for depth-induced aberrations present in the imaging system. In this depth-varying (DV) model, the depth-dependent imaging effects are handled using a stratum-based interpolation method defined on discrete, non-overlapping layers or strata along the Z axis. Recently, a new approximation method based on a principle component analysis (PCA) was developed to predict DV-PSFs1 with improved accuracy over the DV-PSFs predicted by the strata interpolation method of Ref. [11]. In this study, we implemented the PCA-based forward model for DV imaging to further compare the two approaches. DV-PSFs and forward models were computed using both the strata-based and the new PCA-based approximation schemes. Differences are quantified as a function of the approximation, i.e. the number of bases or strata used in each case respectively. A new PCA-based image estimation method was also developed based on the DV expectation maximization (DV-EM) algorithm of Ref. [11]. Preliminary evaluation of the performance of the PCA-based estimation shows promising results and consistency with previous results obtained in previous studies.

Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions.

A depth-variant (DV) image restoration algorithm for wide field fluorescence microscopy, using an orthonormal basis decomposition of DV point-spread functions (PSFs), is investigated in this study. The efficient PSF representation is based on a previously developed principal component analysis (PCA), which is computationally intensive. We present an approach developed to reduce the number of DV PSFs required for the PCA computation, thereby making the PCA-based approach computationally tractable for thick samples. Restoration results from both synthetic and experimental images show consistency and that the proposed algorithm addresses efficiently depth-induced aberration using a small number of principal components. Comparison of the PCA-based algorithm with a previously-developed strata-based DV restoration algorithm demonstrates that the proposed method improves performance by 50% in terms of accuracy and simultaneously reduces the processing time by 64% using comparable computational resources.

Image estimation accounting for point-spread function depth cariation in three-dimensional fluorescence microscopy

An approximate model for optical-sectioning microscopy describing depth-varying imaging is developed. The model incorporates changes in the point-spread function due to refractive index mismatch between the immersion medium and the specimen, which causes spherical aberration that worsens with increasing depth under the coverslip. Comparison of model predictions to measured images from a bead phantom shows that the approximate model captures the main features in the data. The model presented in this paper is the first step towards depth-variant image estimation for optical-sectioning microscopy. An expectation maximization algorithm for maximum-likelihood restoration based on this model is also presented.