beam propagating on the optical axis, proportional to the cross-product , is retained. This signal is then recorded by a slow detector, which measures is exactly the intensity autocorrelation . The generation of the second harmonic in crystals is a nonlinear process that requires high peak power, unlike the previous setup. However, such high peak power can be obtained from a limited amount of energy by ultrashort pulses, and as a result their intensity autocorrelation is often measured experimentally. Another difficulty with this setup is that both beams must be focused at the same point inside the crystal as the delay is scanned in order for the second harmonic to be generated. It can be shown that the intensity autocorrelation width of a pulse is related to the intensity width. For a Gaussian time profile, the autocorrelation width is longer than the width of the intensity, and it is 1.54 longer in the case of a hyperbolic secant squared (sech2) pulse. This numerical factor, which depends on the shape of the pulse, is sometimes called the deconvolution factor. If this factor is known, or assumed, the time duration (intensity width) of a pulse can be measured using an intensity autocorrelation. However, the phase cannot be measured. Interferometric autocorrelation As a combination of both previous cases, a nonlinear crystal can be used to generate the second harmonic at the output of a Michelson interferometer, in a collinear geometry. In this case, the signal recorded by a slow detector is is called the interferometric autocorrelation. It contains some information about the phase of the pulse: the fringes in the autocorrelation trace wash out as the spectral phase becomes more complex. Pupil function autocorrelation The optical transfer function T(w) of an optical system is given by the autocorrelation of its pupil function f(x,y): See also Autocorrelator Convolution Degree of coherence Frequency-resolved optical gating Multiphoton intrapulse interference phase scan Spectral phase interferometry for direct electric-field reconstruction References Optical metrology Nonlinear optics Laser science