A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

On robust estimation of the location parameter

https://wiki.biac.duke.edu/lib/exe/fetch.php?media=biac:jones_etal_2012_the_do_s_and_don_ts_of_diffusion_mri.pdf

White matter integrity, fiber count, and other fallacies: The do's and don'ts of diffusion MRI

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Diffusion Imaging in Python (Dipy) is a free and open source software project for the analysis of data from diffusion magnetic resonance imaging (dMRI) experiments. dMRI is an application of MRI that can be used to measure structural features of brain white matter. Many methods have been developed to use dMRI data to model the local configuration of white matter nerve fiber bundles and infer the trajectory of bundles connecting different parts of the brain. Dipy gathers implementations of many different methods in dMRI, including: diffusion signal pre-processing; reconstruction of diffusion distributions in individual voxels; fiber tractography and fiber track post-processing, analysis and visualization. Dipy aims to provide transparent implementations for all the different steps of dMRI analysis with a uniform programming interface. We have implemented classical signal reconstruction techniques, such as the diffusion tensor model and deterministic fiber tractography. In addition, cutting edge novel reconstruction techniques are implemented, such as constrained spherical deconvolution and diffusion spectrum imaging (DSI) with deconvolution, as well as methods for probabilistic tracking and original methods for tractography clustering. Many additional utility functions are provided to calculate various statistics, informative visualizations, as well as file-handling routines to assist in the development and use of novel techniques. In contrast to many other scientific software projects, Dipy is not being developed by a single research group. Rather, it is an open project that encourages contributions from any scientist/developer through GitHub and open discussions on the project mailing list. Consequently, Dipy today has an international team of contributors, spanning seven different academic institutions in five countries and three continents, which is still growing.

/pdf/dipy-a-library-for-the-analysis-of-diffusion-mri-data-2tds675qhd.pdf

Dipy, a library for the analysis of diffusion MRI data

We developed a novel method to accelerate diffusion spectrum imaging using compressed sensing. The method can be applied to either reduce acquisition time of diffusion spectrum imaging acquisition without losing critical information or to improve the resolution in diffusion space without increasing scan time. Unlike parallel imaging, compressed sensing can be applied to reconstruct a sub-Nyquist sampled dataset in domains other than the spatial one. Simulations of fiber crossings in 2D and 3D were performed to systematically evaluate the effect of compressed sensing reconstruction with different types of undersampling patterns (random, gaussian, Poisson disk) and different acceleration factors on radial and axial diffusion information. Experiments in brains of healthy volunteers were performed, where diffusion space was undersampled with different sampling patterns and reconstructed using compressed sensing. Essential information on diffusion properties, such as orientation distribution function, diffusion coefficient, and kurtosis is preserved up to an acceleration factor of R = 4. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.23064

Accelerated diffusion spectrum imaging in the human brain using compressed sensing.

We demonstrate a novel computational method for high resolution image recovery from a single digital hologram frame. The complex object field is obtained from the recorded hologram by solving a constrained optimization problem. This approach which is unlike the physical hologram replay process is shown to provide high quality image recovery even when the dc and the cross terms in the hologram overlap in the Fourier domain. Experimental results are shown for a Fresnel zone hologram of a resolution chart, intentionally recorded with a small off-axis reference beam angle. Excellent image recovery is observed without the presence of dc or twin image terms and with minimal speckle noise.

Single shot high resolution digital holography

We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography.

Two-dimensional phase unwrapping using the transport of intensity equation.

We use the Whittaker–Shannon sampling theorem to show that the eigenvalue problem for the sinc-kernel is equivalent to a discrete eigenvalue problem. The well-known eigenfunctions, namely, the prolate spheroidal wavefunctions, their corresponding eigenvalues and the orthogonality and completeness properties are determined without invoking the prolate spheroidal differential equation. This analysis based on the sampling theorem may be used for calculating the eigenvalues and eigenfunctions of bandlimited kernels in general as we illustrate with an additional example of the sinc2-kernel.

https://iopscience.iop.org/article/10.1088/0305-4470/36/39/303/pdf

Sampling theory approach to prolate spheroidal wavefunctions

We describe and evaluate a robust method for compressive sensing MRI reconstruction using an iterative soft thresholding framework that is data-driven, so that no tuning of free parameters is required. The approach described here combines a Nesterov type optimal gradient scheme for iterative update along with standard wavelet-based adaptive denoising methods, resulting in a leaner implementation compared with the nonlinear conjugate gradient method. Tests with T₂ weighted brain data and vascular 3D phase contrast data show that the image quality of reconstructions is comparable with those from an empirically tuned nonlinear conjugate gradient approach. Statistical analysis of image quality scores for multiple datasets indicates that the iterative soft thresholding approach as presented here may improve the robustness of the reconstruction and the image quality, when compared with nonlinear conjugate gradient that requires manual tuning for each dataset. A data-driven approach as illustrated in this article should improve future clinical applicability of compressive sensing image reconstruction.

Kedar Khare

Papers

Accelerated diffusion spectrum imaging in the human brain using compressed sensing.

Single shot high resolution digital holography

Two-dimensional phase unwrapping using the transport of intensity equation.

Sampling theory approach to prolate spheroidal wavefunctions

Accelerated MR imaging using compressive sensing with no free parameters