Finite-dimensional matrix treatment of partially coherent optical systems

Methods for calculating the output intensity or the output mutual intensity of partially coherent optical systems have been the subject of much research during the last 50 years. All of the previously developed methods have required evaluating complicated integrals or required limiting approximations regarding the input distribution, the optical system, or the degree of coherence of the illumination. This thesis presents a new method for modeling optical systems of arbitrary degree of coherence using finite dimensional matrix operators. Discrete forms and finite dimensional (size N x N) matrix representations of several optical operations as well as sampling-related restrictions on these transforms are found. The new discrete transforms include the discrete Fresnel transform and the discrete Rayleigh-Sommerfeld transform as well as some new matrix representations for lenses, apertures and phase or amplitude masks. The matrices are then combined and used to operate on input distributions represented as vectors in an N-tuple vector space. Examples of how to model general optical systems are given. A new finite-dimensional matrix form of the mutual intensity function is then introduced and incorporated into the optical system matrix model. A new method for calculating the mutual intensity matrix and the intensity vector at the output of an optical system is demonstrated as is the relationship between the optical system matrices and the Van Cittert-Zernike theorem. The optical operator and mutual intensity matrices are then used to model three different types of microscopes as well as hybrid optical/digital imaging systems in order to predict how an arbitrary input will appear at the output of the given system.