The impulse response function of apertured and misaligned ABCD optical system in phase-space

By expanding the aperture into complex Gaussian functions, the approximate analytical impulse response function of apertured and misaligned ABCD optical system in phase-space is determined, which allows us to formulate the input-output relation completely in terms of Wigner distribution functions. Its shown that the hard-aperture placed before the optical system will change the shape of output signal Wigner distribution and the misalignment of optical system will introduce the output Wigner distribution function a coordinate shift in phase-space. For examining the analytical results some numerical simulation are done and the graphical results as well as the absolute errors between analytical results and numerical integral ones are presented.