“Light” “Measurement”

Thinking Photometrically, Part ILIGHTFAIR 2001 — Las Vegas, NVKevin W. Houser Pa

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Thinking Photometrically, Part I

Kevin W. Houser, Ph.D., LCUniversity of Nebraska-Lincoln

Copyright, 2001 © Kevin W. Houser

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What is Photometrics?

“Light”

“Measurement”

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What is Photometrics?

Photometrics can be thought of in terms of . . .

1. Photometrics for Light Sources(spectral issues)

2. Photometrics for Luminaires(directional issues)

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1. An understanding of the interrelationship between radiometry, the human visual system, and photometry

2. An appreciation of V() based photometry3. An understanding of spectral weighting

functions, including: photopic, scotopic, mesopic, tri-chromacy

What will you get out of today’s workshop?

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1. Review of fundamental quantities2. Relationships between fundamental

quantities3. Radiometry vs. Photometry4. Systems of Photometry

Photopic Scotopic Mesopic Systems based on Tri-Chromacy Systems endorsed by CIE

Presentation Outline


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Review of Fundamental Quantities 1 Luminous Flux

• “Total amount of lamp light in all directions”

• Measured in Lumens• Symbol =

8

Luminous Intensity• “Concentration of light in a

particular direction”• Measured in Candela• Symbol = I

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Illuminance• “Density of light on a

surface”• Measured in Lux (fc) • Symbol = E

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Exitance• “Density of light off or

through a surface”• Measured in Lumens/m2 or

Lumens/ft2

• Symbol = M

11 12

Luminance• “Concentration of light

directed toward the eye”• Measured in Candela/m2

• Symbol = L


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Fundamental Lighting Units

“Total amount of lamp light in all directions”Luminous Flux ( ) Lumen

“Concentration of light in a particular direction”Luminous Intensity (I) Candela

“Density of light on a surface”Illuminance (E) Footcandle, Lux

“Concentration of light directed towards the eye”Luminance (L) Candela

sq. foot or meter

Term Unit

“Density of light off or through a surface”Exitance (M) Lumen

sq. foot or meter

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Lux = LumenSq. Meter

Candela = LumenSteradian

Footcandle = LumenSq. Foot

What’s a Steradian?

Relationships between Fundamental Quantities 2

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Plane Angle: Radians

θ = lr

θ ~ Radians

l

rθ

16

Solid Angle: Steradians

Ω = Ar2

Ω ~ Steradians

17


r = 1

L = 1

W = 1

Ω = Ar2

(L)(W)r2

12

12 = 1 steradian= =18


r = 2

L = 2

W = 2

Ω = Ar2

(L)(W)r2

22

22 = 1 steradian= =


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Relationships Between Units

Consider a uniform one candela light source.

1 Ca

ndel

a

1 Candela

1 Candela

1 Candela 20

Now consider this source at the center of a sphere of unit radius.


1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

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1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

Now consider an opening of 1 sq. ft (or 1 sq. meter) at the surface of the sphere.

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A. 1 steradian

Q. What is the solid angle subtended by the opening?

1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

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1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

Q. How many lumens are passing through the opening?

A. 1 lumen

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1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

Q. What is the illuminance at any point on the inside of the sphere?

A. 1 fc (or 1 lx)



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1 Ca

ndel

a

1 Candela

1 Candela

1 Candela

1 Foot or1 Meter

Q. How many lumens does our uniform 1 cd source produce?

A. The sphere has a total area of 4π ft2 (or m2), and 1 lumen falling on each unit area. Therefore, it produces 4π lumens.


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1. Radiometry Not weighted for human vision Measurement of radiant energy (watts) Extents are the entire spectrum of radiant

energy2. Photometry

Energy that is weighted for some aspect of human vision

Extents are limited to the range of visible energy

Radiometry versus Photometry 3

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RadiantFlux (e ) Watts

RadiantIntensity (Ie )

Irradiance (Ee )

Radiance (Le )Watts

meter2 · sr

Radiometry

RadiantExitance (Me )

Wattsmeter2

Wattsmeter2

Wattssteradian

Counterpart Units

LuminousFlux ( ) Lumen

LuminousIntensity (I) Candela

Illuminance (E) Lux

Luminance (L) Candelameter2

Photometry

Exitance (M) Lumenmeter2

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Spectral Weighting FunctionsAKA: Luminous Efficiency Functions

Definition: Any mathematical function used to weight the spectral power distribution of an illuminant.

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Luminous Efficiency Functions

Underlying Principle

two stimuli produceequivalent visual response

ratio between radiances defines luminous efficiency

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Test t Reference r

Subjects adjust the test field until it matches the reference on a criterion visual response




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550360 830

Wavelength (nm)

100

0

50

Rad

ianc

e %

Test t

Ref r

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Weighting Factor @ t = Radiance rRadiance t



10.5

=

= 2

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550360 830

Wavelength (nm)

100

0

50

Lum

inou

s Ef

ficie

ncy

%

550360 830

Wavelength (nm)

550360 830550360 830

Wavelength (nm)

100

0

50Test t

Ref r

Weighting Factor @ t = Radiance rRadiance t



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There are many ways to quantify how radiant energy stimulates vision.

Spectral Weighting Functions

An Important Concept

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Conditions that could be considered when developing a photometric system fall under two general categories:

1. Visual Response Conditions

2. Viewing Conditions

Spectral Weighting Functions

An Important Concept

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Range of Ways to Quantify Radiant Energy

• Detection threshold• Brightness• Spatial resolution (visual

acuity)• Temporal resolution (flicker

detection)• Spatial contrast• Reaction time• Visual search• Attention• Color & form recognition

• Light level• Adaptation level• Eccentricity (foveal,

parafoveal)• Field size (point, 2°, 10°,

full-field)• Duration (steady, flash)• Observer age (young, adult,

aged)• Surround conditions

Visual Response Viewing Condition


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Photopic Scotopic Mesopic Systems based on Tri-Chromacy Systems endorsed by CIE

Systems of Photometry 4

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Systems of Photometry

Photopic“vision mediated essentially or exclusively by the cones”

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. . . . . . . Mole. . . . . . . . . . . . Ampere

. . . . . . . . . . . . . . . . . . . . . Meter. . . . . . . . . . . Candela

. . . . . . . . . . . . . . . . . . . . . . Gram. . . . . . . . . . . . . . . . Kelvin

. . . . . . . . . . . . . . . . . . . . . . Second

Amount of a Substance Electrical Current Length Luminous Intensity Mass Temperature Time

Base Quantities in the SI System

Defining the Base Unit of Light

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Q: What is Measurement?A: The assignment of numbers to

‘objects’ following some rule


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A: By reference to the V() function

Q: What is the ‘rule’ for assigning numbers to light?

Q: How is the Candela defined?


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550360 830

Wavelength (nm)

100

0

50Relative

Sensitivity(%)

The V() FunctionAKA: Photopic Luminous Efficiency Curve


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Defining the Candela

λλλ dVIKI emv )(830

360 ,=

Where:Iv = luminous intensity in candela [note: cd = lm·steradian-1]

Ie,λ = radiant intensity in W·sr-1·nm-1

V(λ) = spectral luminous efficiency for photopic visionKm = maximum spectral luminous efficiency (683 lm·W-1)

and the limits of integration are wavelength in nanometers44

Defining the Lumen

λλλ dVθKθ emv )(830

360 ,=

Where:θv = luminous flux in lumens [note: lm = cd·sr]θe,λ = radiant flux in W·nm-1

V(λ) = spectral luminous efficiency for photopic visionKm = maximum spectral luminous efficiency (683 lm·W-1)

and the limits of integration are wavelength in nanometers

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SPD for a100W A19

550380 770 nm

V() Function

Lumens

x

=

RelativeEnergy

RelativeSensitivity

ResultantRelativeEnergy

x

=

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SPD for aTL841

V() Function

Lumens

x

=

RelativeEnergy

RelativeSensitivity


x

=

550380 770 nm

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SPD for a70W HPS

V() Function

Lumens

x

=

RelativeEnergy

RelativeSensitivity


x

=

550380 770 nm48

SPD for a100W MH

(NA/SC)

V() Function

Lumens

x

=

RelativeEnergy

RelativeSensitivity


x

=

550380 770 nm


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SPD forD65

V() Function

Lumens

x

=

RelativeEnergy

RelativeSensitivity


x

=

550380 770 nm50

A Deeper Look at V()AKA: Photopic Photometry

It is important to understand the experimental context for V() because of the practical implications on lighting practice.

A Field of View

B Field Luminance

D Additivity Assumption

E Experimental Methods

Experimental Context for V():

C Wavelength Center of Gravity

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V() is based on a 2° to 3° field of view. A 2° field size is only about 0.01% of the total

visual field that we see with both eyes.

A Deeper Look at V()

A. Field of View

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Often less than 10 cd/m2

Field luminance in building interiors is more typically 50 to 200 cd/m2


B. Field Luminance

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Additivity “law” states that the luminance of a mixture of lights will be equal to the arithmetic sum of the component luminances

Only holds under restricted conditions Perhaps this assumption was driven by the

technology available in the early 1900’s


C. Additivity Assumption

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V() is (mostly) based on flicker photometry


D. Experimental Methods


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E. Wavelength Center of Gravity

Wavelength center of gravity is the wavelength that divides in half the area under the “visibility curve”.

It was believed that the “visibility curve” should have a wavelength center of gravity for a Plankian radiator at 2077 K.

Computed to be 581.6 nm, the curve was balanced and smoothed to meet this requirement.

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• Light level (~ 10 cd/m2)• Adaptation level• Eccentricity (foveal,


full-field)• Duration (steady, flash)• Observer age (young, adult,

aged)• Surround conditions (dark

surroundings)



Photopic

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V() works well for the conditions used in its derivation

Problems occur when it is applied out of context


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“Although spectral sensitivity functions are adequate to predict the amount of energy required to stimulate vision, they are very poor at describing the perceived effect of suprathreshold lights. For example, it is well know that perceived brightness differs significantly from photometric luminance under all but very restricted viewing conditions”

Dr. Alan Lewis

Some Interesting Quotations

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“. . . photopic illuminance alone does not adequately characterize the visual system spectral response, implying that lighting design for buildings based only on photopic spectral conditions does not capture an important and potentially valuable lighting attribute.”

Dr. Sam Berman


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“It is worth pointing out that the CIE . . . have come to regard its standard luminous efficiency function, on which all of photometry is based, as an arbitrary wavelength function adopted for its convenience and utility rather than because luminance so evaluated correlates with what the eye sees.”

Dr. Dean Judd



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“. . . There are many instances in which light is measured in the routine way, with light meters and photometers, and the values recorded bear little or no relationship to the visual impression.”

CIE Publication 41


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“. . . it is clear that the normal visual system has definite spectral likes and dislikes (not indicated by the ‘luminous efficiency’ curve) which bear on every light entering it.”

Dr. William Thornton


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Question:

Q: Is V() a rational way to quantify light for typical illuminating engineering applications?

A: . . .

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Scotopic“vision mediated essentially or exclusively by the rods”

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Scotopic

Conventional view is that rods are active at light levels below 0.034 cd/m2

(equal to illuminance of 0.0125 fc on 80% reflective white paper)

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Scotopic

550360 830

Wavelength (nm)

100

0

50Relative

Sensitivity(%)

Photopic V()

Scotopic V’()


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ScotopicApplications for Scotopic Photometry

Applicable when . . .– the visual surrounding is at extremely low

illuminance– the rods dominate the visual function– off-axis viewing (within central 20° field)

If electric lighting is present, we’re probably above the (traditional) scotopic range

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ScotopicModern View of Rod Function (Driven by Dr. Sam Berman)

Rods contribute to visual functioning at light levels above the traditional scotopic range

Rods (may) mediate the dilation and constriction of the pupil

Smaller pupils lead to improvements in:– Depth of field– Visual acuity

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ScotopicImplications of Dr. Berman’s findings for lighting practice

Vision can be improved by providing short wavelength energy in the peripheral field of view

Research suggests lamps with higher S/P ratios will result in better sight

The S/P ratio equals scotopic lumens divided by photopic lumens

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ScotopicS/P Ratios for Common Light Sources

RE875

Sun + Sky (D65)

Daylight

TL841

Warm White

50W HPS

MH (na/sc)

Incandescent

. . . . . . . . . . 2.47

. . . 2.47

. . . . . . . . . 2.15

. . . . . . . . . . . 1.62

. . . . . . 1.00

. . . . . . . . 0.62

. . . . . . . 1.49

. . . . . 1.41

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Mesopiceyes fully adapted to light levels between photopic and scotopic

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Mesopic

“Vision with fully adapted eyes to conditions between those of photopic and scotopic”

Between 3.4 and 0.034 cd/m2

Important region because many outdoor applications fall within this range


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Issues: No single function describes the visual

response – differs with luminance level No “official” mesopic system agreed upon


Mesopic

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550360 830

Wavelength (nm)

100

0

50Relative

Sensitivity(%)


Mesopic

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Mesopic

Issues: What is the most salient visual response for

mesopic photometry?– Brightness (Kinney, Palmer, Kokoschka, Ikeda, Sagawa)

– Reaction Time (He, et. al.)

– They give similar functions (Berman & Clear)

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• Light level• Adaptation level (0.034 – 3.4

cd/m2)• Eccentricity (foveal,


large-field)• Duration (steady, flash)• Observer age (young, adult,

aged)• Surround conditions



Mesopic

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Mesopic

Issues: Multiplying Factors

Use a lookup table with multipliers for equivalent “visual effectiveness” at different luminance levels.

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Mesopic PhotopicLuminance Light Source Multiplying Factor

(relative to HPS)

10 cd/m2

1 cd/m2

0.1 cd/m2

0.01 cd/m2

3000K FL

MHIncandescent

HPS

3000K FL

MHIncandescent

HPS

3000K FL

MHIncandescent

HPS

3000K FL

MHIncandescent

HPS

1.00

1.001.00

1.00

1.37

1.521.40

1.00

1.75

2.041.80

1.00

2.12

2.562.20

1.00

Lookup Method(Bierman, Rea)


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Tri-Chromacy & Brightness

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Tri-Chromacy of Human Vision

550360 830

Wavelength (nm)

100

0

50Relative

Sensitivity(%)

xy

z

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The three inputs act upon our neural system in a complex way


Opponent Colors ModelTri-Chromacy of Human Vision

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Opponent Colors ModelTri-Chromacy of Human Vision

Red/GreenOpponent

(R + B) - G

-

+

+ +

Red/GreenOpponent

(R + B) - G

Red/GreenOpponent

(R + B) - G

---

+++

+++ +++

AchromaticR + G

++

AchromaticR + G

AchromaticR + G

AchromaticR + G

++++++

xy

z

xxyy

zz Gxy

z

xxyy

zz

B xy

z

xxyy

zz Rxy

z

xxyy

zz Gxy

z

xxyy

zz Gxy

z

xxyy

zz

Bxy

z

xxyy

zz

B xy

z

xxyy

zz Rxy

z

xxyy

zz R

Blue/YellowOpponent

(R + G) - B +

++

-

Blue/YellowOpponent

(R + G) - B

Blue/YellowOpponent

(R + G) - B +++

++++++

---

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Opponent Colors Model as the Basis for a System of Photometry

A complex spectral weighing function based on the opponent colors model

General form may look like . . .

|(dR + eG + fB)|p+

|(gR + hG + iB)|p )1/p+

|(aR + bG + cB)|pβ = (

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Opponent Colors Model as the Basis for a System of Photometry

|(aR + bG + cB)|pβ = (

achromatic term

|(dR + eG + fB)|p+

R/G term

|(gR + hG + iB)|p )1/p+

B/Y term


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Rank Rank Rank

MH 100W Metal Halide (Na/Sc) 100 0.3777 9 0.1490 1 0.1698 2 4D65 CIE D65 Illuminant 100 0.4445 2 0.1416 9 0.1697 3 4.7DPLUS Daylight Deluxe Fluorescent 100 0.4251 3 0.1416 10 0.1804 1 4.7C50 5000K Colortone Fluorescent 100 0.4068 5 0.1421 6 0.1681 4 5CW Cool White Fluorescent 100 0.3829 7 0.1424 4 0.1665 6 5.7TL750 5000K RE Fluorescent 100 0.4169 4 0.1420 7 0.1650 7 6CW-EW Cool White EW Fluorescent 100 0.3718 11 0.1436 2 0.1670 5 6TL741 4100K RE Fluorescent 100 0.3786 8 0.1430 3 0.1625 9 6.7C75 7500K Colortone Fluorescent 100 0.4629 1 0.1409 12 0.1627 8 7CDM4K Metal Halide (Na/Tl/Dy/Li) 100 0.3957 6 0.1423 5 0.1600 10 7TL735 3500K RE Fluorescent 100 0.3682 12 0.1420 8 0.1600 11 10.3CDM3K Metal Halide (Na/Tl/Dy/Li) 100 0.3734 10 0.1409 13 0.1583 15 12.7WW Warm White Fluorescent 100 0.3539 16 0.1411 11 0.1598 12 13TL730 3000K RE Fluorescent 100 0.3634 14 0.1408 14 0.1584 14 14Halogen PAR38 Halogen 100 0.3581 15 0.1408 15 0.1589 13 14.3White HPS White SON HPS 100 0.3646 13 0.1408 16 0.1578 16 15Incan. 100W A19 100 0.3538 17 0.1407 17 0.1569 17 17HPS 70W High Pressure Sodium 100 0.3495 18 0.1406 18 0.1552 18 18

HowettThornton MeanRank

GuthPhotopicLumensLamp Description

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Endorsed by CIE

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CIE Spectral Weighting FunctionsAKA: Luminous Efficiency Functions

Function Usage

V() photopic 2°

V10() photopic 10° physiologically meaningful

V’() scotopic >2°

VM() photopic 2° physiologically meaningful

Vb,p() photopic point efficiency for brightness

Vb,2() photopic 2° efficiency for brightness

Vb,10() photopic 10° efficiency for brightness

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Other Lightfair Presentations

Thinking Photometrically, Part IIIan Ashdown

Photoreceptive Systems and Elderly & Others with Low/Poor VisionMark Rea, Alan Lewis

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Thank You

“Light” “Measurement”

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