Integrating sphere

Laboratory setup with integrating sphere, light sensitivity measurement of a CCD camera (video evaluation not shown)

Artwork by Jürgen Schieferdecker based on an Ulbricht sphere in front of the TU Dresden

The integrating sphere , named after the engineer Richard Ulbricht , is a component of technical optics . It is used as a light source to achieve diffuse radiation from directed radiation or to collect radiation from strongly divergent sources.

construction

It is a hollow sphere, which is diffusely reflective on the inside and in the surface of which there is (often) an outlet opening at right angles to a light inlet opening. The light or radiation source is located in front of the light inlet opening. The inner coating consists of materials that are as diffusely reflective as possible. Often, barium sulfate (BaSO ₄ ) were used. However, the best reflective properties over a wide range of wavelengths are achieved with optical PTFE . For infrared radiation with wavelengths over 700 nm, gold is used as a coating on the sand-blasted inner surface.

The diameters of possible openings are significantly smaller than the inner diameter of the sphere, so that only light that has previously been reflected many times on the inner surface reaches the exit plane. The area of ​​all openings should not exceed 5% of the total area of ​​the sphere. Integrating spheres are mostly used for use in the area of ​​visible light. They are also suitable for infrared and ultraviolet, depending on the interior of the ball.

functionality

To explain how it works, the luminous flux emitted by a light source should be measured with the help of an integrating sphere . The light source can shine in different directions with different light levels ; is the total luminous flux emitted in all directions . ${\displaystyle L}$ ${\displaystyle \Phi _{L}}$

In principle it would be possible, but very complex, to view the light source from all possible directions with a photometer and to calculate the total luminous flux as the sum of the components emitted in the individual directions (principle of the goniophotometer). However, if only the luminous flux itself and not the directional distribution is of interest, the measurement is much easier with an integrating sphere.

The light source is placed in the middle of an integrating sphere. The luminous flux emitted directly by it is diffusely reflected on the inner surface of the sphere and, after multiple reflections , finally generates the indirect luminous flux , which fills the inside of the sphere as a diffuse light field . The sum of the direct and indirect luminous flux meets the spherical surface with the degree of reflection . The proportion of this is absorbed and discharged to the outside as heat . After switching on the light source, the intensity of the light field inside the sphere increases until the luminous flux withdrawn from the field by absorption equals the luminous flux supplied by the light source: ${\displaystyle A}$ ${\displaystyle A}$ ${\displaystyle \Phi _{R}}$ ${\displaystyle A}$ ${\displaystyle \rho }$ ${\displaystyle \Phi _{L}+\Phi _{R}}$ ${\displaystyle (\Phi _{L}+\Phi _{R})\cdot (1-\rho )}$

${\displaystyle (\Phi _{L}+\Phi _{R})\cdot (1-\rho )=\Phi _{L}}$.

Solve for delivers: ${\displaystyle \Phi _{L}}$

${\displaystyle \Leftrightarrow \Phi _{L}=\Phi _{R}\cdot {\frac {1-\rho }{\rho }}}$

If the coating of the inner surface of the ball z. B. the reflectance

${\displaystyle \rho =0{,}83}$

the indirect luminous flux accumulated as a result of multiple reflections is approximately five times as large as the direct luminous flux:

${\displaystyle \Rightarrow \Phi _{R}={\frac {0{,}83}{1-0{,}83}}\cdot \Phi _{L}\approx 5\cdot \Phi _{L}}$

Depending on the radiation characteristics , the light source can illuminate different parts of the inner surface of the sphere with its direct luminous flux to different degrees. The indirect luminous flux, on the other hand, is completely diffuse due to the multiple reflections, is evenly distributed and generates the same indirect illuminance component at all points ${\displaystyle A}$

${\displaystyle E_{R}={\frac {\Phi _{R}}{A}}}$

A photometer attached to the inner surface of the sphere only records the indirect illuminance component if the direct component is kept away from the measuring surface by a suitably attached screen , the "shadow". The luminous flux you are looking for results from the measured indirect illuminance component and the known properties of the sphere as: ${\displaystyle E_{R}}$

${\displaystyle \Phi _{L}=E_{R}\cdot A\cdot {\frac {1-\rho }{\rho }}}$

In this example, the integrating sphere is used to collect the originally non-uniformly distributed luminous flux from all directions and to convert it into an easily measurable illuminance that is simply related to the desired luminous flux. The photometer, which actually measures the illuminance in lux , can be calibrated so that it immediately shows the desired luminous flux in lumens .

In other applications, the integrating sphere can be used to investigate the optical properties of materials. For this purpose, the material sample is attached to a spherical opening and illuminated from the outside with a measuring beam. The light that emerges on the back of the sample after irradiation and is mostly unevenly distributed in different directions is collected by the sphere and fed to the transmittance measurement. If the reflection properties of the sample are to be examined, it is illuminated from the inside of the sphere.

The integrating spheres used in practice sometimes deviate from the ideal case described here. The coating, for example, will not be applied completely homogeneously, it will not reflect ideally diffusely (which is partly, but not completely, compensated by the multiple reflection), and it will reflect different wavelengths to different degrees. Real spheres usually have openings whose surfaces are occupied by material samples, light sources or photometers and therefore have different degrees of reflection than the inner surface of the sphere. An effective mean reflectance should therefore be used. These and numerous other sources of error must be taken into account by means of correction factors or eliminated by means of suitable measurement procedures (such as comparative measurements on reference samples).

use

The radiation scattered in the integrating sphere is almost ideally diffuse; it fulfills Lambert's law (Lambert distribution) far better than this is achieved by opaque material (such as a diffuser or frosted glass ) or a flat, diffuse reflective plate (white sheet of paper ) is possible.

The integrating sphere is mostly used in optical measurement technology. On the one hand, it enables the power or the total luminous flux of different light sources to be measured without the measurements being falsified by their directional characteristics . In addition, laser and infrared radiation sources can be measured. On the other hand, the diffuse radiation generated offers the possibility of creating a photometric standard or a reference radiation source in order to compare the properties of different optical detectors with one another.

Measurement of luminous flux and radiant power

In most applications, the integrating effect is used to measure “4-pi / 2-pi emitters” with regard to the luminous flux (spherical photometer) or the radiant power of laser diodes. The integrating sphere can be described as an "integration sphere". The sphere acts as part of a measurement setup. In addition to the sphere, other assemblies include the receiver (e.g. filtered Si photodiode) and the display console / PC.

The advantage lies in the fast measurement; milliseconds to seconds are possible without the necessary setup times for the measurement object.

If the integrating sphere is used for luminous flux measurement, a known luminous flux standard must be used to calibrate the spherical photometer, which has similar properties (spectral, directional characteristic, dimensions) to the test object in order to reduce the measurement uncertainty. Since the spherical photometer only allows relative measurements, the use of a luminous flux standard is essential. If the spectral sensitivity of the measuring head agrees very well with the standard spectral value function and if the coating is as selective as possible with ~ 80%, the spectral distribution of the luminous flux standard can deviate from the test object. The measurement uncertainty is also insignificantly impaired if the test object and standard have significantly different dimensions, but both are small in relation to the ball diameter. ${\displaystyle \rho }$

According to DIN 5032, a reflectance of the sphere color of = 80% is specified for the sphere photometer ; EN 13032-1, which is relevant in Europe, extends the range to = 75 - 85%. Every increase in the degree of reflection leads to better mixing and deterioration of the adaptation as well as to a reduction in long-term stability due to increased sensitivity to dirt. ${\displaystyle \rho }$ ${\displaystyle \rho }$ ${\displaystyle v(\lambda )}$

It is possible to use the integrating sphere as an attachment in front of a photodiode (detector) as an attenuator, with attenuations of 100 to 10,000 being achieved. In this case, the Ulbricht sphere has a second opening (light inlet), the aperture of which receives the radiation to be measured with good cosine characteristics (Lambertian distribution). It is therefore recommended to use it as an illuminance measuring head, as the incident light is evaluated at the correct angle.

The diameter of the integrating sphere as a light receiver is a few centimeters when measuring laser diodes and up to three meters when measuring fluorescent tubes or linear luminaires.

Homogeneous light source

Integrating spheres are also used as a homogeneous light source. Such applications are adjustment or balancing of camera systems, it can be adjusted with or without optics. Typical diameters of the free aperture are a few centimeters (white balance of focal plane arrays (FPA), CCD sensors etc.) up to one meter (white balance of satellite cameras including optics), with the diameter of the integrating sphere being at least three times the aperture diameter should in order to ensure sufficient mixing.

Measurements of substance indicators

For transmittance and reflectance measurements , as well as for scattering studies , the diffuse scattering in front of or behind a sample can be integrated with the integrating sphere in order to enable quick measurements. The structures are to be created in accordance with DIN 5036 Part 3 in order to achieve comparable results.

Web links

Commons : Integrating sphere  - collection of images, videos and audio files

• Camera measurement technology luminance distribution (PDF; 824 kB)

Individual evidence

1. ↑ ^{a b c} S. Banda: The basic lighting parameters. expert verlag, Renningen-Malmsheim 1999, ISBN 3-8169-1699-6 , p. 64.