This invention provides a method and apparatus for analyzing the propagation of optical fields between arbitrarily oriented planes using full scalar diffraction theory. One aspect of the invention allows propagation between tilted planes. A second aspect allows propagation between offset planes. To analyze the propagation of an input optical field from a first plane to a second plane, the input field in the spatial domain is Fourier transformed to obtain the plane wave distribution in the spatial frequency domain. Within the spatial frequency domain the field is propagated from the first plane to the second plane by first multiplying the plane wave distribution by the spatial frequency domain phase accumulation between the first and second planes, and then converting the plane wave distribution from the coordinate system of the first plane to that of the second plane. Finally, the propagated plane wave distribution is inverse Fourier transformed to obtain the propagated optical field. This propagation sequence forms the building block for a numerical method to analyze optical systems using full scalar diffraction theory. To analyze optical systems, the input field is propagated from the plane of the source to the plane of the first optical element and the propagated optical field is multiplied by the transmittance function of the optical element. This invention further includes tolerance analysis of each parameter that affects the image quality and coupling efficiency of the optical system.