Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses

Frequency-resolved optical gating (FROG), a technique for measuring ultrashort laser pulses, involves producing a spectrogram of the pulse and then retrieving the pulse intensity and phase with an iterative algorithm. We study how several types of noise—multiplicative, additive, and quantization—affect pulse retrieval. We define a convergence criterion and find that the algorithm converges to a reasonable pulse field, even in the presence of 10% noise. Specifically, with appropriate filtering, 1% rms retrieval error is achieved for 10% multiplicative noise, 10% additive noise, and as few as 8 bits of resolution. For additive and multiplicative noise the retrieval errors decrease roughly as the square root of the amount of noise. In addition, the background induced in the wings of the pulse by additive noise is equal to the amount of additive noise on the trace. Thus the dynamic range of the measured intensity and phase is limited by a noise floor equal to the amount of additive noise on the trace. We also find that, for best results, a region of zero intensity should surround the nonzero region of the trace. Consequently, in the presence of additive noise, baseline subtraction is important. We also find that Fourier low-pass filtering improves pulse retrieval without introducing significant distortion, especially in high-noise cases. We show that the field errors in the temporal and the spectral domains are equal. Overall, the algorithm performs well because the measured trace contains N2 data points for a pulse that has only 2N degrees of freedom; FROG has built in redundancy.  1995 Optical Society of America