Shakil Rehman

Advanced optical microscopy methods for in vivo imaging of sub-cellular structures in thick biological tissues

Optical microscopy has become an indispensable tool for visualizing sub-cellular structures and biological processes. However, scattering in biological tissues is a major obstacle that prevents high-resolution images from being obtained from deep regions of tissue. We review common techniques, such as multiphoton microscopy (MPM) and optical coherence microscopy (OCM), for diffraction limited imaging beyond an imaging depth of 0.5 mm. Novel implementations have been emerging in recent years giving higher imaging speed, deeper penetration, and better image quality. Focal modulation microscopy (FMM) is a novel method that combines confocal spatial filtering with focal modulation to reject out-of-focus background. FMM has demonstrated an imaging depth comparable to those of MPM and OCM, near-real-time image acquisition, and the capability for multiple contrast mechanisms.

Experimental 4D compressive phase space tomography

We experimentally retrieve 4D mutual intensity with limited data using compressive phase space tomography. The complete coherent modes can be recovered by our low-entropy assumption.

Empirical concentration bounds for compressive holographic bubble imaging based on a Mie scattering model

We use compressive in-line holography to image air bubbles in water and investigate the effect of bubble concentration on reconstruction performance by simulation. Our forward model treats bubbles as finite spheres and uses Mie scattering to compute the scattered field in a physically rigorous manner. Although no simple analytical bounds on maximum concentration can be derived within the classical compressed sensing framework due to the complexity of the forward model, the receiver operating characteristic (ROC) curves in our simulation provide an empirical concentration bound for accurate bubble detection by compressive holography at different noise levels, resulting in a maximum tolerable concentration much higher than the traditional back-propagation method.

Factored form descent: a practical algorithm for coherence retrieval

We formulate coherence retrieval, the process of recovering via intensity measurements the two-point correlation function of a partially coherent field, as a convex weighted least-squares problem and show that it can be solved with a novel iterated descent algorithm using a coherent-modes factorization of the mutual intensity. This algorithm is more memory-efficient than the standard interior point methods used to solve convex problems, and we verify its feasibility by reconstructing the mutual intensity of a Schell-model source from both simulated data and experimental measurements.

Analytic method to optimize aperture design in focal modulation microscopy

Focal modulation microscopy (FMM) has been demonstrated more effective than confocal microscopy for imaging of thick biological tissues. To improve its penetration depth further, we propose a simple analytical method to enlarge the modulation depth, the unique property of FMM directly linked to its signal-to-noise ratio. The modulation depth increases as the excitation intensity of the binary phase aperture status is pushed further away from the focal region of the detection optics, thereby creating a dark region in the focal volume, which we call maximally flat crater (MFC). By direct algebraic manipulation, MFCs are achieved for both scalar and vector diffraction optics. Numerical results show that the modulation depth from MFC is very close to the maximum values, with a small difference less than 3% for the same number of subapertures. Applications of bifocus produced by MFC apertures are also discussed.

Beam collimation in the presence of aberrations

Abstract This paper describes the application of multiple beam shearing interferometry to beam collimation in the presence of lens aberrations. To realize multiple beam shearing interferometry, a shear plate is used, wedged slightly in thickness at an angle of 2.7 ″ , with coatings of 90% reflectance. The beam collimation in the presence of aberrations is analyzed in terms of the effects apparent at the paraxial focus, circle of least confusion and marginal focus. It is shown to be possible to collimate a beam very accurately by moving a lens under test around the position of circle of least confusion while observing the fringe line.

Phase imaging using shifted wavefront sensor images

We propose a new approach to the complete retrieval of a coherent field (amplitude and phase) using the same hardware configuration as a Shack-Hartmann sensor but with two modifications: first, we add a transversally shifted measurement to resolve ambiguities in the measured phase; and second, we employ factored form descent (FFD), an inverse algorithm for coherence retrieval, with a hard rank constraint. We verified the proposed approach using both numerical simulations and experiments.

Picosecond time-gated microscopy of UV-damaged plant tissue

We demonstrate that picosecond time-gated fluorescence microscopy can be used to monitor subtle changes in the kinetics and spatial distribution of perturbations to the molecular and cellular structure of plant tissue caused by ultraviolet radiation. Single-molecule experiments on Photosystem II and chloroplast preparations give picosecond fluorescence decay kinetics that are similar to those obtained previously on bulk samples. For green plant leaves, localized and well-defined cellular structure is seen for normal material whereas relatively diffuse and non-specific features are seen after UV-irradiation indicating significant UV-induced rupture of the cellular structure. The changes in the chlorophyll fluorescence decay kinetics indicate uncoupling of chlorophyll molecules in the light-harvesting system leading to inhibition of energy reorganization and transfer in the antennae and subsequent exciton transfer to the reaction centers.

Starlet transform applied to digital Gabor holographic microscopy.

In this paper, we show how the starlet transform can be used to process holograms from a digital Gabor holographic microscope. The starlet transform is an undecimated wavelet transform with the property that when performing reconstruction, we only need to add all scales without the use of a synthesis filter bank. When the starlet transform is applied to a hologram, we divide the hologram into a certain number of scales, process them separately, and propagate each one using a numerical diffraction method. After diffraction propagation, we perform processing on complex amplitudes that correspond to individual scales. With the aforementioned procedure, it is possible to reduce the background and effects of parasitic fringes caused by high coherence of a laser, enhance the contrast, and reduce the effects of the twin image. Experimental results confirming the method are presented.

Quantitative measurement of oil droplets using compressive digital holography

Compressive holography is applied to characterize the oil droplet in oil spill experiment. The compressive reconstruction method demonstrates good performance in the real experimental data compared with traditional back-propagation based method. The phase transition curve in simulation illustrates the effects of sparsity of object function on the compressive reconstruction success rate, which indicates the effectiveness of free space propagation as a signal mixer in compressive measurement.