Here - PMOD/WRC
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1) Select the initial values of power coefficients<br />
( 0<br />
k<br />
)<br />
i , i = 1...<br />
n of i-th LED; they can be any positive<br />
number.<br />
2) Calculate the j -th value of k i from the (j-1)-th<br />
value, based on the partial derivative with respect to k i<br />
of the square of the difference between the target<br />
spectrum and the STS spectrum built up from the LED<br />
spectra weighted by the variables k:<br />
( )<br />
( j−1<br />
j<br />
)<br />
k = k − a<br />
i<br />
i<br />
780<br />
⎛<br />
⎜<br />
⎝<br />
n<br />
∂ ∑ ∑<br />
k<br />
i<br />
380 i=<br />
1<br />
( j −1) S ( λ) − S ( λ)<br />
LED<br />
i<br />
( j −1<br />
∂k<br />
)<br />
i<br />
TARGET<br />
where a should be between 0 and 1. To<br />
achieve an optimal calculation time while still<br />
ensuring convergence of the solution, a<br />
parameter was set to 0.001.<br />
3) Continue the iterations until the solution<br />
converges, i.e. when<br />
780 n<br />
i LEDi<br />
380 i=<br />
1<br />
780 n<br />
= i LEDi<br />
380 i=<br />
1<br />
( j) ∑∑k<br />
S ( λ) − S ( λ)<br />
TARGET<br />
( j−1) ∑∑k<br />
S ( λ) − S ( λ)<br />
TARGET<br />
The equality is obtained from a large number of iterations<br />
where the individual LED currents (power coefficients k)<br />
are increased or decreased in small increments. It can be<br />
interpreted that the algorithm stops when the values k i<br />
reach a steady-state solution. The individual LED currents<br />
are obtained from the optimization. The integral-sum of<br />
the differences at each wavelength is an indication of the<br />
quality of the realized spectral match.<br />
3. Realized STS spectral distributions<br />
Figs. 2 to 4 shows examples of the output spectra of the<br />
STS source matched to the given spectra. The deviations<br />
from the given spectra are mainly caused by limitations in<br />
the availability of LEDs with the appropriate peak<br />
wavelengths, their finite spectral widths (SPD curves), as<br />
well as drifts due to temperature dependence, instability,<br />
and aging of the LEDs. The matching will be improved by<br />
changing the selection of LEDs used. The average<br />
luminance of the STS, which depends on the specific<br />
spectral distribution desired, is between several hundred<br />
-2<br />
and one thousand [ cd ⋅ m ]. Further results of<br />
characterizaion of the STS source developed will be<br />
presented in the full paper.<br />
4. Conclusions<br />
A spectrally tunable LED source (STS) has been<br />
developed. The source can approximate various CIE<br />
illuminants (D65, etc.) as well as common source spectral<br />
distributions for other photometric and colorimetric<br />
applications, and may be useful for visual experiments on<br />
colorimetry as well.<br />
⎞<br />
⎟<br />
⎠<br />
2<br />
,<br />
Relative distribution<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
350 450 550 650 750<br />
Wavelength (nm)<br />
Fig. 2. SPD of CIE illuminant D65 (dashed line) and the STS<br />
output measured by spectroradiometer (solid line).<br />
Relative distribution<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
350 450 550 650 750<br />
Wavelength (nm)<br />
Fig. 3. SPD of a CRT green (dashed line) and the STS output<br />
measured by spectroradiometer (solid line).<br />
Relative distribution<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
350 450 550 650 750<br />
Wavelength (nm)<br />
Fig. 4. SPD of a Cool White FL (dashed line) and the STS output<br />
measured by spectroradiometer (solid line).<br />
References<br />
[1] ISO/CIE 10527-1991, CIE standard colorimetric observers,<br />
1991.<br />
[2] ISO/CIE 10526-1991, CIE standard colorimetric illuminants,<br />
1991.<br />
[3] S. W. Brown, C. Santana, and G. P. Eppeldauer, Development<br />
of a tunable LED-based colorimetric source, J. Res. Nat’l. Inst.<br />
Stands. Technol. 107, 363-371, 2002.<br />
[4] I. Fryc, S. W. Brown, G. P. Eppeldauer, Y. Ohno, A spectrally<br />
tunable solid-state source for radiometric, photometric, and<br />
colorimetric applications, Proceedings of SPIE, 5530, 150 –<br />
159, 2004.<br />
296