Search

The performance of optically coherent imaging systems can be limited by measurement and speckle noise. In this paper, we develop an image formation framework for computing the maximum a posteriori estimate of an object's reflectivity when imaged using coherent illumination and detection. The proposed approach allows for the use of Gaussian denoising algorithms (GDAs), without modification, to mitigate the exponentially distributed and signal-dependent noise that occurs in coherent imaging. Several GDAs are compared using both simulated and experimental data. The proposed framework is shown to be robust to noise and significantly reduce reconstruction error compared to the standard inversion technique.

Here we expand on the current methods of characterizing small astronomical bodies, particularly asteroids, by viewing stellar occultation events. Stellar occultation has proven to be a viable method for determining the size of moons and asteroids; however, it comes with some limitations. In general the method does not consider or use all of the known diffraction effects that occur and thus provides a nominal radius--not a shape--of the occluder. We show that most stellar occultation events involving small near-Earth asteroids occur with low Fresnel numbers. This in effect renders the traditional methods useless to characterize the shape, because no sharp shadow exists. We show that using similar data collection to that of the traditional occultation method and inverting a Fresnel diffraction equation by a phase retrieval process can yield a complete reconstruction of the silhouette of the occluder. The effect of noise in the measurements is also discussed. A practical example applied to the asteroid 25143 Itokawa is shown.

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern's frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform's modulus, without background constraints. A practical example is shown.

Here a modification to the hybrid input-output (HIO) method of phase retrieval is presented which aides in mitigating the negative effects of low signal-to-noise ratios (SNRs). Various type of interferometers measure diffraction patterns which are used to determine the Fourier transform modulus of an objective. Interferometry often suffers from very low SNRs making phase retrieval difficult because of the sensitivity of most phase retrieval algorithms to local minima. Here we analyze the effect of noise on the HIO method. The result is used as a rationale for the proposed modification to the HIO method. The algorithm presented here introduces a filtering scheme which removes much of the Fourier modulus noise. Examples are shown and the results are compared to the HIO method with and without the proposed modification. Comparisons are also made to other methods of filtering the Fourier modulus noise.