  The integrating sphere (IS) is an indispensable tool for measuring
transmission and scattering of materials and their colorimetry, as well as
other photometric tasks. The accuracy of its data depends critically on port
sizes used for measurement and control, usually defined by trial and error or
brute-force optical simulations. To find the optimal port sizes of this
powerful tool, a sample visibility function is defined and optimized using the
energy conservation principle. This yields an analytical expression that should
be useful in a variety of applications, especially those where signal is rather
small (low-haze materials).
