Physical Methods for Cultural Heritages Radiometry and Fotometry

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

2. l Electromagnetic waves • Electromagnetic wave In a transparent medium n= refraction index n=1,5 l = wavelenght n = frequency c = vacuum light speed T = period

3. The electromagnetic spectrum

4. Foundamental laws of optics (1) • Reflection: • Refraction: • Dispersion • (n2 depends on l)

5. Foundamental laws of optics (2) • Diffraction • Interference 5

6. Foundamental laws of optics (3) • Polarization • Diffusion 6

7. Real and virtual images • An optical system forms a real image of an objectwhenthe 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 objectwhen 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

8. Light diffraction 8

9. Elements of Radiometry • Radiometry refers to the measure of the energetic content of a radiation field and study the energy propagation in free space or in an optical system • Radiometry mainly deals with incoherent radiation sources and assumes that the optical field propagates according to the laws of the geometrical optics Radiometric quantities

10. Radiometric quantities • Radiant flux • Power carried by a radiation field [W] • Foundamental radiometric quantity • Radiant exitance • Radiant flux emitted by an extended source per unit of area [W·m-2] • Irradiance • Radiant flux incident onto a surface per unit area [W·m-2] • Radiance • Radiant flux emitted by an extended source per unit of solid angle and unit of projected area [W·m-2·sr-1] • Radiant intensity • Radiant flux emitted toward the direction (θ,φ) per unit of solid angle (useful for pointlike radiant sources) [W ·sr-1]

11. J1 J0 dA0 dW0 dW1 dA1 r 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 dA0 to dA1 is: • The radiance measured on surface dA1 in direction r is given by: Solid angle subtended by dA1 for an observer in dA0 Solid angle subtended by dA0 for an observer in dA1 E = Etendue of the optical system L0 = radiance measured on surface A0

12. Lambertian sources • A lambertian source is a source whose radiance does not depend on the observation angle  L(J) = constant = L0 • The radiant intensity (W/sr) emitted by a lambertian source of small area A0 and radianceL0 in a generic direction J is given by: • The radiant intensity changes with the cosine of the observation angle • The change of I as a function of J depends on the variation of the apparent area of the source • Let’s consider a small size lambertian source (dA0) • The radiant flux that impinges on dA1 is: • L(J) is independent on angle J • The radiant exitance of a lambertian source is: J dA0 dW0 dW1 dA1

13. Disk-like lambertian source • Irradiance produced by a disk-like lambertian source of radius R on a surface dA1 located at distance z • A ring element on the disk has area given by: • The solid angle dW0 subtended by dA1from any point on dA0 is given by: • The radiant flux transferred from dA0to dA1 is given by: • The irradiance on the surface dA1 is then: z z0 z∞

14. Aplanatic image forming system • Within paraxial approximation the angle between any ray and the optical axis is small (J << 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 stigmaticfor P and P’ that also obeys the Abbe condition is said to be aplanatic for the two points and is not affected by coma n n’ h, h’ small J, J’ arbitrary For any ray leaving P under any angle J

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/n2) 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 dW1 is: • According to Snell law: • Diefferentiating the previous equation: • The ratio between solid angle dW1 e dW2in polar coordinates is: n1 n2  

16. x→y,diffJ Radiance of an image • Let’s calculate the radianceof the image of a light source produced by an aplanatic optical system • The radiant flux produced by the source(dx0, dy0) within solid angle dW0 at the entrance pupil of the optical system is: • In a lossless optical system the flux dF impinges onto the image element (dx1,dy1) and produces the radiancein direction (J1,f1) given by: • Using the Abbe condition: • The image of a lambertiansource is still lambertianand has the same radiance of the source • Given a light source, the radiance (L/n2) of its image can never be greater than that of the source n0 n1 

17. Irradiance given on dA1 by the exit pupil having uniform irradiance: Irradiance of an image • Let’s calculate the irradiancegiven by an optical system in the image plane • The fluxtransferred from a lambertian surface dA to a ringelement dW is: • The fluxcollected by the optical system taking into account its aperture is: • The irradianceof 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 n0 n1

18. 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 activationof cones • Gives a clear perception ofcolours • Can be experienced duringdaylight 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

19. ba bt bm 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 (l) • Scotopic vision (CIE, 1951) → V’(l) Luminous flux Fv [lm] 19

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 1 candle = luminous intensity produced by a source emitting monocromatic radiation @ n = 540 1012 Hz (l = 555 nm) with a Radiant intensity of 1/683 W/sr 20

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

22. 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

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

24. Light sources - Colour temperature of the daylight 24

25. Light sources - The Planck blackbody 25

26. “Planckian locus” and colour temperature 26

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

28. S1 S1’ e- hnF hnA knr kf S0 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 characterisedby sharp lines and bands • Emission by semiconductor • The emission occurs via inter-bandtransitions (electron- hole recomb.) • The emission spectrum shows a band 20-30 nm wide 28

29. 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 theefficiency of the lamp increases with the temperature of the filament(distribution temperature) • Halogen lamps have a temperaturehigher than that of normal lamps • The presence of iodine makes theevaporated tungsten to come backto the filament Stefan-Boltzmann law Wien law Blackbody spectral power density 29

30. 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

31. 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 furtherionization and excitation of the atoms that emitvia 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

32. 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

33. High pressure xenon lamp 33

34. Flashtube xenon lamp 34

35. 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