The previous section gave the theoretical basis for deriving an effective F-Number definition.  Now, the integral in Eq. (1) is also known as the image space "projected solid angle" or PSA in classical radiometry.  As such, we can write:

   [Eq. 3]

If we again write f/No._eff = 1/(2NA_eff), and substitute Eq. (3) into this, we arrive at the defined effective F-Number as written in the Zemax manual.  The PSA of an imaging system is routinely calculated in Zemax to determine the relative illumination of the optical design. 

Since the PSA may be calculated for all off axis field points, the effective F-Number may also be defined for all off axis points on the image plane.  Try it! - Open up your favorite lens design in Zemax and click on the drop down menu for relative illumination under Analysis > Illumination > Relative Illumination.  A window appears displaying the system relative illumination.  Then click on the text button of that window and you see a list of effective F-Number values as a function of field (you must of course define your field points first). 

For other details, consult the Zemax user's manual⁴.  Thus, we now have a very practical way of calculating the effective F-Number of an optical imaging system with arbitrary stop shape, based on very fundamental radiometric principles.