Lambert's Cosine Law (also known as Lambert's cosine emission law) is the mathematical statement that a radiance of certain idealized optical sources is directly proportional to the cosine of the angle - with respect to the direction of maximum radiance - from which the source is viewed. Lamberts cosine law also applies to certain idealized diffuse reflectors or coatings.

Based upon the principle of multiple diffuse reflection (resulting from the Lambertian coating), the integrating sphere is used to spatially integrate radiant flux, either from an external or an internal source of radiation. The efficiency of an integrating sphere is determined by a number of factors, including the size and number of ports, the size and location of baffles or screens, the number of inclusions in the sphere, and most importantly, the reflectance and diffuse nature of the sphere coating that has to be "Lambertian" (ideally diffuse reflecting).
Depending on port position, baffling, and to an extent, sphere size, integrating spheres can be configured for a number of applications, including:

• Light collection from internal or external source (lamp measurement photometry)
• Uniform light sources
• Laser power measurement
• LED spectral and flux measurement
• Reflectance of either specular or scattering samples
• Total or diffuse only transmittance measurement
• Cosine receptors

Lamp measurement systems

The oldest application for the integrating sphere is the measurement of total geometric luminous flux from electric lamps. The technique originated at the turn of the 20th century (by Richard Ulbricht in Germany, which is why it is also called an Ulbricht sphere) as a simple and fast method of comparing the lumen output of different lamp types. It is still widely used in the lamp industry for quality control during manufacture. The alternative method is a goniophotometer which would need to rotate a photodetector in a complete sphere around the lamp (or rotate the sample in relation to a detector). Each discrete intensity point (lm/sr) is then integrated over 4π steradians.

In contrast to the absolute measuring method using a goniophotometer that scans the complete intensity distribution of the lamp and integrates the flux, the integrating sphere is the relative measuring method requiring calibration of the sphere with a calibrated flux (or spectral distribution) bulb that should be traceable to a national standard (e.g. PTB or NIST).

In a sphere photometer, the lamp to be measured is mounted at the center of the integrating sphere and baffled from a viewing port equipped with a diffuser and photopic response detector. The baffle is usually positioned at 2/3 of the radius from the sphere center. Its size should be as small as possible yet large enough to screen the maximum dimension of the lamp.

The lumen output from the test lamp is determined by first calibrating the photodetector signal using a lamp standard of known luminous flux. The lamps are alternately substituted into the integrating sphere. An auxiliary lamp can be permanently mounted inside the sphere to compensate for the substitution error caused by different self-absorption from the test and standard lamps.

Optronik - Labsphere Product Selection Chart

Transmittance and reflectance measurement
A possible application for integrating spheres is the measurement of the reflectance and transmittance of diffuse or scattering materials. The measurements are performed photopically or spectrally, as a function of wavelength. The measurement of luminous reflectance or transmittance is performed using a photopic response detector. A transmittance measurement places a material sample at the entrance port to the sphere.

In reflectance measurements, the sample can be placed at a port opening opposite the entrance port. The incident flux is reflected by the sample. The total hemispherical reflectance, both the diffuse and specular components, is collected by the integrating sphere. There are special applications such as ECER46 that also require a specific sphere design.

Luminance standards / Uniform Sources
Integrating spheres provide the ideal means for creating a uniform light source. Light collected by a sphere is diffusely reflected many times, so that any spatial characteristics are integrated for light leaving the sphere exit port plane.

The emitted light is nearly perfectly Lambertian. Our uniform source sphere LDN10 is internally coated with a special photometer paint, a proprietary diffuse white coating that produces excellent diffuse reflectance over the VIS-NIR wavelength region.

The functional principle is that a lamp or several lamps are placed inside the integrating sphere around the perimeter of the viewing port. The lamps are baffled from the port. The radiance of the sphere is a function of the wattage rating of the lamp.

Tungsten halogen lamps are most commonly used with integrating sphere sources. These lamps provide a continuous spectrum free of emission lines or temporal instability when operated from a regulated current power supply. The spectral radiance of the sphere source can be estimated by combining the sphere radiance equation with blackbody equations for the spectral radiant flux.

Integrating Sphere its 10
serving for measuring luminous flux (luminous power) and luminous colour

Luminance standard ldn 10
Creates on it’s light emitting surface a luminance which is accurately defined

Integrating Sphere with diffuse and directional light source kms 10
Highly specialized measurement device with two color temperature
regulated (standard illuminant A) light sources

digilumen 9500

Other Sphere diameters on request.

The Optronik "Integrating Spheres" Brochure (PDF 0.7 MB)