Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors

Abstract

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). The etching of the CGH pattern must be highly accurate to create desired wavefronts. Variations of line width, etching depth, and surface roughness cause unwanted wavefront errors. The sensitivity to these manufacturing errors is studied using scalar diffraction analysis. We provide a parametric model that can be used for optimizing the CGH design to give good diffraction efficiency and limited sensitivity to manufacturing errors.

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

“…2. The focus 0 I of the transmission sphere is first imaged to 1 I by CGH (the first subsystem), then 1 I is imaged to 2 I by the testing part (the second subsystem), and 2 I is finally imaged to 3 I by the CGH again (the third subsystem). For convenience in discussing the disturbed area on CGH, we assume the exit pupil of the CGH null system is placed on CGH in the image space of the third subsystem.…”

“…6, the sphere 1 sp , centered at the Gaussian image point 3 I , is the Gaussian reference sphere and the sphere 2 sp , centered at the focus 0 I (cat eye), is the cat-eye reference sphere. The ray intersects with 1 sp and 2 sp at 1 N and 2 N , respectively.…”

“…The aberration in Eq. (14) is observed at the sphere 1 sp , but to analyze the spurious diffraction orders, we need to obtain the aberration coefficients at the sphere 2 sp . This change of the reference sphere results in an extra aberration …”

“…However, since aspheric surface is not self-collimated under spherical wavefront, i.e., the testing rays do not impinge normally on aspheric part, it cannot be directly tested under standard interferometer. Computer-generated hologram (CGH) is often inserted between the aspheric part and the transmission sphere to transfer spherical wavefront to match the aspheric one [1][2][3].…”

Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

“…Enough carrier frequency must be applied to the CGH to spatially isolate the wanted order, followed by a pinhole placed at the focal plane to block the unwanted ones. However, superfluous carrier frequency merely decreases the line spacing of the CGH, thus driving the cost up and the accuracy down [9,10]. Searching for an admissible carrier frequency within the fabrication limits is one of the designers' destinies.…”