High-accuracy Fourier transform interferometry, without oversampling, with a 1-bit analog-to-digital converter

摘要

We demonstrate a new technique for performing accurate Fourier transform interferometry with a 1-bit analog-to-digital (AD) converter that does not require oversampling of the interferogram, unlike in other 1-bit coding schemes that rely on delta-sigma modulation. Sampling aims at locating the intersections {z_(i)} of the modulation term s(z) of the interferogram and a reference sinusoid r(z)=A cos(2πf_(r)Z), where z is the optical path difference. A new autocorrelation-based procedure that includes the accurate recovery of the equally sampled amplitude representation {s(k)} of s(z) from {z_(i)} is utilized to calculate the square of the emission spectrum of the light source (sample). The procedure is suitable for interferograms that are corrupted with additive noise. Sinusoid-crossing sampling satisfies the Nyquist sampling criterion, and a z_(i) exists within each sampling interval △=1/2f_(r), if A≥|s(z)| for all z, and f_(r)≥f_(c), where f_(c) is the highest frequency component of s(z). By locating a crossing at an accuracy of 1 part in 2~(16), we determine the multimode spectrum of an argon-ion laser with a 1-bit AD converter that performs like a 13-bit amplitude-sampling AD converter.