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of the lamp housing (halogen lamp) were used as reference<br />
planes of these lamps. Distances were measured on an<br />
optical rail using a magnetic length measuring device with<br />
0.1 mm resolution and accuracy.<br />
Figure 2. Images of the measured spectroradiometer diffusers<br />
(from left to right): Bentham D3 (∅ 25 mm), Bentham D7<br />
(∅ 10 mm), Bentham D5 (∅23.5 mm), and the Schreder<br />
diffuser with the quartz glass dome.<br />
Measurement results<br />
Reference planes of the photometer diffusers: The<br />
reference planes of the tested photometer heads were<br />
determined by illuminance values measured at six<br />
distances between 500 mm and 1500 mm. The results for<br />
the photometer diffusers are presented in Table 1. All<br />
offsets of the reference planes were found out to be several<br />
millimeters behind the outermost surfaces of the diffusers. 3<br />
Table 1. Dimensions and offsets of the photometer diffusers.<br />
Uncertainties are deviations of the mean of four measurements.<br />
Diffuser (a) (b) (c)<br />
D 24.3 16.0 30.0<br />
Dimensions<br />
[mm]<br />
L 8.0 7.1 15.0<br />
W - - 26.1<br />
Offset ∆d D<br />
[mm]<br />
5.0•±•0.5 7.8•±•0.3 8.5•±•0.7<br />
Reference planes of the spectroradiometer diffusers:<br />
Measurements with spectroradiometer heads were carried<br />
out at 10 distances between 300 mm and 2000 mm. This<br />
range includes typical calibration distances of 500 mm and<br />
370 mm used. The results at each wavelength and for each<br />
diffuser are presented in Table 2.<br />
Table 2. Measured reference plane offsets [mm] of the<br />
spectroradiometer diffusers.<br />
Filter /<br />
Diffuser<br />
Bentham<br />
D3<br />
Bentham<br />
D7<br />
Bentham<br />
D5<br />
Schreder<br />
UV 2.3 -0.3 0.4 6.4<br />
V(λ) 2.6 0.1 1.2 7.1<br />
700 nm 3.6 0.3 3.2 7.1<br />
The measurement result, 5.0 mm in the UV region,<br />
indicates that the quartz dome increases the observed shift<br />
of the reference plane.<br />
Conclusions<br />
We have presented a method with which the location of the<br />
reference planes of photometers and radiometers with<br />
diffusers can be determined. Inverse square law works only,<br />
if distance measurements are made with respect to this<br />
reference plane.<br />
The method has been demonstrated with various<br />
photometers and spectroradiometer diffusers. From the<br />
measurement results, we may discover that the distance<br />
reference plane is shifted with measuring heads having<br />
either thick mesa-shaped or dome-shaped diffusers. The<br />
material of the diffuser contributes to the shift. Large<br />
errors appear in the regions where the materials are<br />
transparent.<br />
If these effects are not accounted for, systematic errors<br />
may occur in the calibrations of photometers and<br />
spectroradiometers. For the studied photometers, errors up<br />
to 3 % at a calibration distance of 500 mm would arise.<br />
There would also be inevitable distance dependence on the<br />
correction factors.<br />
With the Schreder diffuser, the observed distance shift<br />
of 6.4 mm in the UV region may cause an error as large as<br />
2 % in the calibration at a distance of 500 mm. This is a<br />
significant contribution in the uncertainty of spectral<br />
global UV irradiance measurements that is nowadays at the<br />
level of a few percent.<br />
The uncertainty of the method may be estimated from<br />
the repeatability noted during the measurements that is of<br />
the order of 1 mm (k=2). It was checked that the<br />
wavelength dependence of the reference plane of the lamp<br />
is of the order of 0.4 mm.<br />
References<br />
1. Y. Ohno, Photometric Calibrations, NIST Special Publication<br />
250-37, U.S. Government Printing Office, Washington DC,<br />
1997.<br />
2. H. J. Kostkowski, Reliable spectroradiometry, La Plata, Md.,<br />
Spectroradiometry Consulting, 1997.<br />
3. J. Hovila, M. Mustonen, P. Kärhä, E. Ikonen, “Determination<br />
of the diffuser reference plane for accurate illuminance<br />
responsivity calibrations,” Appl. Opt. (in press).<br />
It can be seen that the mesa-shaped diffuser D3 has a<br />
significant offset, which is surprising for a planar diffuser.<br />
This is probably due to the poor material used to obtain a<br />
wide wavelength region. The other diffusers are made of<br />
Teflon, which results in increasing offset towards infrared<br />
wavelengths, where Teflon is not a very good diffuser<br />
material. The reference plane of the Schreder diffuser is<br />
surprisingly deep inside the measuring head. The effect is<br />
too large to be explained by the dome-shape only.<br />
The influence of the quartz dome of the Schreder<br />
diffuser on the reference plane position was studied by<br />
repeating the measurement without the quartz glass dome.<br />
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