Online Model-based Estimation for Automated Optical System Alignment and Phase Retrieval Algorithm
Online model-based estimation is applied to two major applications in optics: Automated optical component alignment and wavefront reconstruction with simultaneous system parameter estimation. Both applications utilize mechanical perturbation in the optical system to generate phase diversity in real-time stochastic systems. The first part of this study proposes a novel automated alignment method which improves efficiency and increases the flexibility of an optical system. Current optical systems with automated alignment capabilities are typically designed to include a dedicated wavefront sensor. Here, we demonstrate a self-aligning method for a reconfigurable system using only focal plane images. We define reconfigurable and reflective optical systems and simulate the images given misalignment parameters using ZEMAX software. We perform a principal component analysis (PCA) on the simulated dataset to obtain Karhunen-Loeve (KL) modes, which form the basis set whose weights are the system measurements. A model function which maps the state to the measurement is learned using nonlinear least squares fitting and serves as the measurement function for the extended Kalman filter (EKF) and unscented Kalman filter (UKF) used to estimate the state and control the system. The observability and stability of the system are discussed. We present both simulated and experimental results of the full system in operation. The second part of this study presents a novel algorithm for phase retrieval and optical system parameter estimation. Many wavefront reconstruction techniques estimate the amplitude and phase from multiple intensity measurements. One can generate phase diversity among these intensity measurements by varying certain parameters in the optical system. These parameters are subject to noise and disturbances, which might strongly degrade the accuracy of the reconstruction. The parallel algorithm iterative amplitude and phase retrieval (APR) have been proven to accurately reconstruct arbitrary wavefronts from multiple intensity measurements when system parameters are known exactly, given the ability to induce phase diversity between images. Such sets of intensity images with phase diversity can be generated by moving a lens in the optical system, but any position error on the lens will degenerate the reconstruction result. We demonstrate the use of an expectation-maximization (EM) algorithm with Kalman smoothing for recovering both the complex field and the lens position from a stack of intensity images. Our method successfully reduces the mean-squared-error of the estimated wavefront in comparison to an approach without position error estimation. We present and discuss the results of using a Kalman smoother and nonlinear least-square optimization for the estimation of the moving lens position. We modify and extend the system variable estimation method to serial phase retrieval algorithm. We present the use of iterated extended Kalman filter (IEKF) to estimate the system variables in a multiple-image phase retrieval framework. An iterated extended Kalman filter is shown to effectively reduce the normalized mean-square-error of the reconstructed wavefront by estimating the defocus and transverse shifts of a moving camera in simulation. Experiments are conducted using two different test objects, and the results clearly demonstrate the enhancement of detail and contrast of the wavefront when using the filter. A quadratic phase introduced by a convex lens is used with a binary mask as one of the test objects. The focal length estimated from the unwrapped phase agrees with the (1% tolerance) value provided by the manufacturer.
Automated alignment; Computational imaging; Kalman filtering; Phase retrieval; Optics; Engineering
Lloyd, James; Kress Gazit, Hadas
Ph. D., Mechanical Engineering
Doctor of Philosophy
dissertation or thesis