Holographic radius test plates for spherical surfaces with large radius of curvature

We describe a novel interferometric method, based on nested Fresnel zone lenses or photon sieves, for testing and measuring the radius of curvature of precision spherical surfaces that have radii in a range between several meters and a few hundred meters. We illustrate the measurement concept with radius measurements of a spherical mirror with a radius of about 10 m. The measured radius is 9877 mm±10 mm for a coverage factor k=2. Our measurements also demonstrate, for the first time to the best of our knowledge, the utility of photon sieves for precision surface metrology because they diffuse higher diffraction orders of computer generated holograms, which reduces coherent noise.