Abstract

The SPIDER technique has become one of the most important tools for characterizing femtosecond laser pulses [1], As a self-referencing variant of spectral interferometry, SPIDER allows for direct analytical reconstruction of the spectral phase from measured data. The absence of iterative reconstruction steps makes SPIDER the ideal choice for video-rate measurements of the pulse shape and has been demonstrated with acquisition rates up to 1 kHz [2], So far phase retrieval has nearly exclusively been based on the Takeda algorithm [3], i.e., a Fourier filtering technique originally proposed for application in holography. The Takeda algorithm greatly benefits from the fast Fourier transform and enables real-time pulse characterization with update rates beyond 10 Hz. Recently, it has been suggested that wavelet based phase retrieval is more robust for phase extraction in spectral interferometry applications [4], Wavelet spectrograms allow for localization of the energy content of a waveform in frequency and time, limited only by Heisenberg’s uncertainty principle. These properties translate into an increased robustness and reduced artifacts of the phase retrieval procedure as compared to traditional Takeda-based retrieval. Unfortunately, complete mapping out of the wavelet spectrogram is numerically very intense. Even on modem computers it may still require several minutes of CPU time as the required computation time scales with the third power of the number of data points. Similar to fast Fourier transforms, accelerated wavelet algorithms exist but are restricted to efficient computation of the wavelet transform for a sparse sequence of delay coordinates δτ ∝2ⁿ, which makes them impractical for precise phase retrieval applications.

© 2007 IEEE