Improving speed and precision of local frequency analysis using Gaussian ridge interpolation for wavelet and windowed Fourier ridge algorithms

• Wavelet and windowed Fourier analysis allow to extract local phase and frequency of fringe images.
• A 3-point Gaussian ridge interpolation is used to improve precision and speed of local frequency estimation.
• For wavelet ridge analysis, the speed-up was 3 times while using 4 times less memory.
• For windowed Fourier ridge analysis, the speed-up was 15 times while using 16 times less analysing frequencies.
• The improvement in precision for both techniques can go up to 2 times for moderate signal to noise ratios (SNR=20)(SNR=20).

When analysing fringe images, wavelet and windowed Fourier ridge algorithms allow to extract phase and local frequency even in the presence of considerable noise levels. However, the precision of the local frequency information is often limited by the relatively small number of analysing frequencies used in practice. This on account of the direct trade-off between frequency precision and processing time, which can become prohibitive in some cases. In the present paper, a method is shown capable of reducing the processing time by a factor 3 for the wavelet ridge technique and by up to 15 times for the windowed Fourier ridge algorithm. This is accomplished by a 3-point Gaussian ridge interpolation. This approach is also shown to lead to an improved frequency precision for moderate noise levels.