## High-Accuracy Fourier Transform Interferometry, Without Oversampling, with a 1-Bit Analog-to-Digital Converter

Applied Optics, Vol. 39, Issue 1, pp. 108-113 (2000)

http://dx.doi.org/10.1364/AO.39.000108

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### 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(2π

*f*

*), where*

_{r}z*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*} 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

_{i}*z*exists within each sampling interval Δ = 1/2

_{i}*f*, if

_{r}*A*≥ ‖

*s*(

*z*)‖ for all

*z*, and

*f*≥

_{r}*f*, where

_{c}*f*is the highest frequency component of

_{c}*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.

© 2000 Optical Society of America

**OCIS Codes**

(070.4790) Fourier optics and signal processing : Spectrum analysis

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

**Citation**

Vincent Ricardo Daria and Caesar Saloma, "High-Accuracy Fourier Transform Interferometry, Without Oversampling, with a 1-Bit Analog-to-Digital Converter," Appl. Opt. **39**, 108-113 (2000)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-1-108

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