Here - PMOD/WRC

Relative Signal
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
1.0E-05
1.0E-06
1.0E-07
light are significant in the wings for measurements of all
three LEDs. After the stray-light correction, the errors are
reduced more than one order of magnitude, which
corresponds to a reduction of measurement error in
chromaticity coordinates (x, y) from 0.01 (original) to less
than 0.001 (after correction) for the green LED.
1.0E+01
1.0E+00
1.0E-01
1.0E-08
200 300 400 500 600 700 800
Wavelength (nm)
Measured Sig Corrected Sig 1 count level
Relative Signal
1.0E-02
1.0E-03
1.0E-04
1.0E-05
Figure 2. An example of the stray-light correction for a laser
source measurement. Thick solid line: measured raw signals
from the array spectrometer; thin symbol line: stray-light
corrected signals; horizontal dashed line: one-count level of the
15-bit array spectroradiometer.
Improvement in measurement uncertainty
The stray-light correction can significantly reduce the
errors in both the calibration of an array spectroradiometer
and measurements of test sources. Figure 3 shows plots of
the raw output signal, the stray-light corrected ‘true’ signal,
and the percentage of the stray-light signal relative to the
‘true’ signal for a calibration of an array spectrometer
system with stray light of 10 -4 , using an incandescent
standard lamp. The stray-light signals are significant
compared to the ‘true’ signals below 400 nm. The error
without correction reaches 30 % of the ‘true’ signal at 350
nm. By applying the stray-light correction, the
spectroradiometer errors arising from stray light in the
measurement of the standard lamp are reduced
significantly below 400 nm.
Relative Signal
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-03
1.0E-04
0
300 400 500 600 700 800
Wavelength (nm)
Raw Signal Corrected Signal Stray-light Signal (%)
Figure 3. Stray-light correction for calibration of the spectral
responsivity of an array spectrometer system. Thick solid line:
raw output signal from the spectrograph; thin solid line:
stray-light corrected ‘true’ signal; thick symbol line: percentage
of stray-light signal relative to the ‘true’ signal.
Correction for stray light is critical when measuring
test sources that have dissimilar spectra compared to that
of the calibration source. As an example, an array
spectroradiometer was used to measure the color of a blue
LED, a green LED, and a red LED. The measurement
results are shown in Figure 4. Errors arising from stray
100
90
80
70
60
50
40
30
20
10
Stray-light Signal (%)
1.0E-06
1.0E-07
200 300 400 500 600 700 800
Blue raw
Green raw
Red raw
Wavelength (nm)
Blue corrected
Green corrected
Red corrected
Figure 4. Stray-light corrections for measurements of a blue, a
green, and a red LEDs. Thick solid line: measured raw signals
from the spectrograph; thin symbol line: stray-light corrected
signals.
Conclusion
A stray-light correction matrix has been developed for
spectrometers to perform a simple, fast correction of
stray-light errors in measured raw signals. This approach
corrects stray-light errors using a simple matrix
multiplication, which can be readily incorporated in an
instrument’s software for real-time stray-light correction.
After the correction was applied, stray-light errors were
reduced by one to two orders of magnitude, to a level less
than 10 -5 of the measured signal of broad-band sources,
equivalent to less than one count of the 15-bit-resolution
instrument. The principle of the stray-light correction can
be used to correct other types of errors resulting from
different mechanisms, for example, fluorescence of optical
materials used in a spectrometer system. By correcting
spectroradiometers for stray light, significant reductions in
overall measurement uncertainties are expected in
colorimetry (as shown in the LED example), radiometry,
photometry, spectroscopy, and other areas where these
instruments are commonly used.
The theory, the validation, and the example
applications of the stray-light correction matrix approach
will be presented.
References
Brown, S. W., Johnson, B. C., Feinholz, M. E., Yarbrough, M. A.,
Flora, S. J., Lykke, K. R., and Clark, D. K., Stray light
correction algorithm for spectrographs, Metrologia, 40,
S81-83, 2003.
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