Integrating sphere

An integrating sphere (also known as an Ulbricht sphere) is an optical component consisting of a hollow spherical cavity with its interior covered with a diffuse white reflective coating, with small holes for entrance and exit ports.

An integrating sphere may be thought of as a diffuser which preserves power but destroys spatial information.

In 1892, W. E. Sumpner published an expression for the throughput of a spherical enclosure with diffusely reflecting walls.

[1] R. Ulbricht developed a practical realization of the integrating sphere, the topic of a publication in 1900.

[2] It has become a standard instrument in photometry and radiometry and has the advantage over a goniophotometer that the total power produced by a source can be obtained in a single measurement.

[3] Even small commercial integrating spheres cost many thousands of dollars, as a result their use is often limited to industry and large academic institutions.

However, 3D printing and homemade coatings have seen the production of experimentally accurate DIY spheres for very low cost.

An integrating sphere can be used to create a light source with apparent intensity uniform over all positions within its circular aperture, and independent of direction except for the cosine function inherent to ideally diffuse radiating surfaces (Lambertian surfaces).

An integrating sphere can be used to measure the diffuse reflectance of surfaces, providing an average over all angles of illumination and observation.

A number of methods exist to measure the absolute reflectance of a test object mounted on an integrating sphere.

[7] Subsequent work by A. H. Taylor,[8][9] Frank A. Benford,[10][11] C. H. Sharpe & W. F. Little,[12] Enoch Karrer,[13] and Leonard Hanssen & Simon Kaplan[14][15] expanded the number of unique methods which measure port-mounted test objects.

Edwards et al.,[16] Korte & Schmidt,[17] and Van den Akker et al.[18] developed methods which measure center-mounted test objects.

The sphere creates a reference radiation source that can be used to provide a photometric standard.

High-powered illumination sources may heat or damage the coating, so an integrating sphere will be rated for a maximum level of incident power.

The theory of the integrating sphere assumes a uniform inside surface with diffuse reflectivity approaching 100%.

Openings where light can exit or enter, used for detectors and sources, are normally called ports.