Sudhakar Prasad

Engineering the pupil phase to improve image quality

By suitably phase-encoding optical images in the pupil plane and then digitally restoring them, one can greatly improve their quality. The use of a cubic phase mask originated by Dowski and Cathey to enhance the depth of focus in the images of 3-d scenes is a classic example of this powerful approach. By using the Strehl ratio as a measure of image quality, we propose tailoring the pupil phase profile by minimizing the sensitivity of the quality of the phase-encoded image of a point source to both its lateral and longitudinal coordinates. Our approach ensures that the encoded image will be formed under a nearly shift-invariant imaging condition, which can then be digitally restored to a high overall quality nearly free from the aberrations and limited depth of focus of a traditional imaging system. We also introduce an alternative measure of sensitivity that is based on the concept of Fisher information. In order to demonstrate the validity of our general approach, we present results of computer simulations that include the limitations imposed by detector noise.

A quantum description of the beam splitter

Abstract We derive the unitary transformation that embodies the action of a lossless plane-parallel beam splitter on an incident light beam. We use the transformation to illustrate with some examples how fluctuations and noise in one light mode may get coupled with those in another mode.

Computational imaging systems for iris recognition

Computational imaging systems are modern systems that consist of generalized aspheric optics and image processing capability. These systems can be optimized to greatly increase the performance above systems consisting solely of traditional optics. Computational imaging technology can be used to advantage in iris recognition applications. A major difficulty in current iris recognition systems is a very shallow depth-of-field that limits system usability and increases system complexity. We first review some current iris recognition algorithms, and then describe computational imaging approaches to iris recognition using cubic phase wavefront encoding. These new approaches can greatly increase the depth-of-field over that possible with traditional optics, while keeping sufficient recognition accuracy. In these approaches the combination of optics, detectors, and image processing all contribute to the iris recognition accuracy and efficiency. We describe different optimization methods for designing the optics and the image processing algorithms, and provide laboratory and simulation results from applying these systems and results on restoring the intermediate phase encoded images using both direct Wiener filter and iterative conjugate gradient methods.

Pupil-phase optimization for extended-focus, aberration-corrected imaging systems

The insertion of a suitably designed phase plate in the pupil of an imaging system makes it possible to encode the depth dimension of an extended three-dimensional scene by means of an approximately shift-invariant PSF. The so-encoded image can then be deblurred digitally by standard image recovery algorithms to recoup the depth dependent detail of the original scene. A similar strategy can be adopted to compensate for certain monochromatic aberrations of the system. Here we consider two approaches to optimizing the design of the phase plate that are somewhat complementary - one based on Fisher information that attempts to reduce the sensitivity of the phase encoded image to misfocus and the other based on a minimax formulation of the sum of singular values of the system blurring matrix that attempts to maximize the resolution in the final image. Comparisons of these two optimization approaches are discussed. Our preliminary demonstration of the use of such pupil-phase engineering to successfully control system aberrations, particularly spherical aberration, is also presented.

High-Resolution Imaging Using Integrated Optical Systems

Certain optical aberrations, such as defocus, can significantly degrade the signal collected by an imaging system, producing images with low resolution. In images with depth‐dependent detail, such degradations are difficult to remove due to their inherent spatially varying nature. In 1995, Dowski and Cathey introduced the concept of wavefront coding to extend the depth of field. They showed that wavefront coding and decoding enables quality control of such images using integrated optical‐digital imaging systems. With wavefront coding, a high‐resolution image can be efficiently obtained without the need to resort to expensive algorithms for spatially varying restoration. In this article, we discuss a novel and effective multiple‐design‐parameter approach for optimizing the processes of encoding and decoding the wavefront phase in integrated optical‐digital imaging systems. Our approach involves the use of information metrics, such as the Strehl ratio and Fisher information, for determining the optimal pupil‐phase distribution for which the resulting image is insensitive to certain aberrations, such as focus errors. The effectiveness of this approach is illustrated with a number of numerical simulation experiments, and applications to the development of iris recognition systems with high‐resolution capabilities are briefly discussed.

Joint segmentation and reconstruction of hyperspectral data with compressed measurements

This work describes numerical methods for the joint reconstruction and segmentation of spectral images taken by compressive sensing coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene, resulting in significant savings in acquisition time and data storage. The reconstruction process decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene and is therefore an indispensable component of the spectral imager. In this study, we seek a particular form of the compressed sensing solution that assumes spectrally homogeneous segments in the two spatial dimensions, and greatly reduces the number of unknowns, often turning the underdetermined reconstruction problem into one that is overdetermined. Numerical tests are reported on both simulated and real data representing compressed measurements.

Statistical-information-based performance criteria for Richardson–Lucy image deblurring

Iterative image deconvolution algorithms generally lack objective criteria for deciding when to terminate iterations, often relying on ad hoc metrics for determining optimal performance. A statistical-information-based analysis of the popular Richardson-Lucy iterative deblurring algorithm is presented after clarification of the detailed nature of noise amplification and resolution recovery as the algorithm iterates. Monitoring the information content of the reconstructed image furnishes an alternative criterion for assessing and stopping such an iterative algorithm. It is straightforward to implement prior knowledge and other conditioning tools in this statistical approach.

Rotating point spread function via pupil-phase engineering

A simple approach based on the use of a properly designed pupil-phase profile can yield a 3D point-spread function (PSF) that rotates with changing defocus, while keeping its transverse shape approximately invariant over ±3-4 waves of defocus. Unlike Gauss-Laguerre mode-based approaches, it generalizes readily for encoding spherical aberration too via PSF rotation.

Digital superresolution and the generalized sampling theorem

The technique of reconstructing a higher-resolution (HR) image of size MLxML by digitally processing LxL subpixel-shifted lower-resolution (LR) copies of it, each of size MxM, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.

Noncompact simulations of SU(2)3

Abstract The action density and Wilson loops for SU(2) in three dimensions have been measured using both a noncompact version of lattice gauge theory and Wilsons version. As a standard of comparison, the Creutz ratio χ of a quartet of Wilson loops has been calculated in the exact theory to order 1/β 2 . The noncompact method gave χs that are between 2 and 23% below the one-loop calculation for the smaller loops at β = 30 and 60 on a 24 3 lattice. Wilsons method gave χs that are above the one-loop calculation by comparable amounts. For β ⩽10, the noncompact χs are closer than the Wilson χs to the one-loop calculation. Also some noncompact simulations were done in the temporal gauge; the results agree subtantially with those done without gauge fixing, providing evidence for the gauge independence of the noncompact method. By comparing the χs of the 12 3 lattice at β = 30 with those of the 24 3 lattice at β = 30 and 60, evidence was found that the accuracy of the noncompact method improves both as the volume of the lattice grows and as the lattice spacing shrinks.