Precise phase theory for accuracy improvement in a fiber probe interferometer for nanometric sensing, taking into account fiber coupling

In a single-mode-fiber probe type of interferometer, the effect of fiber coupling on the sensing performance is theoretically comprehensively investigated in order to analyze and improve the achievable sensing accuracy for nanometric sensing. In both direct and via-lens coupling schemes for the interferometer, the scale factors to deduce optical path length change from the measured phase are analytically and numerically examined in terms of deviation from the plane wave assumption of conventional use. It is manifested that the scale factor deviation is of considerable magnitude in the case of direct coupling, but, by the incorporation of suitable collimating optics for coupling, the degree of deviation can be drastically reduced to as small as typically 10 − 8 , supporting achievement of ultrahigh accuracy such as picometer in displacement sensing. The effect of reflector tilting is also addressed.