The effect of a parasitic light mode in length measurements by interferometry

Light sources are typically assumed to be monochromatic when these are used for length measurements by interferometry, especially for the primary realization of the length. From the calibrated frequency of the light source, the (vacuum-) wavelength can be calculated which is generally assumed to be identical with the path length which corresponds to a single interference order (l = 1/2 lambda). While this assumption is correct for an ideal interference of two plane waves, it does not hold when the light is not perfectly monochromatic. This paper demonstrates that a certain amount of 'parasitic light', originating from an unwanted mode of a laser's resonator, can lead to a relative error in the order of 10(-7) in a length measurement although the light frequency of the main mode was calibrated on a relative level of 10(-12). The theoretical concept comprising a four-beam interference was confirmed experimentally by comparative length measurements in vacuum. Moreover, for a single parasitic light mode it was demonstrated that the maximum effect onto a length measurement is approximately given by 0.16/eta interference orders, in which eta is the ratio between the intensity of the main light mode with respect to that of the parasitic light mode. As a conclusion it seems necessary to formulate additional requirements for light sources to be used in length measurements by interferometry, especially when these are intended to be used for the primary realization of the length.