Four-dimensional calibration of a Multiple Aperture Shear-Interferometer

In full-field metrology of wave fields there may be a range of incident angles (α, β) of surveyed wave fields permitted at every point (x, y) in the measurement plane. These incident angles each correspond to a different path through the measurement system. Thus, systematic errors of the system depend on coordinates in the measurement plane as well as incident angles. To calibrate such a system a four-dimensional calibration function Δ(x, y, α, β) is necessary. A recently developed full-field method is the Multiple Aperture Shear-Interferometry (MArS) for measuring aspheric and freeform surfaces. MArS uses the mutual coherence function as a primary measurand allowing for simultaneous measurement of multiple independent wave fields. Consequently, partially overlapping illumination apertures are permitted which implies a variety of incident angles at any given point. We present a strategy for calibration of a MArS-interferometer which may be generalized for other full-field methods. The calibration is based on spherical waves of known origin and uses nested Zernike-polynomials as a calibration function. We test this calibration for the case of multiple superpositioned wave fields.