For instance we have shown that the PSF approximation has a complexity which is independent of certain system parameters such as defocus. We have studied the detailed properties of our approximations. 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 derived rigorous bounds on the accuracy of these expressions and established their fast convergence. In this PhD thesis, we have developed approximate analytical expressions for MTF and PSF of an imaging system. In particular, it is often impossible to guarantee that one has reached the global optimum. (cont.) In practice, however, evaluating these functions is computationally expensive this makes the design and optimization problem hard. 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. These two functions are standard measures for evaluating the performance of an imaging system. 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). We have developed analytical approaches in designing imaging systems by engineering the pupil function. Numerical methods in general have many drawbacks including long processing time and no guarantee that one has reached the global optimum. Currently these design processes are performed mostly by using numerical optimization methods. This includes designing a pupil surface and often involves the simultaneous design of a post-processing algorithm. Perhaps the most important way to make an imaging system meet a particular purpose is to engineer the pupil function of the imaging system. Applications of imaging systems range from simple photography to advanced lithography machines. Journal of General Psychology, 1937, 17, 307–322.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. Binocular relations in macular adaptation. The luminous efficiency of rays entering the eye pupil at different points. Journal of the Optical Society of America. Brightness function: Effects of adaptation. Brightness function: Binocular versus monocular stimulation. Further validation of subjective scales for loudness and brightness by means of cross-modality matching. Mach bands: Quantitative studies on neural networks in the retina. The relation between area of stimulation and intensity of light at various levels of visual excitation as measured by pupil constriction. Journal of the Optical Society of America, 1961, 51, 667–673. Light adaptation and the brightness of brief foveal stimuli. Brightness as a function of retinal locus. Journal of the Optical Society of America, 1970. Variables determining flicker sensitivity in small fields. Proceedings of the International Colour Meeting (Lucerne). Threshold and suprathreshold relations in vision. Brightness scales for monochromatic light. Quantitative description of contrast phenomena. Neural inhibitory units of the eye and skin.
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