You seem unaware of the fact that the effective wavelength varies as the cosine of the angle of incidence. This was established about a century ago (Tolansky, Williams and Francon and others cover this in their books on interferometry). Haidinger fringes (fringes of equal inclination) demonstrate this effect clearly.
Haidinger fringes are readily visible in microscope slides and cover glasses for example preferably in reflection for increased contrast. However despite some textbook claims they are also visible in transmission (at least by some).
The variation of effective wavelength with angle of incidence is important in gauge block interferometry particularly with large airgaps. NRC have shown that due to this effect the finite source diameter also has to be taken into account.
The consequence is that if one has a wedge airgap bounded by a pair of perfectly plane surfaces the fringes will not be perfectly straight if the angle of incidence (and consequently its cosine) vary along the fringe. The significance depends on the actual airgap and the change in the angle of incidence along the fringe. The effect is smallest for near normal incidence.
If the flat is viewed from an angle far from normal incidence the effect becomes more significant.
If for example the airgap were 10 microns for a particular fringe near and parallel to the edge of a square flat viewed from a distance of 10 times the length of a side of the flat being tested, then for near normal incidence the cosine of the angle of incidence varies from 0.99875 to 0.9975 from the center to the edge of the fringe. The fringe will deviate from a straight line by about 1/20 of a wave. The effect becomes worse for shorter viewing distances quadrupling to 0.2 waves when viewed from half the distance.
Should the flat be viewed from and angle of incidence of 45 degrees then the effect is much larger (around 14x for the above example).
Without an accurate value for the actual airgap correction for this effect isn't possible. If one has 20 fringes across the flat then for a 500nm source wavelength at best all that is known is that (for near normal incidence) the airgap varies by 5 microns in a direction normal to the fringes. In principle measurement at several wavelengths could be used as in gauge block interferometry to determine the actual airgap.
Edited by BGRE, 22 April 2019 - 05:28 PM.