A Parallel Product-Convolution approach for representing the depth varying Point Spread Functions in 3D widefield microscopy based on principal component analysis.

Keck Advanced Microscopy Center and the Dept. of Biochem. and Biophys., University of California at San Francisco, San Francisco, CA-94158, USA.
Optics Express (Impact Factor: 3.53). 03/2010; 18(7):6461-76. DOI: 10.1364/OE.18.006461
Source: PubMed

ABSTRACT We address the problem of computational representation of image formation in 3D widefield fluorescence microscopy with depth varying spherical aberrations. We first represent 3D depth-dependent point spread functions (PSFs) as a weighted sum of basis functions that are obtained by principal component analysis (PCA) of experimental data. This representation is then used to derive an approximating structure that compactly expresses the depth variant response as a sum of few depth invariant convolutions pre-multiplied by a set of 1D depth functions, where the convolving functions are the PCA-derived basis functions. The model offers an efficient and convenient trade-off between complexity and accuracy. For a given number of approximating PSFs, the proposed method results in a much better accuracy than the strata based approximation scheme that is currently used in the literature. In addition to yielding better accuracy, the proposed methods automatically eliminate the noise in the measured PSFs.

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    ABSTRACT: Imaging thick biological samples with wide-field fluorescence microscope is a challenge since microscope objectives are designed to be operated within its depth of field. Refractive Index (RI) variation between the immersion medium of the objective lens, the coverslip, and the specimen changes the spherical wave-front of the emitted light and introduces aberration, known a spherical aberration (SA). Modeling the response of the system allows the use of model based computational methods for data processing to improve resolution and contrast by mitigating the effect of SA and defocus blur. To simplify the complexity of the problem, the specimen is either assumed to be thin, or in the case of depth-variant algorithms to have a constant RI. It is a well-known fact that the RI of a sample varies throughout the volume. Therefore, images acquired through the sample volume are subjected to space variant (SV) imaging, i.e., variance both in the lateral and axial directions. Computation of image intensity using a SV model requires a different point spread functions (PSF) for each pixel is not computationally feasible, hence a approximate forward model that accounts for SV imaging based on a block-based representation is introduced. The block-based forward model is evaluated using experimental and simulated data in this paper.
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    ABSTRACT: Imaging thick biological samples introduces spherical aberration (SA) due to refractive index (RI) mismatch between specimen and imaging lens immersion medium. SA increases with the increase of either depth or RI mismatch. Therefore, it is difficult to find a static compensator for SA1. Different wavefront coding methods2,3 have been studied to find an optimal way of static wavefront correction to reduce depth-induced SA. Inspired by a recent design of a radially symmetric squared cubic (SQUBIC) phase mask that was tested for scanning confocal microscopy1 we have modified the pupil using the SQUBIC mask to engineer the point spread function (PSF) of a wide field fluorescence microscope. In this study, simulated images of a thick test object were generated using a wavefront encoded engineered PSF (WFEPSF) and were restored using space-invariant (SI) and depth-variant (DV) expectation maximization (EM) algorithms implemented in the COSMOS software4. Quantitative comparisons between restorations obtained with both the conventional and WFE PSFs are presented. Simulations show that, in the presence of SA, the use of the SIEM algorithm and a single SQUBIC encoded WFE-PSF can yield adequate image restoration. In addition, in the presence of a large amount of SA, it is possible to get adequate results using the DVEM with fewer DV-PSFs than would typically be required for processing images acquired with a clear circular aperture (CCA) PSF. This result implies that modification of a widefield system with the SQUBIC mask renders the system less sensitive to depth-induced SA and suitable for imaging samples at larger optical depths.
    Proceedings of SPIE - The International Society for Optical Engineering 02/2014; DOI:10.1117/12.2040191 · 0.20 Impact Factor
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    SIAM Journal on Imaging Sciences 10/2014; 7(4). DOI:10.1137/130945776 · 2.87 Impact Factor

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