Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology

Computer-generated hologram (CGH) has been widely used as a wavefront compensator in symmetric aspheric metrology. As a diffractive element, it generates different diffraction orders, but only the 1st-order diffraction is used to test aspheric surface. The light from spurious diffraction orders (SDO) will produce many high-frequency fringes in interferogram and reduce measurement accuracy. In this paper, we regard the CGH null system as an imaging system and develop an aberration model in Seidel formalism to analyze the SDO. This model has the advantage to address the difference between the SDO (k₁, k₂) and (k₂, k₁). We consider the effect of the pupil distortion so that our model can analyze the SDO with a large pupil distortion. We derive the condition to ensure the 2^nd-order and 4^th-order aberrations have the same sign and calculate the minimum defocused distance (power carrier frequency) of CGH. According to the marginal-ray heights (h₁ and h₃ ) on the CGH in the first and second passes, we determine the condition that the SDO covers the whole CGH in the second pass. We analyze the SDO of 4 CGH designs and compare the results from our aberration model with these from real ray trace. These results validate that our aberration model is feasible whether the aspheric part is convex or concave and whether CGH is inside or outside the focus of the transmission sphere.