Simple Analytical Model for Optimizing Integrating Sphere Port Sizes

TL;DR

This paper presents an analytical model to optimize port sizes in integrating spheres, improving measurement accuracy for low-haze materials by using energy conservation principles.

Contribution

It introduces a new analytical expression for optimizing integrating sphere port sizes, reducing reliance on trial-and-error or extensive simulations.

Findings

Derived an explicit formula for port size optimization

Enhanced measurement accuracy for low-signal applications

Simplified the design process for integrating spheres

Abstract

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).