Study of the Errors in Interpolated Fast Fourier Transform for Interferometric Applications

Abstract

Frequency estimation is often the basis of various measurement techniques, among which optical distance measurement stands out. One of the most used techniques is interpolated fast Fourier transform due to its simplicity, combined with good performance. In this work, we study the limits of this technique in the case of real signals, with reference to a particular interferometric technique known as self-mixing interferometry. The aim of this research is the better understanding of frequency estimation performances in real applications, together with guidance on how to improve them in specific optical measurement techniques. An optical rangefinder, based on self-mixing interferometry, has been realized and characterized. The simulation results allow us to explain the limits of the interpolated fast Fourier transform applied to the realized instrument. Finally, a method for overcoming them is proposed by decorrelating the errors between the measurements, which can provide a guideline for the design of frequency-modulated interferometric distance meters.