Aspheric surface metrology: Fringe phase modeling and iterative optimization with radial shearing interferometry

We propose a nonnull testing method for aspheric surfaces using a radial shearing interferometer (RSI) combined with iterative optimization. The RSI minimizes the departure of aspheric surfaces, making it suitable for surfaces with large asphericity due to its self-reference property. First, we modeled the RSI using ray-tracing software, allowing the resulting interference fringes to be easily revealed. An experimental setup was constructed based on this modeling, and the corresponding interference fringes were collected. The modeling's geometrical constraints and aspheric parameters were iteratively optimized to achieve good agreement between the departure wavefronts in the experiment and the simulation. We identified the positions and parameters in the modeling that represent the experimental setup, enabling the accurate measurement of the waviness of the aspheric surface under test.