Fourier transform with matched non-linear frequency modulation in femtosecond laser ranging with imbalanced dispersion

We propose a new algorithm based on the Fourier transform with matched non-linear frequency modulation for processing femtosecond laser ranging data. The algorithm allows us to compensate for both the influence of the third-order dispersion in the fiber-based dispersive Fourier spectrometer and the influence of imbalanced second- and third-order dispersions in the interferometer. Computer simulations and experimental results show that the proposed algorithm significantly increases the accuracy of measuring the position of an object at larger displacements than the well-established non-linear time stretching.