Evaluation of centricity of optical elements by using a point spread function

Our work describes a technique for testing the centricity of optical systems by using the point spread function. It is shown that a specific position of an axial object point can be found for every optical element, where the spherical aberration is either zero or minimal. If we image such a point with an optical element, then its point spread function will be almost identical to the point spread function of the diffraction-limited optical system. This consequence can be used for testing the centricity of precisely fabricated optical elements, because we can simply detect asymmetry of the point spread function, which is caused by the decentricity of the tested optical element. One can also use this method for testing optical elements in connection with a cementing process. Moreover, a simple formula is also derived for calculation of the coefficient of third-order coma, which is caused by the decentricity of the optical surface due to a tilt of the surface with respect to the optical axis, and a simple method for detecting the asymmetry of the point spread function is proposed