Timothy J. Schulz

Single-shot compressive spectral imaging with a dual-disperser architecture

This paper describes a single-shot spectral imaging approach based on the concept of compressive sensing. The primary features of the system design are two dispersive elements, arranged in opposition and surrounding a binary-valued aperture code. In contrast to thin-film approaches to spectral filtering, this structure results in easily-controllable, spatially-varying, spectral filter functions with narrow features. Measurement of the input scene through these filters is equivalent to projective measurement in the spectral domain, and hence can be treated with the compressive sensing frameworks recently developed by a number of groups. We present a reconstruction framework and demonstrate its application to experimental data.

Deblurring subject to nonnegativity constraints

Csiszars I-divergence is used as a discrepancy measure for deblurring subject to the constraint that all functions involved are nonnegative. An iterative algorithm is proposed for minimizing this measure. It is shown that every function in the sequence is nonnegative and the sequence converges monotonically to a global minimum. Other properties of the algorithm are shown, including lower bounds on the improvement in the I-divergence at each step of the algorithm and on the difference between the I-difference at step k and at the limit point. A method for regularizing the solution is proposed. >

Multiframe blind deconvolution of astronomical images

Maximum-likelihood estimation techniques are presented for the problem of forming object estimates from turbulence-degraded images when the point-spread functions are unknown. The inability of unconstrained maximum-likelihood methods to form meaningful estimates is acknowledged, and iterative algorithms are derived for estimating the object by using both a penalized maximum-likelihood method and a physically meaningful parameterization of the point-spread functions by phase errors distributed over an aperture.

Hubble Space Telescope characterized by using phase-retrieval algorithms.

We describe several results characterizing the Hubble Space Telescope from measured point spread functions by using phase-retrieval algorithms. The Cramer-Rao lower bounds show that point spread functions taken well out of focus result in smaller errors when aberrations are estimated and that, for those images, photon noise is not a limiting factor. Reconstruction experiments with both simulated and real data show that the calculation of wave-front propagation by the retrieval algorithms must be performed with a multiple-plane propagation rather than a simple fast Fourier transform to ensure the high accuracy required. Pupil reconstruction was performed and indicates a misalignment of the optical axis of a camera relay telescope relative to the main telescope. After we accounted for measured spherical aberration in the relay telescope, our estimate of the conic constant of the primary mirror of the HST was - 1.0144.

Thin infrared imaging systems through multichannel sampling

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

Compressive holography of diffuse objects

We propose an estimation-theoretic approach to the inference of an incoherent 3D scattering density from 2D scattered speckle field measurements. The object density is derived from the covariance of the speckle field. The inference is performed by a constrained optimization technique inspired by compressive sensing theory. Experimental results demonstrate and verify the performance of our estimates.

Practical methods for automated reconstruction and characterization of particles in digital in-line holograms

Hologram reconstruction algorithms often undersample the phase in propagation kernels for typical parameters of holographic optical setups. Given in this paper is an algorithm that addresses this phase undersampling in reconstructing digital in-line holograms of particles for these typical parameters. This algorithm has a lateral sample spacing constant in reconstruction distance, has a diffraction limited resolution, and can be implemented with computational speeds comparable to the fastest of other reconstruction algorithms. This algorithm is shown to be accurate by testing with analytical solutions to the Huygens–Fresnel propagation integral. A low-pass filter can be applied to enforce a uniform minimum particle size detection limit throughout a sample volume, allowing this method to be useful in measuring particle size distributions and number densities. Tens of thousands of holograms of cloud ice particles are digitally reconstructed using the algorithm discussed. Positions of ice particles in the size range of 20 µm–1.5 mm are obtained using an algorithm that accurately finds the position of large and small particles along the optical axis. The digital reconstruction and particle characterization algorithms are implemented in an automated fashion with no user intervention on a computer cluster. Strategies for efficient algorithm implementation on a computer cluster are discussed.

Optimal beams for propagation through random media

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Greens function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Greens function.

Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements

Conventional Hartmann sensor processing relies on locating the centroid of the image that is formed behind each element of a lenslet array. These centroid locations are used for computing the local gradient of the incident aberration, from which the phase of the incident wave front is calculated. The largest aberration that can reliably be sensed in a conventional Hartmann sensor must have a local gradient small enough that the spot formed by each lenslet is confined to the area behind the lenslet: If the local gradient is larger, spots form under nearby lenslets, causing a form of cross talk between the wave-front sensor channels. We describe a wave-front reconstruction algorithm that processes the whole image measured by a Hartmann sensor and a conventional image that is formed by use of the incident aberration. We show that this algorithm can accurately estimate aberrations for cases in which the aberration is strong enough to cause many of the images formed by individual lenslets to fall outside the local region of the Hartmann sensor detector plane defined by the edges of a lenslet.

Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope.

Multiframe blind deconvolution - the process of restoring resolution to blurred imagery when the precise form of the blurs is unknown - is discussed as an estimation-theoretic method for improving the resolving power of ground-based telescopes used for space surveillance. The imaging problem is posed in an estimation-theoretic frame- work whereby the objects incoherent scattering function is estimated through the simultaneous identication and correction of the distorting effects of atmospheric turbulence. An iterative method derived via the expectation-maximization (EM) procedure is reviewed, and results obtained from telescope imagery of the Hubble Space Telescope are presented.