Photoelectric Fringe Signal Information and Range in Interferometers with Moving Mirrors*

Abstract

Photoelectric receptors and electronics have greatly increased the accuracy and simplicity of interferometric measurements. Theoretical and experimental investigations of instrumental and light source conditions required to ensure adequate information content and “visibility” of fringe signals have been made. Mirror parallelism requirements needed to maintain maximum signal modulation and to reduce apparent local displacement errors, for use with equal inclination interferometers, are expressed by the fractional number of equal thickness fringes within the mirror aperture, the sensitivity to varying rotation along the mirror traverse being reducible by decreasing this aperture and ensuring best local parallelism. The “effective” length per fringe, determined by photoelectric flux integration over an angular range within the source angular radius αs is approximately (λ/n)/2(1−αs2/4). Theoretical expressions obtained for the fringe “visibility” with simple single isotope lines of Gaussian shape are in good accord with experiments, showing that the fringe amplitude with perfectly adjusted continuously moving interferometers is governed by an expression of the form exp[-4π2l2σ2n2][sin(πlαs2n/λ)/(πlαs2n/λ)]×[cos{[2πl(1-αs2/4)]/[(λ/n)/2]}],usable for estimating interferometric range with such sources as the green Hg 198 line with an effective Gaussian width of about two Doppler widths at room temperatures. The further extension of interferometric range with measurement precisions of 1 part in 108 over traverses exceeding 300 mm appears feasible.