A practical method for determining the accuracy of computer-generated holograms for off-axis aspheric surfaces

• We introduce two different design methods for CGH.
• In ray tracing, B-spline is suitable to fit discrete compensated phase and get the phase function.
• Surface intersection is used to compute CGH fringe position.
• Dummy glass is very easy to get the vertical direction of the off-axis aspheric surface, so that it can be used to simulate CGH in Zemax.
• When compared phase distribution, all the fitting surface should unify the same coordinate system.
• B-spline interpolation can achieve the comparison of the CGH fringe position.
• An off-axis paraboloid is tested by CGH and autocollimation to prove the correction.

To design a computer-generated hologram (CGH) to measure off-axis aspheric surfaces with high precision, two different design methods are introduced: ray tracing and simulation using the Zemax software program. With ray tracing, after the discrete phase distribution is computed, a B-spline is used to obtain the phase function, and surface intersection is a useful method for determining the CGH fringe positions. In Zemax, the dummy glass method is an effective method for simulating CGH tests. Furthermore, the phase function can also be obtained from the Zernike Fringe Phase. The phase distributions and CGH fringe positions obtained from the two results were compared, and the two methods were determined to be in agreement. Finally, experimental outcomes were determined using the CGH test and autocollimation. The test result (PV=0.309λ, RMS=0.044λ) is the same as that determined by autocollimation (PV=0.330λ, RMS=0.044λ). Further analysis showed that the surface shape distribution and Zernike Fringe polynomial coefficient match well, indicating that the two design methods are correct and consistent and that the CGH test can measure off-axis aspheric surfaces with high precision.