Effect of an optical coating on in-band and out-of-band transmitted and reflected wavefront error measurements

The wavefront error (WE) of a surface with an optical coating ("filter") is ideally measured at the in-band wavelength of the filter. However, quite often this is not possible, requiring that the filter be measured at an out-of-band wavelength (typically 633 nm), assuming that the filter transmits (for transmitted WE, or TWE) or reflects (for reflected WE, or RWE) at this wavelength. This out-of-band TWE/RWE is generally assumed to provide a good estimation of the desired in-band TWE/RWE. It will be shown in this paper that this is not the case for a large class of filters (i.e., bandpass) where the group delay is significantly different at the in-band and out-of-band wavelengths and where the optical filter exhibits a thickness non-uniformity across the surface. A theoretical explanation will be given along with an approach to predict the in-band TWE/RWE based on the coating non-uniformity, the measured out-of-band TWE/RWE, and the theoretical properties of the optical filter at the in-band and out-of-band wavelengths. A reasonable agreement between theory and measurement was demonstrated by measuring the TWE of an 11 nm wide bandpass filter (centered at 1048 nm) at both in-band (λ=1048nm) and out-of-band (λ=625nm) wavelengths. A similar treatment is provided for RWE.