APPENDIX: Measuring Light

Where vision is concerned, light is generally specified in photometric units, not in quanta (photons) and energy

Radiometry is the measure of radiant energy in the

electromagnetic spectrum

Photometry is the measure of the luminous effect of

radiant energy

For radiant energy to be “luminous”, it must be absorbed by

the photoreceptors and be effective for vision.

Photometry measures the luminous effect of radiant energy.

Commission Internationale de l’Eclairage (CIE)

Wavelength (nm)

400 450 500 550 600 650 700

RelativeLuminousEfficiency

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Photopic, VScotopic, V'

Fig. A-1. The photopic (V) and scotopic (V’)curves of relative luminosity as standardized by the Commission Internationale de l’Eclairage (CIE). Modified from Wright (1958)

Figure A1- 1. The photopic (V) and scotopic (V’) curves of relative spectral luminosity as standardized by the CIE. “m“ is the same as nanometers. Modified from Wright (1958).

V is the relative luminous efficiency of radiant energy:

the luminous efficiency relative to the maximum at 555

nm.

The scotopic (rod mediated) luminous efficiency

function, V (V lambda prime), is similar in shape to the

photopic curve but has a maximum (1.0) at a shorter

wavelength, 507 nm.

Wavelength (nm)

400 450 500 550 600 650 700

RelativeLuminousEfficiency

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Photopic, VScotopic, V'

Luminous efficiency is not brightness.

Just because something is twice as intense does not mean it is twice as bright!!

Photometric Terminology

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

P h o t o m e t r i c t e r m i n o l o g y

T h e o u t p u t o f a p o i n t s o u r c e i s c a l l e d l u m i n o u s f l u x a n d t h e

u n i t o f m e a s u r e i s t h e l u m e n .

A t a w a v e l e n g t h o f 5 5 5 n m , o n e l u m e n i s e q u a l t o

a p p r o x i m a t e l y 4 . 0 7 x 1 0 1 5 q u a n t a p e r s e c o n d e m i t t e d f r o m

t h e p o i n t s o u r c e . I n e n e r g y t e r m s , t h i s i s 1 . 4 6 x 1 0 4 e r g s o r

1 / 6 8 5 t h o f a w a t t .

L u m i n o u s i n t e n s i t y i s l u m i n o u s f l u x p e r u n i t s o l i d a n g l e .

I f o n e l u m e n i s e m i t t e d p e r s t e r a d i a n t h e n , b y d e f i n i t i o n , t h e

l u m i n o u s i n t e n s i t y i s e q u a l t o o n e c a n d e l a .

P o i n tS o u r c e

L u m i n o u s f l u x i s e m i t t e di n a l l d i r e c t i o n s f r o m ap o i n t s o u r c e o f l i g h t . Al u m e n i s e q u i v a l e n t t o4 . 0 7 x 1 0 5 q u a n t a / s e c o n da t 5 5 5 n m .

L u m i n o u s i n t e n s i t y i sl u m i n o u s f l u x i n a s o l i da n g l e . A c a n d e l a i sd e f i n e d a s o n e l u m e n /s t e r a d i a n .

L u m i n a n c e i s t h el i g h t t h a t c o m e s o f fa s u r f a c e w h e t h e rr e f l e c t e d o r e m i t t e d .I t i s m e a s u r e d i nc a n d e l a s / u n i t a r e a

I l u m i n a n c e i s w h a tf a l l s o n a s u r f a c e . I t i sm e a s u r e d i n l u m e n s /u n i t a r e a

q

rB

A

A steradian is "the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r2."

Table A.1 Luminous intensity of various sources.

SOURCE Approximate luminous Intensity

(candelas)

Sun 10 27

Electric arc 10 3

40 W light bulb 10 2

Candle flame 10 0

Illuminance is a photometric measure of the density of light

falling on a surface. It is expressed in lumens per unit area.

One lumen per m2 is a lux. One lumen per ft2 is a foot candle,

which is equal to approximately 10.8 lux.

Fig. A.2

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

Table A.2. Illuminance from various sources.

TARGET/SOURCE Illuminance

(lux)

On the earth from the sun at noon 10 5

On an eye chart from room lights 10 2.5

On walls of a typical room interior

from incident lighting 10 2

On the earth from a full moon 10 –1

Illuminance decreases in proportion to the square of the distance from the

light source

If F is the total luminous flux (in lumens) emitted by a point source at the center

of a sphere of radius r, then the illuminance (in lux) on the surface of the sphere

is given by:

Illuminance = F/4r2 Eq. A.1

This is the “famous” Inverse-square Law.

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

I l l u m i n a n c e d e c r e a s e s w i t h s u r f a c e o r i e n t a t i o n r e l a t i v e

t o t h e s o u r c e

T h e C o s i n e L a w o f I l l u m i n a n c e .

q cos )(1/r eIlluminanc 2 E q . A . 2

w h e r e r i s t h e p e r p e n d i c u l a r d i s t a n c e f r o m t h e s o u r c e o f

l u m i n o u s i n t e n s i t y , I , t o t h e s u r f a c e a n d q i s t h e a n g l e o f t i l t o f

t h e s u r f a c e .

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

Luminance is a photometric measure of the light emitted from

a surface.

The luminous intensity of the reflected or emitted light is

expressed in candelas per unit area of the emitting surface,

usually as candelas per square meter (cd/ m2).

PointSource

Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 1015 quanta/ secondat 555 nm.

Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.

Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area

iIluminance is whatfalls on a surface. It ismeasured in lumens/unit area

q

rB

A

Table A.3. Luminance of various sources. Modified from

Riggs (1965), Boynton, (1966) and Bartley (1951)

SOURCE Luminance (cd/m2)

Surface of sun at noon (clear day) 10 9

Tungsten filament 10 6

Upper limit of visual tolerance 10 4.7

White paper in sunlight (clear day) 10 4

Candle flame 10 4

Clear blue sky 10 3.8

Surface of moon (clear night) 10 3.3

Upper limit for rods (approximate) 10 2

White page in good reading light 10 1.7

Cone threshold (approximate) 10 –2

White paper in moonlight (clear night) 10 –2

White paper in starlight (clear night) 10 –4

Absolute threshold 10 –6

Photopic

Scotopic

Mesopic

For Reference:

1 lumen/m2 = 0.0929 lumen/ft2 (e.g., foot candles)

1 cd/m2 = 3.1416 apostilbs

= 0.2919 foot-lamberts

= 0.3142 millilamberts

T h e t r o l a n d ( t d ) , t h e u n i t o f r e t i n a l i l l u m i n a n c e , i s d e f i n e d a s

L , t h e l u m i n a n c e o f a s u r f a c e ( i n t h e d i r e c t i o n o f v i e w i n g )

m u l t i p l i e d b y t h e a r e a o f t h e e y e p u p i l , S . T h u s :

Sxtd L E q . A . 3

A s t i m u l u s w i t h a l u m i n a n c e o f 1 c d / m 2 v i e w e d t h r o u g h a

p u p i l w i t h a n a r e a o f 1 m m 2 ( 1 . 1 3 m m d i a m e t e r ) p r o v i d e s 1

t r o l a n d o f r e t i n a l i l l u m i n a n c e .

Reflectance is not a photometric term. Reflectance is the

ratio of the amount of light reflected from a surface divided by

the light incident on the surface.

Contrast is not a photometric term. Contrast is an expression of luminous

difference between two surfaces . The standard quantitative definition of contrast

for a target on a background is:

BBT /L)L(L - Eq. A.4

where LB is the luminance of the ref erence surface and L T is the luminance of the

second surface. If L T > LB then the contrast is positive; otherwise it is negative.

This is sometimes called “Weber Contrast ”

0 200 400 600 800 1000

RelativeLuminance

0

20

40

60

80

100

0

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100

0

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40

60

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100

Horizontal Position (arbitrary units)

0 200 400 600 800 1000

0

20

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60

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100

A

B

C

D

The contrast of sine-wave gratings is measured differently

Fig. 6.6

Horizontal Position (arbitrary units)

0 90 180 270 360 450 540 630 720

Relative Luminance

0

20

40

60

80

Width of 1 cycle

B

ALmax of A

Lmax of B

Lmin of B

Lmin of A

Mean Luminance

Sine-wave gratings are measured in terms of their spatial frequency defined as the number of cycles per degree of visual angle Fig. 6.7

There is a second definition of contrast used for gratings

(alternating light and dark bars) called “Michelson contrast” This

is defined as:

)L/(L)L(Lminmaxminmax

- Eq. A.5

where Lmax is the highest luminance in the grating and Lmin is

lowest luminance in the grating.

Specifying and Using Visual AngleStimulus size is often expressed in terms of visual angleFig. A.3

Specifying and Using Visual AngleStimulus size is often expressed in terms of visual angle

Two advantages:1) Provides a measure of the stimulus size on the retina2) That allows investigators in other labs to duplicate

the stimulus size (without needing to duplicate the equipment)

Objects A and B are the same size, but subtend different angles on the retina because they are at different distances from the cornea

Object C subtends the same angle as object A, so A and C would be indistinguishable based on retinal size and position alone

Can calculate the visual angles subtended by the visual stimuli:

Visual angles are expressed in degrees, minutes or seconds of arc

Large stimuli subtend visual angles expressed in degrees ()(e.g., a 10 spot) There are 360 in a circle

Smaller stimuli are described in minutes (’) of arc There are 60’ in 1 of arc

Still smaller stimuli are expressed in second (”) of arc There are 60” in 1’ of arc