Theoretical analysis of interferometer wave front tilt and fringe radiant flux on a rectangular photodetector

This paper is a theoretical analysis of mirror tilt in a Michelson interferometer and its effect on the radiant flux over the active area of a rectangular photodetector or image sensor pixel. It is relevant to sensor applications using homodyne interferometry where these opto-electronic devices are employed for partial fringe counting. Formulas are derived for radiant flux across the detector for variable location within the fringe pattern and with varying wave front angle. The results indicate that the flux is a damped sine function of the wave front angle, with a decay constant of the ratio of wavelength to detector width. The modulation amplitude of the dynamic fringe pattern reduces to zero at wave front angles that are an integer multiple of this ratio and the results show that the polarity of the radiant flux changes exclusively at these multiples. Varying tilt angle causes radiant flux oscillations under an envelope curve, the frequency of which is dependent on the location of the detector with the fringe pattern. It is also shown that a fringe count of zero can be obtained for specific photodetector locations and wave front angles where the combined effect of fringe contraction and fringe tilt can have equal and opposite effects. Fringe tilt as a result of a wave front angle of 0.05° can introduce a phase measurement difference of 16° between a photodetector/pixel located 20 mm and one located 100 mm from the optical origin.