# Physical Methods for Cultural Heritages Radiometry and Fotometry G. Valentini - Tel. 6071 - Robert W. Boyd Radiometry and.

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Physical Methods for Cultural Heritages Radiometry and Fotometry G. Valentini - Tel. 6071 - gianluca.valentini@polimi.it Robert W. Boyd Radiometry and the Detection of Optical radiation John Wiley & Sons

Gianluca Valentini Electromagnetic wave Electromagnetic waves  = wavelenght  = frequency c = vacuum light speed T = period  = wavelenght  = frequency c = vacuum light speed T = period In a transparent medium n= refraction index In a transparent medium n= refraction index n=1,5 2

Gianluca Valentini The electromagnetic spectrum 3

Gianluca Valentini Reflection: Refraction: Foundamental laws of optics (1) Dispersion ( n 2 depends on  4

Gianluca Valentini 5 Foundamental laws of optics (2) Diffraction Interference 5

Gianluca Valentini 6 Foundamental laws of optics (3) Polarization Diffusion 6

Gianluca Valentini 7 Real and virtual images An optical system forms a real image of an object when the light exiting any point M of the object (spherical wave) is focused to a point M’ of a plane called “conjugated plane”  The eye forms a real image of the observed objects to the retina  A photographic lens forms a real image of the scene to the film (CCD) An optical system forms a virtual image of an object when the spherical wave exiting any point of the object O is converted to a spherical wave exiting a new point O’  Optical devices designed for direct eye observation (microscope, telescope, binoculars, etc.) form virtual images 7

Gianluca Valentini 8 Light diffraction 8

Gianluca Valentini r d0d0 d1d1 dA 1 dA 0 1 0 11 Law of conservation of the radiance (free space propagation) Let’s suppose that the radiation field propagates in a non-absorbing homogneous medium from a source to a receiver We define: The flux transferred from dA 0 to dA 1 is: The radiance measured on surface dA 1 in direction r is given by: Solid angle subtended by dA 1 for an observer in dA 0 L 0 =radiance measured on surface A 0 Solid angle subtended by dA 0 for an observer in dA 1 E = Etendue of the optical system

Gianluca Valentini 12 Lambertian sources A lambertian source is a source whose radiance does not depend on the observation angle  L( ) = constant = L 0 The radiant intensity (W/sr) emitted by a lambertian source of small area A 0 and radiance L 0 in a generic direction is given by:  The radiant intensity changes with the cosine of the observation angle  The change of I as a function of depends on the variation of the apparent area of the source Let’s consider a small size lambertian source (dA 0 )  The radiant flux that impinges on dA 1 is:   L( ) is independent on angle The radiant exitance of a lambertian source is: dA 0 dA 1 d1d1 d0d0

Gianluca Valentini 13 Disk-like lambertian source Irradiance produced by a disk-like lambertian source of radius R on a surface dA 1 located at distance z A ring element on the disk has area given by: The solid angle d  0 subtended by dA 1 from any point on dA 0 is given by: The radiant flux transferred from dA 0 to dA 1 is given by: The irradiance on the surface dA 1 is then: z z0z0 z∞z∞

Gianluca Valentini 14 Aplanatic image forming system Within paraxial approximation the angle between any ray and the optical axis is small ( << 1)  The images are exact replica of the objects because the spherical aberration is negligible An optical system is called stigmatic for the two axial points P and P’ if P’ is a perfect image of P (no aberrations) For a system stigmatic for P e P’ to be aberration free for points slightly off axis it is required that the Abbe condition is satisfied: A system stigmatic for P and P’ that also obeys the Abbe condition is said to be aplanatic for the two points and is not affected by coma For any ray leaving P under any angle h, h’ small, ’ arbitrary n n’

Gianluca Valentini 15 Radiance Theorem The radiance L of a radiation field is conserved as the beam propagates through a uniform lossless medium or through an aplanatic optical system Let’s demonstrate that the radiance (L/n 2 ) is conserved when the beam crosses the interface between two media with different refraction indexes  The radiant flux carried by a beam falling onto the surface element dA from the solid angle d  1 is: According to Snell law: Diefferentiating the previous equation: The ratio between solid angle d  1 e d  2 in polar coordinates is:  n1n1 n2n2

Gianluca Valentini 16 Radiance of an image Let’s calculate the radiance of the image of a light source produced by an aplanatic optical system The radiant flux produced by the source (dx 0, dy 0 ) within solid angle d  0 at the entrance pupil of the optical system is: In a lossless optical system the flux d  impinges onto the image element (dx 1,dy 1 ) and produces the radiance in direction ( 1,  1 ) given by: Using the Abbe condition: The image of a lambertian source is still lambertian and has the same radiance of the source  Given a light source, the radiance (L/n 2 ) of its image can never be greater than that of the source x→y,diff  n0n0 n1n1

Gianluca Valentini 17 Irradiance of an image Let’s calculate the irradiance given by an optical system in the image plane The flux transferred from a lambertian surface dA to a ring element d  is: The flux collected by the optical system taking into account its aperture is: The irradiance of the image is then: Using the Abbe condition one gets: Introducing the definition of focal ratio (f # ): The irradiance of the image depends on the radiant exitance of the source and on the aperture of the optical system Irradiance given on dA 1 by the exit pupil having uniform irradiance: n0n0 n1n1

Gianluca Valentini The spectral sensitivity of the human eye The visual stimulus produced by a radiation depends on its spectral power density according to the spectral sensitivity of the human eye The vision process is triggered by the isomerisation reaction of Rhodopsin Photopic vision  It is characterized by activation of cones  Gives a clear perception of colours  Can be experienced during daylight vision  Mainly corresponds to the maximum visual acuity (macula) Scotopic vision  It is characterized by the activation of rods  Can be experienced during night vision  Chromatic sensitivity is very low  It is more effective in the peripheral region of the retina 18

Gianluca Valentini Spectrophotometric sensitivity of the eye Through experiment made with bipartite colour fields it has been possible to measure the Spectral Luminous Efficiency for the Standard Observer Photopic vision (CIE, 1924)→ V ( ) Scotopic vision (CIE, 1951)→ V’( ) Luminous flux Fv [lm] 19 baba bmbm btbt

Gianluca Valentini 20 The photometric quantities Photometry deals with the measurement of the visual response caused by radiation fields with wavelength within the visible range (380-700 nm) Photometric quantities stem from the analogous radiometric quantities “weighted” by the spectral response of the eye of a normal observer (i.e. not affected by ocular diseases) Photometric quantities QuantitySymbolDefinitionMeas. UnitSymbol Luminous energyQvQv talbotlm·s Luminous densityuvuv dQ v /dVlumen·s·m -3 lm·s·m -3 Luminous flux vv dQ v /dtlumenlm Luminous exitanceMvMv d  v /dA lux lm·m -2 = lx IlluminanceEvEv d  v /dA lux lm·m -2 = lx LuminanceLvLv d  v 2 /(dA pr  d  nitlm·m -2 ·sr -1 = nt Luminous intensity*IvIv d  v /d  candlelm·sr -1 = cd 1 candle = luminous intensity produced by a source emitting monocromatic radiation @ = 540 10 12 Hz ( = 555 nm) with a Radiant intensity of 1/683 W/sr

Gianluca Valentini Light sources - the sun Spectral irradiance of the sun (W·m -2 ·  m -1 ) outside the atmosphere and at earth’s surface 21

Gianluca Valentini Daylight Daylight corresponds to the direct illumination by the sun + light from the sky on a horizontal surface:  Colour temperature Tc = 5.000 – 7.000 K (temperature of the solar corona Ts  5.780 K) Overcast sky  Colour temperature is Tc = 5.000 – 7.000 K Bright sky without direct sun light (shadow)  Colour temp Tc > 7.000 K up to 40.000 K for bright sky in north direction Solar disk with “atmospheric filter”  Colour temperature Tc ≈ 5000 K The conventional colour temperature of the daylight is Tc = 6.500 K 22

Gianluca Valentini Light sources - Daylight Relative spectral power distribution for different phases of the daylight Fraunhofer absorption lines in the solar spectrum (H, Na,etc.) 23

Gianluca Valentini Light sources - Colour temperature of the daylight 24

Gianluca Valentini Light sources - The Planck blackbody 25

Gianluca Valentini “Planckian locus” and colour temperature 26

Gianluca Valentini Light sources - Daylight Colorimetric coordinates of daylight (cromaticy diagram) Cromaticy of the blackbody at differen temperatures (Plankian locus) White light x=y=1/3 Daylight locus: 27

Gianluca Valentini Light emission mechanisms The major light emission mechanisms are:  Thermal emission: High temperature bodies The emission spectrum is continouos  Emission by excited electronic states Discharge lamps The emission spectrum is characterised by sharp lines and bands  Emission by semiconductor The emission occurs via inter-band transitions (electron- hole recomb.) The emission spectrum shows a band 20-30 nm wide k nr S0S0 S1S1 S1’S1’ h A h F kfkf e - 28

Gianluca Valentini Incandscence lamps The emission is produced by a tungsten filament at temperature from 2200 to 3400 °K The emission spectrum is similar to that of a blackbody with temperature about 40 K lower than that of the filament The emission obeys the following physical laws: The quality of the light and the efficiency of the lamp increases with the temperature of the filament (distribution temperature) Halogen lamps have a temperature higher than that of normal lamps  The presence of iodine makes the evaporated tungsten to come back to the filament Stefan-Boltzmann law Wien law 29 Blackbody spectral power density

Gianluca Valentini Discharge lamps Emission is mainly produced by electronic treansitions The atom excitation is achieved by an electric discharge ia a gas or in an ionized vapour Emission spectrum is made by lines that undergo collision widening up to a quasi-continuous spectrum Direct emission lamps  The emitted light comes directly from electronic transitions  The quartz or glass bulb absorbs only the harmful UV radiation Lamp with wavelength conversion  The radiation emitted by electronic transitions (typically UV) is converted to visible light by a phosphor layer covering the internal wall of the glass bulb  The phosphor emission takes place by the luminescence/fluorescence effect  the name “fluorescent lamps” 30

Gianluca Valentini Discharge lamp mechanism The active medium is a gas or vapour in a glass or quartz bulb or tume The current flows into the lamp through two electrodes (anode + e cathode – ) The electron – and ion + flux causes further ionization and excitation of the atoms that emit via radiative transitions When the current reaches high density, an arc established between the electrodes  The gas reaches high temperature and is almost completely ionized  The thermal emission contributes to the light generation in addition to atomic transition Efficiency goes down but the light quality greatly improves 31

Gianluca Valentini Discharge lamp types Sodium lamps  Low pressure (  > 120 lm/W) High efficiency, almost monochromatic light  street lighting  High pressure (   50 lm/W) Good efficiency and higher chromatic quality Xenon lamps (  = 30...50 lm/W)  High chromatic quality, high efficiency  Emission spectrum close to the solar one Metal halide lamps (  > 90 lm/W)  High efficiency and chromatic CRI=90  Low cost Mercury lamps  Direct emission High UV emission  special uses  Wavelength conversion by phosphors Good efficiency, but low light quality 32

Gianluca Valentini High pressure xenon lamp 33

Gianluca Valentini Flashtube xenon lamp 34

Gianluca Valentini Fluorescent lamps They are made by low pressure mercury lamps  A small quantity of noble gas (neon) assists the discharge setup  Mercury emission is mainly in the UV range  Light is produced by a mixture of phosphors with high quantum efficiency (  = 60...100 lm/W)  A higher number of phosphor improves the light quality, but lower the efficiency  Different light “tones” can be achieved by changing the phosphor recipe (cool white, warm white, daylight, etc.) 35