KEYWORDS: 3D modeling, Point spread functions, 3D image processing, Luminescence, Lung, Tissues, Principal component analysis, Microscopy, Computer simulations, Algorithm development
Development of a block-based restoration (BBR) method that addresses spatially variant (SV) imaging in wide-field fluorescence microscopy of thick samples is presented. The BBR method is based on a block-based imaging model, which approximates SV imaging using an efficient orthonormal basis decomposition of multiple SV point-spread functions computed at block vertices. The effect of reducing the number of blocks needed to account for SV imaging on the restoration accuracy was investigated with simulations using a numerical lung tissue phantom relevant to biological studies. Results show that reducing the number of blocks by 82% and 98% resulted in a 19% and 27% reduction in restoration accuracy, respectively, thereby establishing a reasonable tradeoff between computational resources and accuracy. Comparison of the BBR method to existing methods (deconvolution) that do not account for SV imaging demonstrates a 90% improvement in restoration accuracy. BBR results from synthetic and experimental images of a controlled test sample with SV refractive index (RI) show consistency, providing a validation of the BBR approach. In this study, information from DIC and fluorescence images was combined to identify regions with changing RI within the imaging volume. The BBR method provides a first step toward computationally tractable reconstruction of images from thick samples.
A three-dimensional (3-D) point spread function (PSF) model for wide-field fluorescence microscopy, suitable for imaging samples with variable refractive index (RI) in multilayered media, is presented. This PSF model is a key component for accurate 3-D image restoration of thick biological samples, such as lung tissue. Microscope- and specimen-derived parameters are combined with a rigorous vectorial formulation to obtain a new PSF model that accounts for additional aberrations due to specimen RI variability. Experimental evaluation and verification of the PSF model was accomplished using images from 175-nm fluorescent beads in a controlled test sample. Fundamental experimental validation of the advantage of using improved PSFs in depth-variant restoration was accomplished by restoring experimental data from beads (6 μm in diameter) mounted in a sample with RI variation. In the investigated study, improvement in restoration accuracy in the range of 18 to 35% was observed when PSFs from the proposed model were used over restoration using PSFs from an existing model. The new PSF model was further validated by showing that its prediction compares to an experimental PSF (determined from 175-nm beads located below a thick rat lung slice) with a 42% improved accuracy over the current PSF model prediction.
In typical fluorescence imaging systems the refractive index (RI) variability between the immersion medium of the objective lens, the coverslip, and the specimen, changes the spherical wave-front of the emitted light and introduces spherical aberrations (SA) in the acquired 3D image. In existing computational optical sectioning algorithms (COSM) 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 which is an invalid assumption for biological samples. Accurate modeling of biological samples requires a space variant (SV) imaging system i.e. a different point spread functions (PSF) for each pixel. To reduce the computational load an approximate block-based forward model is introduced in this study. The entire object space is divided into a collection of small 3D blocks where the PSFs at the faces of the blocks are known. An optimized combination of overlap-save and overlap-add methods of interpolation are used to obtain the final SV (axially and laterally variant) image. Simulated SV images using the new imaging model, of a numerical object comprising of similar structures dispersed in a medium with spatially variant RI are discussed. Images of fluorescent microspheres (6-μm in diameter) dispersed in a controlled sample with two distinct RIs are compared to simulated images of a numerical object subjected to the same imaging condition, to evaluate the new model. The accuracy of the block-based forward model to model the effect of space variance within a specimen was assessed using intensity profiles through the microspheres. The qualitative similarities in the appearance of the experimental and simulated image indicate the validity of the blockbased forward model to appropriately model samples with lateral variability in RI.
Three-dimensional (3D) imaging with optical sectioning microscopy uses computational methods to obtain the true fluorescence distribution by ameliorating the effect of defocus, spherical aberration and noise. Inverse algorithms improve image quality at a fraction of the cost of implementing an optical system by accurate modeling of the imaging system. Good inverse imaging algorithms need to be accurate as well as fast. Better understanding of the image formation model is vital to obtain improved restoration through model-based algorithms. Forward imaging models 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. PSFs at every layer can be represented using their principal components. Computation of the forward imaging model using a principal component analysis (PCA) representation of the DV-PSF requires fewer convolutions than a strata based approach investigated in the past. In this paper we present a new algorithm for maximum likelihood image restoration developed based on a PCA representation of the DV-PSF and an accelerated conjugate gradient (CG) iteration scheme. Results obtained with this PCA-CG algorithm from both simulated and experimental fluorescence microscope data are discussed and compared with results obtained from a CG iteration method based on the strata model and linear interpolation of the DV-PSF. The performance of the PCA-CG algorithms is shown to be promising for practical applications.
KEYWORDS: Calibration, Point spread functions, 3D image processing, Particles, Microscopy, 3D modeling, Imaging systems, Computing systems, Luminescence, Modulation transfer functions
We characterize the three-dimensional (3-D) double-helix (DH) point-spread function (PSF) for depth-variant fluorescence microscopy imaging motivated by our interest to integrate the DH-PSF in computational optical sectioning microscopy (COSM) imaging. Physical parameters, such as refractive index and thickness variability of imaging layers encountered in 3-D microscopy give rise to depth-induced spherical aberration (SA) that change the shape of the PSF at different focusing depths and render computational approaches less practical. Theoretical and experimental studies performed to characterize the DH-PSF under varying imaging conditions are presented. Results show reasonable agreement between theoretical and experimental DH-PSFs suggesting that our model can predict the main features of the data. The depth-variability of the DH-PSF due to SA, quantified using a normalized mean square error, shows that the DH-PSF is more robust to SA than the conventional PSF. This result is also supported by the frequency analysis of the DH-PSF shown. Our studies suggest that further investigation of the DH-PSF’s use in COSM is warranted, and that particle localization accuracy using the DH-PSF calibration curve in the presence of SA can be improved by accounting for the axial shift due to SA.
Point spread function engineering with a double helix (DH) phase mask has been recently used in a joint computationaloptical
approach for the determination of depth and intensity information from fluorescence images. In this study,
theoretically determined DH-PSFs computed from a model that incorporates different amounts of depth-induced
spherical aberration (SA) due to refractive-index mismatch in the three-dimensional imaging layers, are evaluated
through a comparison to empirically determined DH-PSFs measured from quantum dots. The theoretically-determined
DH-PSFs show a trend that captures the main effects observed in the empirically-determined DH-PSFs. Calibration
curves computed from these DH-PSFs show that SA slows down the rate of rotation observed in a DH-PSF which results
in: 1) an extended range of rotation; and 2) asymmetric rotation ranges as the focus is moved in opposite directions.
Thus, for accurate particle localization different calibration curves need to be known for different amounts of SA.
Results also show that the DH-PSF is less sensitive to SA than the conventional PSF. Based on this result, it is expected
that fewer depth-variant (DV) DH-PSFs will be required for 3D computational microscopy imaging in the presence of
SA compared to the required number of conventional DV PSFs.
Double Helix point-spread functions (DH-PSFs), the result of PSF engineering, are used for super resolution microscopy.
The DH-PSF design features two dominant lobes in the image plane which rotate with the change in axial (z) position of
the light point source. The center of the DH-PSF gives the precise XY location of the point source, while the orientation
of the lobes gives the axial location. In this paper we investigate the effect of spherical aberrations on the DH-PSF.
Physical parameters such as the lens used, the size of the particle, refractive index of medium, and depth i.e., location
within the underlying object, contribute to the amount of spherical aberration. DH-PSFs with spherical aberrations are
computed for different imaging conditions. Three-dimensional images were generated of computer-generated objects
using both space-invariant and depth-variant approach. Different approaches to estimate intensity and location of points
from these images were investigated. Our results show that the DH-PSFs are susceptible to spherical aberration leading
to an apparent shift in the location of the point source with increasing spherical aberrations which is comparable to the
conventional PSF. Estimation algorithms like the depth variant expectation maximization (DVEM) can be used to obtain
estimates of the true underlying object from the image obtained with DH-PSFs.
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