Interferometry at the Physical Limit: How to Measure Sub-Parts-Per-Million Optical Homogeneity in Fused Silica

Inspection of the refractive-index distribution in fused silica is very sensitive to thermally induced measurement errors. A model is derived for the estimation and interpretation of thermal errors applicable to interferometric homogeneity investigations. The outlines of the model are supported by experimental investigations and numerical calculations. The results state a mandatory temperature stability of (delta)T = 0 .02 K for a required reproducibility of (sigma)((delta)n ) <= 1 x 10^-7 and a lower sensitivity of higher-order Zernike terms. Requirements of the interferometer environment include spatial and temporal stability. Only a small part of the frequency spectrum of temporal instabilities contributes significantly to the measurement error and is therefore critical for the system. Experimental values are given for different environmental conditions.