with the incidence angle. Thus, the initial focus must be tight enough to include the entire spectrum of the pulse. After the SHG crystal, cylindrical lenses are used to image the signal onto a camera with wavelength mapped vertically while the delay is mapped horizontally. Overall, a number of things occur in the crystal: First, the two beams or pulses from the biprism are being crossed at a very large angle which acts as a single-shot autocorrelator, self-gating the pulse to produce a varying delay in the horizontal direction. In the vertical direction, the limited phasematched bandwidth of the crystal phasematches a different small portion of the input pulse bandwidth for each incidence angle, effectively acting as a spectrometer. The end result is the wavelength spectrum in the vertical direction for each amount of delay in the horizontal direction. It is important to consider the ‘thick’ SHG crystal requirements. In a normal second harmonic generation, the goal is to minimize the group-velocity mismatch (GVM) in order to maximize phase-matching bandwidth. This is typically achieved by requiring the fundamental and second harmonic wavevectors to overlap throughout the crystal length, L. However, in a GRENOUILLE the goal is to only phasematch a portion of the pulse bandwidth in order to act as a frequency filter. This leads to the constraint that the product of the GVM and L must be much greater than the pulse length, . Using the definition of GVM for SHG where is the group velocity at wavelength, , the constraint is In addition, if the crystal is too thick, the accumulation of group-velocity dispersion (GVD) will cause excessive pulse spreading. To prevent this, the product of GVD and crystal length L should be much less than the pulse coherence time, , which is the reciprocal of the bandwidth. Using the definition of GVD where is the pulse bandwidth, leads to the form These two constraints can be rearranged and combined to get The time-bandwidth product (TBP) of a pulse is defined as the ratio of pulse length to pulse coherence time, . This means that a crystal length L will satisfy the simultaneous condition above if which is considered the fundamental relationship of the system. From this, it can be seen that material properties and crystal dimensions will affect GRENOUILLE's temporal and spectral resolution. In addition, the depth of focus into the crystal can produce an effectively shorter