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Radiant Flux Is a Radiometric Quantity Denoted by #E

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Radiant Flux Is a Radiometric Quantity Denoted by #E 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 ;
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