Phase imaging based on wavefront propagation

Abstract

Light is a wave which has both amplitude and phase. Since the vibration of the wave is too fast, phase needs to be recovered from the time–averaged energy—intensity by computational methods. In this thesis, we choose defocus as a way to mix phase into measured intensity images, because it is not only efficient in transferring phase to intensity but also advantageous due to its simplicity and flexibility in the experiment. In this thesis, we develop computational methods to recover phase from defocused intensity images which contain phase information. We first propose methods based on complex Kalman filtering, which updates the complex field from the noisy intensity images by maintaining pair–wise pixel error correlation. We prove that the pixel–wise correlation is sparse and it reduces computational complexity of the method from cubic to linear of the total number of the pixel numbers. Secondly, we introduce an exponential spacing measurement scheme to efficiently re-duce the number of defocused intensity images. We perform Gaussian process regres-sion over the exponentially spaced intensity images to estimate the axial derivative in the transport of intensity equation (TIE) phase retrieval. It alleviates the nonlinear-ity error in the derivative estimation by using the prior knowledge of how intensity varies with defocus propagation in the spatial frequency domain. Finally, we also consider the phase recovery of partially coherent illumination created by any arbitrary source shape in K¨ohler geometry. By extending the Kalman filtering algorithms to the partially coherent case, we recover not only the phase but also an estimate of the unknown illumination source shape. In conclusion, we consider the issues of noise, intensity measurement scheme, nonlinearity error in TIE and partially coherent illumination. We validate our techniques experimentally with a brightfield microscope. Since the measurement of defocused in-tensity images is experimentally simple and flexible, the methods in this thesis should find use in optical, X–ray and other phase imaging systems.