Simultaneous estimation of phase and itspth order derivatives

Abstract

One unaddressed challenge in optical metrology has been the measurement of higher order derivatives of rough specimens subjected to loading. In this paper, we investigate an approach that allows for the simultaneous estimation of the phase and its higher order derivatives from a noisy interference field. The interference phase is represented as a weighted linear combination of linearly independent Fourier basis functions. The interference field is represented as a state space model with the weights of the basis functions as the elements of the state vector. These weights are accurately estimated by employing the extended Kalman filter. The interference phase and phase derivatives are subsequently computed using the estimated weights. Since the Fourier basis functions are infinitely differentiable, phase derivatives of any arbitrary order can be estimated. Simulation and experimental results are provided to substantiate the effectiveness of the proposed method in the presence of high noise.

Disease, illness, sickness and related terms: A note for non-epidemiologists

“…Disease is a medical condition caused by a pathological process that manifests as specific signs and symptoms that may affect a specific tissue/organ or the entire body. It is any abnormal condition of an organism (interruption, cessation, or disorder) that impairs a physiological or psychological function of systems or organs (5,6,7).…”

“…It is a subjective feeling or concept of not feeling well based on personal disease experience. It refers to self-reported physical or mental symptoms ranging from minor temporary issues to severe health issues or acute suffering (4,6,7). Medical conditions include all types of illnesses.…”

“…Sickness (being ill) can refer to either a non-medical or a medical condition. When a person adopts a sickness role and is unable to fulfill his social role, he is in a state of social and cultural dysfunction (7,29). Sickness is associated with the social role that a person with illness takes or is assigned in society in a variety of fields of life (4).…”