Abstract
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 2nd-order and 4th-order aberrations have the same sign and calculate the minimum defocused distance (power carrier frequency) of CGH. According to the marginal-ray heights (h1andh3) 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.
Highlights
Aspheric surface can improve the performance of the optical system and reduce its complexity, so it is widely used in modern optical systems, such as astronomical telescopes and photolithographic lenses
Since the stray rays pass through Computer-generated hologram (CGH) twice, we denote the spurious diffraction orders (SDO) as (k1, k2), where k1 and k2 is the diffraction order of CGH in the first and second pass, respectively
Since our model considers the effect of the pupil distortion, even if there are two rays passing the same point on the CGH in the second pass, the ray error calculated by our model agrees well with that calculated by real ray trace
Summary
Aspheric surface can improve the performance of the optical system and reduce its complexity, so it is widely used in modern optical systems, such as astronomical telescopes and photolithographic lenses. Lindlein derived the 1storder ray model to analyze the SDO of symmetric CGH when testing convex aspheric part and CGH was laid close to convex aspheric part [6] They argued the SDO (−1, 3) and (3, −1) has the most significant effect on measurement accuracy and calculated the minimum amount of power carrier frequency to separate SDO. They analyzed the SDO of non-symmetric CGH and calculated the minimum amount of tilt carrier frequency when testing conic surfaces with a large F# (larger than 4) They proposed the necessary condition to separate SDO by tilt carrier frequency when testing paraboloid: the paraxial center of the paraboloid should be inside the focus of transmission sphere. The ray error on pinhole calculated by our model is compared with that calculated by real ray trace to validate our model
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