Cyclic error compensation in interferometry systems

Abstract

The invention features a method including: (i) providing an interference signal S(t) from two beams directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time; (ii) providing one or more coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form Acos(ωt+φ(t)+ζ), where Aand ζare constants, ωis an angular frequency difference between the two beams before being directed along the different paths, and φ(t)=nk{tilde over (L)}(t), with k=2π/λ and λ equal to a wavelength for the beams; (iii) calculating a linear combination of values of the signal S(t); and (iv) reducing the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal generated from the coefficients and one or more error basis functions derived at least in part from the linear combination of values of the signal S(t).