System design of a single-shot reconfigurable null test using a spatial light modulator for freeform metrology

We report the simulation of an adaptive interferometric null test using a high-definition phase-only spatial light modulator (SLM) to measure form and mid spatial frequencies of a freeform mirror with a sag departure of 150 μm from its base sphere. A state-of-the-art commercial SLM is modeled as a reconfigurable phase computer generated hologram (CGH) that generates a nulling phase function with close to an order of magnitude higher amplitude than deformable mirrors. The theoretical uncertainty in form measurement arising from pixelation and phase quantization of the SLM is 50.62 nm RMS. The calibration requirements for hardware implementation are detailed.