Radiometry is the science of measuring radiation, including separate wavelengths across the electromagnetic spectrum. Photometry specifically measures light visible to the human eye. Key radiometric quantities include radiant flux (watts), irradiance (watts/m2), and radiance (watts/m2/sr). Key photometric quantities are luminous flux (lumens), illuminance (lux), and luminance (candelas/m2). These radiometric and photometric quantities are related through the CIE luminous efficiency curve. Blackbody radiation follows Planck's law, Stefan-Boltzmann law, and Wien's displacement law, describing the spectral distribution and total power of electromagnetic radiation emitted by a

1. Radiometry and Photometry
Definition
Radiometry: The science of radiation measurement. The detection and
measurement of radiant energy, either as separate wavelengths or
integrated over a broad wavelength band, and the interaction of
radiation with matter in such ways as absorption, reflectance and
emission.
Photometry: The science of the measurement of light intensity, where
"light'' refers to the total integrated range of radiation to which the eye is
sensitive. It is distinguished from radiometry in which each separate
wavelength in the electromagnetic spectrum is detected and measured,
including the ultraviolet and infrared.

2. Radiometry and Photometry
F, Flux M, Flux/Proj. Area
I, Flux/W L,Flux/AWE, Flux/Area Rcd.
Radiant Flux
Watts
Luminous Flux
Lumens
Radiant Exitance
Watts/m2
Luminous Flux
Lumens/m2=Lux
A /
Radiance
Watts/m2/sr
Luminance
Lumens/m2/sr
1 Lambert=
(1L/cm2/sr)/p
1 ft Lambert = (1L/ft2/sr)/p
1m Lambert = (1L/m2/sr)/p
Radiant
Intensity
Watts/sr
Luminous
Intensity
Lumens/sr
1 Candela=1cd=1L/sr
W/
Irradiance
Watts/m2
Illuminance
Lumens/m2=
Lux
1 Ft Candle=1L/ft2
1 W is 685 L
at 555 nm.
Radiometric quantities
are related to photometric
quantities through the
CIE luminous efficiency
curve
Photometric unit = K() 
radiometric unit
Where K() = 685 V()

3. Radiometry and Photometry
Radiometric quantities
Radiometry is the science that allows us to answer “how much light is there?”
Quantity Symbol Units
Energy Q J
Power (flux) P, Φ W
Intensity I W / sr
Irradiance E W / m2
Exitance M W / m2
Radiance is the
most fundamental
radiometric quantity
Radiance W / (m2 sr)
“spectral” anything = per unit wavelength or frequency
ex. “spectral radiance” W / (m2 sr nm)
L
Q
t


P
W
P
A


2
P
A

 W
incident
exiting

4. CIE Luminous Efficiency Curve
Radiometric quantities are related
to photometric quantities through
the luminous efficiency curve.
The luminous flux corresponding
to 1W of radiant power at any
wavelength is given by the
product of 685lm and luminous
efficiency at the same
wavelength.

5. The Unit Solid Angle
One of the key concepts to understand the relationship between the
different photometric quantities is that of the solid angle, or
steradian. A steradian is defined as the solid angle which, from the
centre of a sphere, cuts off an area of the surface of that sphere equal
to the square of its radius. A full sphere therefore contains 4p
steradians.
The solid angle (W) in steradians is equal to the spherical surface
area (A) over which it is measured divided by the square of the
radius (r) at which it is measured.
W = A/r²

6. Radiant flux is a measure of how much radiometric power is being emitted by
a source. Flux, expressed in watts, is a measure of the rate of energy flow in
joules per second (J/s).
Luminous flux, on the other hand, is a measure of the power of visible light.
This measure depends on the sensitivity of the human eye and is therefore
based on the CIE Luminous Efficacy Curve for photopic conditions.
Thus the radiosity of any given light can be vastly different from its
luminosity depending on the spectral content of its emission, meaning that we
have to distinguish between the flow of energy (radiometric) and the flow of
light (photometric).
Radiant and Luminous Flux

7. Irradiance is a measure of radiometric flux per unit area, or flux density,
and is typically expressed in Watts per square meter (W/m²). It is
basically the amount of radiometric energy flowing in a particular
direction.
Illuminance, however, is a measure of photometric flux per unit area, or
visible flux density. Illuminance is typically expressed in lumens per
square meter (lux) or lumens per square foot (foot-candles).
Irradiance and Illuminance

8. Radiance is a measure of the flux density per unit solid viewing
angle, expressed in W/m²/Sr. Luminance is a measure of the
photometric brightness of a surface and is given in cd/m² or asb. As
such it is based on the amount of light being output or reflected off
surfaces in the environment. The human eye and the camera both
respond only to luminance.
Radiance and Luminance

9. Radiant Intensity is a measure of
radiometric power per unit solid angle,
expressed in watts per
steradian. Similarly, luminous
intensity is a measure of visible power
per solid angle, expressed in candela
(lumens per steradian).
Inverse Square Law
Radiant Intensity (I) is related to
irradiance (E) by the inverse square
law, as shown below:
I = E * r²
The flux leaving a point source within
any solid angle is distributed over
increasingly larger areas, producing an
irradiance that decreases with the
square of the distance
Radiant Intensity and luminous Intensity

10. Lambert's cosine law
Flux per unit solid angle leaving a surface in any direction is
proportional to the cosine of the angle between that direction
and the normal to the surface. A material that obeys Lambert's
cosine law is said to be an isotropic diffuser; it has the same
sterance (luminance, radiance) in all directions.
I() = I(0)cos (Lambert’s cosine law)
If the radiance at each angle is constant then
Le = I()/Acos()=I(0)cos()/Acos()= I(0) / A
Thus, when a radiating surface has a radiance that is
independent of the viewing angle, the surface is said to be
perfectly diffuse or a Lambertian surface.

11. Blackbody Radiation
 “Glowing red hot”--blackbody radiation is the name given to
electromagnetic radiation emitted by a heated object.
 Solids and dense gases give off blackbody radiation
 Thermal radiation spectrum range: 0.1 to 100 mm
 It includes some ultraviolet (UV) radiation and all visible (0.4-0.76
mm) and infrared radiation (IR).

12. Blackbody Radiation
 A blackbody is an ideal absorber: all radiation falling on a
blackbody, irrespective of wavelength or angle of incident, is
completely absorbed.
 A blackbody is also a perfect emitter: no body at the same
temperature can emit more radiation at any wavelength or
into any direction than a blackbody.

13. Blackbody Radiation
 Planck’s Law
 1900, Max Planck derived mathematical law describing distribution of
brightness in blackbody spectrum
 Stefan-Boltzmann Law
 Energy emission is greater at every wavelength as temperature increases;
total amount of radiant energy emitted increases with increasing temperature
 Wien’s Displacement Law
 Maximum emission found toward shorter wavelengths (blue end of
spectrum) as temperature increases

14. Radiation Laws
 Planck’s Law
The formula describing the spectral radiant emittance of a perfect blackbody
as a function of its temperature and the wavelength of the emitted radiation.
 Stefan-Boltzmann Law
The formula that indicates the total radiation at all wavelengths from a
perfect blackbody.
W Total = 5.67 x 10-12 T 4(W/cm2)
 Wien’s Displacement Law
The formula that gives the wavelength of maximum spectral radiant
emittance of a perfect blackbody:
lmax = 2898/T(µm)









1
110745.3
/143885
8
T
e
M 

(W/m2-m)

15. Blackbody Radiation
 Radiation emitted by stars tends to
be much like that emitted by
blackbody
 Planck’s Law
 Stephan-Boltzmann Law
 Wien’s Displacement Law

16. Colour
 White light, or nearly white light from the Sun, contains a
continuous distribution of wavelengths.
 The light from the Sun is essentially that of a blackbody
radiator at 5780 K.
 The wavelengths (spectral colours) of white light can be
separated by a dispersive medium like a prism.
 Even more effective separation can be achieved with a
diffraction grating.
http://www.educypedia.be/education/physicsjavacolor.htm

17. Colour
Approximate model for sunlight:
 Assume the intensities for red (R), blue (B) and green (G)
are roughly equal.
 Also: Ignore its emissions in the colors orange, yellow,
and violet.
 We call the colours R, G, and B the primary additives.

18. Colour
 R, G, and B
Why are they the primary additives?
Because experiment shows:
Any perceived colour can be matched by an additive combination of
R, G and B.
Just choose appropriate relative intensities.
Reason: The eye has three types of sensors in the retina. They are each
sensitive to either R, G, or B light.
Note: One way we perceive white is when all primary colors enter the
eye in equal amounts.

19. Rules of colour mixing: additive
Additive Combining
You need to know these four facts:
R + G = Y (yellow).
R + B = M (magenta).
G + B = C (cyan).
R + G + B = W (white).
Important note:
We are combining light sources.
That is, each colour in the sum is entering our eye, simultaneously.

20. Rules of colour mixing: additive

21. Example: Colour TV
 Most TV tubes produce color as follows:
 Use three different phosphors on the screen, arranged in tiny dots.
 The three phosphors produce red, green or blue light, when struck
by the electron beam of the tube.
 The eye integrates the tiny dots to produce a mixture of the three
primaries.
 The three types produce red, green or blue light when an electron
beam impinges.
http://www.educypedia.be/education/physicsjavacolor.htm

22. Rules of colour mixing: subtractive
Subtractive combining
Subtractive colour mixing is the kind of mixing you get if you
illuminate colored filters with white light from behind
The commonly used subtractive primary colours are cyan,
magenta and yellow, and if you overlap all three in
effectively equal mixture, all the light is subtracted giving
black. Subtractive colour mixing is more complex than the
additive colour mixing you get with coloured spotlights.

23. Rules of colour mixing
http://www.educypedia.be/education/physicsjavacolor.htm

24. Subtractive Colour Mixing: Filters
Filters
 A filter absorbs light of certain colours. It lets
through the other colours.
 Example
 An ideal red filter absorbs all colours but red light. It
transmits red light.
 In the model W = R + G + B, the red filter absorbs
blue and green light, transmits red.
Subtractive Mixing Problems
 Two colors are mixed finely.
Or, two filters overlap.
 What is the resulting colour?
(Always assume white light is incident.)
http://www.educypedia.be/education/physicsjavacolor.htm

25. Exercise
1. We make a fine mixture of R and B paints. What color is
the mixture?
2. A yellow filter is put on an overhead projector above a
slit. What primary colours are absent? Why?
3. White light is incident on a pair of overlapping green and
red filters. What light emerges?
4. Mix cyan and yellow paint. What is the color of the
mixture?
http://www.educypedia.be/education/physicsjavacolor.htm