Iterative Phase Estimation Algorithms In Interferometric Systems PDF Download

"Coherent optical interferometry has a long history of enabling extremely precise measurements at length scales of less than the wavelength of light used in the interferometer. It is the ability of these systems to measure both the relative phase and amplitude information of the optical field that makes them so useful. As the name would imply, measuring phase and amplitude is accomplished by interfering two or more beams of light. Interferometric techniques have been adopted for use in both imaging/sensing technologies. For imaging systems under ideal conditions, the ability to measure both phase and amplitude information in one transverse plane allows for the calculation of that field's phase and amplitude distribution in any other transverse plane. However, the presence of atmospheric turbulence unpredictably alters the index of refraction in the propagation medium thereby adversely affecting the reliability of calculation of phase and amplitude in other transverse planes. To address this problem, we demonstrate iterative sharpness maximization (ISM) correction of anisoplanatic turbulence effects in simulated range-compressed holography (RCH) fields and their corresponding range images. Our turbulence correction estimated four phase screens placed along the path of optical propagation using nonlinear optimizations aided by the method of sieves technique. We conducted a study of range images created from simulated single speckle realization 3D RCH fields subjected to twenty different turbulence profiles at five different strengths of turbulence, D/r0 = 7, 14, 21, 28, and 36. Range images showed significant improvement for all strengths of turbulence. To assist in correction, we introduced a novel constraint limiting the spread of energy in the corrected pupil. Corrected range images were qualitatively very similar to unaberrated range images in all but the most severe turbulence case, D/r0 = 36. Additionally, our algorithm was tested for fields affected by shot noise. Mean target photons per speckle ranged from 10 -2 to 10 2 in these simulations. For an effective D/r0 = 36, range images corrected from fields with 102 mean photons per speckle had very similar RMSE when compared to corrected noiseless range images. On average, corrected range images created from fields with 1 mean target photon per speckle differed by less than 5% RMSE from noiseless corrected range images. We went on to construct a RCH system in a laboratory setting using a linear frequency modulated CW laser and a high frame rate camera which allowed us to create 3D images of laboratory targets. Data was collected both with and without the effects of turbulence. In the former, multiple Lexitek turbulence screens were used to aberrate the image fields of our lab target at two different effective strengths of anisoplanatic turbulence, D/r0 = 7 and D/r0 = 16, respectively. Both of these sets of real aberrated image fields showed profound improvement in quality after correction with our phase ISM turbulence mitigation algorithm. Novel interferometric systems are also being developed which enable modal analysis of an optical field. This generalized optical interferometry (GOI) treats coherent optical fields as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. In order to maximize the utility of these systems, we used phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Algorithms were developed both for use with an array detector and for use with a bucket detector. Information diversity increased the robustness of both algorithms by better constraining the solutions. In our array detection phase retrieval, the algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise. Similarly, the algorithm we developed using data from a simulated bucket detector was able to consistently recover better than 95% of coefficient phases for simulated random fields consisting of up to 21 superpositioned Hermite Gaussian modes using between three and seven measurements per unknown phase coefficient. With shot noise, the algorithm achieved performance on par with noiseless simulations with 106 mean signal photons per measurement. The role played by number of measurements per unknown (mpu), photons per unknown per measurement (ppu), and order of superposition in the bucket detection algorithm's performance was also explored"--Pages xvi-xix