Diffraction effects in length measurements by laser interferometry

Abstract

High-accuracy dimensional measurements by laser interferometers require corrections because of diffraction, which makes the effective fringe-period different from the wavelength of a plane (or spherical) wave λ₀. By using a combined X-ray and optical interferometer as a tool to investigate diffraction across a laser beam, we observed wavelength variations as large as 10^-8λ₀. We show that they originate from the wavefront evolution under paraxial propagation in the presence of wavefront- and intensity-profile perturbations.

Fake tilts in differential wavefront sensing

“…By comparing the laser-beam wavefront against the diffracting planes, our x-ray/optical interferometer highlighted λ/10 (peak-to-valley) errors having a periodicity equal to about the beam radius [20,21]. These observation suggests that the interfering beams might be contaminated by high-frequency modes, e.g., due to the imprinting of imperfections by the surfaces hit or crossed in the beam ways through the interferometer.…”

“…Since the interfering beams are made collinear to better than 20 µrad and the distance of the detection plane from the interferometer mirrors is less than 1 m, the 0.14w 0 ≈ 160 µm offset explaining the 1.3 nrad/mm gradient is more than the maximum 20 µm expected. The deviation from flatness of the interferogram -λ/10 peak-to-peak, see [20,21] -implies that |γ r,m |<35 mrad. By equating and differentiating Eqs.…”

“…expected when the offset between the axes of the interfering beams is 2 √ 2ξ 0 (solid line). The dashed line is the approximation Eq (21)…”

Wavefront errors in a two-beam interferometer

“…As shown in Figs. 2 and 3, they have σ ϕ = 10 nm and σ A = 0.025 standard deviations and were filtered so has to have the same correlation length of about 0.5 mm observed experimentally [17,18]. We did not consider the wavefront curvature and imperfect recombinations of the interfering beams, which might be modelled by amplitude and phase perturbations [6].…”

“…Characterizations of the laser beams leaving a combined x-ray and optical interferometer brought into light wavefront and wavelength ripples having a spatial bandwidth of a few mm −1 and amplitudes as large as ±20 nm [17] and ±10 −8 λ [18], respectively, which might have a detrimental effect on the accuracy of the measurements. Since the differential wavefront-errors -i.e., a non-uniform phase profile of the interference pattern -cannot be explained by aberrations of beam feeding the interferometer, we carried out an analysis of the effect of wavefront aberrations due to the interferometer optics.…”