 physics  measurement  norm  perception Glossiness & colour of a transparent glass:  physics  measurement  norm  perception Claudio Oleari Università degli Studi di Parma Dipartimento di Fisica claudio.oleari@fis.unipr.it

Light TRANSMISSION and REFLECTION are considered in relation to the perception in order to open a debate useful to define the most meaningful specification of the APPEARANCE of a transparent glass.

In practice: How to judge visually the appearance of a glass? Transmitted and reflected lights are present at the same time in a glass object. In practice: How to judge visually the appearance of a glass? In science: How to specify and measure the appearance of a glass?

1) Optics For an optical characterization of a non scattering glass i) appearance characterization spectral transmittance t(l) spectral reflectance r(l) ii) optical characterization spectral refraction index n(l) absorption coefficient k(l)

Colour stimulus VISIBILE SPECTRUM violet blue green yellow orange red 380 430 490 560 580 620 780 nm gamma X radio ray ray UV IR microwave wave long radio wave l 10-14 10-12 10-10 10-8 10-6 10-4 10-2 1 102 104 106 108 m Colour stimulus

Refraction index  reflection & refraction n(l) 1 l - Snell laws (geometrical properties of light) Fresnel laws (energetic properties of light) reflectance & transmittance

Snell laws geometrical optics From Wikipedia

Fresnel laws Surface reflectance

What geometry for illumination and light collection? Biconical Transmittance and Reflectance spectral Distribution Function (BTDF) (BRDF) wi w ji j Ji J

2) CIE norm (Commission Internationale de l’Éclairage) for transmittance measurement (a standard reflectance measurement of a transparent medium is not defined) Norms for light-modulation measurement CIE publication No. 15:2004, Colorimetry, 3rd Ed.

specimen 10° W to the spectrometer CIE geometry (0°:0°)

specimen 10° W 2° to the spectrometer CIE geometry (di:0°), (de:0°)

specimen W =2p to the spectrometer CIE geometry (d:d)

absorption Incident light CIE geometry (0°:0°) Transparent glass reflected light refracted light absorption Transparent glass CIE geometry (0°:0°)

Absorption and Internal transmittance Lambert-Bouguer and Beer laws F,l(s=0) F,l(s) s

Fi Ft Fr Physical quantities directly related to the perception nair(l) nglass(l) a ≈ 0 Fi Ft Fr Measured by spectrophotometer Total spectral transmittance Total spectral reflectance

For an (approximate) complete optical characterization n(l), k(l) t(l), r(l)

Transmittance for orthogonal incidence Approximate equation Zero-thickness transmittance

For a complete optical (approximate) characterization From measures of transmittance for two different thicknesses absorption coefficient refraction index

For an (approximate) complete characterization of appearance t(l), r(l)

For an (approximate) complete characterization of appearance Total transmittance is measured Total reflectance is function of n(l) and k(l), obtained by approximation from two transmittance measurements refraction index

3) Colour perception & specification of transmitted and reflected lights CIE observers CIE colorimetric systems CIE colorimetric computation

Macular absorbance [a. u.] MACULA LUTEA Macula lutea Fovea Blind point 400 500 600 700 nm lunghezza d’onda Macular absorbance [a. u.] CIE 1931 CIE 1964 CIE observers

typical of the psycho-physical and psycho-metric colorimetry aperture mode typical of the psycho-physical and psycho-metric colorimetry

CIE colorimetric systems: (X, Y, Z) linear vector space (tristimulus space) Luminance factor, ld dominant wavelength, purity CIELAB metric space (L*,a*,b*), (L*, hab, C*ab) + colour-difference formulae CIELUV metric space (L*,u*,v*), (L*, huv, C*uv) Luminance factor, whiteness, tint

L* b* a* C*ab hab CIELAB – CIELUV A colour specification close to the perception unique hues (red, yellow, green, blue) binary hues colour opponency Binary hues L* a* b* hab C*ab

Colorimetric computation: Colour specification depends on  the observer (CIE 1931 or CIE 1964)  the spectral transmittance/reflectance  the illuminant (A, D65, F11) (X, Y, Z)

Few warnings

TRISTIMULS COMPUTATION according to CIE[1] and ASTM [2] RAW SPECTRAL DATA IF Dl  1 nm THEN ELSE OR CHOICES observer (CIE 1931, CIE 1964,., …) illuminant (A, B, C, D65,…, F11, …) deconvolution interpolation ASTM 1996 Weighting Functions ASTM 1985 1 nm CIE TRISTIMULUS VALUES (X, Y, Z) [1]Publication CIE N° 15:2004, Colorimetry, 3rd edition, Central Bureau of the CIE, A-1033 Vienna, P.O. BOX 169 Austria. [2] ASTM E 308-96 Standard Practice for Computing the Colors of Objects by Using the CIE System, Annual book of ASTM Standard, American Society for Testing and Materials, Philadelphia, USA.

? What means “COLOR CALCULATION ACCORDING TO CIE RECOMMENDATION (D65/10° - CIE 15:2004)” ?

RECOMMENDATIONS CONCERNING THE CALCULATION OF TRISTIMULUS VALUES AND CHROMATICITY COORDINATES The CIE Standard (CIE, 1986) on standard colorimetric observers recommends that the CIE tristimulus values of a colour stimulus be obtained by multiplying at each wavelength the value of the colour stimulus function () by that of each of the CIE colour-matching functions and integrating each set of products over the wavelength range corresponding to the entire visible spectrum, 360 nm to 830 nm. The integration can be carried out by numerical summation at wavelength intervals, , equal to 1 nm. (7.1) In the above equations () denotes the spectral distribution of the colour stimulus function, i.e. () = d()/d, see CIE International Lighting Vocabulary item 845-01-17 (CIE,1987). X, Y, Z are tristimulus values, X(), Y(), Z() (or ) are colour-matching functions of a standard colorimetric observer, and k is a normalising constant defined below. Each of these may be specified for the CIE 1931 standard colorimetric system by being written without a subscript, or for the CIE 1964 standard colorimetric system by the use of the subscript 10. The fundamental colorimetric tables are the 1 nm tables in CIE standards. All rigorous calculations should use these 1 nm tables. For most practical purposes, the summation may be approximated by using wavelength intervals,  equal to 5 nm over the wavelength range 380 nm to 780 nm. Values of the CIE colour-matching functions at 5 nm intervals suitable for use in summation over this range of wavelengths are given in Tables T.4 and T.5. In case measurement have been made at smaller intervals than 5 nm, the appropriate values from the tables in the standards should be used.

What about “WHITENESS and TINT ” ?

The evaluation of whiteness To promote uniformity of practice in the evaluation of whiteness of surface colours, it is recommended that the formulae for whiteness, W or W10, and for tint, Tw or Tw,10, given below, be used for comparisons of the whiteness of samples evaluated for CIE standard illuminant D65. The application of the formulae is restricted to samples that are called "white" commercially, that do not differ much in colour and fluorescence, and that are measured on the same instrument at nearly the same time. Within these restrictions, the formulae provide relative, but not absolute, evaluations of whiteness, that are adequate for commercial use, when employing measuring instruments having suitable modern and commercially available facilities. W = Y + 800(xn – x) + 1700(yn – y) W10 = Y10 + 800(xn,10 – x10) + 1700(yn,10 – y10) (9. 11) Tw = 1000(xn – x) – 650(yn – y) Tw,10 = 900(xn,10 – x10) – 650(yn,10 – y10) where Y is the Y-tristimulus value of the sample, x and y are the x, y chromaticity coordinates of the sample, and xn, yn are the chromaticity coordinates of the perfect diffuser, all for the CIE 1931 standard colorimetric observer; Y10, x10 , y10, xn,10 and yn,10 are similar values for the CIE 1964 standard colorimetric observer.

Conclusion:  deep physical specification refraction index n(l) {measured, approximate from 2 transmittances} absorption coefficient k(l) {approximate from 2 transmittances}  appearance physical specification spectral transmittance t(l,s) {measured by spectrophotometer} spectral reflectance r(l,s) {measurement?} {approximate from 2 transmittances}  Colorimetric specification of the appearance- physical specification observer: CIE 1931 illuminants: A, D65, F11 colorimetric system: CIELAB (L*, C*ab, hab)

About the VISUAL JUDGEMENT of the appearance ?

Thank you for your attention Claudio Oleari