Continuous wavelet transform ridge extraction for spectral interferometry imaging

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a monomode fiber in a small endoscope. The local depth of the imaged object is encoded in the local spatial frequency of the signal measured at the output of the fiber-decoder system. We propose a procedure to retrieve the depth-map by determining the signal's instantaneous frequency. First, we compute its continuous, complex-valued, wavelet transform (CWT). The frequency signature at every position is contained in the resulting scalogram. We then extract the ridge of maximal response by use of a dynamic programming algorithm thus directly recovering the object's topography. We present results that validate this procedure based on both simulated and experimental data.