Optical Methods in Experimental Physics Radiometry - photometry
November 2007
Experimental Methods in Physics Ganiere Jean-Daniel IPEQ - EPFL
IPEQ - SB - EPFL Station 3 CH - 1015 LAUSANNE
Spectroscopy
Spectroscopy is the study of the interaction between radiation (electromagnetic radiation, or light, as well as particle radiation) and matter
excitation signal source detector
excitation energy probe filter signal
specimen
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Spectroscopy
The objective in spectroscopy is typically to measure the intensity of a signal as a function of the energy of a proposed event occuring in the sample
name probe signal
PL Photons Photons
CL Electrons Photons
EDS Electrons X-photons
AES X-rays Electrons
EELS Electrons Electrons
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Optical Spectroscopy
light light light sample source analyzer detector
incoherent light sources crystallogenesis monochromator (eg quantum detectors - blackbody types prism , grating type) (eg photographic plate, - arc lamps epitaxy PM. PD, CCD, ...) - LED PF analyzer cryogenic Thermal detectors coherent light sources (eg photoacoustic, ...) - laser light magnetic field light light sample synchrotronsour lightces analyzers detectors
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Optical spectroscopy
excited excited Motivations singulet state triplet state
Information on the electronic
S2 structure
internal conversion vibrational relaxation S 1 10 fs - 100 ps Information on the dynamics of the radiative processes (life absorption - 10 fs time !) T1 fluorescence 100 fs - 100 ns
phosphorescence 1 ms - 10 ms Important for the realization of intersystem efficient device (lasers, Crossing
non-radiative detector) relaxation
ground state Better understanding of the physics ! Jablonski diagram
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Optical spectroscopy
• The optical spectroscopy of solids is only a pretext to approach various important subjects in MEP
• nothing too specific.
• Also useful in other domains (life science, chemistry, ...)
Raman map showing a horitzontal section of a carrot root. Based on miscoloured pictures the concentration profiles of betacarotin in plant tissue can be clearly illustrated.
Credit: IPA [Institute of Plant Analysis, www.bafz.de]
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Units
E = ho mo = c/n
It is difficult to measure directly the frequency, that is why we use mostly the wavelength ! .
From the theoretical point of view, it is the frequency which plays a fundamental role, that is why we introduce a new unit, the wave number, ", who expresses itself in cm-1. The wave number is measured with the same precision as the wavelength ! 1 o v = = m c
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Units
Wavelength Wavenumber Frequency Photon energy
-1 Symbol m [nm] v [cm ] o [Hz] Ep [eV] m 107 /m 3 $ 1017 /m 1224/m 107 /v v 3 $ 1010 $ v 1.22 $ 10-4 v
3 $ 1017 /o 3.33 $ 1011o o 4.1 $ 10-15 o
14
Factor of conversion 1224/Ep 8197 $ Ep 2.44 $ 10 Ep Ep
200 5 $ 104 1.5 $ 1015 6.12
500 2 $ 104 6 $ 1014 2.45 Examples 1000 104 3 $ 1014 1.224
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 International Sytem of Units (SI)
Unit of length meter
Unit of mass kilogram
Unit of time second
Unit of electric current ampere
Unit of thermodynamic! temperature kelvin
Unit of amount of substance mole
Unit of luminous intensity candela
The candela was first defined as 1/60 the luminous intensity, in the perpendicular direction, of a 1 cm2 blackbody radiator at the freezing temperature of platinum (about 2042 K) and a pressure of 1 atmosphere
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Radiometry, photometry
optical system
object image
Radiometry the measurement of optical radiation over the entire spectrum from the ultra-violet to the infra-red.
Photometry the measurement of visible light as it appears to the human eye.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Radiometry, photometry
Although describing fundamentally similar parameters, namely flux, energy, intensity, power per unit area a different system of units is used to distinguish between radiometric and photometric quantities.
The assumptions (radiometry and photometry)
! incoherent radiation ! optical geometric laws apply ! no diffraction ...
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Photometry
Photometric units Units Photometry MKS CGS British
Luminous energy Talbot
Luminous power Lumen
Illuminance Lux Phot Footcandle
Nit Stilb Luminance Apostilb, Blondel Lambert Footlambert
Luminous intensity Candela (Candle, Candlepower, Carcel, Hefner)
Thus one nit is one lux per steradian is one candela per square meter is one lumen per square meter per steradian. Got it ? James Kajiya
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Photometry versus radiometry
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Photometry, radiometry
A particular algebraic symbol is used to describe the optical parameter, be it radiometric or photometric, the subscript "e" added to denote a radiometric quantity (e, like energetic) , the subscript "v" to denote a photometric quantity (v, like visual).
radiant flux is a radiometric quantity denoted by #e
luminous flux is a photometric quantity denoted by #v
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Photometry, radiometry
Note that radiometric and photometric parameters relate to the total amount of radiation emitted over all wavelengths (EM spectrum or visible).
Sometimes need to define a parameter over a specific frequency or wavelength interval.
For example, spectral radiance is the flux per unit area per
unit solid angle per unit frequency interval denoted as Lv(!) or
Le(!)
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Photometry, radiometry
The distinction between radiometry and photometry is necessary because the eye responds unequally to the various wavelengths of light.
Two monochromatic light sources of wavelengths !1 and
!2 may have same radiant flux but will have different values of luminous flux.
A green light emitting diode, for example, will appear brighter than a red one of the same radiance or flux. Radiant flux and luminous flux are related via the photopic response curve of the human eye.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Luminous efficiency
low light levels everyday light levels (scotopic curve) (phototopic curve)
1.0
0.8
0.6 V At the peak of the Vn! d ! curve, 550 nm, 0.4 1 W = 674 lm
luminous efficiency factor (spectral) 0.2
0.0 400 500 600 700
Wavelength [nm]
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Worked example
A particular light emitting diode made from GaAsP emits 25 !W of flux at its peak wavelength of 650 nm (red). Another diode made from GaP emits the same flux at its peak of 550 nm (green).
1.0
0.8
0.6 V V n! d ! the photopic sensitivity of 0.4 the GaAsP diode at 650 nm is
luminous efficiency factor (spectral) 0.2 0.107, for the GaP diode at
0.0 400 500 600 700 550 nm it is 0.967.
Wavelength [nm]
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Worked example
The luminous flux of the GaAsP diode is -6 -1 !v= 25 x 10 W x 674 lm x 0.107 lm W = 1.9 mlm
The corresponding flux for the GaP diode is -6 -1 !v = 25 x 10 W x 674 lm x 0.967 lm W = 16.3 mlm
For the GaAsP diode to produce the same visual effect as the GaP diode, its radiant flux has to be increased by ratio of the luminous fluxes
Hence, the required radiant output is -6 !e = 25 x 10 W x 16.3 mlm / 1.9 mlm = 214 !W
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Photometric, radiometric quantities
Radiant Energy Total amount of light emitted from Qe J
Luminous Energy source Qv J
Radiant Flux Rate of energy emitted or $e W #=dQ/dt Luminous Flux transferred from source $v lm
-1 Radiant Intensity Flux emitted from a point source per Ie W sr # % I=d /d -1 Luminous Intensity unit solid angle Iv lm sr = cd
-2 Radiant Emittance Flux emitted per surface unit area of Me W m M=d#/dA -2 Luminous Emittance extended source Mv lm m = lx
Flux emitted per unit surface area of 2 -2 -1 Radiance Le L=d #/ W m sr extended source, per unit solid angle -2 -1 -2 Luminance Lv (dAd%cos&) lm m sr = cd m at angle normal to surface n
Flux arriving at a surface per unit -2 Irradiance Ee W m surface area at an angle normal to E=d#/dA -2 Illuminance Ev lm m = lx the surface
Radiant Energy Density Energy emitted per unit volume of J m-3 w w= dQ/dV Luminous Energy Density source J m-3
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Radiometry
angle and solid angle
l angle= 2D R cercle has 2' radians
A solid angle= X= sphere has 4' steradians 3D R2
Projected area
Shape area projected area
flat rectangle A = L•w A = L•w
circular disc A = "•r2 A = "•r2•cos#
sphere A = 4"•r2 A = "•r2
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Radiant energy
Q is the total energy emitted, transferred or collected in a radiative process. Unit of Q is [J]
The energy density, u, per volum unit is defined as: dQ u = dV
Unit of u is [J/m3]
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Radiant flux
The radiant flux, # (or sometimes noted P), represents the quantity of EM energy, transferred from one region to another per time unit:
dQ U = dt
Unit of # is [W]
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Radiant excitance
The radiant (luminous) excitance, M(x), is the energy per unit area leaving a surface:
dUo M(x) = dA
W ; E Unit of radiant excitance, M, is: m2
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Irradiance
The surface radiance (illuminance), E(x), is the power per unit area incident on a surface:
dUi E(x) = dA
W ; E Unit of irradiance is: m2
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Irradiance measurement
Credit: Newport http:// www.newport.com
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Irradiance Practical importance
Characteristics of light sources
credit: www.newport.com
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Radiant intensity
The radiant intensity, I((,)), is the power per unit solid angle:
dU I(i,{) = dX
( ) W Unit of radiant intensity, I( , ), is: :sr D
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Radiant intensity Practical importance
Characteristics of LED
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Radiance
The radiance (luminance), L(x,*), is the intensity per unit area leaving a surface:
dI(x,~) d2 U(x,~) L(x,~) = = dA d~dA
W ; E Unit of radiance is: sr m2
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Isotropic point source
U= # I d~= 4r S2
U I = 4r
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Irradiance - isotropic point source
U I = 4r
U cos i U cos3 i dU = Id~= E dA = dA = 4r r2 4r h2
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Lambertian source (uniform diffuser)
A source whose radiance is independent of angle is called Lambertian. Thermal sources and LED are lambertian emitters.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Lambertian source relationship between M and L
M(x) = # L0 cos i d~ H2
= L0 # cos i d~ H2
= rL0
M L0 = r
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Some interesting results
• Conservation of radiance (formerely called “brightness theorem”)
In an optical system the radiance measured in the direction of propagation is an invariant (in fact, this is the quantity L/n2 which is an invariant)
In an optical system the radiance of the image is equal to the radiance of the source
optical system
object image
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Geometrical extent
In an optical system we will try to maximize theamount of radiant power transferred from the source to the detector. If the system is aberration free and has no internal aperture, we verify the relation:
G = As Xs = Ai Xi= cste
The quantity, G, which is the same for the source and for the image is called the geometrical extent
Credit: http:www.newport.com
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Geometrical extent 1D case
If the optical system has a cylindrical symmetry, the 1D version of the optical extent ia applicable:
G = h1 i1 = h2 i2= cste
Credit: http:www.newport.com
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Geometrical extent coupling light into a monochromator
monochromator
excitation
sample
the lowest geometrical extent of any component in an optical system limits system throughput. Generally the monochromator is the component with the lowest geometrical extent. The geometrical extent of the monochromator is the product of the entrance slit width and the angle of acceptance.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Flux measurement - integration sphere
integration sphere (radius = R, reflection factor = r)
detecteur (area: dAd)
☀ baffle
light source (flux = ?)
dAd r dzm = 2 $ zes 4rR ;(1 - r)E
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
Practical importance
Visual perception of colours
credit: www.gameonline.co.il
Illumination
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008 Summary
Radiometry and photometry deal with the same subject: the measurement of the electromagnetic tradiation. In radiometry we use physical detectors, while in photometry we use the eye as detector.
Radiance is invariant in an optical system
the basic unit is the candela (W/sr)
Conversion between radiometric and photometric units possible only in the visible part of EM spectrum.
Most of the time you need to know the response of the eye and/or the spectral distribution of the EM radiation.
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008
References
• http://www.optics.arizona.edu/Palmer/rpfaq.htm
• Introduction to radiometry by William Wolfe (SPIE tutorial text in optical engineering Vol. TT29)
• Radiometry and the Detection of Optical Radiation Rober W. Boyd, John Wiley & Sons, ISBN-10 047186188X
• Electro-optical Devices and Systems by Mohammad Karim PWS-Kent, ISBN 0-534-91630-9
• A guide to integrating sphere - Theory and Applications (Labsphere) (pdf file available on wiki.epfl.ch/mep)
J-D Ganiere IPEQ / EPFL MEP _ 2007-2008