Large segmented and distributed aperture telescopes increasingly rely on innovative imaging techniques such as phase diversity and phase retrieval. These algorithms obtain the phase aberration in a dynamic system by different estimation techniques using the information from in-focus and out-of-focus images of extended objects and point objects, respectively. These estimation techniques are generally iterative and suffer from the usual pitfalls of CPU demands and failure modes.
An alternative method would be to obtain an expression for the wavefront directly from the phase diversity measurements. The optimal wavefront expression would be expressed as a polynomial times the unaberrated OTF derived from the aberrated PSF. In this paper, we first obtain the expansion of the aberrated PSF with an explicit dependence on the amount of diversity and explore the implications of varying amounts of diversity as well as different numbers of diversity planes. Finally, we discuss solutions for the wavefront expression.
The use of segmented mirrors for the primary elements of large telescope systems is becoming increasingly popular owing to the cost effectiveness of the design. Likewise, the use of non-optical flat glass in large collectors can further reduce cost. Unfortunately, both non-optical flatness and segment misalignment do result in phase errors. We have used a computer simulation to study the effects of these phase errors on the polarization state of an optical beam. We report herein on the effects of surface warping and of segment piston and tilt on the Stokes parameters of an optical beam reflected from a segmented mirror.
This paper discussed a simulation fo the imaging of a space- based object through cirrus clouds. The wavefront reflected by the object is propagated to the top of the cloud using Huygens-Fresnel propagation theory. At the top of the cloud, the wavefront is divided into an array of input rays, which are in turn transmitted through the cloud model using the CIRIS-C software. At the bottom of the cloud, the output ray distribution is used to reconstruct a wavefront that continues propagating to the ground receiver. Images of the object as seen through cirrus clouds with different optical depths are compared to a diffraction-limited image. Turbulence effects from the atmospheric propagation are not included.
Statistical variations in the size, position, shape and orientation of hexagonal ice crystals in a 3D volume complicates the modeling of image transfer through cirrus clouds. These variations will give rise to fluctuations in image quality as measured by the MTF of a single realization of a cloud/receiver combination. Computing the average MTF from several realizations of the cloud/receiver combination, allowing for a different cloud composition on every realization can alleviate these fluctuations. In this paper, we present the result of the multiple MTF for clouds of different optical depths, distinguishing the separate contributions of scattered as well as unscattered light. Finally, we apply the MTF thus generated to create images of objects as seen through the cloud.
The authors present a wavefront reconstruction technique for beams forward scattered and back scattered through cirrus clouds. The technique uses ray distributions from the Coherent Illumination and Ray Trace Imaging Software for Cirrus which traces the propagation and E field vectors through a 3D volume of ice crystals in the shape of columns, plates, bullets, and bullet rosettes with random positions and polydisperse sizes and orientations. The wavefronts are then propagated to a telescope receiver on the ground and imaged in the receiver focal plate. A modification transfer function for each of these images is calculated and compared to the MTF for a diffraction-limited system.
We apply out previously-developed turbid-media backpropagation algorithm to imaging extended objects imbedded in turbid media such as clouds. Although the backpropagation algorithm was developed initially for biomedical applications, the underlying development is general enough to encompass imaging objects imbedded in any sort of turbid media whose scattering properties dominate their absorption properties. For non-biomedical applications, imaging data is usually obtained only for a limited number of view angles. As a result, we look at the potential of the backpropagation algorithm to reconstruct an image of an object, imbedded in a cloud, from a single view. Using both computer-simulated data and laboratory data, we show that the backpropagation algorithm successfully increases resolution in these types of images. Because the backpropagation algorithm incorporates a depth-dependent deconvolution filter, it turns out that the optimal image quality obtained in the reconstruction occurs for the deconvolution filter which corresponds to the location of the object in the medium. This surprising result permits object localization in the range dimension even when the illuminating radiation is continuous-wave illumination, such as sunlight.
The authors present a novel simulation for studying the interaction of coherent illumination with cirrus clouds. The software traces the propagation and E field vectors through a 3D volume of ice crystal in the shape of columns, plates, bullets, and bullet rosettes with random positions, sizes, and orientations. The magnetic (B) field vectors can be found from a cross product of the two. Back-scattered depolarization results are compared to published studies. The use of this simulation for detailed studies of the impact of cirrus clouds on the wavefront of an illuminating beam is discussed.
The speckle size metric known as power-averaged speckle size (PASS), which is based on the integral of the power spectral density of the data, is insensitive to target asymmetry. PASS is defined as the inverse of the median frequency of the power spectral density of the reconstructed pupil. Implementation of the metric using simulated data from different targets under a variety of imaging conditions illustrates the impact of the environment. In this paper, we deconvolve the imaging environment using power spectral density of the detected speckle in the error function. Different targets are simulated in the presence of a variety of imaging situations as well as noise and we compare the resultant deconvolved images with undistorted images as well as with the unimproved ones.
The effect of atmospheric phase perturbations on the diffractive and coherent properties of the uplink and downlink paths of an active imaging illumination beam has been studied in some detail. Similarly, the scattering and depolarization induced by water and ice cloud particles in the path of coherent laser illumination is currently an area of much production research. In contrast, the effect of cloud particles on the diffractive properties of a laser illumination beam has not received as much attention due primarily to the daunting mathematics of the physical mode. This paper seeks to address some of the mathematical issues associated with modeling the interaction of a coherent illumination beam with a cloud of ice particles. The simulation constructs a 3D model of a cirrus cloud consisting of randomly oriented hexagonal ice crystals in the shape of plates, columns, and bullet rosettes. The size, shape, and vertical distribution of the crystals are modeled after measured particles concentrations and distributions. An illumination pattern, in the form of grid of rays, is traced through the cloud, and the properties of the exiting wavefronts are analyzed.
Robust reconstruction of coherent speckle images from non- imaged laser speckle patterns in the aperture plane of an optical system requires adequate sampling of the speckle intensity at the focal plane. Although detector size cannot be changed dynamically in the course of an experiment to achieve the necessary sampling in every frame, a measure of speckle size could be used to accept or reject individual frames in post-processing software to improve the final reconstructed image. This paper investigates the use of a speckle size metric to gauge the integrity of speckle sampling in each frame of a series of coherent speckle images. Frames containing inadequate sampling are sorted out of the final reconstructed image. The quality of the final recovery for a variety of targets and imaging conditions are compared for sorted and non-sorted reconstructions.
In classical imaging, the optical transfer function (OTF) conveys information about how well the optical system transmits individual spatial frequencies of the object. This OTF is based on the point spread function of the system; that is, the ability of the optics to form a point image given either coherent or incoherent illumination. In contrast, nonconventional imaging systems consist of an innovative combination of optics and software to form a final image. Such a system does not easily lend itself to the concept of a point spread function although individual spatial frequencies will be affected differently by the system as a whole. This paper investigates a phase differencing technique for deriving OTF information from a single frame of a coherent speckle image. A multiframe transfer function is obtained by averaging the OTFs of several single frames.
In previous work, a new family of exact, closed-form, analytic solutions to the scalar Helmholtz equation was derived in the oblate-spheroidal coordinate system. The 0,0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam which is not limited to the paraxial region, but reduces to the traditional Kogelnik and Li model in the paraxial limit. This present work compares the higher-order terms of the spheroidal-Gaussian modes with both the Hermite-Gaussian and Laguerre-Gaussian modes. Distinction is made between magnitude and phase results for paraxial modes (Hermite, Laguerre, and spheroidal) and nonparaxial ones (spheroidal only).
The recovered object in speckle imaging is generally an accumulated average of instantaneous speckled image frames. Misregistration of individual frames with respect to each other degrades image quality by blurring the average resultant image. In particular, atmospheric perturbations can cause random tilts in the phase of the detected speckle pattern, which tilts in turn induce random translations in each reconstructed image. Various techniques have been proposed to deal with this registration problem. We present here a maximum likelihood estimator to estimate and correct for the random tilts when each speckle frame is further corrupted by shot noise. The noise is modeled as a Poisson- distributed random variable. Results of this correction technique are compared with the performance of previous registration routines.
In sheared beam imaging, a target is coherently illuminated with three sheared and modulated beams. Both target motion and the temporal distribution of the laser illumination affect image recovery. Movement of the target will cause a corresponding motion of the target's speckle pattern on the ground. As the speckle pattern travels across the detector, each integration period, or bin, in a single laser pulse, or frame, will record a slightly different speckle distribution. This phenomenon effects a smearing of the speckle formation from bin to bin within a single frame, and subsequently degrades the recovered image. Image recovery is further complicated by temporally nonuniform illumination. Both smearing and nonuniform pulse shapes create distortions in the spatial and temporal distributions of the speckle patterns that garble image recovery. This paper documents the derivation of the governing equations for the simulation of sheared beam imaging in the presence of these space-time distortions. In addition, we present algorithms for alleviating these distortions prior to image reconstruction. We conclude with simulation results showing the effect of the space-time distortions on sheared beam image recovery and the improvement achieved with the post-detection deblurring and pulse correction algorithms.
A new mathematical model for the fundamental mode of a Gaussian beam is presented. Unlike the Kogelnik and Li model, this new model is an exact, closed-form solution of the scalar Helmholtz equation for beams with a Gaussian amplitude distribution. The model is the 0,0 order of a family of solutions to the wave equation in the oblate spheroidal coordinate system. A geometrical interpretation of the model, based on the concept of a skew line, is also presented that allows simple, straight-line modeling of intracavity and extracavity beam propagation.