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

Area of Science:

• Optical Physics
• Metrology
• Signal Processing

Background:

• Fourier transform interferometry is crucial for spectral analysis.
• Existing 1-bit analog-to-digital (AD) converter schemes often require oversampling, increasing complexity.
• Accurate spectral recovery from limited-bit data remains a challenge.

Purpose of the Study:

• To introduce a new technique for accurate Fourier transform interferometry using a 1-bit AD converter.
• To demonstrate a method that circumvents the need for oversampling.
• To enable high-resolution spectral analysis with simplified hardware.

Main Methods:

• Utilized sinusoid-crossing sampling to locate interferogram modulation term intersections with a reference sinusoid.
• Developed a novel autocorrelation-based procedure for recovering equally sampled amplitude data from crossing points.
• Applied the technique to determine the spectrum of an argon-ion laser.

Main Results:

• Achieved accurate Fourier transform interferometry with a 1-bit AD converter without oversampling.
• The developed method recovers the spectrum even in the presence of additive noise.
• Demonstrated performance equivalent to a 13-bit amplitude-sampling AD converter.

Conclusions:

• The proposed 1-bit AD converter technique offers a simplified and accurate approach to Fourier transform interferometry.
• Sinusoid-crossing sampling combined with autocorrelation-based recovery meets Nyquist criteria for spectral analysis.
• This method provides a cost-effective solution for high-resolution spectral measurements.