Joseph C. Marron

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.

Three-dimensional lensless imaging using laser frequency diversity.

A laser radar system for three-dimensional (3-D) lensless imaging is analyzed in theory and experiment. 3-D imaging is accomplished by making use of the relationship between the angular and wavelength dependence of the scattered light and an objects 3-D Fourier transform. The concept is demonstrated by obtaining a 3-D image of an extended object by using a charge-coupled device detector array and an argon-ion laser with a tunable intracavity étalon.

Three-dimensional imaging using a tunable laser source

A method for obtaining 3-D images by illuminating an object with frequency tunable laser light and recording information interfero- metrically is discussed. The instrumentation requirements include a telecentric imaging system and a tunable laser source capable of serially illuminating the object with multiple laser frequencies. Complex-valued image plane data is recorded interferometrically and processed using Fourier transform algorithms, and 3-D images obtained from a variety of objects are presented. These results demonstrate the wide range of measurement applications that can be addressed with this method.

Phase retrieval from experimental far-field speckle data.

Phase retrieval from experimental (laboratory) data has been successfully demonstrated. A diffuse object was coherently illuminated and Fourier intensity data were collected by a charge-coupled device detector and a video digitizer. By using the data and an a priori triangular image support constraint, an iterative Fourier-transform algorithm was used to estimate the phase of the Fourier transform of the object. The reconstructed image compares favorably with a conventional image with the same spatial-frequency bandwidth.

Three-dimensional, fine-resolution imaging using laser frequency diversity

Experimental results obtained using a fine-resolution, three-dimensional imaging method are presented. The method consists of flood illuminating an extended object with a laser beam and recording the scattered light as the laser frequency is varied. An image is recovered by three-dimensional Fourier transformation of the recorded data. For the results presented here, a tunable dye-laser source is used, and the obtained range resolution is 287 microm.

Wavelength decorrelation of laser speckle from three-dimensional diffuse objects

Abstract The wavelength dependence of laser speckle produced by scattering from 3-D diffuse objects is considered. A simple Fourier transform relationship between the cross-spectral correlation function and an objects range profile is derived.

Digital shearing laser interferometry for heterodyne array phasing

A laser radar using an array of heterodyne detectors offers the possibility of fine resolution angle-angle imaging. The heterodyne measurements, however, are subject to phase errors due to atmospheric turbulence and mechanical misalignment. A method is described that employs digital shearing of the heterodyne measurements as a means to remove phase errors. By this method large phase errors can be corrected without requiring a beacon or a glint. This digital shearing laser interferometry method was investigated theoretically and demonstrated via computer simulations which included photon noise and various types of phase errors. The method was also successfully applied to data collected in a simple laboratory experiment.

Higher-order kinoforms

Several arguments are made for using higher-order, rather than first-order, kinoforms for producing low f-number diffractive lenses. It is shown that improved efficiency can be achieved with higer-order kinoforms when the f-number of the lens is very low. A procedure for the fabrication of higher-order kinoforms is also presented.

Use of an opacity constraint in three-dimensional imaging

Three-dimensional imaging provides profile information not available with conventional 2D imaging. Many 3D objects of interest are opaque to the illuminating radiation, meaning that the object exhibits surface, as opposed to volume, scattering. We investigate the use of an opacity constraint to perform 3D phase retrieval. The use of an opacity constraint in conjunction with frequency-diverse pupil-plane speckle measurements to reconstruct a 3D object constitutes a novel unconventional-imaging concept. This imaging modality avoids the difficulties associated with making phase measurements at a cost of increased computations.

Speckle from rough rotating objects

Dynamic speckle from rough rotating objects with nonplanar underlying shape is considered in theory and experiment. The theoretical treatment is based on modeling the optical field as a sum of contributions from discrete scatterers on the surface of the object. It follows that computation of the speckle correlation function requires knowledge of the objects average scattering strength as a function of position and the underlying shape of the object. Calculation of the speckle correlation function reduces to tracing a series of rays that coarsely sample the object and for each ray computing the relative phase shift resulting from object rotation. This method is quite simple compared to previous analytic techniques. Theory and experiment are compared for cylinders with a variety of surface coatings. Dynamic speckle from multiple rotating objects and objects with complicated underlying shape is also considered.