Sharon V. King

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.

Quantitative structured-illumination phase microscopy

We introduce a quantitative phase imaging method for homogeneous objects with a bright field transmission microscope by using an amplitude mask and a digital processing algorithm. A known amplitude pattern is imaged on the sample plane containing a thick phase object by placing an amplitude mask in the field diaphragm of the microscope. The phase object distorts the amplitude pattern according to its optical path length (OPL) profile, and the distorted pattern is recorded in a CCD detector. A digital processing algorithm then estimates the objects quantitative OPL profile based on a closed form analytical solution, which is derived using a ray optics model for objects with small OPL gradients.

Calibration of a phase-shifting DIC microscope for quantitative phase imaging

Phase-shifting differential interference contrast (DIC) provides images in which the intensity of DIC is transformed into values linearly proportional to differential phase delay. Linear regression analysis of the Fourier space, spiral phase, integration technique shows these values can be integrated and calibrated to provide accurate phase measurements of objects embedded in optically transparent media regardless of symmetry or absorption properties. This approach has the potential to overcome the limitations of profilometery, which cannot access embedded objects, and extend the capabilities of the traditional DIC microscope, which images embedded phase objects, but does not provide quantitative information.

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.

A Phase-Shifting DIC Technique for Measuring 3D Phase Objects: Experimental Verification

Experimental verification of our previously proposed linear phase imaging technique for differential inference contrast microscopy (DIC) microscopy is presented. This technique first applies phase-shifting methods to DIC to acquire linear phase gradient images in two orthogonal directions. A special Fourier integration algorithm is then applied to the combined phase gradient images to create a single linear phase image in which intensity is proportional to phase. This overcomes the limitations of traditional DIC, which cannot accurately measure the phase (i.e. refractive index or thickness) of embedded 3D phase objects. The linear phase imaging technique is implemented using a standard DIC microscope altered to allow controlled phase shifting, a low noise CCD camera, and post-processing in Matlab. The results presented confirm the linear proportionality of intensity to phase in these images.

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.

Enhanced Extended Depth-of-Field Microscopy via Modeling of SLM Effects on the Applied Phase Mask

To represent the imaging model precisely for wavefront encoded systems, we modified our forward model to take into consideration the diffraction inefficiency of spatial light modulator response and its effect on the ideal phase mask.

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.

Real-time quantitative differential interference contrast (DIC) microscopy implemented via novel liquid crystal prisms

A phase shifting differential interference contrast (DIC) microscope, which provides quantitative phase information and is capable of imaging at video rates, has been constructed. Using a combination of phase shifting and bi-directional shear, the microscope captures a series of eight images which are then integrated in Fourier space. In the resultant image the intensity profile linearly maps to the phase differential across the object. The necessary operations are performed by various liquid crystal devices (LCDs) which can operate at high speeds. A set of four liquid crystal prisms shear the beam in both the x and y directions. A liquid crystal bias cell delays the phase between the e- and o-beams providing phase-shifted images. The liquid crystal devices are then synchronized with a CCD camera in order to provide real-time image acquisition. Previous implementation of this microscope utilized Nomarski prisms, a rotation stage and a manually operated Sénarmont compensator to perform the necessary operations and was only capable of fixed sample imaging. In the present work, a series of images were taken using both the new LCD prism based microscope and the previously implemented Sénarmont compensator based system. A comparison between these images shows that the new system achieves equal and in some cases superior results to that of the old system with the added benefit of real-time imaging.

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.