Beam-astigmatism in laser interferometry

Abstract

We have developed a null laser interferometer capable of picometer resolution in fringe division for the measurement of the silicon (220) lattice spacing by X-ray interferometry., With a view to achieving 10(-9) measurement uncertainty, we hale given special attention to the effects of diffraction, An analysis of the measurements which has brought to Light wavefront astigmatism? the effect of which had so far been overlooked, is presented, This article show's how astigmatism affects measurements, describes how we determine beam parameters, and compares theoretical and experimental results

Scanning X-ray interferometry and the silicon lattice parameter: towards relative uncertainty?

“…Other errors are caused by the way the guiding system is driven [20]. The crystal movement undergoes minute oscillations with periodicity Λ ≈ 0.11 mm and amplitude A ≈ 10 nm.…”

“…We studied diffraction by using the Gaussian approximation [18] of the laser beam, and then we extended the analysis to beam shear [19] and astigmatism [20]. However, millimeter scans, permitting an increase of one order of magnitude in resolution, put the matter in a different light.…”

Diffraction effects in length measurements by laser interferometry

“…In high-accuracy dimensional measurements by laser interferometry, one of the largest corrections required is due to diffraction. Examples are the measurements of Si lattice-parameter by combined X-ray and optical interferometry [1][2][3][4], of gravity by free-fall gravimeters [5][6][7], and of diameters by Fizeau interferometers [8][9][10][11][12][13]. At the 10 −9 level of relative accuracy it is not possible to trace back wavelength to frequency via the plane-wave dispersion equation.…”

Vectorial ray-based diffraction integral

“…Plane or spherical waves were assumed to relate the phase of the interference fringes to the measurand, but, as early as 1976, Dorenwendt and Bönsch pointed out that this is not correct and that diffraction brings about systematic errors [2]. Since then, metrologists have routinely applied corrections based on scalar and paraxial approximations of the interferometer operations [3][4][5][6][7][8][9][10][11][12][13]. In recent years, cutting-edge interferometric measurements carried out to determine the Avogadro constant are looking at 1 × 10 −9 relative accuracies over propagation distances of the order of 1 m and propagation differences of many centimeters.…”