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

Abstract

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 λ). 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/η interference orders, in which η 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.

Corrections of the travelling-fringe period for the interference of aberrated beams

“…The dispersion relation for monochromatic plane waves in vacuum λ = c/ν-where the speed of light c = 299 792 458 ms −1 is prescribed by the International System of units-relates wavelength and frequency. However, plane waves are never realised in practice and limited monochromaticity [2][3][4][5], geometric phase [6][7][8], and diffraction [9][10][11][12][13][14][15][16][17][18][19][20][21][22] threaten the λ = c/ν relationship.…”

The new mise en pratique for the metre—a review of approaches for the practical realization of traceable length metrology from 10−11 m to 1013 m

“…A certain amount of 'parasitic light', which comes from an undesired mode of the resonator of a laser, can even lead to a relative error of a few parts in 10 7 when measuring a length, although the light frequency of the main mode was calibrated to a relative uncertainty of 10 −12 . As shown in [67] for a single parasitic light mode, the maximum effect on a length measurement is given approximately by 0.16/η fractional interference orders, where η is the ratio between the intensity of the main light mode and that of the parasitic light mode. It therefore appears desirable to have information about the amount of parasitic light.…”

Iodine frequency-stabilized HeNe laser amplified by injection locking of a semiconductor laser diode

“…Side-modes induce errors in interferometric measurements [13] thus special care has to be taken to avoid them. Using an optical spectrum analyser, a side-mode suppression ratio within the stable lock region of more than 27 dB is observed, which should induce an error of less than 0.1 nm in any interferometric measurement.…”