Simple Analytical Model for Optimizing Integrating Sphere Port Sizes

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).