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Topics:
Statistics The Human Visual System Color Science Radiometry/Photometry Geometric Optics Tone-transfer Function Image Sensors Image Processing Displays & Output Colorimetry & Color Measurement Image Evaluation Psychophysics
Some Radiometry / Photometry References Grum, F. and Becherer, R. (1979). Optical Radiation
Measurements, Vol. 1 Radiometry. Academic, N.Y. Mooney, W. (1991). Optoelectronic Devices and
Principles. Prentice Hall, N.J. Stimson, A. (1974). Photometry and Radiometry for
Engineers. Wiley & Sons, N.Y. Walsh, J. (1958). Photometry. Constable & Company,
LTD. Wolf, W, (1998). Introduction to Radiometry. SPIE
Press.
Outline Definition of Terms and Units
Radiometry Solid Angle, Point Sources, Projected Area Sources of Radiation
Gas Discharge Fluorescent Blackbody Radiation Incandescent
The Sun and daylight SOURCES LABORATORY
Outline Radiance
Radiance invariance Lamberts Cosine Law and Lambertian Surfaces Relationship between radiance and exitance Relationship between flux and intensity
Photometry and Color Temperature HVS short overview Photometric terminology Planckian locus Color temperature Distribution temperature
Outline Spectral radiometry
Diffraction gratings Spectrometers Wavelength selectors
Absorption and interference filters IR rejection ND filters Monochromators
CALIBRATION LABORATORY Irradiance Variation with Distance and Angle
Point source (inverse square law) Line source Plane source
Outline Irradiance Variation with Distance and Angle
Point source (inverse square law) Line source Plane source
INV SQ LAW LABORATORY
Outline Radiometry and Imaging Systems
Lens falloff and exposure Irradiance onto the focal plane
Non-Point Sources How to handle non-point source calculations Some governing formula’s
Integrating Spheres (if time permits) Governing sphere equation Applications of integrating spheres
Radiometric Quantities and Units
Emmett Ientilucci, Ph.D.Digital Imaging and Remote Sensing Laboratory
Chester F. Carlson Center for Imaging Science
Overview
What is Radiometry? Where does it come from? In the early days Radiometry was “illumination science” (which
is still alive today) In this early era much arcane terminology was developed
Who uses Radiometry? Physicists, vision and psychophysics', EE, etc
They all use different words to mean the same thing You will learn the internationally accepted terminology
What is Photometry?
Radiometric / Photometric Definitions
What is Radiometry?
Measurement or characterization of EM radiation and its interaction with matter
It is the measurement of “how much”
The science of putting “numbers” on things you do in the science of imaging.
What is Photometry?
Measurement or characterization of EM radiation which is detectable by the human eye
Why Develop These Concepts?
Given an optical system, for example Camera, telescope, etc And any optical radiation source, a surface, detector, etc.
Can calculate “how much” radiation gets to the detector array or film in the image plane
e.g., Can calculate the value of the Signal-to-Noise (i.e., SNR) or exposure
2 Second Review …
We will be using units such as micro-meters (um) nano-meters (nm) and will be using the MKS (meter, kilogram, second)
system.
We will be ‘counting’ counting photons (i.e., the particle nature of light)
What is Radiometry?
EM spectrum of interest This is not universal terminology Most remote sensors use this terminology For example, NIR : Where Si detectors respond
Radiometry Definitions: Summary
Units can be divided into two conceptual areas Those having to do with energy or power
Energy, Q (joule or [J] ) Power or flux, (watt or [W] )
Those that are geometric in nature Irradiance, E [W/m2] Exitance, M [W/m2] Intensity, I [W/sr] Radiance, L [W/m2 sr]
Photometry Definitions: Summary
Units can be divided into two conceptual areas Those having to do with energy or power
Energy, Q (lumen second or [lm s] or Talbots) Power or flux, (lumen or [lm] = [cd sr] )
Those that are geometric in nature Illuminance [lm/m2 = lux or lx] Emittance [lm/m2 = lux or lx] Intensity [lm/sr = candela or cd] Luminance [lm/m2 sr = cd/m2 = nit]
Sometimes called Luminosity
Systeme International d’Unites (SI)
SI developed in 1960 7 SI Base Units
Kilogram [kg] Second [s] Meter [m] Ampere [A] Kelvin [K] Mole [mol] Candela [cd]
All others are SI derived units Previous slide: Radiometric definitions are all
SI derived units
Radiometric Definitions
Photon Energy, q We think of energy as being transferred in terms of
energy packets or quanta The energy carrier is a “photon” Each photon carries energy,
Shorter wavelength photons carry more energy than longer wavelength photons
h = Planck Constant (6.6 E-34 J s)c = Speed of Light (3 E8 m s-1) = Wavelength (meters)
Radiometric Definitions
Radiant Energy, Q Since we are counting photons, lets sum them up!
The total energy (Q) in a beam is a function of: Frequency or wavelength of the photons, or Number of photons (n), of a particular frequency or
wavelength, i
Radiometric Definitions
Radiant Energy, Q Example: HeNe LASER (632 nm)
Example: 632 nm AND 1000 nm sources
Radiometric Definitions
Radiant Flux or Power, We are looking at light continuously hitting a surface.
How many photons over a period of time?
DEF: Quantity of energy propagating onto, through, or emerging from, a specified surface of a given area in a given period of time
2
Time Interval
Radiometric Definitions
Radiant Flux or Power DEF: Quantity of energy propagating onto, through, or
emerging from, a specified surface of a given area in a given period of time
- P = iv, electrical power [watts] dissipated by a resistor.- Some of this power is turned into light
- That is, electrical power is converted to radiant power
Radiometric Definitions
Irradiance, E Change of power ONTO a surface. Rate at which radiant flux, is delivered onto a surface
(e.g., a detector surface)
- These are spatially dependant terms !!- However, we will often not write this. Will look at bulk average
Projected Area
Radiometric Definitions
Radiant Exitance, M Rate at which radiant flux, F is delivered away from a
surface (e.g., a diffuser, reflected surface)
- If the surface is opaque, then there is flux onto the surface- Since we can see it, there must be flux OFF the surface- M can be related to E via the transmission, “tau”
Radiometric Definitions
Radiant Intensity, I Rate of change at which radiant flux, is incident on,
passing through, or emerging from a point in space in a given direction
“steradian”
- No spatial dependency here- Associated with sources (points sources)
Point Source
Point Source or Point Location A point is a location in space that occupies no space.
How do you get photons through a point?
Really, we will be looking a photons that emerge from a very small source that approximates a point source
Approximations: A point source is “small” compared to how far we are away from it R.O.T.: Should be 10x the radius of source away, for example
(about a 1% error in this assumption)….I will show you later…
Errors in Point Source Approximations, In General
About 0.002% error in assuming Sun is a point source
If the sensor is 10xthe source radius away,we have a 1% errorin our assumptions.
Radiometric Definitions
Radiant Intensity, I Rate of change at which radiant flux, is incident on,
passing through, or emerging from a point in space in a given direction
“steradian”
- No spatial dependency here- Associated with sources (points sources)
Plane Angle
Plain angle or linear angle, Length of arc, s divided by the radius, r Plain angle is dimensionless However, to aid in
communication it is assigned the SI unit of measure … radian
s
ss
r=1
C = 2r
For any s :
2 radians in a full circle
Plane Angle
So… A straight line or even a curved line can subtend
the same angle as an arc on the circle
So…DEF: A plane angle is the projection of a line on a unit circle, and the line need not be straight
Solid Angle
Solid angle, 3D equivalent of a plane angle Projection of a area (or a closed curve in space) onto a unit
sphere “square radians” or steradian
SA = 4r2
r=1
dAFor any A
4 steradians in a sphere2 steradians in a hemi-sphere- Lets derive it !
d
Solid Angle
Solid angle, Sphere of radius, r has a (surface) area SA = 4r2
SA = 4r2
r=1
dA
d
4 steradians in a sphere
2 steradians in a hemi-sphere
Example: Def, Sphere, Pt Source
Radiometric Definitions
Radiance, L One of the problems with M, is we don’t know
where any of the flux goes ! They might go straight or make a left turn?
Same thing with irradiance, E
So we combine the concepts if irradiance with Intensity
This is called “radiance”
Radiometric Definitions
Radiance, L Function of both position and direction
DEF: Flux, incident on, passing through, or emerging in a specified direction from a specified point in a specified surface
Formal Definition
[W/m2 sr]
Radiometric Definitions
Radiance, L Element ofFlux d2
Element ofSolid Angle d
Element ofArea dA0
Radiometric Definitions
Radiance, LElement ofFlux d2
Element ofSolid Angle d
Element ofProjected Area dA = dA0 cos
Element ofArea in the Surface dA0
The “area” in the units (m2) is now with respect to the projected area dA.
Radiometric Definitions
Radiance, L- Radiance can be used for a source or a receiver- It is a much more universal definition
- It does not change with distance (as we will derive later)
- e.g., If I know L headed in a certain direction (lossless), then the radiance leaving that surface will be the same radiance hitting any surface along that direction
-We need (x,y,,) dependency because the radiance can be different in any location on a surface and different in any direction
- We will devote an entire section to Radiance
Sources of Radiation
Emmett Ientilucci, Ph.D.Digital Imaging and Remote Sensing Laboratory
Chester F. Carlson Center for Imaging Science
Classes of Emitted Radiation
Line spectra sources Continuous spectra sources Monochromatic sources
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CIE A CIE D65 Solar (ASTM G173-03) CW-Fluorescent
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CIE A CIE D65 Solar (ASTM G173-03) CW-Fluorescent
Methods of Producing Radiation
Gas Discharge Sodium street lamp
Incandescence The Sun, tungsten light bulb
Chemical Fluorescence, phosphorescence
Electroluminescence Semiconductors and LED’s
Sodium Vapor Lamp
Gas Discharges
Gases are not good conductors at STP However, in some cases, insulation properties can break
down… e.g., Plug in a power supply. Current across air !
Contents of Gas Discharge lamp Noble gas such as
Argon, neon, krypton, xenon, etc. Combination of Nobel gases And/or materials such as
Sodium or mercury
Gas Discharges
The gas can be under low or high pressure 5-15 torr (low pressure) 760 – 1520 torr (1-2 atm), (high pressure)
Apply a high voltage 1000 – 5000 volts Creates an electric field EF creates free electrons across tube
Gas Discharges
Conditions: (Overview)1. Create an electric field between electrodes
2. Free electrons will accelerate away from (-) electrode
3. Free electrons can collide with gas molecules
4. e- can transfer energy to molecule (excited)
5. Light is generated from de-excitation
Gas Discharges
Comments:1. We get non-continuous line spectrum
2. The type of gas in the tube determines the glow Neon emits a red glow, naturally Mercury emits blue Sodium emits yellow Helium produces a pale yellow Argon yields purple
Gas DischargesArgon
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Gas Discharges
Low Pressure Sodium Lamps Very efficient (ratio of electrical power in to radiant power out) Entire output in visible consists of
589.0 and 589.6 nm (poor color rendering)
Efficacy [lm / W] Term to help characterize “human perceived brightness”…. We use the term efficacy (not to be confused with efficiency)
Ratio of emitted luminous flux [lm] to radiant flux [W]
The “lumen is a measure of perceived brightness” of light The maximum efficacy for any source is 683 lm/W
Since DEF of a lumen is 1/683 watts at 555 nm.
Gas Discharges
Example A monochromatic source that emits at 1000 nm
Has an efficacy of zero (since there is no useful radiation in the visual portion of the spectrum)
Sodium Source Very efficient and large “efficacy” 183 – 200 lm/W
Gas Discharges
This makes them ideal for mass street lighting Cheap !! But poor color rendering …
Low Pressure Sources Sodium gas lamp Mercury gas lamp (and also a fluorescent tube) Neon tube
Gas Discharge
This makes them ideal for mass street lighting
- Cheap !!- But poor color rendering …
Gas Discharges
High Pressure sodium (and mercury) Lamps (high) pressure 1 -2 atm (760 torr = 1atm)
Proximity of atoms is closer Concentration of excited molecules is much higher Lines of emission becomes broader (line broadening) Much brighter than (low) pressure lamps
Better color rendering (i.e., pale pink-orange) Good for flood lighting, parking lot lighting
Efficacy of about 150 [lm/W]
Gas Discharge
Gas Discharge
Mercury Lamps (low and high pressure) Low pressure produces lines at
253.7, 365.4, 404.7, 435.8, 546.1 and 578.0 nm
We will see that 253.7 and 365.4 nm are used in a fluorescent lamp to excite phosphors That is, a fluorescent lamp is basically a better quality
(mercury) gas discharge lamp
Gas Discharge
Mercury Vapor Source
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Wavelength [nm]
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Gas Discharge
Metal Halide lamps (high pressure) Same as high pressure mercury lamps …add some metal halides to the mix
Extra lines can be provided in the spectrum Improved color rendering Efficacies around 80 [lm/W]
Applications Floodlighting in stadiums
High Intensity Discharge (HID)
Basically…class of lamps with large luminous output High pressure Mercury vapor lamps High pressure Metal halide lamps High pressure sodium lamps
Efficacy [lm/W]
Applications
Xenon Arc Lamps
http://en.wikipedia.org/wiki/Xenon_arc_lamp
Xenon Arc Lamps
http://en.wikipedia.org/wiki/Image:Xenon_short_arc_1.jpg
15,000 W Xenon short-arc lamp used inIMAX projectors.
-Filled with xenon gas-At very high pressure-Large current draw (450 W: 18V at 25 A)
Xenon Arc Lamps
http://ncr101.montana.edu/Light1994Conf/5_9_Kofferlein/Fig%20Pay%201.jpg
-Contains spectral lines-Also fair amount of incancescence-Very bright-Color rendering resembles “daylight”
Efficiency
Tungsten 5% of energy consumed by 100 watt bulb is converted to
visible light The rest is in the IR and/or heat !!
Discharge Lamps 30% of the energy consumed is converted to visible light
Fluorescent lamps can approach 50%
Fluorescent Lamps
Conditions: Low pressure mercury gas in tube Inside is coated with phosphors that can be
excited by UV lines of the mercury spectrum
Phosphors selected so as to provide additional light at long wavelengths i.e., Light does come from gas discharge but mainly
from phosphors
Fluorescent Lamps
Process: Contains Hg and inert gas such as Argon
We excite the Hg vapor in Ar gas Power on: Cathode heats up to emit electrons Electrons migrate across due to potential difference e- ionize the argon gas
Fluorescent Lamps
Process: Electron and ionized argon atoms move through tube
This allows higher currents to flow Which, in turn, (vaporizes) and ionizes the mercury De-excitation of the Hg gas emits UV radiation
A black light !!
Fluorescent Lamps
Process: Efficiency is mainly due to the fact that
65% of total light is at the 253.7 nm line. UV radiation absorbed by phosphor coating Phosphor re-radiates at longer wavelength
440 and 546 nm
Fluorescent Lamps
Fluorescent and Mercury Sources
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Wavelength [nm]
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Mercury Source [radiance]
Fluorescent Source [irradiance]
Spectral Line Broadening
In Gases We have seen that when gas pressure is raised, spectral
lines in the emission are broadened This is due to the effects of the neighboring atoms in the
gas
… and In liquids and solids….. Atoms are much more closely packed than in a gas Line broadening effects are so great that emission is
continuous throughout the spectrum
Incandescent Light Sources
The most important natural incandescent light source is the Sun
The most important man-made incandescent source is the tungsten filament lamp
The amount of power radiated by incandescent sources depends on their temperature
Incandescent and Fluorescent
Blackbody Radiation: Solids
Max Planck (1901) Derived an expression for the spectral radiant
exitance, M, from a “blackbody”
k = Boltzmann gas constant (1.381 x 10-23 [J K-1])h = Planck constant (6.63 x 10-34 [J s])c = speed of light (3.0 x 108 [m s-1])
Max Karl Ernst Ludwig Planck, 1901
Blackbody Radiation: Solids
- A “blackbody” is an idealized surface where the reflectivity is zero and the absorpitivity is one
- That is, it has the property that all incident EM flux can be perfectly absorbed and can be re-radiated- The spectrum emitted by a solid, when heated, resembles a blackbody
Similar to your:
-Toaster-Stove-Hair dryer-Etc…-(those these are not “Ideal” blackbodies)
Blackbody Radiation: Solids
Blackbody Radiation: Solids
Sources: Solid
http://www.csr.utexas.edu/projects/rs/hrs/pics/
Sources: Solid and Gas
Incandescent Lamp
Fluorescent Lamp
Blackbody Radiation: Solids
Can you see energy atT = 300 K?
- Is the Sun a perfect BB?- What about things that “almost” look like BB’s……….
Blackbody Radiation: Solids
Emissivity In reality, objects are NOT perfect absorbers To describe this phenomenon, we introduce the
concept of emissivity, ()
Ratio of the spectral exitance from an object at temperature T to the exitance from a blackbody at that SAME temperature
( )M (T)
MBB (T )- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
Emissivity i.e., how “poor” does it resemble a BB. The Sun has an emissivity < 1
Can’t have negative emissivities That would suck photons out of existence !!
Can’t have greater than one (>1) That would mean you are radiating better than an ideal
BB!
( )M (T)
MBB (T )- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
Emissivity Objects whose emissivity is constant with wavelength are
called Gray bodies
Objects with spectrally varying emissivities are called Selective Radiators
( )M (T)
MBB (T )- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
Transmissivity, transmittance, transmission Ability of the material to allow the flux
to propagate through it
MEi
E M
- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
Reflectivity, Reflectance Ability of the material to turn incident flux back into the
hemisphere above the material
E
M
r MrEi
r
- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
Absorptivity, absorptance Ability of the material to remove EM flux from the system by
converting incident flux to another form of energy (e.g., heat)
How much EM energy is “lost” to the system i.e., How much of the exitance is lost (absorbed) by the
system
E
M
MEi
- Ranges from 0 to 1- [unitless]
Blackbody Radiation: Solids
In General Conservation of energy requires all the incident flux to be
absorbed, transmitted or reflected. We have:
(I don’t really know what else to do with the photons !)
For an opaque material or surface we have:
r 1
r 1
Blackbody Radiation: Solids
In General (with out proof…) There’s a law from thermodymanics that comes into play
regularly when dealing with radiative surfaces
Kirchhoff’s law (kirk-offs) states that emissivity must be numerically equal to the absorptance surface in thermodynamic equilibrium (TDE)
That is, good absorbers are good emitters (in TDE) TDE, T is constant. Therefore I can write….
r 1Gustav Robert Kirchhoff1861
Blackbody Radiation: Solids
…And for opaque objects I have
This is a very useful substitution… Because it is often easier to measure the reflectivity
of an object than its emssivity
When are you not in TDE? i.e., When can’t I use Kirchhoff’s rule? When something is heating and cooling However, in “normal” operating conditions in the world,
you can set =
r 1
Blackbody Radiation: Solids
Total exitance from a blackbody Is the area under the Planck function curve
Stefan-Boltzmann Law (or Stefan’s Law)
= Stefan-Boltzmann constant
Joseph Stefan, 1879 Ludwig Eduard Boltzmann, 1884
Blackbody Radiation: Solids
Total exitance from a blackbody Area under the Planck function curve
But when would we use this result?
In imaging, we never look at ALL the photons over the entire EM spectrum ?
I really care about an interval from 1 to 2
So, I need to solve the Planck equation from 1 to 2 Anyone know this closed form solution?
Blackbody Radiation: Solids
Exitance within a bandpass Solved numerically for no closed form
solution exists
I will demonstrate how to do this through example in a minute……but first..
Blackbody Radiation: Solids
Wien Displacement Law Where is the peak in the Planck function ??
This says that the peak exitance from the Sun will be approximately 500 nm (yellow-green)
Wilhelm Wien, 1893
A = Wien displacement constant (2898 um K)
Integrate Planck Function
Trapezoid:(a+b)/2 x wa b
w
Integrate Planck Function
So the exitance in an interval , is
And the total exitance summing all intervals is
Integrate Planck Function
Tungsten Lamps
Make an incandescent source… Heat a conductor by passing electrical current through it
(above 1000 K)!! In air, you get rapid oxidation of the material In vacuum…much more stability
Most stable conductor today is “tungsten” Spectral emissivity is constant in visible
i.e, it looks like a Planckian radiator Melts at 3683 K
Greater temperature = more light = more evaporation? = early failure
Tungsten Lamps
Thermionic Emission (Thomas Edison, 1883) Flow of electrons from a metal surface caused by thermal
vibrational energy overcoming the electrostatic forces holding electrons to the surface
So, - Some e- de-excite (produce light)- Some leave the surface altogether
Tungsten Lamps
Use inert gas such as Argon to reduce effects of Thermionic Emission Inert gas will not react with other elements
Tungsten Lamps
As tungsten evaporates it “may” collide with an argon atom and bounce back to the filament
Tungsten-Halogen Lamps
Fill envelope with a halogen gas Iodine, bromine
This create a reaction such that the tungsten is preferentially re-deposited on the filament Preferentially because the filament thickness actually
varies, thus the temperature has spatial variation across the filament
Therefore we can run this at higher temperatures !! But need to use different glass casing (i.e., quartz)
Tungsten, Tungsten-Halogen
Tungsten (2650 to 3200 K). Typically 2800 K 10 to 25 [lm/W]
Tungsten-Halogen (2850 to 3300 K). Typ 3200 K 15 to 35 [lm/W]
Efficacy [lm/W]
LED’s
Group IV semiconductors are Indirect bandgap Si (1.12 ev = 1.1um), Ge (0.66 eV = 1.9um), SiC Recombination is a non-radiative transition
i.e., no optical emission under forward bias
Direct band gap materials Recombination produces optical radiation
i.e, Near UV, VIS, NIR, under forward bias
LED’s
LED’s
LED’s
Blue LED’s
Wide bandgap material GaN (3.4eV = 364nm), used in Blu-ray DVD players (PS3)
First blue LED 1971: very fragile 1980’s: New, more robust, process 1993: Shuji Nakamura, new process
This facilities the creation of white LED’s 450, 470 nm Blue LED
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White LED’s (1996) Modified blue LED’s Uses a phosphor (inside) coating Re-emits at 580 nm Mix of blue and yellow gives appearance of white light
White Light LED
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White LED
LASER
HeNe LASER
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SOURCES LABORATORY
Radiance
Emmett Ientilucci, Ph.D.Digital Imaging and Remote Sensing Laboratory
Chester F. Carlson Center for Imaging Science
Constancy of Radiance
Radiance does not change with distance. As you move away, the sampled area increase effectively cancelling any inverse square law losses.
Diffus
ing
Surfa
ce
Detector measuring radiance[W / m^2 sr]
- Lossless Medium
Responsivity and Radiance
Silicon Response
Lamberts Law and Lambertian Surfaces
Johann Heinrich Lambert (1728-1777)
Relationship between L and M
For a Lambertian surface ONLY M = L [W/m2] = [W/m2 sr] * [sr]
That is, if you know the radiance from a LAMBERTIAN surface, the exitance (M) can be found by scaling the radiance by a factor of steradians.
Photometry and Color Temperature
Emmett Ientilucci, Ph.D.Digital Imaging and Remote Sensing Laboratory
Chester F. Carlson Center for Imaging Science
Photometry
Radiometry for the human visual system (HVS)
Photometry (predates Radiometry)
- The eye is just another detector
-You do the radiometry problem first, then turn it into something the HVS sees.
-Q. But how do we get a signal out of your eye?
-A. We ask people “how much”-Not very calibrated !
-Visual response is in terms of perceived brightness
Photometry
-HVS responses to radiance- It’s an “apertured” system-Solid angle is formedby the pupil
Detectors
-Cones (RGB)-Rods (BW)
-Flux perceived by HVS quantified in terms of Lumens
Photometry Units
Energy or Power Energy, Q (lumen second or [lm s] or Talbots) Power or Luminous flux, , (lumen or [lm] = [cd sr] )
Those that are geometric in nature Illuminance [lm/m2 = lux or lx] Emittance [lm/m2 = lux or lx] Intensity [lm/sr = candela or cd] Luminance [lm/m2 sr = cd/m2 = nit]
Sometimes called Luminosity Used to characterize brightness
Photometry Units
Other arcane units sometimes used Illuminance
1 metre-candle = 1 lux 1 phot = 1 lm/cm2 = 104 lux 1 foot-candle = 1 lumen/ft2 = 10.76 lux 1 milliphot = 10 lux
Luminance 1 stilb = 1 cd/cm2 = 104 cd/m2 = 104 nit 1 cd/ft2 = 10.76 cd/m2 = 10.76 nit
Photometry Units – Illuminance/Exitance
1m21ft21cm2
Source of 1 [cd](1 lm/sr)
1 lux = 1 lm/m2
1 fc = 1 lm/ft2
1 phot = 1 lm/cm2
(intensity)
Normalized Std. Response Functions
(average) Human visual response functions Developed in 1931 Based on many observations
i.e., standard observed response functions
http://retina.umh.es/Webvision/Psych1.html
V()V’()
Pea
k N
orm
aliz
edTo calculate the “output” ofthe HVS (in terms of perceivedflux), we need the VRF’s.
Standard Response Functions
http://retina.umh.es/Webvision/Psych1.html
Lum
inou
s E
ffic
acy
[lm /
W]
-Flux perceived by HVS quantified in terms of lumens (lm)
-Can we map flux in (W) to flux out (lm)?
-Scaled by luminous efficacy scalar [lm/W]
-Scales radiometry flux levels to be consistent with historical scales of perceived brightness
-Now looks like a “responsivity”-How many lumens do I get out per watt in….
Photometry
Can take any radiometry problem and make it a photometric problem using the relation
which calculates the luminous flux.- [lm] = [W/um] *[lm/W]*[um]
- k = 683 [lm/W] (photopic) - k’ = 1700 [lm/W] (scotopic)
Photometry
Can also do for: Illuminance Emittance Intensity Luminance [lm/m2] = [W/m2 um] *[lm/W]*[um]
Plotting Color in 2D
-Given a radiance L, we can find-Tristimulus Values
-From the tristimulus values we can find-Chromaticity coordinates (x, y)
-Calculate x,y for monochromatic radiation-Which produces this “horseshoe shape”
-Horseshoe shape is often called “spectrum locus”
-Region inside is called the “color gamut”
-A given system will be capable of displaying some subset of this gamut
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap17/chap17.htm
Displaying Sources
-Chromaticity coordinates of blackbodies form a (Planckian) locus in the chromaticity diagram
-We have a way to describe its color
http://en.wikipedia.org/wiki/Planckian_locus
Displaying Sources
-A fluorescent source is NOT a blackbody.
-But we can STILL compute chromaticity coordinates
-But this will NOT be on the BB locus
-We compute the closest BB radiator. (perceived not Euclidian closest)
-And give it a…- (correlated) color temperature (CCT)
http://en.wikipedia.org/wiki/Planckian_locus
5000K Fluorescent Bulb
Can “look” the same to the eye
Distribution Temperature
Has nothing to do with color and the CIE diagram
Distribution temperature is for curves that look like a blackbody