Abstract

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 Δ = 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 2¹⁶, 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.

© 2000 Optical Society of America

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