For radiometric calibration of our devices (sky-scanner, pollution spectrometer, DSLR camera) we need a short term stable cosine light source with a continuous spectrum. An integration sphere is a commonly used solution. For our purposes we need the diameter of the output port ca 8 cm (to fit the fish-eye lens of the camera) and corresponding diameter of the sphere should be 30 - 40 cm. Standard spheres have the diameters of 5-10 cm for fiber optics measurements or 1-1.5 m for the measurement of standard luminaires. So, our decision was to build our own integration sphere.
The sphere is based on a hollow styrofoam sphere with diameter of 30 cm, that is easily available in creative shops.
The principle of an integration sphere as a cosine light source is in the next picture. The baffle blocks the direct light from the bulb.
The inner surface is covered by a layer of baryum sulphate (BaSO4) powder with the reflectance about 98% in visible spectrum. The powder was mixed with small amount of white latex and some water was added to obtain a viscous paint. The paint was applied manually using a brush.
As a light source we use a small halogen light bulb 4.2V/0.5A. The amount of light escaping the bulb is measured by a fototransistor and regulated using PWM and Arduino. The schematics of the circuit is in the next picture.
The photos of the control unit:
The components of the light source are 3D-printed from white PETG:
The photo of the output port shows a very homogenous light source:
The properties of our integration sphere were analysed using OceanOptics USB650 spectrometer. The difference in the brightness measured in various places of the output port was found to be less than 3%.
Next, the warming time was investigated. Parameters of both light bulb and phototransistor are temperature dependent, so the temperature of the integration sphere has to be settled before the measurement. We measured the mean voltage delivered to the bulb in per-cent (relative to the maximum allowed voltage of 4.2V). The next plot shows the difference in the mean voltage regulated by the phototransistor as a function of time:
We can see, that after 15 minutes is the difference less than 1%. During the real calibration session, the user should wait until the value stops changing.
After testing the basic functionality of the sphere, we designed and built the stand.
Final look on the built integration sphere:
Finaly, a basic calibration of the integration sphere was done. A professional luxmeter showed the illumination level of 118 +/-5% lux (= lumen/m2) at the output port. The luminance of the output port is 118/3.14 lux/m2/srad = 37.6 +/- 5% cd/m2. Such simple calibration can be done everytime the sphere is used.
To be sure that the luminance of the sphere is homogenous enough (a simple relation between the luminance of the output port L(cd/m2) and the illuminance at the output port E(lux) in the form L = E/PI can be used), we analysed numerically the (linearized) pictures of the interior of the sphere taken by DSLR camera with fish-eye lens. We compared the average luminance of the region opposite to the output port (i.e. the luminance of the output port seen by narrow angle of view devices) to the luminance calculated from the illuminance at the output port (measured by the luxmeter). The following picture shows the interior of the sphere as "seen" by the luxmeter (a cosine correction is applied to the picture). Dark circle in the centre corresponds to the region oposite to the output port, the bright circle around corresponds to the viewing angle of 90 deg.
The numerical integration shows, that the difference in luminances is less than 0.9%. It suggests that the "physical integration" works well within the sphere, and darker region (baffle and its shadow) is well compensated by the brighter regions (illuminated by direct light from the bulb).
František Kundracik
Department of Experimental Physics
Faculty of Mathematics, Physics and Informatics
Comenius University
Bratislava, Slovakia