and when multiplied by MTFDL. The smallest RMS error is for the version (Formula 10) in which there are three parameters. However we sought a formula with fewer parameters, in part because when there are many parameters, they tend not to be well-behaved with respect to pupil diameter. As will be seen below, we would also like to model the parameter variation with pupil diameter. None of the prior formulas (1–5) provided good fits, especially when number of parameters is considered. In most cases, the inclusion of the MTFDL or =MTFDL term reduces the error, sometimes by a large amount. Of the formulas we considered with two or fewer parameters, the lowest error (RMS¼0.33) was for Formula 9, using =MTFDL. The error was almost as low (RMS¼0.37) for a variant (Formula 8, multiplied by =MTFDL) in which the second parameter (the exponent on the Lorentzian) is fixed at 0.62.