Errors in phase-measurement interferometry with high numerical apertures

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Abstract
If phase-measurement interferometry (PMI) is applied for a high numerical aperture (NA), specific errors can occur. The resulting phase no longer varies linearly with the height difference in the test surface. Thus, for height measurements, a constant correction factor or NA scaling factor, which depends only on the NA and the illumination of its stop, does not exist here. This is shown for several pupil illuminations (intensity ∼ cos2 α, intensity ∼ cos α, intensity constant; α is the incident angle). For example (NA = 0.9, pupil illumination intensity is constant, wedge angle ≈ 0, PMI phase increments = π/2 for normal incidence), the correction factor can vary from 1.20 (height difference ≈ 0) to 1.37 (height difference ≈ λ/4), i.e., by 17%.