Fizeau interferometer is widely used to test the surface deformation of the optical lens surface profile. However, in some
measurement circumstances the common path condition of the Fizeau configuration does not hold. For example, the subaperture
scanning interferometry of asphere or the non-null aspherical element testing has dense fringe spacing.
Systematic aberrations of non-null testing are introduced into the measurement wavefront with the high wavefront slope
of the returning beam. We propose to use a two-dimension scanning device to drive a test ball to different fields of the
Fizeau interferometer for the the interference phase at each field. By least square fitting the measurement, we can get the
double Zernike polynomial coefficients representing the field dependent aberrations in the interferometer system.
According to the coefficients, the off-axis aberrations in the interferometer can be identified
Most of the practical optical systems have circular shape lens pupil and rectangular shape image field. This paper
proposes a four dimensional polynomial to describe the full-field wavefront with orthogonal polynomials set in both
circular pupil and rectangular field. The basic functions of both the pupil wavefront and the field wavefront are Zernike
circle polynomials, multiplying each other to a four dimensional double Zernike polynomial (DZP) function. The double
Zernike polynomial coefficients of the full-field wavefront represent the global optical aberration of the image system.
The misalignment perturbation changes the corresponding least squares fitted DZP coefficients. The changed DZP
coefficients shows both linear and nonlinear response to the misalignment status when the misalignment is large. The
Tri-Mirror Anastigmatic Telescope is used as one of the implemented example showing the changed DZP due to
perturbation.
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