UNEP-lites.asia Laboratory Training Workshop GELC Training 2015 3 Outline 1. Background of CIE 1931...
Transcript of UNEP-lites.asia Laboratory Training Workshop GELC Training 2015 3 Outline 1. Background of CIE 1931...
UNEP-lites.asia Laboratory Training Workshop
Beijing, China
22-24 April 2015
2 UNEP GELC Training 2015
Fundamentals of Colorimetry and
Practical Color Measurements
Yoshi Ohno CIE VP-Technical Elect, President-Elect
NIST Fellow, Sensor Science Division
National Institute of Standards and Technology
Gaithersburg, Maryland
UNEP GELC Lamp Performance Testing Training Workshop
April 22-24, 2015, Beijing
3 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
4 UNEP GELC Training 2015
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
Outline
5 UNEP GELC Training 2015
Three cone sensitivities
6 UNEP GELC Training 2015
Color Matching Experiments
Broadband Primaries (lamp+filters)
Guild (1931) Wright (1929)
lR=650 nm
lG=530 nm
lB=460 nm
2°
7 UNEP GELC Training 2015
Results
Wright (1929)
• Monochromatic
primaries (460, 530,
650 nm)
• 10 observers • 2° field of view
Guild (1931)
• red, green, blue filters
plus lamp
• 7 observers
• 2° field of view
B B R R G G
8 UNEP GELC Training 2015
CIE 1931 XYZ Color Matching Functions
Tristimulus Values
0. 0
1. 0
2. 0
350 400 450 500 550 600 650 700 750
Wavelengt h ( nm )
x牋?
y牋?
z牋?
()
()
()
X = k f(l)xl
ò (l)dl
Y = k f(l) yl
ò (l)dl
Z = k f(l)zl
ò (l)dl
f(l)
2° field of view observer
(applicable to 1° to 4° field of view)
(CIE 1931 Standard Colorimetric Observer)
9 UNEP GELC Training 2015
CIE 1964 10° Color Matching Functions
(CIE 1964 Supplementary Standard Colorimetric Observer)
Tristimulus Values
• Applicable to field of view greater than 4°.
• Used for some applications in object color, but not used
for light source specification.
X10 = k f(l)x10lò (l)dl
Y10 = k f(l)yl
ò10
(l)dl
Z10 = k f(l)zl
ò10
(l)dl
10 UNEP GELC Training 2015
Chromaticity coordinates
Tristimulus Values Chromaticity Coordinates
•Y is a measure of visual intensity of light stimulus.
• x, y, Y fully describes a light stimulus.
x =X
X +Y + Z
y =Y
X +Y + Z
X
Y
Z
11 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
12 UNEP GELC Training 2015
CIE 1931 (x, y) Chromaticity Diagram
Spectrum
locus
Purple
line
Color mixing
Chromaticity of a
mixture of two lights
lies along the line
between the two
chromaticity points
of the lights.
13 UNEP GELC Training 2015
Just noticeable
color differences.
(magnified by 10
times)
If the color space
were uniform,
these ellipses
would be circles
of the same size.
MacAdam Ellipses
14 UNEP GELC Training 2015
CIE 1960 (u, v) Chromaticity Diagram
(Now obsolete)
u =4X
X +15Y + 3Z
v =6Y
X +15Y + 3Z
In 1960, the CIE
developed Uniform
Chromaticity Scale
diagram, based on the
work of MacAdam.
u =4x
(-2x +12y + 3)
v =6y
(-2x +12y + 3)
15 UNEP GELC Training 2015
CIE 1976 (u’, v’) Chromaticity Diagram
¢u =4X
X +15Y + 3Z
¢v =9Y
X +15Y + 3Z
In 1976, CIE adopted an
amended Uniform
Chromaticity Scale which
gave better agreement
with experimental data:
u ' = u ; v ' =1.5v
¢u =4x
(-2x +12y + 3)
¢v =9y
(-2x +12y + 3)
16 UNEP GELC Training 2015
CIE (u’,v’) for chromaticity difference specification
CIE 1931 (x, y) Diagram CIE 1976 (u’, v’) Diagram
7-step MacAdam ellipses a circle with radius 0.008 on (u’v’) diagram.
Do not use MacAdam ellipses. x-step MacAdam ellises radius 0.00x
R=0.008
»
7 step
MacAdam
Ellipses
7 step
MacAdam
Ellipses
»
17 UNEP GELC Training 2015
CIE TN 001 (2014)
Primary author Y Ohno
Published July 2014
18 UNEP GELC Training 2015
The u'v' circle is specified with a centre point
and radius r on the (u',v') diagram, and expressed by,
Recommended to replace n-step
MacAdam ellipses
Available free at: http://files.cie.co.at/738_CIE_TN_001-2014.pdf
CIE TN 001 (2014)
19 UNEP GELC Training 2015
Conversions
¢u =4x
(-2x +12y + 3)
¢v =9y
(-2x +12y + 3)
(x,y) (u’,v’)
(u’,v’) (x, y)
x =9 ¢u
(6 ¢u -16 ¢v +12)
y =2 ¢v
(3 ¢u -8 ¢v + 6)
x =9u
(6u - 24v +12)
y =3v
(3u -12v + 6)
u =4x
(-2x +12y + 3)
v =6y
(-2x +12y + 3)
(x,y) (u,v)
(u,v) (x, y)
20 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
21 UNEP GELC Training 2015
Temperature [K] of a Planckian radiator whose radiation
has the same chromaticity as that of a given stimulus.
0.0
1.0
2.0
3.0
4.0
5.0
300 400 500 600 700 800
1000 K
2000 K
3000 K
5000 K
10000 K
20000 K
Re
lati
ve
Sp
ec
tra
l P
ow
er
Dis
trib
uti
on
Wav elength (nm)
Color Temperature
Planckian radiation
22 UNEP GELC Training 2015
Correlated Color Temperature (CCT)
Temperature [K] of a Planckian radiator whose chromaticity is closest to that of a given stimulus on the CIE (u’,2/3 v’) coordinate.
CIE (u’,2/3 v’) is the CIE
1960 (u, v) diagram,
which is now obsolete.
(CIE 15:2004)
23 UNEP GELC Training 2015
Chromaticity expression for lighting
CCT (Correlated Color Temperature)
(u’, v’) =
(0.245, 0.528)?
Duv
Duv (Shift from Planckian locus)
24 UNEP GELC Training 2015
Duv
Duv scale on (u’, v’) diagram
Closest distance from the Planckian locus on the (u', 2/3 v') diagram,
with + sign for above and - sign for below the Planckian locus.
Defined in ANSI C78.377
25 UNEP GELC Training 2015
CCT- Duv chart
3000 K 4000 K 5000 K 6500 K
2700 K 3500 K 4500 K 5700 K
7-step MacAdam
ellipses
(CCT in log scale)
26 UNEP GELC Training 2015
Direct approach (1) to calculate CCT and Duv
Triangular solution
(1) Create a table of CCT vs
distance di to BB locus on (u,v)
coodinate.
(2) Find the closest point in the
table.
(3) Solve the triangle for the
neighboring 2 points
x =dm-1
2 - dm+1
2 + l2
2l
Tx = Tm-1 + Tm+1 - Tm-1( ) ·x
l
Duv = [±sign] dm-1
2 - x2( )1/ 2
l
CCT u v distance d
Tx
Tx
Tm+1
Tm
Use Planck’s equation and color matching functions at 1 nm interval.
27 UNEP GELC Training 2015
Parabolic solution
Duv = [±sign] aTx
2+ bTx + C( )
d(T) = aT 2 +bT +C
(1) Create a table of CCT vs
distance di to BB locus on (u,v)
coodinate.
(2) Find the closest point in the
table.
(3) Parabolic fit for the neighboring
3 points.
Tx
Direct approach (2) to calculate CCT and Duv
Tm+1
Tm
28 UNEP GELC Training 2015
CCT Error in Triangular Solution
29 UNEP GELC Training 2015
Conversion from (CCT, Duv) back to (x, y)
Input: CCT T (K)
Duv Duv
1) Calculate (u0, v0) of the Planckian
radiator at T (K).
2) Calculate (u1, u1) of the Planckian
radiator at T+DT (K). DT=0.01 (K)
3) Calculate
(u0, v0)
(u1, v1)
(u, v)
du = u1 - u0
dv = v1 - v0
u = u0 + Duv × sinq
= u0 + Duv × dv / du2 + dv2
v = v0 + Duv × cosq
= u0 + Duv × du / du2 + dv2
¢ u = u
¢ v =1.5v
x = 9 ¢ u /(6 ¢ u -16 ¢ v + 12)
y = 2 ¢ v /(3 ¢ u - 8 ¢ v + 6)
(Included in Revision draft of C78.377)
30 UNEP GELC Training 2015
Simple calculation of Duv from (x, y) or (u’,v’)
Duv is normally calculated in the process of calculating CCT.
Below is a simple approximation formula, without calculation of CCT.
1) Convert (x, y) or (u’, v’) to (u, v)
u = ¢ u
v = 2 ¢ v / 3
2) Duv is obtained by
LFP = (u - 0.292)2 + (v - 0.24)2
a = arccosu - 0.292
LFP
æ
è ç
ö
ø ÷
LBB = k6 a6 + k5 a5 + k4 a4 + k3 a3 + k2 a2 + k1 a + k0
Duv =LFP - LBB
k6 -0.00616793
k5 0.0893944
k4 -0.5179722
k3 1.5317403
k2 -2.4243787
k1 1.925865
k0 -0.471106 (Included in C78.377-2011)
u = 4x/(-2x +12y + 3)
v = 6y/(-2x +12y + 3)or
31 UNEP GELC Training 2015
Simple calculation from (x,y) or (u’,v’) to Duv
Accuracy of this method
within 0.00001 in the range
from 2600 K to 20000 K and
Duv 0.000 ± 0.010
within 0.0001 in the range
from 2160 K to 20000 K and
Duv 0.000 ± 0.010
(Included in C78.377-2011)
32 UNEP GELC Training 2015
LEUKOS 10:1, 47-55, 2014 (DOI: 10.1080/15502724.2014.839020)
33 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
34 UNEP GELC Training 2015
ANSI and IEC (for Fluorescent Lamps)
CIE 1931 (x, y) Diagram
ANSI C78.376-2001 IEC 60081 for Fluorescent Lamps
35 UNEP GELC Training 2015
ANSI C78.377 for Solid State Lighting Products
2015 revision (in ballot)
Duv
±0.006
2011 revision (current)
First published in 2008.
Used in Energy Star and many
regulations worldwide
36 UNEP GELC Training 2015
Annex C. 4-step u’v’ circles Annex B. 4-step quadrangles
4-step version in C78.377-2015 (Informative Annex)
37 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
38 UNEP GELC Training 2015
Chromaticity below Planckian Locus
Lights below Planckian
locus look better.
Anecdotes say …
An example in neodymium
lamp
Current standard
39 UNEP GELC Training 2015
NIST Spectrally Tunable Lighting Facility
40 UNEP GELC Training 2015
41 UNEP GELC Training 2015
Experiments made at 4
CCTs, at 6 Duv points at
each CCT, at total 23
points.
Total 50 spectra used.
• 18 subjects participated.
• Subjects viewed fruits on
the table, his/her skin tone
and the whole room.
• Selected lights that looked
―more natural‖.
2013 Vision Experiment at NIST
on Preferred and Acceptable level of Duv
42 UNEP GELC Training 2015
2013 Vision Experiment at NIST
on Preferred and Acceptable level of Duv
Results
Y. Ohno and M. Fein, Vision Experiment on Acceptable and Preferred White Light
Chromaticity for Lighting, CIE x029:2014, pp. 192 – 199 (2014)
Duv ≈
-0.015
Proposal made to ANSI
C78.377 to allow such products.
Another experiment planned for
summer 2015 at NIST.
43 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
44 UNEP GELC Training 2015
Object Color Measurement
Reflectance factor
R(λ)
sample
Eye or detector
Wavelength (nm)
Rela
tive p
ow
er
Wavelength (nm)
Rela
tive r
eflecta
nce
Light source
S()
Reflected light
S(λ) • R(λ)
Wavelength (nm)
Rela
tive r
eflection
45 UNEP GELC Training 2015
Y gives luminance factor of the surface in %
(for the given illumination).
Trisimulus values
R(): Spectral reflectance factor of object surface
S(): Spectral distribution of illumination (standard illuminant).
Tristimulus Values for Object Colors
k =100 S(l)l
ò y(l)dl Y= 100 (%) for a
perfect diffuser.
X = k S(l)R(l)l
ò x(l)dl
Y = k S(l)R(l)l
ò y(l)dl
Z = k S(l)R(l)l
ò z(l)dl
46 UNEP GELC Training 2015
CIE Standard Illuminants
Standard Illuminant A: Representative of tungsten-filament lighting with
a color temperature of 2856 K.
Standard Illuminant D65: Representative of average daylight with a CCT
of ~6500 K.
Other Daylight Illuminants D50, D55, D75
<Now obsolete> Illuminant B: direct sun light with a CCT of ~4900 K
Illuminant C: average daylight with a CCT of ~6800 K
( realized by a tungsten source with a prescribed liquid filter.)
*Formulae to calculate values of Illuminants A and D are available in CIE 15:2004
Wavelength (nm)
Rela
tive p
ow
er
Wavelength (nm)
Rela
tive p
ow
er
To Calculate Object Color, one of standard illuminants is used.
47 UNEP GELC Training 2015
Light Color vs. Object Color
Chromaticity diagrams such as
(x,y), (u’,v’) are two-dimensional
and are only for light color. These
are not for object color.
No black, grey, or brown
Object color needs another axis: black—white
Object color needs a 3-dimensional color space.
48 UNEP GELC Training 2015
Object Color Space
Three attributes of object
color are hue, chroma
(saturation), and lightness,
and are expressed in a three
dimensional space.
To allow accurate
specification of object colors
and color differences, CIE
recommended
CIELAB and
CIELUV
in 1976.
3D color space
Lig
htn
ess
Hue
Chroma
white
black
49 UNEP GELC Training 2015
CIE 1976 (L*a* b*) color space
(CIELAB color space)
L*=0
L*=100
: for object surface
: white reference
(perfect diffuser)
L* =116 (Y /Yn )1/3 -16
a* = 500 (X / Xn )1/3 - (Y /Yn )1/3éë
ùû
b* = 200 (Y /Yn )1/3 - (Z / Zn )1/3éë
ùû
(when X / Xn, Y /Yn, Z / Zn > 0.008856)
X, Y, Z
Xn, Yn, Zn
See CIE 15:2004 for more details.
50 UNEP GELC Training 2015
Example: (a*,b*) plots of 1200 Munsell color samples
Ref. D65
51 UNEP GELC Training 2015
Color difference formulae
CIELAB space
CIEDE2000 (Improved formula)
See CIE 142:2001 DE00
*
• is occasionally used for displays
as they simulate object colors.
• is used for uncertainties of object
color measurements.
52 UNEP GELC Training 2015
Comparison of object color spaces
Illum. A
D65
CIE L*a* b* (CIELAB) or CIE L*u* v* (CIELUV)
are the current CIE recommendations.
Plot of 15 saturated
Munsell samples
(used in CQS).
CIELAB CIELUV W*U*V* (used in CRI, obsolete)
53 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
54 UNEP GELC Training 2015
Investigating problems of the CRI
Color Rendering Index (CRI) CIE 13.3
Reference source Test source
Planckian
(CCT<5000 K)
CIE
Dxx
Standard Daylight
(CCT > 5000 K)
Same CCT [K]
#1 #2 #3 #4 #5 #6 #7 #8
#9 #10 #11 #12 #13 #14
Ra
R9
55 UNEP GELC Training 2015
1. CRI (Ra) badly penalizes visually preferred lights
Problems of CRI
2. Good CRI (Ra) score does not guarantee good color rendering
CCT 4929 K, Duv-0.001
CRI Ra = 70
CCT 5020 K, Duv 0.000
CRI Ra = 82, R9 = -99
56 UNEP GELC Training 2015
15 saturated test color samples
Update the old formulae in CRI • CIELAB color space
• CMCCAT2000 chromatic adaptation
• 0 to 100 scale
• RMS averaging of color differences
Saturation factor (address the Hunt effect)
Standards work for new metric is still on-going (in CIE, IES)
CQS is used as a tool for color quality design.
Color Quality Scale (CQS) Proposed by NIST to improve CRI on these problems
Improvement of CRI, produces one number score that
correlates well with perceived naturalness for real objects.
W. Davis and Y. Ohno, Color Quality Scale, Optical Engineering 49 (3), 033602 March 2010
57 UNEP GELC Training 2015
CQS 9.0 EXCEL sheet (Color Rendering Simulation)
Used by many companies as a design tool for color quality
58 UNEP GELC Training 2015
Narrowband theoretically more efficient
~20 to 25 % increase
B-Y + broad Red RGBA (simulation)
LER= 310 lm/W LER= 375 lm/W LER= 382 lm/W
B-Y + narrow Red
Looking at ―Luminous Efficacy of Radiation‖
59 UNEP GELC Training 2015
Outline
1. Background of CIE 1931 colorimetry system
2. Chromaticity diagrams and MacAdam ellipses
3. CCT and Duv
4. ANSI chromaticity specification for SSL
5. Preferred white light chromaticity
6. Object color specification, CIELAB space
7. CRI and color quality
8. Practical color measurements of LED products
60 UNEP GELC Training 2015
Color Quantities of Light Sources
All light sources:
Chromaticity coordinates (x,y), (u’, v’)
White light sources:
Correlated color temperature Tc(K)
Duv Duv
Color Rendering Index (CRI) Ra
Narrow-band sources (LEDs):
Dominant wavelength d (nm)
61 UNEP GELC Training 2015
Dominant Wavelength
Wavelength of the monochromatic stimulus that, when additively
mixed in suitable proportion with a specified achromatic stimulus,
yields a color match with the color stimulus considered.
Achromatic stimulus is usually equal energy spectrum:
(x,y)=0.3333, 0.3333)
If this is the
colored
stimulus
and this is the
achromatic
stimulus,
then a line
connecting the two
and going to the
spectral locus ends
at the dominant
wavelength
62 UNEP GELC Training 2015
Peak wavelength vs. Dominant wavelength
Peak wavelength
(628 nnm)
Dominant
wavelength
(618 nm)
63 UNEP GELC Training 2015
Examples of real LEDs Peak WL
(nm)
Dom. WL
(nm)
Difference
(peak-dom)
(nm)
443 450 -7
454 459 -5
457 462 -5
458 463 -6
463 468 -6
471 475 -3
476 479 -3
497 499 -2
504 506 -2
517 523 -6
522 529 -7
525 532 -7
530 538 -9
592 590 3
599 596 3
628 618 9
638 626 12
Peak vs. Dominant Wavelength
64 UNEP GELC Training 2015
Conversion from Photometric to Radiometric Quantities
Conversions can be made by knowing the relative
spectral power distribution S ) of the light
source:
[cd] [W/sr]
[lm] [W]
Km = 683 [lm/W]
Xv: photometric quantity (e.g., Iv [cd])
Xe: radiometric quantity (e.g., Ie [W/sr])
This ratio K is called luminous efficacy of radiation (LER).
[lm/W]
Xv
Xe
= K =Km S
lò (l)V (l)dl
S(l)dll
ò
65 UNEP GELC Training 2015
Measurement of Spatially-averaged color
A sphere-spectroradiometer directly measures the spatially
averaged color quantities.
< Sphere-spectroradiometer system >
66 UNEP GELC Training 2015
Gonio-spectroradiometer
This method may be used when a sphere-
spectroradiometer system is not available, or the
test sample is too large for such a system.
1. A goniometer equipped with a
spectroradiometer
(gonio-spectroradiometer)
2. A goniometer equipped with a colorimeter
(gonio-colorimeter) …. This must be calibrated
against a spectroradiometer for each SSL product
measured.
LM-79
67 UNEP GELC Training 2015
Calculation of spatially averaged color
Example for chromaticity x
LM-79
68 UNEP GELC Training 2015
Sources of uncertainty in a spectrometer
• Uncertainty of reference standards (spectral irradiance,
total spectral radiant flux)
• Input optics geometry
• Wavelength scale error
• Bandpass and scanning interval
• Random noise
• Stray light
• Detector non-linearity
• Detector zero drift
Ref: Colorimetry – Understanding the CIE System, edited by J. Schanda, John
Wiley and Sons, pp.101-134 (2008).
Chapter 5 Spectral Color Measurement (Y. Ohno)
Appendix 2 Uncertainties in Spectral Color Measurement (G. Gardner)
69 UNEP GELC Training 2015
Bandpass error
0.0
0.2
0.4
0.6
0.8
1.0
1.2
460 510 560
Wavelength (nm)
LED model
Measured (10 nm BP)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
350 450 550 650 750
Wavelength (nm)
Cool White FL
Measured (5 nm BP)
Error in u’v’
• Bandwidth of 5 nm (FWHM) or less is
acceptable for colorimetry of most light sources.
• Error is proportional to the square of bandwidth
increase.
70 UNEP GELC Training 2015
Bandpass error correction
• Applies only to a triangular bandpass
• Bandwidth and scanning interval
must be matched.
S0 =1
98M-2 -
12
98M-1 +
120
98M0 -
12
98M1 +
1
98M2
Corrected value: S0
Stearns and Stearns method (S-S method) (also, ASTM E308)
71 UNEP GELC Training 2015
Corrected value S0 is obtained from the neighboring five points.
I0 = s(l, l0 )ò dl
I1 = s(l,l0 )lò dl
I2 = s(l, l0 ) l2ò dl
Calculated numerically
for any bandpass function
æ
è ç
ö
ø ÷
S0 = b-2 × M-2 + b-1 × M-1 + b0 × M0 + b1 × M1 + b2 × M2
with b-2 =a-1
2
X, b-1 = -
a-1
X, b0 =
a0
X, b1 = -
a1
X, b2 =
a1
2
X,
and X = a0
2- 2a-1a1.
Ohno-Gardner method for bandpass correction
Y. Ohno, A Flexible Bandpass Correction Method for Spectrometers (AIC 2005)
J. Gardner, Bandwidth correction for LED chromaticity, Color Res. Appl. 31(5) 374-380
Applicable to any bandpass functions, non-triangular, asymmetric, not
matched with scanning interval.
72 UNEP GELC Training 2015
How to determine the bandpass of an array spectrometer
(3) Fit to a model
(2) Wavelength-reversed data.
(1) Measure emission line.
(4) Normalize it
b(m, l0 ) =brel(m, l0 )
brel(m, l0 )m
ò
Y. Ohno, Measurement of Bandpass for Array Spectrometers, Proc., CIE 27th Session, July 2011
73 UNEP GELC Training 2015
Stray Light Error
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
400 450 500 550 600 650 700 750
Wavelength (nm)
Re
lati
ve
po
wer
Diode-array
NI ST/5nm BP
RED # 9 9 56
x=0.7055
y=0.2945
x=0.7035(∆x= -0.0020)
y=0.2951(∆y=+0.0006)
Example
Correction methods
available
Ref: Y. Zong et al, Appl. Opt. 45-6 (2006)