Design and optimization of imaging systems by engineering the pupil function

Abstract

It is expected that the ability to accurately and efficiently design an imaging system for a specific application will be of increasing importance in the coming decades. Applications of imaging systems range from simple photography to advanced lithography machines. Perhaps the most important way to make an imaging system meet a particular purpose is to engineer the pupil function of the imaging system. This includes designing a pupil surface and often involves the simultaneous design of a post-processing algorithm. Currently these design processes are performed mostly by using numerical optimization methods. Numerical methods in general have many drawbacks including long processing time and no guarantee that one has reached the global optimum. We have developed analytical approaches in designing imaging systems by engineering the pupil function. Two of the most important merit functions that are used for the analysis of imaging systems are the modulation transfer function (MTF) and the point spread function (PSF). These two functions are standard measures for evaluating the performance of an imaging system. Usually during the design process one finds the PSF or MTF for all the possible degrees of freedom and chooses the combination of parameters which best satisfies his/her goals in terms of PSF and MTF.

(cont.) In practice, however, evaluating these functions is computationally expensive; this makes the design and optimization problem hard. In particular, it is often impossible to guarantee that one has reached the global optimum. In this PhD thesis, we have developed approximate analytical expressions for MTF and PSF of an imaging system. We have derived rigorous bounds on the accuracy of these expressions and established their fast convergence. We have also shown that these approximations not only reduce the calculation burden by several orders of magnitude, but also make the analytic optimization of imaging systems possible. We have studied the detailed properties of our approximations. For instance we have shown that the PSF approximation has a complexity which is independent of certain system parameters such as defocus. Our results also help in better understanding the behavior of imaging systems. In particular, using our results we have answered a fundamental question regarding the limit of extension of the depth of field in imaging systems by pupil function engineering. We have derived a theoretic bound and we have established that this bound does not change with change of phase of pupil function. We have also introduced the concept of conservation of spectral signal-to-noise ratio and discussed its implications in imaging systems.