Chapter 1 radiometry_and_photometry

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.


, Flux M, Flux/Proj. Area

I, Flux/ L,Flux/AE, Flux/Area Rcd.

Radiant FluxWattsLuminous FluxLumens

Radiant ExitanceWatts/m2

Luminous FluxLumens/m2=Lux

A /

RadianceWatts/m2/srLuminanceLumens/m2/sr1 Lambert=(1L/cm2/sr)/

1 ft Lambert = (1L/ft2/sr)/1m Lambert = (1L/m2/sr)/

Radiant IntensityWatts/srLuminous IntensityLumens/sr

1 Candela=1cd=1L/sr

/

IrradianceWatts/m2

IlluminanceLumens/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 unitWhere K() = 685 V()


Radiometric quantitiesRadiometry 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 themost fundamentalradiometric quantity

Radiance W / (m2 sr)

“spectral” anything = per unit wavelength or frequencyex. “spectral radiance” W / (m2 sr nm)

L

Q

t

P

P

A

2P

A

incident

exiting

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.

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

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

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

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

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 LawRadiant 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

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.

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).

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.

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

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

TeM

(W/m2-m)

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

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

ColourApproximate 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.

Colour

R, G, and BR, G, and BWhy are they the Why are they the primary additivesprimary additives??

Because experiment shows: Because experiment shows: Any perceived colour can be matched by an additive combination of Any perceived colour can be matched by an additive combination of R, G and B.R, G and B.

Just choose appropriate relative intensities.Just choose appropriate relative intensities.Reason: The eye has three types of sensors in the retina. They are each Reason: The eye has three types of sensors in the retina. They are each sensitive to either R, G, or B light.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.

Rules of colour mixing: additiveAdditive 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.

Rules of colour mixing: additive

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.


Rules of colour mixing: subtractiveSubtractive 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.

Rules of colour mixing


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.)


Exercise1. 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?


Chapter 1 radiometry_and_photometry

Science

Transcript of Chapter 1 radiometry_and_photometry