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. Its relevant property is a uniform scattering or diffusing effect. Light rays incident on any point on the inner surface are, by multiple scattering reflections, distributed equally to all other points. The effects of the original direction of light are minimized. An integrating sphere may be thought of as a diffuser which preserves power but destroys spatial information. It is typically used with some light source and a detector for optical power measurement. A similar device is the focusing or Coblentz sphere, which differs in that it has a mirror-like (specular) inner surface rather than a diffuse inner surface.

The practical implementation of the integrating sphere was due to work by R. Ulbricht (1849–1923), published in 1900. It has become a standard instrument in photometry and radiometry. It has the advantage over a goniophotometer for measuring the light produced by a source that total power can be obtained in a single measurement.

The theory of a light-collecting cubical box was described by W. E. Sumpner in 1910.

The theory of integrating spheres is based on these assumptions:

Using these assumptions the sphere multiplier can be calculated. This number is the average number of times a photon is scattered in the sphere, before it is absorbed in the coating or escapes through a port. This number increases with the reflectivity of the sphere coating and decreases with the ratio between the total area of ports and other absorbing objects and the sphere inner area. To get a high homogeneity a recommended sphere multiplier is 10-25. The theory further states that if the above criteria are fulfilled then the irradiance on any area element on the sphere will be proportional to the total radiant flux input to the sphere. Absolute measurements of instance luminous flux can then be done by measuring a known light source and determining the transfer function or calibration curve.

Light scattered by the interior of the integrating sphere is evenly distributed over all angles. The integrating sphere is used in optical measurements. The total power (flux) of a light source can be measured without inaccuracy caused by the directional characteristics of the source, or the measurement device. Reflection and absorption of samples can be studied. The sphere creates a reference radiation source that can be used to provide a photometric standard.

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