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New source and detector technology for the realization of photometric units
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2014 Metrologia 51 S276
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Bureau International des Poids et Mesures
Metrologia
Metrologia 51 (2014) S276–S281
doi:10.1088/0026-1394/51/6/S276
New source and detector technology for
the realization of photometric units
1,2
¨
Timo Donsberg
, Tomi Pulli2 , Tuomas Poikonen1 ,
Hans Baumgartner1,2 , Anna Vaskuri2 , Meelis Sildoja2 ,
¨ a¨ 1,2 and Erkki Ikonen1,2
Farshid Manoocheri1,2 , Petri Karh
1
2
Centre for Metrology and Accreditation (MIKES), PO Box 9, FI-02151 Espoo, Finland
Metrology Research Institute, Aalto University, PO Box 13000, FI-00076 Aalto, Finland
E-mail: [email protected]
Received 9 June 2014, revised 27 August 2014
Accepted for publication 28 August 2014
Published 20 November 2014
Abstract
The production of incandescent light bulbs is bound to end, as incandescent lighting is being
phased out globally in favour of more energy-efficient and sustainable solutions. Temporally
stable light-emitting diodes (LEDs) are potential candidates to replace incandescent lamps as
photometric source standards. However, traditional V(λ) filter based photometers may have
large uncertainty when LEDs are measured instead of incandescent lamps. This is due to the
narrow and complicated spectra of LEDs. When the spectra of LEDs are limited to the visible
wavelength range, new silicon detector technology can be advantageously exploited in
photometry. We present a novel method—based on the recently introduced Predictable
Quantum Efficient Detector (PQED)—for the realization of photometric units which
completely eliminates the need to use V(λ) filters. Instead, the photometric weighting is taken
into account numerically by measuring the relative spectral irradiance. The illuminance values
of a blue and a red LED were determined using the new method and a conventional reference
photometer. The values obtained by the two methods deviated from each other by −0.06% and
0.48% for the blue and red LED, respectively. The PQED-based values have much lower
standard uncertainty (0.17% to 0.18%) than the uncertainty of the values based on the
conventional photometer (0.46% to 0.51%).
Keywords: photometry, light-emitting diode, silicon photodetector, induced junction, optical
standards
(Some figures may appear in colour only in the online journal)
1. Introduction
Incandescent lamps are widely used as measurement standards
in photometry [1–3]. However, their mass production will end
as incandescent lighting is being phased out globally in favour
of more energy-efficient, sustainable and cost-effective light
sources [4–7]. Eventually, the industry and the know-how
needed for the manufacturing of incandescent lamps will be
lost, and incandescent standards may not be available—or the
costs will be exceedingly high. Therefore, it is worth looking
at new photometric source standards to replace the traditional
incandescent lamps.
Light-emitting diodes (LEDs) are widely used in
photometric applications [8–11]. Prospects for the new
technology as photometric standards seem promising, as
0026-1394/14/060276+06$33.00
certain types of commercial LED light sources have been
shown to be temporally stable within 0.2% in luminous flux
over a time period of 20 000 h of operation [12]. However,
the uncertainties of the measurement methods based on V(λ)
filtered photometers may increase when measuring LEDs
instead of incandescent lamps. This is due to the narrow and
complicated spectra of LEDs. The situation is problematic in
the red and blue regions of the visible spectrum, where the
relative uncertainty of the V(λ) weighted spectral responsivity
is high [13, 14].
We present a novel method for the realization of
photometric units based on the recently introduced Predictable
Quantum Efficient Detector (PQED) operated at room
temperature [15–18]. The PQED is a primary standard
of optical power that consists of two induced-junction
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© 2014 BIPM & IOP Publishing Ltd Printed in the UK
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Metrologia 51 (2014) S276
photodiodes with almost unity internal quantum efficiency
(IQE), meaning that almost all absorbed photons produce
a collectable charge carrier. The photodiodes are mounted
in a wedged trap configuration [19] for the elimination of
specular reflectance losses. At room temperature, the IQE
of the PQED can be modelled with an estimated standard
uncertainty of 70 ppm in the visible wavelength range [20],
whereas the uncertainty due to reflectance of unpolarized
radiation is less than 30 ppm for most of the visible wavelength
range [15, 21]. The predicted responsivity of the PQED has
been confirmed experimentally with measurements against
cryogenic radiometers [16].
The new method to realize the photometric units
completely eliminates the need to use V(λ) filters. Instead,
the photometric weighing is carried out numerically using
separately measured relative spectral irradiance of the light
source and the predicted spectral responsivity of the PQED.
The method is applicable to light sources whose emission
spectra do not extend outside the visible wavelength range,
such as LED light sources. In order to validate the new method,
illuminance values were determined using the new method
and a conventional reference photometer. Such measured
illuminances of a blue and red LED deviated by −0.06% and
0.48%, respectively. Moreover, the PQED-based illuminance
values have a factor of three lower standard uncertainty than the
illuminance values measured with the reference photometer.
2. Method
Photometric quantities are obtained from corresponding
radiometric quantities by weighting the radiation with the
spectral luminous efficiency function V(λ) which represents
the relative spectral responsivity of the human eye under
daylight illumination levels. Thus, the relation between a
photometric quantity Xv and the corresponding radiometric
quantity Xe,λ is
(1)
Xv = Kcd Xe,λ (λ)V(λ) dλ,
λ
where constant Kcd = 683 lm W−1 is the maximum luminous
efficacy for photopic vision [3]. A conventional photometric
measurement is carried out by using a filtered detector, a
photometer, the spectral responsivity of which closely follows
the V(λ) curve. The deviation between the V(λ) and the relative
spectral responsivity of the photometer, srel (λ) = s(λ)/s(λ0 ),
is taken into account by using the so-called spectral mismatch
correction factor
e (λ)V(λ) dλ
F =
,
(2)
e (λ)srel (λ) dλ
where e (λ) is the incident spectral radiant flux. For
example, illuminance Ev is then obtained from the measured
photocurrent i using the equation [22]
Ev =
Kcd F i
,
As(λ0 )
(3)
Figure 1. Schematic structure of the PQED and the precision
aperture in front of it. Without the aperture the field-of-view (FOV)
of the PQED is θ = 21.5◦ . The precision aperture limits the FOV to
4.4◦ . At the distance of 3 m, and with the source diameter of 3 mm,
the maximum entrance angle of the incident light is 0.06◦ when the
3 mm aperture is used.
where A is the area of the limiting aperture and s(λ0 ) is
the absolute responsivity of the photometer at the V(λ) peak
wavelength of λ0 = 555 nm.
The new method utilizes the PQED together with a
precision aperture placed in front of the photodiodes to limit
the field of view. The schematic structure of the assembly is
shown in figure 1. It should be emphasized that there is no
filter or any other optical element between the light source and
the detector. Seven reflections of the incident light take place
between two 11 mm × 22 mm silicon photodiodes and a small
fraction of light is reflected back. Typical shunt resistance
and capacitance of the PQED are 3 M and 1 nF. The dust
and moisture contamination of the photodiodes is prevented
by using a nitrogen flow system [17].
The reflectance loss of the PQED is affected by the
spectral distribution and state of polarization of the incident
light. The reflectance loss and the photocurrent ratio of the
two photodiodes have been modelled for monochromatic light
at s and p polarization by using a multilayer model of the
photodiodes and ray transfer matrix analysis. As described
in [21], these modelled values, together with the measured
photocurrent ratio, can be used to determine the reflectance
loss of the PQED at individual wavelengths without direct
measurement of the reflectance. The method to calculate the
responsivity s(λ) of the PQED to be used in equations (2)
and (3) with unknown polarization distribution is derived in
the appendix.
As the V(λ) filter is not used, the new method relies
on accurate determination of the relative spectral flux e (λ)
in equation (2). The reliability of the measurement of
relative spectra can be addressed by measuring the same
LED with different calibrated spectroradiometers [23]. In
conventional photometry, the relative responsivity of the
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T Donsberg
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Metrologia 51 (2014) S276
Figure 2. Schematic of the measurement setup. The distance between the LED and the detector plane is 3 m. The dashed line indicates the
locations where white reflecting material was fixed during the stray light studies.
photometer resembles the V (λ) function in equation (2), and
the uncertainty of the spectral mismatch correction factor due
to uncertainty in the incident spectral flux is small. In the
absence of V(λ) filter, the relative spectral responsivity srel (λ)
is simply that of the PQED—very near to the responsivity of
an ideal quantum detector, that is srel (λ) ≈ λ/λ0 . Moreover,
the absolute responsivity s(λ0 ) in equation (3) is accurately
known. The effect of the measured spectral flux on the spectral
mismatch correction factor is the main uncertainty component
when measuring photometric quantities with the PQED.
In the case of a narrow bandwidth light source, integrating
the noise floor of the spectroradiometer over the entire visible
wavelength range causes an error in the spectral mismatch
correction factor. This effect can be corrected by extrapolating
the tails of the peak in the LED spectrum. The most suitable
function for extrapolation is an exponential function of photon
energy [24–26].
3. Measurements and results
Figure 3. Normalized spectra of the measured blue and red LEDs
and the V(λ) function (dashed line).
The illuminance values produced by a blue and a red LED with
peak wavelengths of 462 nm and 664 nm, respectively, were
measured with the reference photometer and with the PQED
as described above. The design of the reference photometer is
similar to the filter radiometer described in [27]. The schematic
of the measurement setup in a light tight enclosure around
the photometric bench is shown in figure 2 [22]. With both
methods, a precision aperture with a diameter of 3 mm was
used. The detectors were located at a distance of 3 m from
the light source. Both LEDs were mounted on a heat sink
stabilized to the temperature of 40 ◦ C and they were driven at
currents of 700 mA (blue LED) and 1 A (red LED).
The relative spectral fluxes e (λ) of the measured LEDs
and the V(λ) curve are shown in figure 3. The spectra
were measured using a double monochromator scanning
spectroradiometer with 1 nm bandwidth. The relative intensity
scale of the spectroradiometer was calibrated against the
traceable spectral irradiance of an FEL lamp [28], whereas the
argon ion laser line at 457.94 nm and the helium–neon laser
line at 632.82 nm were used to calibrate the wavelength scale
in air. The calculated spectral mismatch correction factors,
measured photocurrents and the corresponding illuminance
values are given for the PQED and the reference photometer
in table 1. As described above, the spectra of the LEDs were
extrapolated below the noise floor of the spectroradiometer (see
figure 4). LEDs were also studied with the spectroradiometer
at a close distance to confirm that their spectra are limited to
the single peak.
The uncertainty components of the illuminance measurements using the reference photometer and the PQED are given
in table 2. The uncertainty due to the spectral mismatch
correction factor is dominated by the transmittance of the
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Table 1. Measured spectral mismatch correction factors, photocurrents and the corresponding illuminance values for the PQED-based
method and for the reference photometer.
Blue LED
Spectral mismatch correction factor F
Photocurrent i/nA
Illuminance Ev /lx
Red LED
PQED
Photometer
PQED
Photometer
0.103 86
47.454
1.0378
0.942 13
2.7298
1.0384
0.071 918
135.514
2.0521
1.012 52
4.9954
2.0422
Figure 4. Normalized spectra of the measured blue and red LED
and the extrapolated slopes of the peaks (dashed lines).
V(λ) filter when the reference photometer is used, and by the
measurement of the relative LED spectrum when the PQED
is used. These components include the uncertainty due to the
wavelength scale, which is 0.08% to 0.10% for the PQED and
0.43% to 0.48% for the reference photometer. Other sources
of uncertainty in the spectral mismatch correction factor of the
photometer, such as spectral transmittance of the filter and its
angular and temperature dependence, were evaluated similarly
to [22]. The uncertainties in the LED spectrum due to the
non-linearity of the spectroradiometer, temporal drift and the
angular dependence were estimated by measuring the spectra
of the LEDs at distances of 1.5 m and 3 m. The combined effect
of these on the standard uncertainty was concluded to be less
than 0.1% for both LEDs when the PQED is used. In addition,
the uncertainty of the spectral extrapolation was estimated by
changing the wavelength range used for the curve fitting and
the wavelength range where the extrapolation was applied. The
standard uncertainty due to extrapolation was found to be less
than 0.08% for both LEDs.
The uncertainty components due to absolute responsivity
at λ0 are obtained similarly to [20] and [22]. In addition,
the effect of polarization distribution of the source on the
responsivity of the PQED was studied. The polarization
distribution of the LEDs was measured using a polarizer in
front of the reference photometer. The proportions of p
polarized components were 49.9% and 50.3% for the blue and
the red LED, respectively. On the other hand, the calculation
described in the appendix gave corresponding values of
(35 ± 16)% and (55 ± 6)%. The quoted standard uncertainty
of the calculation is dominated by the uncertainty of the
predicted ratio given in [21]. Even without the measurement
of the polarization distribution, the standard uncertainty in
the responsivity of the PQED due to polarization is less than
0.002% for both LEDs, if the method described in the appendix
is used.
Two similar precision apertures were used for the
reference photometer and the PQED, and their areas had the
same uncertainty indicated in table 2. The PQED and the
reference photometer were aligned using a laser [29] in such
a way that the back-reflections from the wedged trap and
the V(λ) filter, respectively, were parallel with the incident
beam. The small angle between the aperture normal and the
optical axis was then measured and corrected. The transverse
movement of the PQED near optical axis was found to have
an effect of 0.05% mm−1 in the measured signal. The residual
uncertainty due to aperture alignment after the centring and
angular correction is 0.02%.
The uncertainty due to stray light was estimated to
be 0.01% by covering the detector side of the baffle
shown in figure 2 with white diffusely reflecting material.
On-site calibrations were performed after the photometric
measurements for the current-to-voltage converters and
multimeters used for photocurrent measurements.
The
uncertainty due to repeatability of the measurements was
estimated on the basis of data collected during one day. Finally,
the apertures of the reference photometer and the PQED were
at the same entrance plane within a standard uncertainty of
0.2 mm, causing a negligible standard uncertainty of 0.01% in
the comparison of illuminance measurements.
4. Conclusions
A new method has been developed for the basic realization
of photometric units based on the PQED operated at room
temperature. The PQED is used without the V(λ) filter, and
the photometric weighting is taken into account in the spectral
mismatch correction factor F . As a result, the new method
overcomes the problems associated with V(λ) filters, such as
low values at the blue and red slopes as well as temporal and
temperature drifts. The method is applicable to light sources
whose spectral irradiance is limited to silicon region, i.e. the
region where PQED has predictable responsivity.
In both the PQED-based method and the traditional
photometry, the accuracy of the wavelength scale produces
the largest contribution to the uncertainty when narrowband sources in the blue and red region are measured.
However, the wavelength scale of the spectroradiometer
can be conveniently calibrated using lasers as wavelength
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T Donsberg
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Metrologia 51 (2014) S276
Table 2. Uncertainty components of illuminance measurements using the reference photometer and the PQED. If the uncertainties for the
blue and red LED deviate, the value for the red LED is given in parenthesis.
100 × Relative standard uncertainty
Source of uncertainty
Photometer
PQED
Spectral mismatch correction factor, F
LED spectrum
relative spectral responsivity of the photometer/detector
Absolute responsivity of the detector, s(λ0 )
Aperture area, A
Aperture alignment
Stray light
Photocurrent measurement, i
Repeatibility of the measurement
0.006 (0.004)
0.44 (0.49)
0.10
0.07
0.02
0.01
0.006
0.03
0.15 (0.16)
0.002
0.007
0.07
0.02
0.01
0.003
0.03
Combined standard uncertainty
0.46 (0.51)
0.17 (0.18)
Expanded uncertainty (k = 2)
0.92 (1.01)
0.34 (0.36)
standards, and the method is more accurate than the wavelength
scale calibration of spectrophotometers using wavelength
transmission standards.
Illuminance values of narrow-band blue and red LED were
measured with the PQED-based method and with the reference
photometer. The congruent measurement results demonstrate
that the new method is suitable for characterization of narrowband LED sources, such as separately measured colours
of RGB lamps. In addition, the PQED-based method has
significantly lower uncertainty than the reference photometer
in the illuminance measurements of both LEDs. As the spectral
weighting is not dependent on a physical device, i.e. the filter,
the new method is not limited to photopic weighting. Thus, any
weighting in the visible spectrum can be used, such as mesopic,
scotopic, or spectrally flat for determination of broadband
radiometric quantities.
The PQED-based method was here demonstrated to
be applicable to illuminance measurements of narrow-band
LEDs. The method can also be extended to the realization
of other photometric units as with traditional photometers.
Furthermore, the new method is in principle applicable to
broadband solid state light sources based on phosphor LEDs.
In conclusion, realizing the illuminance and luminous intensity
units without a V(λ) filter using the PQED may give lower
uncertainty and a simpler method than with V(λ) weighted
photometers when narrow-band or white LEDs are measured.
Acknowledgments
Minna Santaholma is acknowledged for the design of precision
mechanics.
The research leading to these results has
received funding from the European Metrology Research
Programme (EMRP) project SIB57 ‘New Primary Standards
and Traceability for Radiometry’. The EMRP is jointly funded
by the EMRP participating countries within EURAMET and
the European Union.
Appendix
light source with uncontrolled state of polarization is used.
The method requires the measurement of the relative spectral
distribution of the light source and the photocurrent ratio of
the PQED photodiodes. As the photocurrents of the two
photodiodes can be measured separately, the photocurrent ratio
is easily obtained.
The photocurrent ratio, denoted here as α, is defined as
α=
i1
,
i2
(A1)
where i1 and i2 are the photocurrents measured by the first and
second photodiode, respectively, and the total photocurrent i
is the sum
(A2)
i = i1 + i2 .
From equations (A1) and (A2) we can obtain
i1 =
αi
1+α
and
i2 =
i
.
1+α
(A3)
The photocurrent ratio can be predicted for monochromatic
light at s and p polarization [21], denoted here as αs (λ)
and αp (λ). In turn, the photocurrents can be divided into
components due to incident light at s and p polarization:
i1 = i1,s + i1,p and i2 = i2,s + i2,p . By applying equation (A3),
the photocurrent ratio α can be written as
i1,s + i1,p
α=
i2,s + i2,p
α (λ)
αs (λ)
dλ + e,p (λ)Rp (λ) 1+αp p (λ) dλ
e,s (λ)Rs (λ) 1+α
s (λ)
=
,
e,s (λ)Rs (λ) 1+α1s (λ) dλ + e,p (λ)Rs (λ) 1+α1p (λ) dλ
(A4)
where e,s (λ) and e,p (λ) are the incident spectral fluxes and
Rs (λ) and Rp (λ) are the responsivities of the PQED at s and p
polarization, respectively. If the polarization distribution of the
light source is assumed to be wavelength independent—a good
approximation for narrow-band light source—we can define a
wavelength independent polarization ratio
This appendix describes the method to determine the
reflectance losses of the PQED when a non-monochromatic
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b=
e,p (λ)
.
e,s (λ)
(A5)
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T Donsberg
et al
Metrologia 51 (2014) S276
From (A4) and (A5) we can then obtain
s (λ)
e (λ)Rs (λ) α−α
dλ
1+αs (λ)
.
b = −
α−αp (λ)
e (λ)Rp (λ) 1+αp (λ) dλ
(A6)
Further, this can be used to calculate the responsivity of the
PQED at given polarization ratio b
Rb (λ) =
Rs (λ) + bRp (λ)
,
1+b
(A7)
which can be used as the absolute responsivity s(λ) for
equations (2) and (3).
References
[1] Metzdorf J 1993 Network and traceability of the radiometric
and photometric standards at the PTB Metrologia
30 403–8
[2] Ohno Y and Jackson J K 1995 Characterization of modified
FEL quartz-halogen lamps for photometric standards
Metrologia 32 693–6
[3] Zwinkels J C, Ikonen E, Fox N P, Ulm G and Rastello M L
2010 Photometry, radiometry and ’the candela’: evolution
in the classical and quantum world Metrologia 47 R15–32
[4] Jacob B 2009 Lamps for improving the energy efficiency of
domestic lighting Light. Res. Technol. 41 219–28
[5] Tsao J Y, Saunders H D, Creighton J R, Coltrin M E and
Simmons J A 2010 Solid-state lighting: an
energy-economics perspective J. Phys. D: Appl. Phys.
43 354001
[6] Khan N and Abas N 2011 Comparative study of energy saving
light sources Renew. Sust. Energy Rev. 15 296–309
[7] Haitz R and Tsao J Y 2011 Solid-state lighting: ‘the case’ 10
years after and future prospects Phys. Status Solidi a
208 17–29
[8] Fryc I, Brown S W, Eppeldauer G P and Ohno Y 2005
LED-based spectrally tunable source for radiometric,
photometric, and colorimetric applications Opt. Eng.
44 111309
[9] Park S, Kim Y W, Lee D H and Park S N 2006 Preparation of a
standard light-emitting diode (LED) for photometric
measurements by functional seasoning Metrologia
43 299–305
[10] Voigt D, Hagendoorn I A and van der Ham E W M 2009
Compact large-area uniform colour-selectable calibration
light source Metrologia 46 S243–7
[11] Hirvonen J-M, Poikonen T, Vaskuri A, K¨arh¨a P and Ikonen E
2013 Spectrally adjustable quasi-monochromatic radiance
source based on LEDs and its application for measuring
spectral responsivity of a luminance meter Meas. Sci.
Technol. 24 115201
[12] K¨arh¨a P, Baumgartner H, Vaskuri A, Renoux D and Ikonen E
2014 Natural and accelerated ageing of solid state lamps
Proc. NEWRAD 2014 Conf. (Espoo, Finland, 2014) pp
310–11
[13] Sametoglu F 2008 Influence of the spectral power distribution
of a LED on the illuminance responsivity of a photometer
Opt. Laser Eng. 46 643–7
[14] Poikonen T, K¨arh¨a P, Manninen P, Manoocheri F and Ikonen E
2009 Uncertainty analysis of photometer quality factor f1
Metrologia 40 75–80
[15] Sildoja M, Manoocheri F, Merimaa M, Ikonen E, M¨uller I,
Werner L, Gran J, K¨ubarsepp T, Smid M and Rastello M L
2013 Predictable quantum efficient detector: I. Photodiodes
and predicted responsivity Metrologia 50 385–94
[16] M¨uller I et al 2013 Predictable quantum efficient detector:
II. Characterization and confirmed responsivity Metrologia
50 395–401
[17] D¨onsberg T, Sildoja M, Manoocheri F, Merimaa M, Petroff L
and Ikonen E 2014 A primary standard of optical power
based on induced-junction silicon photodiodes operated at
room temperature Metrologia 51 197–202
[18] Manoocheri F, Sildoja M, D¨onsberg T, Merimaa M and
Ikonen E 2014 Low-loss photon-to-electron conversion Opt.
Rev. 21 320–4
[19] Sildoja M, Manoocheri F and Ikonen E 2009 Reflectance
calculations for a predictable quantum efficient detector
Metrologia 46 S151–4
[20] Gran J, K¨ubarsepp T, Sildoja M, Manoocheri F, Ikonen E and
M¨uller I 2012 Simulations of a predictable quantum
efficient detector with PC1D Metrologia 49 S130–4
[21] Sildoja M, D¨onsberg T, M¨antynen H, Merimaa M,
Manoocheri F and Ikonen E 2014 Use of the predictable
quantum efficient detector with light sources of uncontrolled
state of polarization Meas. Sci. Technol. 25 015203
[22] Toivanen P, K¨arh¨a P, Manoochehri F and Ikonen E 2000
Realization of the unit of luminous intensity at the HUT
Metrologia 37 131–40
[23] Baumgartner H, Vaskuri A, Poikonen T, D¨onsberg T, Pulli T,
Oksanen J, K¨arh¨a P and Ikonen E 2014 Measurement of
relative spectra of LEDs Proc. NEWRAD 2014 Conf.
(Espoo, Finland, 2014) pp 142–3
ˇ
[24] Vaitonis Z, Vitta P and Zukauskas
A 2008 Measurement of the
junction temperature in high-power light-emitting diodes
from the high-energy wing of the electroluminescence band
J. Appl. Phys. 103 093110
[25] Keppens A, Ryckaert W R, Deconinck G and Hanselaer P
2010 Modeling high power light-emitting diode spectra and
their variation with junction temperature J. Appl. Phys.
108 043104
[26] Brody J, Weiss D and Young P 2010 Observing the
Maxwell–Boltzmann distribution in LED emission spectra
Am. J. Phys. 78 933–5
[27] K¨arh¨a P, Toivanen P, Manoochehri F and Ikonen E 1997
Development of a detector-based absolute spectral
irradiance scale in the 380–900-nm spectral range Appl.
Opt. 36 8909–18
[28] K¨ubarsepp T, K¨arh¨a P, Manoocheri F, Nevas S, Ylianttila L
and Ikonen E 2000 Spectral irradiance measurements of
tungsten lamps with filter radiometers in the spectral range
290 nm to 900 nm Metrologia 37 305–12
[29] Bi-directional two-beam alignment laser, OMTec, Teltow,
Germany
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