Waveform metrology and a quantitative study of regularized deconvolution

We present methodology and preliminary results of a Monte-Carlo simulation to perform a quantified analysis of regularized deconvolution in the context of full waveform metrology. We analyze the behavior of different regularized inversion methods with varying dimensionless parameters that serve as indicators of the problem difficulty, including: the ratio of input pulse duration to that of the system impulse response, signal to noise ratio, pulse shape, and/or the ratio of high frequency roll-off of input to system response. We characterize the waveform estimates in terms of pulse parameters and total error, comparing different Tikhonov deconvolution algorithms as well as commonly used heuristic approaches. We present a quantitative comparison of the relative merits of the different procedures, and compare the numerical performance with asymptotic analyses.