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

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(2pif(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 Delta = 1/2f(r), if A >or= |s(z)| for all z, and f(r) >or= 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.