Generalized Image Reconstruction in Optical Coherence Tomography Using Redundant and Non-Uniformly-Spaced Samples.

In this paper, we use Frame Theory to develop a generalized OCT image reconstruction method using redundant and non-uniformly spaced frequency domain samples that includes using non-redundant and uniformly spaced samples as special cases. We also correct an important theoretical error in the previously reported results related to OCT image reconstruction using the Non-uniform Discrete Fourier Transform (NDFT). Moreover, we describe an efficient method to compute our corrected reconstruction transform, i.

Tensor Least Angle Regression for Sparse Representations of Multidimensional Signals.

Sparse signal representations have gained much interest recently in both signal processing and statistical communities. Compared to orthogonal matching pursuit (OMP) and basis pursuit, which solve the and constrained sparse least-squares problems, respectively, least angle regression (LARS) is a computationally efficient method to solve both problems for all critical values of the regularization parameter . However, all of these methods are not suitable for solving large multidimensional sparse least-squares problems, as they would require extensive computational power and memory.

Massively parallel simulator of optical coherence tomography of inhomogeneous turbid media.

Background And Objective: An accurate and practical simulator for Optical Coherence Tomography (OCT) could be an important tool to study the underlying physical phenomena in OCT such as multiple light scattering. Recently, many researchers have investigated simulation of OCT of turbid media, e.g.

Monte Carlo simulation of optical coherence tomography for turbid media with arbitrary spatial distributions.

We developed a Monte Carlo-based simulator of optical coherence tomography (OCT) imaging for turbid media with arbitrary spatial distributions. This simulator allows computation of both Class I diffusive reflectance due to ballistic and quasiballistic scattered photons and Class II diffusive reflectance due to multiple scattered photons. It was implemented using a tetrahedron-based mesh and importance sampling to significantly reduce computational time.

Fast calculation of multipath diffusive reflectance in optical coherence tomography.

We show how to efficiently calculate the signal in optical coherence tomography (OCT) systems due to the ballistic photons, the quasi-ballistic photons, and the photons that undergo multiple diffusive scattering using Monte Carlo simulations with importance sampling. This method enables the calculation of these three components of the OCT signal with less than one hundredth of the computational time required by the conventional Monte Carlo method. Therefore, it can be used as a design tool to characterize the performance of OCT systems, and can also be used in the development of novel signal processing techniques that can extend the imaging range of OCT systems.

Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography.

We developed an importance sampling based method that significantly speeds up the calculation of the diffusive reflectance due to ballistic and to quasi-ballistic components of photons scattered in turbid media: Class I diffusive reflectance. These components of scattered photons make up the signal in optical coherence tomography (OCT) imaging. We show that the use of this method reduces the computation time of this diffusive reflectance in time-domain OCT by up to three orders of magnitude when compared with standard Monte Carlo simulation.

Inversion of the Debye-Wolf diffraction integral using an eigenfunction representation of the electric fields in the focal region.

The forward problem of focusing light using a high numerical aperture lens can be described using the Debye-Wolf integral, however a solution to the inverse problem does not currently exist. In this work an inversion formula based on an eigenfunction representation is derived and presented which allows a field distribution in a plane in the focal region to be specified and the appropriate pupil plane distribution to be calculated. Various additional considerations constrain the inversion to ensure physicality and practicality of the results and these are also discussed.

Eigenfunction expansion of the electric fields in the focal region of a high numerical aperture focusing system.

The Debye-Wolf electromagnetic diffraction integral is now routinely used to describe focusing by high numerical (NA) lenses. We obtain an eigenfunction expansion of the electric vector field in the focal region in terms of Bessel and generalized prolate spheroidal functions. Our representation has many optimal and desirable properties which offer considerable simplification to the evaluation and analysis of the Debye- Wolf integral.

Statistics of the depth-scan photocurrent in time-domain optical coherence tomography.

We derive the time-variant second-order statistics of the depth-scan photocurrent in time-domain optical coherence tomography (TD-OCT) systems using polarized thermal light sources and superluminescent diodes (SLDs). Since the asymptotic-joint-probability-distribution function (JPDF) of the photocurrent due to polarized thermal light is Gaussian and the signal-noise-ratio in TD-OCT is typically high (>80 dB), the JPDF of the depth-scan photocurrent could be approximated as a Gaussian random process that is completely determined by its second-order statistics. We analyze both direct and differential light detection schemes and include the effect of electronic thermal fluctuations.

Effect of detector noise in incoherent hybrid imaging systems.

Hybrid imaging systems involve the joint design of an optical image-gathering module and digital processing algorithms to obtain a required final image. They have the potential to achieve imaging performance hitherto unobtainable by conventional imaging techniques. A reduction in the signal-to-noise ratio of the final image is one of their main disadvantages when one is considering linear signal processing.

Phase plate to extend the depth of field of incoherent hybrid imaging systems.

A hybrid imaging system combines a modified optical imaging system and a digital postprocessing step. We describe a spatial-domain method for designing a pupil phase plate to extend the depth of field of an incoherent hybrid imaging system with a rectangular aperture. We use this method to obtain a pupil phase plate to extend the depth of field, which we refer to as a logarithmic phase plate.

Reduced depth of field in incoherent hybrid imaging systems.

A hybrid imaging system combines a modified optical imaging module and a digital postprocessing step. We define what to our knowledge is a new metric to quantify the blurring of a defocused image that is more suitable than the defocus parameter for describing defocused hybrid imaging systems. We use this metric to design a pupil phase grating to reduce the depth of field, thereby increasing the axial resolution, of an incoherent hybrid imaging system using quasi-monochromatic illumination.