HOME

TheInfoList



OR:

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 Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
white reflective coating, with small holes for entrance and exit ports. Its relevant property is a uniform
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
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 Diffuser may refer to: Aerodynamics * Diffuser (automotive), a shaped section of a car's underbody which improves the car's aerodynamic properties * Part of a jet engine air intake, especially when operated at supersonic speeds * The channel betw ...
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. In 1892, W. E. Sumpner published an expression for the throughput of a spherical enclosure with diffusely reflecting walls. Ř. Ulbricht developed a practical realization of the integrating sphere, the topic of a publication in 1900. It has become a standard instrument in
photometry Photometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
and
radiometry Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...
and has the advantage over a goniophotometer that the total power produced by a source can be obtained in a single measurement. Other shapes, such as a cubical box, have also been theoretically analyzed. 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.


Theory

The theory of integrating spheres is based on these assumptions: * Light hitting the sides of the sphere is scattered in a diffuse way i.e.
Lambertian reflectance Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. More technically, the su ...
* Only light that has been diffused in the sphere hits the ports or detectors used for probing the light 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 In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...
or
calibration In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of know ...
curve.


Total exit irradiance

For a sphere with radius r, reflection coefficient ρ, and source flux Φ, the initial reflected irradiance is equal to: E = \rho \frac \Phi \, Every time the irradiance is reflected, the reflection coefficient exponentially grows. The resulting equation is E = \frac \Phi \,\rho(1 + \rho + \rho^2 + ...) Since ρ ≤ 1, the
geometric series In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series :\frac \,+\, \frac \,+\, \frac \,+\, \frac \,+\, \cdots is geometric, because each succ ...
converges and the total exit irradiance is: E = \frac \Phi \,\frac \rho \,


Applications

Integrating spheres are used for a variety of optical, photometric or
radiometric Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which cha ...
measurements. They are used to measure the total light radiated in all directions from a lamp. 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. In 1916, E. B. Rosa and A. H. Taylor published the first such method. Subsequent work by A. H. Taylor, Frank A. Benford, C. H. Sharpe & W. F. Little, Enoch Karrer, and Leonard Hanssen & Simon Kaplan expanded the number of unique methods which measure port-mounted test objects. Edwards et al., Korte & Schmidt, and Van den Akker et al. developed methods which measure center-mounted test objects. 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. Since all the light incident on the input port is collected, a detector connected to an integrating sphere can accurately measure the sum of all the ambient light incident on a small circular aperture. The total power of a laser beam can be measured, free from the effects of beam shape, incident direction, and incident position, as well as polarization.


Materials

The optical properties of the lining of the sphere greatly affect its accuracy. Different coatings must be used at visible, infrared and ultraviolet wavelengths. High-powered illumination sources may heat or damage the coating, so an integrating sphere will be rated for a maximum level of incident power. Various coating materials are used. For visible-spectrum light, early experimenters used a deposit of
magnesium oxide Magnesium oxide ( Mg O), or magnesia, is a white hygroscopic solid mineral that occurs naturally as periclase and is a source of magnesium (see also oxide). It has an empirical formula of MgO and consists of a lattice of Mg2+ ions and O2− ions ...
, and
barium sulfate Barium sulfate (or sulphate) is the inorganic compound with the chemical formula Ba SO4. It is a white crystalline solid that is odorless and insoluble in water. It occurs as the mineral barite, which is the main commercial source of barium an ...
also has a usefully flat reflectance over the visible spectrum. Various proprietary
PTFE Polytetrafluoroethylene (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene that has numerous applications. It is one of the best-known and widely applied PFAS. The commonly known brand name of PTFE-based composition is Teflon by Chemour ...
compounds are also used for visible light measurements. Finely-deposited gold is used for infrared measurements. An important requirement for the coating material is the absence of fluorescence. Fluorescent materials absorb short-wavelength light and re-emit light at longer wavelengths. Due to the many scatterings this effect is much more pronounced in an integrating sphere than for materials irradiated normally.


Structure

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. The total area of all ports must be small, less than about 5% of the surface area of the sphere, for the theoretical assumptions to be valid. Unused ports should therefore have matching plugs, with the interior surface of the plug coated with the same material as the rest of the sphere. Integrating spheres vary in size from a few centimeters in diameter up to a few meters in diameter. Smaller spheres are typically used to diffuse incoming radiation, while larger spheres are used to measure integrating properties like the
luminous flux In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of electromagnetic radiation (including infrared, ultraviolet, and visible light), in th ...
of a lamp or luminaries which is then placed inside the sphere. If the entering light is incoherent (rather than a laser beam), then it typically fills the source-port, and the ratio of source-port area to detector-port area is relevant. Baffles are normally inserted in the sphere to block the direct path of light from a source-port to a detector-port, since this light will have non-uniform distribution.


See also

*
Lambert's cosine law In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle ''θ'' between the direction ...


References


External links

* RP Photonics, ''Encyclopedia of Laser Physics and Technology''
Integrating spheres
* Pike Technologies, ''Integrating Spheres – Introduction and Theory''
Pike Technologies Application Note
* Newport
''Flange Mount Integrating Spheres''
* *{{cite journal , first=Alfred , last=Ducharme , first2=Arnold , last2=Daniels , first3=Eric , last3=Grann , first4=Glenn , last4=Boreman , title=Design of an Integrating Sphere as a Uniform Illumination Source , journal=IEEE Transactions on Education , volume=40 , issue=2 , year=1997 , pages=131–134 , doi=10.1109/13.572326 , bibcode = 1997ITEdu..40..131D , url=https://semanticscholar.org/paper/41ddbe9c6b90efa06b7569dbeb2fa714b1633791 * Peter Hiscocks
''Integrating Sphere for Luminance Calibration''
Rev 6, May 2016 * Ci Systems
''Integrating sphere introduction, mechanical structure, calibration and sources''
* Electro-Optical Industries
''Integrating Spheres''


Photometry Optical devices Laser science