NOISE SENSITIVITY IN FREQUENCY-RESOLVED OPTICAL-GATING MEASUREMENTS OF ULTRASHORT PULSES

Frequency-resolved optical gating(FROG), a technique for measuring ult rashort laser pulses, involves producing a spectrogram of the pulse an d then retrieving the pulse intensity and phase with an iterative algo rithm. We study how several types of noise-multiplicative, additive, a nd quantization--affect pulse retrieval. We define a convergence crite rion and find that the algorithm converges to a reasonable pulse held, even in the presence of 10% noise. Specifically, with appropriate fil tering, 1% rms retrieval error is achieved for 10% multiplicative nois e, 10% additive noise, and as few as 8 bits of resolution. For additiv e and multiplicative noise the retrieval errors decrease roughly as th e square root of the amount of noise. In addition, the background indu ced 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 measure d 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 tr ace. Consequently, in the presence of additive noise, baseline subtrac tion is important. We also find that Fourier low-pass filtering improv es pulse retrieval without introducing significant distortion, especia lly in high-noise cases. We show that the field errors in the temporal and the spectral domains are equal. Overall, the algorithm performs t ell because the measured trace contains N-2 data points for a pulse th at has only 2N degrees of freedom; FROG has built in redundancy. (C) 1 995 Optical Society of America