Principal components generalized projections: a review [Invited]

Frequency-resolved optical gating (FROG) is a technique used to measure ultrafast laser pulses by optically producing a spectrogram, or FROG trace, of the measured pulse. While a great deal of information about the pulse can be gleaned from its FROG trace, quantitative pulse information must be obtained using an iterative two-dimensional phase retrieval algorithm. A general spectrogram/sonogram inversion algorithm called principal components generalized projections (PCGP) that can be applied to pulse measurement schemes, such as FROG, is reviewed. The algorithm is fast, robust, and can invert FROG traces in real time, making commercial pulse measurement systems based on FROG a reality. Measurement rates are no longer algorithm limited; they are data-acquisition limited. Also, because of some of its unique properties, the PCGP algorithm has found applications in measuring attosecond pulses and measuring telecommunications pulses. In addition, the PCGP structures the inversion and measurement process in a way that can allow new insights into convergence properties of spectrogram and sonogram inversion algorithms. (C) 2008 Optical Society of America.