New approach to high-precision Fourier transform spectrometer design

Laser fringes have long been used to establish the x axis in interferometric spectrometry, but solutions for the intensity axis have been less satisfactory. Now we are seeing the rapid commercial development of low-cost, medium-speed, sigma-delta analog-to-digital converters developed for stereo audio applications. A single chip provides two channels of 20-bit precision at 50 kHz, a significant improvement over many current systems of much greater cost and complexity. But while the laser works in the spatial domain, this converter operates strictly in the time domain; it cannot be triggered. I have developed a bridge between these two domains, the adaptive digital filter, which not only permits us to use this converter to obtain measurements at arbitrary times but as a bonus shows us how to move much of the complexity of an interferometric-control and data-acquisition system from hardware to software. For example, flexible fringe subdivision (to increase the free spectral range) is easily obtained with a simple and efficient algorithm, completely free of laser ghosts. Compensation for drive velocity variation is also possible, requiring only a modest increase in computer memory.