Mark F. Spencer

Physical optics solution for the scattering of a partially-coherent wave from a statistically rough material surface.

The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.

Performance characterization of Phase Gradient Autofocus for inverse synthetic aperture LADAR

Phase Gradient Autofocus (PGA) is an effective algorithm for estimating and removing piston-phase errors from spotlight-mode synthetic aperture radar (SAR) data. For target scenes dominated by a point source, the algorithm has been shown to be optimal in the sense that it approaches the Cramér-Rao bound for carrier-to-noise ratios (CNRs) as low as -5 dB. In this paper, we explore PGAs effectiveness against ground-based inverse synthetic aperture LADAR (ISAL) observations of spacecraft, where the target characteristics and phase errors are quite different than in the SAR case. At optical wavelengths, the power spectrum of the piston-phase errors will be dominated less by platform motion and more by atmospheric variations. In addition, space objects will have fewer range-resolution cells across them than would a typical extended SAR scene. This research characterizes the performance limitations of PGA for an ISAL system as a function of CNR and the number of range-resolution cells across the scene. A high-fidelity wave-optics simulation is used to generate representative test data for input to the PGA algorithm. Emphasis is placed on finding the lower limits of performance for which image reconstruction is possible.

Inverse synthetic aperture ladar: a high-fidelity modeling and simulation tool

A wave-optics model is developed which allows simulation of an Inverse Synthetic Aperture LADAR (ISAL) imaging system. This end-to-end tool models the complex interactions of Linear Frequency Modulated (LFM) chirped pulses, object/beam interactions including object articulation, speckle phenomenology, heterodyne detection with noise, atmospheric turbulence, and laser-guide star adaptive optics. Detected signal outputs are simulated and processed to explore system design trades and to test and compare image processing algorithms. Model verification results will be presented as well as reconstructed images.

An investigation of stair mode in optical phased arrays using tiled apertures

With an optical phased array, the individual phases of a multi-fiber laser source can be manipulated by exploiting high-bandwidth phase loops to correct for aero-optical flow over the turret and free-stream atmospheric effects along the line of sight; however, rough surface scatter through laser-target interaction adds the additional constraints of speckle and depolarizing effects. In particular, speckle phenomena can cause unobservable modes to arise in the beam control system of optical phased arrays. One such unobservable mode is termed stair mode and is appropriately identified by a stair-step pattern of piston phase across the individual subapertures that comprise a tiled aperture. This paper investigates the effects of stair mode using wave-optics simulations. To represent different array fill factors in the source plane, both seven and 19 element hexagonal close-packed tiled apertures are used in the simulations along with both Gaussian and flat-top outgoing beamlets. Peak Strehl ratio and power in the bucket are calculated in the target plane for all simulation setups and are then averaged for multiple random realizations of stair mode step sizes. In addition, the stair mode target irradiance patterns are imaged with cameras which have decreasing aperture stop diameters. Initial results show that low resolution imaging conditions, i.e. an aperture stop on the order of a subaperture diameter, makes it difficult to distinguish between different realizations of stair mode using a separate camera sensor.

Scalar wave solution for the scattering of a partially coherent beam from a statistically rough metallic surface

The scattering of a spatially partially coherent wave from a one-dimensional statistically rough metallic surface is investigated. Assuming a Gaussian Schell-model form for the incident field autocorrelation function, a closed-form expression for the scattered field autocorrelation function is derived using the physical optics approximation (Kirchhoff approximation). Two forms of the solution are derived—one applicable to very rough surfaces and the other applicable to moderately rough surfaces. It is shown that for very rough surfaces, the solution, under certain circumstances, remains Gaussian Schell model as has been previously reported. As such, closed-form expressions for the angular coherence radius and angular scattering radius are derived. These expressions are, in general, complicated functions of both the source (size and coherence properties) and surface parameters (surface height standard deviation and correlation length). It is demonstrated that for many scenarios of interest, the angular coherence radius can be safely approximated as a function of just the source parameters and the angular scattering radius can be simplified to a function of just the surface parameters. For the moderately rough surface solution, the scattered field autocorrelation function is, in general, not Gaussian Schell model and it is therefore not possible to derive analytical forms for the angular coherence radius or angular scattering radius. Nonetheless, the form of the autocorrelation function is physically intuitive and is discussed in this work. To verify the presented theoretical analysis, wave optics simulation results are presented and compared to the predictions of the analytical models. This analysis is concluded with a discussion of future work.

Deep-turbulence wavefront sensing using digital-holographic detection in the off-axis image plane recording geometry

Abstract. This paper develops wave-optics simulations which explore the estimation accuracy of digital-holographic detection for wavefront sensing in the presence of distributed-volume or “deep” turbulence and detection noise. Specifically, the analysis models spherical-wave propagation through varying deep-turbulence conditions along a horizontal propagation path and formulates the field-estimated Strehl ratio as a function of the diffraction-limited sampling quotient and signal-to-noise ratio. Such results will allow the reader to assess the number of pixels, pixel field of view, pixel-well depth, and read-noise standard deviation needed from a focal-plane array when using digital-holographic detection in the off-axis image plane recording geometry for deep-turbulence wavefront sensing.

Impact of spatial resolution on thermal blooming phase compensation instability

Phase compensation instability (PCI) is the time-dependent development of spatial perturbations that occur within thermally bloomed high-energy laser (HEL) beams. These types of spatial perturbations act as local hot spots that create small negative lenses within the HEL beam. Closed-loop adaptive optics (AO) corrects for these spatial perturbations by applying small positive-lens phase compensations, which only increases the strength of the local hot spots and leads to runaway in the adaptive-optics servo. This study uses a straightforward wave-optics code to model horizontal propagation with the effects of thermal blooming for a focused Gaussian beam. The strength of the thermal blooming effects is characterized using the classic dimensionless distortion number. A nominal AO system is used to mitigate phase distortions accumulated from thermal blooming. Parameters within the AO system, such as the number of actuators on the deformable mirror and the resolution of the wavefront sensor, are varied to determine the impact of spatial resolution in the development of the PCI. A discussion is given on the potential use of control theory to diminish the effects of the PCI.

Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework

The estimation of phase errors from digital-holography data is critical for applications such as imaging or wavefront sensing. Conventional techniques require multiple i.i.d. data and perform poorly in the presence of high noise or large phase errors. In this paper, we propose a method to estimate isoplanatic phase errors from a single data realization. We develop a model-based iterative reconstruction algorithm that computes the maximum a posteriori estimate of the phase and the speckle-free object reflectance. Using simulated data, we show that the algorithm is robust against high noise and strong phase errors.

Experimental method of generating electromagnetic Gaussian Schell-model beams

The purpose of this research effort is to experimentally generate an electromagnetic Gaussian Schell-model beam from two coherent linearly polarized plane waves. As such, the approach uses a sequence of mutually correlated random phase screens on phase-only liquid crystal spatial light modulators at the source plane. The phase screens are generated using a published relationship between the screen parameters and the desired electromagnetic Gaussian Schell-model source parameters. The approach is verified by comparing the experimental results with published theory and numerical simulation results. This work enables the design of an electromagnetic Gaussian Schell-model source with prescribed coherence and polarization properties.

Digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming

Digital holography wave-front sensing in the off-axis image plane recording geometry shows distinct potential for directed-energy and remote-sensing applications. For instance, digital holographic detection provides access to the amplitude and wrapped phase associated with an optical field. From the wrapped phase, one can estimate the atmospheric aberrations present and perform adaptive-optics compensation and high-resolution imaging. This paper develops wave-optics simulations which explore the estimation accuracy of digital holography wave-front sensing in the presence of strong atmospheric turbulence and thermal blooming. Specifically, this paper models spherical-wave propagation through varying atmospheric conditions along a horizontal propagation path and formulates the field-estimated Strehl ratio as a function of the image-plane sampling, the coherence diameter, the log-amplitude variance, and the distortion number. Such results will allow one to assess the number of pixels needed in a detector array when using digital holographic detection in the presence of strong atmospheric turbulence and thermal blooming.