Nurmohammed Patwary

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.

Spatial light modulator phase mask implementation of wavefront encoded 3D computational-optical microscopy.

Spatial light modulator (SLM) implementation of wavefront encoding enables various types of engineered point-spread functions (PSFs), including the generalized-cubic and squared-cubic phase mask wavefront encoded (WFE) PSFs, shown to reduce the impact of sample-induced spherical aberration in fluorescence microscopy. This investigation validates dynamic experimental parameter variation of these WFE-PSFs. We find that particular design parameter bounds exist, within which the divergence of computed and experimental WFE-PSFs is of the same order of magnitude as that of computed and experimental conventional PSFs, such that model-based approaches for solving the inverse imaging problem can be applied to a wide range of SLM-WFE systems. Interferometric measurements were obtained to evaluate the SLM implementation of the numeric mask. Agreement between experiment and theory in terms of a wrapped phase, 0-2π, validates the phase mask implementation and allows characterization of the SLM response. These measurements substantiate experimental practice of computational-optical microscope imaging with an SLM-engineered PSF.

Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering

Point-spread function engineering (PSF), achieved by placing a phase mask at the pupil plane of the imaging lens to encode the wavefront emerging from an imaging system, can be employed to reduce the impact of spherical aberration (SA) in 3D microscopy. In a previous study, the effect of SA on a confocal scanning microscope using a squared cubic phase mask (SQUBIC) was investigated using computer simulations. Here the effect of the SQUBIC design parameter on the insensitivity of the engineered PSF to SA is investigated using a metric based on the second-order moment of the axial variability of the PSF. We show that it is possible to find the optimum SQUBIC for the insensitization to SA.

Reducing depth induced spherical aberration in 3D widefield fluorescence microscopy by wavefront coding using the SQUBIC phase mask

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.

Computationally tractable approach to PCA-based depth-variant PSF representation for 3D microscopy image restoration

Application of a previously developed PCA-based expectation maximization algorithm to experimental data is made possible through an interpolated PCA approach. Simulated and experimental results confirm achieved accuracy in image restoration of thick samples.

Reducing effects of aberration in 3D fluorescence imaging using wavefront coding with a radially symmetric phase mask.

In this work, a wavefront encoded (WFE) imaging system built using a squared cubic phase mask, designed to reduce the sensitivity of the imaging system to spherical aberration, is investigated. The proposed system allows the use of a space-invariant image restoration algorithm, which uses a single PSF, to restore intensity distribution in images suffering aberration, such as sample-induced aberration in thick tissue. This provides a computational advantage over depth-variant image restoration algorithms developed previously to address this aberration. Simulated PSFs of the proposed system are shown to change up to 25% compared to the 0 µm depth PSF (quantified by the structural similarity index) over a 100 µm depth range, while the conventional system PSFs change up to 84%. Results from experimental test-sample images show that restoration error is reduced by 29% when the proposed WFE system is used instead of the conventional system over a 30 µm depth range.

Comparison of two structured illumination techniques based on different 3D illumination patterns

Manipulating the excitation pattern in optical microscopy has led to several super-resolution techniques. Among different patterns, the lateral sinusoidal excitation was used for the first demonstration of structured illumination microscopy (SIM), which provides the fastest SIM acquisition system (based on the number of raw images required) compared to the multi-spot illumination approach. Moreover, 3D patterns that include lateral and axial variations in the illumination have attracted more attention recently as they address resolution enhancement in three dimensions. A threewave (3W) interference technique based on coherent illumination has already been shown to provide super-resolution and optical sectioning in 3D-SIM. In this paper, we investigate a novel tunable technique that creates a 3D pattern from a set of multiple incoherently illuminated parallel slits that act as light sources for a Fresnel biprism. This setup is able to modulate the illumination pattern in the object space both axially and laterally with adjustable modulation frequencies. The 3D forward model for the new system is developed here to consider the effect of the axial modulation due to the 3D patterned illumination. The performance of 3D-SIM based on 3W interference and the tunable system are investigated in simulation and compared based on two different criteria. First, restored images obtained for both 3D-SIM systems using a generalized Wiener filter are compared to determine the effect of the illumination pattern on the reconstruction. Second, the effective frequency response of both systems is studied to determine the axial and lateral resolution enhancement that is obtained in each case.

3D microscope imaging robust to restoration artifacts introduced by optically thick specimens

We demonstrate 3D microscope imaging using computational optical sectioning microscopy (COSM) with an engineered point-spread function (PSF) robust to depth-induced spherical aberration (SA). Earlier we demonstrated that wavefront encoding (WFE) using a squared cubic (SQUBIC) phase mask reduces the PSF depth-variance in the presence of SA and that space-invariant (SI) restoration of simulated images using a single WFE-PSF does not lead to artifacts as in the conventional case. In this study, we show experimental verification of our WFE COSM approach. The WFE system used is a commercial microscope with a modified side port imaging path, where a spatial light modulator projects the SQUBIC phase mask on the back focal plane of the imaging lens. High resolution images of a test sample with 6 μm in diameter microspheres embedded in UV-cured optical cement (RI = 1.47) were captured using both the engineered and the conventional imaging paths of the system. The acquired images were restored using a regularized SI expectation maximization algorithm based on Tikhonov-Miller regularization with a roughness penalty. A comparative study quantified in terms of the correlation coefficients between the XZ medial sections of the restored images, from experimental data, shows an 11% reduction in depth sensitivity in the SQUBIC system compared to the conventional system.

Wavefront encoded computational optical sectioning microscopy reduces depth variability in 3D imaging

Wavefront encoded (WFE) computational optical sectioning microscopy (COSM) is evaluated in simulation and experiment. Experimental results show that restoration variability due to spherical aberration is reduced by 23% in WFE-COSM compared to traditional COSM.

Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM

Wavefront coding techniques are currently used to engineer unique point spread functions (PSFs) that enhance existing microscope modalities or create new ones. Previous work in this field demonstrated that simulated intensity PSFs encoded with a generalized cubic phase mask (GCPM) are invariant to spherical aberration or misfocus; dependent on parameter selection. Additional work demonstrated that simulated PSFs encoded with a squared cubic phase mask (SQUBIC) produce a depth invariant focal spot for application in confocal scanning microscopy. Implementation of PSF engineering theory with a liquid crystal on silicon (LCoS) spatial light modulator (SLM) enables validation of WFC phase mask designs and parameters by manipulating optical wavefront properties with a programmable diffractive element. To validate and investigate parameters of the GCPM and SQUBIC WFC masks, we implemented PSF engineering in an upright microscope modified with a dual camera port and a LCoS SLM. We present measured WFC PSFs and compare them to simulated PSFs through analysis of their effect on the microscope imaging system properties. Experimentally acquired PSFs show the same intensity distribution as simulation for the GCPM phase mask, the SQUBIC-mask and the well-known and characterized cubic-phase mask (CPM), first applied to high NA microscopy by Arnison et al.10, for extending depth of field. These measurements provide experimental validation of new WFC masks and demonstrate the use of the LCoS SLM as a WFC design tool. Although efficiency improvements are needed, this application of LCoS technology renders the microscope capable of switching among multiple WFC modes.