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Abstract
The wavefront distortion (WFD) of a surface with an optical filter coating is ideally measured at the operating wavelength ($\lambda$) and angle of incidence (${\theta}$) of the filter. However, this is not always possible, requiring that the filter be measured at an out-of-band wavelength and angle (typically $\lambda = {633}\;{\rm nm}$ and ${\theta} = 0^{\circ}$). Since the transmitted wavefront error (TWE) and reflected wavefront error (RWE) can depend on the measurement wavelength and angle, an out-of-band measurement may not give an accurate characterization of the WFD. In this paper, we will show how to predict the wavefront error (WFE) of an optical filter at the in-band wavelength and angle from a WFE measurement at an out-of-band wavelength and different angle. This method uses (i) the theoretical phase properties of the optical coating, (ii) the measured filter thickness uniformity, and (iii) the substrate’s WFE dependence versus the angle of incidence. Reasonably good agreement was achieved between the RWE measured directly at $\lambda = {1050}\;{\rm nm}$ (${\theta} = \;{45}^\circ$) and the predicted RWE based on an RWE measurement at $\lambda = {660}\;{\rm nm}$ (${\theta} = {0}^\circ$). It is also shown through a series of TWE measurements using a light emitting diode (LED) and laser light sources that, if the TWE of a narrow bandpass filter (e.g., an 11 nm bandwidth centered at $\lambda = {1050}\;{\rm nm}$) is measured with a broadband LED source, the WFD can be dominated by the chromatic aberration of the wavefront measuring system—hence, a light source that has a bandwidth narrower than the optical filter bandwidth should be used.
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