Temperature-programmed desorption (TPD) measurements ate carried out in a molecular beam epitaxy (MBE) growth chamber on pseudomorphic GaAs/In0.22Ga0.78As(125 Angstrom)/GaAs single quantum wells in various stages of growth, using a line-of-sight mass spectrometer for quantitative desorption analysis. The presence of surface-segregated indium is inferred from the appearance of a relatively low binding energy (E(b) approximate to 1.5 eV) peak in the indium TPD spectra. Integration of this TPD peak provides a quantitative measure of the surface-indium population Theta(In). By incorporating the TPD experiment as a subroutine in the MBE growth program, systematic variations of growth parameters are effected and their influence on Theta(In) established. Detailed composition profiles are calculated and found to be in excellent agreement with previous results [Nagle et al., J. Cryst. Growth 127, 550 (1993)]. We find that both the bottom (InGaAs on GaAs) and top (GaAs on InGaAs) interfaces are graded over as much as 10 monolayers, with the bottom interface being indium-poor, due to the sacrificial buildup of Theta(In), and the top interface being characterized by segregation of indium into the GaAs cap, due to relatively slow incorporation of Theta(In) into the lattice after closing the indium shutter. A mon "squarelike" bottom interface is obtained by predeposition of a thin indium layer just before InGaAs growth, while a more "squarelike" top interface is obtained by "flash-off" of Theta(In) just after InGaAs growth. It is believed that the combination of predeposition plus flash-off produces a more truly square InGaAs/GaAs quantum well than that obtained by more standard MBE growth approaches.