UNEP-lites.asia Laboratory Training Workshop GELC Training 2015 3 Outline 1. Background of CIE 1931 colorimetry system 2. Chromaticity diagrams and MacAdam ellipses 3. CCT and Duv

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


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




3. CCT and Duv






Outline


Three cone sensitivities


Color Matching Experiments

Broadband Primaries (lamp+filters)

Guild (1931) Wright (1929)

lR=650 nm

lG=530 nm

lB=460 nm

2°


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


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)


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


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


Outline



3. CCT and Duv







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.


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


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)


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)


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

»


CIE TN 001 (2014)

Primary author Y Ohno

Published July 2014


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)


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)


Outline



3. CCT and Duv







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


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)


Chromaticity expression for lighting

CCT (Correlated Color Temperature)

(u’, v’) =

(0.245, 0.528)?

Duv

Duv (Shift from Planckian locus)


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


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)


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.


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


CCT Error in Triangular Solution


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)


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


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)


LEUKOS 10:1, 47-55, 2014 (DOI: 10.1080/15502724.2014.839020)


Outline



3. CCT and Duv







ANSI and IEC (for Fluorescent Lamps)

CIE 1931 (x, y) Diagram

ANSI C78.376-2001 IEC 60081 for Fluorescent Lamps


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


Annex C. 4-step u’v’ circles Annex B. 4-step quadrangles

4-step version in C78.377-2015 (Informative Annex)


Outline



3. CCT and Duv







Chromaticity below Planckian Locus

Lights below Planckian

locus look better.

Anecdotes say …

An example in neodymium

lamp

Current standard


NIST Spectrally Tunable Lighting Facility



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


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.


Outline



3. CCT and Duv







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


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


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.


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.


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


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.


Example: (a*,b*) plots of 1200 Munsell color samples

Ref. D65


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.


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)


Outline



3. CCT and Duv







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


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


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


CQS 9.0 EXCEL sheet (Color Rendering Simulation)

Used by many companies as a design tool for color quality


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‖


Outline



3. CCT and Duv







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)


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


Peak wavelength vs. Dominant wavelength

Peak wavelength

(628 nnm)

Dominant

wavelength

(618 nm)


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


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


Measurement of Spatially-averaged color

A sphere-spectroradiometer directly measures the spatially

averaged color quantities.

< Sphere-spectroradiometer system >


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


Calculation of spatially averaged color

Example for chromaticity x

LM-79


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)


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.


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)


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.


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


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)


THANK YOU for your

attention.

Contact: [email protected]

Documents

UNEP-lites.asia Laboratory Training Workshop GELC Training 2015 3 Outline 1. Background of CIE 1931 colorimetry system 2. Chromaticity diagrams and MacAdam ellipses 3. CCT and Duv