Frequency-resolved Optical Gating - Measurement Confirmation

Measurement Confirmation

One important feature of a FROG measurement is that many more data points are collected than are strictly necessary to find the pulse electric field. For example, say that the measured trace consists of 128 points in the delay direction and 128 points in the frequency direction. There are 128x128 total points in the trace. Using these points, an electric field is retrieved that has 2x128 points (128 for magnitude and another 128 for the phase). This is a massively overdetermined system, meaning that the number of equations is much larger than the number of unknowns. Thus the importance of each individual data point being absolutely correct is greatly reduced. This is very helpful for real world measurements that can affected by detector noise and systematic error. Noise is extremely unlikely to affect the measured trace in a way that could be confused with a physical phenomenon in the pulse. The FROG algorithm tends to “see through” these effects due to the amount of extra information available and the use of a mathematical form constraint in finding a solution. This means that the error between an experimental FROG trace and a retrieved FROG trace is rarely zero, although it should be quite small for traces without systematic error.

Consequently, significant differences between measured and retrieved FROG traces should be investigated. The experimental setup may be misaligned, or there may be significant spatio-temporal distortions in the pulse. If the measurement averages over several or many pulses, then those pulses may vary significantly from each other.