Numerical fringe pattern demodulation strategies in interferometry

The performance of two different numerical frequency demodulation strategies for evaluating sampled fringe patterns in interferometric applications and optics is discussed. Namely, these techniques involve traditional Fourier filtering techniques and a strategy based on the Gabor wavelets. While the latter is found to be more precise, it is generally difficult to implement wavelet-based frequency demodulation with equal performance as methods based on the fast Fourier transform. Here, we demonstrate a specialized fast wavelet algorithm that outperforms Fourier-based strategies for array sizes up to a few thousand data points and is yet more precise. The performance is investigated in numerical examples, indicating that the required choice of a global filter bandwidth is one of the main problems of the Fourier filtering strategy. Wavelet frequency demodulation, in contrast, always appears to perform slightly better, does not require judicious choice of filtering, and can often be made equally fast without loss of precision. Finally, applying this new algorithm to an ideal sinusoidal signal without noise, the precision of the numerical frequency demodulation is increased by nearly two orders of magnitude.