**
Project title: Colour and colour vision with Ostwald, device, and elementary colours -
Antagonistic colour-vision models TUBJND and TUBLAB, and properties for many applications
Chapter E: Colour Metrics, Differences, and Appearance (2023),
Main part eea_s, under work**

eea_s41 in English or ega_s41 in German.

eea_s42 in English or ega_s42 in German.

eea_s43 in English or ega_s43 in German.

eea_s44 in English or ega_s44 in German.

eea_s45 in English or ega_s45 in German.

eea_s46 in English or ega_s46 in German.

For links to the main chapter E

Content list of chapter E (links and file names use small letters), see

eea_s in English or ega_s in German.

_________________________

**Title of part 4.2: Achromatic and chromatic colour metric for the surface colour range**

Richter (2020) has studied the colorimetric properties of the complementary

For the download of this figure in the VG-PDF format, see eeh91-5a.pdf.

Two complementary

The spectral power distribution of 8 Planck (Pxx) illuminants with colour temperatures between 3000K and 6500K define both the

For the download of this figure in the VG-PDF format, see eeh90-7n.pdf.

Two complementary

A change of the spectral power distribution from P65 to P30 increase the colour temperature, and changes the chromaticity of the illuminant and the wavelength limits from

For the download of this figure in the VG-PDF format, see eeh91-7n.pdf.

All illuminants between P65 and P30 produce approximately the same tristimulus value ratio between Yellow (Y) and Blue (B). The ratio

An explanation seems the following: For the change from P65 to P30 the spectral power increases in the yellow-red area. However the wavelength range decreases. Therefore the tristimulus value of Yellow may be approximately constant. If this is true, then the tristimulus value of Blue is also constant because both mix to white.

The colour temperature of the CIE standard inlluminants D65, D50 and A change in the same range, see the above Fig. 4.21-3

For the tristimulus values, wavelength limits, chromaticities and chromatic values for the standard illuminant D50, see Fig. 4.22-1.

For the download of this figure in the VG-PDF format, see eeh30-7n.pdf.

The wavelenght on the purpur line are described with a "c=complementary to illuminant E".

For the download of this figure in the VG-PDF format, see eew41-3n.pdf.

The

For the download of this figure in the VG-PDF format, see eew41-7n.pdf.

All Ostwald colours (o) of a colour half have different tristimulus values Yo, see Fig. 4.22-4.

For the download of this figure in the VG-PDF format, see eeg81-5n.pdf.

However, the two chromatic values

For the download of this figure in the VG-PDF format, see eeg81-5n.pdf.

All Ostwald colours (o) of a colour half have approximately equal radial chromatic values

For the download of this figure in the VG-PDF format, see eet40-4n.pdf.

The mate surface colour range is limited to the range 3,6 <=

For White the tristimulus value it is

The tristimulus-value ratio

For the radial chromatic values

For the download of this figure in the VG-PDF format, see eet00-3n.pdf.

Different constants

For the download of this figure in the VG-PDF format, see eet00-7n.pdf.

The colorimetric data of the

For all illuminants the CIE

The hue angles are approximately equal for

Additional Figures (only for download) show the above properties for the radial chromatic values

For the download of these two figures in the VG-PDF format, see

http://farbe.li.tu-berlin.de/eet3/eet3l0np.pdf and http://farbe.li.tu-berlin.de/eet4/eet4l0np.pdf.

CIE 230:219

The colour-difference formula LABJND 1985 of CIE 230:2019 includes chromaticity coordinates (

For the download of this figure in the VG-PDF format, see eeg10-7n.pdf.

The chromaticity coordinates

For the download of this figure in the VG-PDF format, see eeg11-3n.pdf.

For a constant

The radial scaling factor

This book shows on page 85 for colours of equal

For the download of this figure in the VG-PDF format, see een10-7a.pdf.

In CIE 230 the

The hue dependent properties of different antagonistic pairs of

For the download of the the figure in the VG-PDF format, see

eew40-7n.pdf

The radial chromatic values of all antagonistic

Instead of the hue independent

For the download of this figure in the VG-PDF format, see eeg11-7n.pdf.

On can compare the chromatic values of the colour-difference formulae LABJND 1985 and TUBJND 2023:

compare LABJND 1985 in Fig. 4.24-2: |

compare TUBJND 2023 in Fig. 4.24-5: |

In LABJND 1985

In TUBJND 2023

The colour-difference formula TUBJND 2023 uses the relative tristimulus values

One can consider the equation

Then there are alternate versions of equation [4] in Fig. 4.24-5 without the trstimulus value

Different versions of TUBJND 2023 are under consideration. The performance of LABJND 1985 in CIE 230 may increase by the use of the formula TUBJND 2023 for the defined CIE datasets for small and larger clour differences

For all experimental data of thresholds

For the download of this figure in the VG-PDF format, see een40-2a.pdf.

In offices the surround luminance is

For

For

It is often appropriate to use a log instead of a linear scale for the contrast

For the download of this figure in the VG-PDF format, see een40-3a.pdf.

The log output shows a slope near 1 in the dark range and a slope -1/3 in the light range compared to the surround. The slope in the light range depends to a large degree on the viewing time of the two adjacent samples. The slope changes from -1 to 0 for very short (<0,1s) to long viewing times (> 25s) by local adaptation.

The experimental viewing time for the thresholds of

MG480-7N 2x2, Fig. 4.25-1

MG481-7N 2x2, Fig. 4.25-2

MG030-8N, Fig. 4.25-3

MG031-1N, Fig. 4.25-4

MG031-3N, Fig. 4.25-5

MG031-4N, Fig. 4.25-6

For the download of this figure in the VG-PDF format, see

eew50-7n.pdf

For the download of this figure in the VG-PDF format, see

eew51-3n.pdf

For the download of this figure in the VG-PDF format, see

eew60-3n.pdf

For the download of this figure in the VG-PDF format, see

eew70-3n.pdf

For the download of this figure in the VG-PDF format, see

eew70-7n.pdf

This section includes a revision of a paper presented at the AIC conference in Jeju/Korea, 2017, see a draft: AIC17.PDF.

For the original AIC version, see AIC 2017, 13th Congress, paper OS07_6,

https://aic-color.org/publications-proceedings.

Introduction.

There are different colour vision properties for related surface colours and unrelated colours in lighting technology. This paper studies special surface colours which are complementary optimal colours of a colour half and which are called

The spectral reflection on any

Theory and experimental results

BE640-4A_1, Fig. 4.26-1a

BE640-5A_1, Fig. 4.26-1b

BE640-6A_1, Fig. 4.26-1c

Fig. 4.26-1a to c: HPE-cone sensitivities and parable functions with maximum values at 570, 540, 430nm

The cone sensitivities, the cone excitations, and the tristimulus value excitations are modeled by parables as function of wavelength. Fig. 4.26-1b is based on this model and allows to understand the existence of elementary colours and their spectral distribution. Fig. 4.26-1c shows the chromatic values of the

The Fig. 4.26-1a to c show the cone sensitivities LMS which are calculated by the

BE641-7A_1, Fig. 4.26-2a

BE641-8A_1, Fig. 4.26-2b

BE640-7A_1, Fig. 4.26-2c

Fig. 4.26-2a to c: CIE spectral tristimulus value and cone excitations

The Fig. 4.26-2a to c show excitations of the CIE tristimulus values

BE860-1A, Fig. 4.26-3a

BE860-3A, Fig. 4.26-3b

BE860-5A, Fig. 4.26-3c

For the download of this figure in the VG-PDF format, see

eew61-7n.pdf

For the download of this figure in the VG-PDF format, see

eew21-3n.pdf

For the download of this figure in the VG-PDF format, see

eew20-3n.pdf

For the download of this figure in the VG-PDF format, see

eex20-3n.pdf

For the download of this figure in the VG-PDF format, see

eex21-3n.pdf

For the download of this figure in the VG-PDF format, see

eex30-3n.pdf

For the download of this figure in the VG-PDF format, see

eex31-3n.pdf

Fig. 4.26-2a to c: Logarithmic sum and differences of the spectral cone sensitivities

The Fig. 4.26-2a to c show example calculations of the sum and differences of the spectral cone sensitivities

The peak values of

Therefore a decision of a linear or logarithmic sum is not possible in the case of surface colours. There is a long expert discussion about the ratio of the weighting factors. The ratio 1:1 is used in Fig. 4.26-3c and the ratio 1:2 is used in the HPE transformation. Recent studies show that there are large individual variations in the relative numbers of cone types and their distribution in the retina [3, section 5.4.6].

A logarithmic calculation in Fig. 4.26-3a to c allow to calculate the same shape for these experimental variations in cone distributions. Equations (1) to (5) show examples used in the plots of Fig. 4.26-3a to c.

logVa = 0.5[logMo +logLo] (1) or

Va =(Mo xLo)0,5 (2)

or logMo = 2logVa –logLo (3) with

log Vo = log Va + 0.03 (4)

The cone excitation is the logarithmic (linear ratio) or the logarithmic difference

log (Mo/Va) = logMo - logVa (5)

If the peak values are normalized to one the index (o) is used. The sum and differences produce peak values below one and in this paper then the index (a) is used. The symbols Va (white-black curve) and Vo (white curve), see Fig. 4.36-3a are proportional to the luminous tristimulus value Y. Va(λ) is smaller compared to Vo(λ) by the factor 0,97 in logarithmic units and 0,93 in linear units. See also more values in Fig. 4.26-3b and c.

In Fig 2f-3a the functions Va(lambda) and Vo(lambda) are calculated according to equation (1).

Similar in Fig. 4.26-3b the La(lambda) and Lo(lambda) functions are calculated from calculated sensitivities Ro(lambda) and Go(lambda). All calculated sensitivities are shown by dashed curves. Fig. 4.26-3c uses the red and green colours according to the location in the spectral range.

Fig. 4.26-3c is similar with peak values 570, 520, and 470 nm. These are the peak values of the spectral elementary colours, for example the elementary (e) green Ge as neither yellowish nor bluish.

BE860-2A, Fig. 4.26-4a

BE860-4A, Fig. 4.26-4b

BE860-6A, Fig. 4.26-4c

Fig. 4.26-4(a, b, c): Cone excitation as logarithmic ratio of the spectral or calculated cone sensitivities

The Fig. 4.26-4 show the logarithmic ratio of the real or calculated cone sensitivities in Fig. 4.26-4a to b as function of wavelength according to equation (5). The slope increases with the difference of the peak values.

BE830-3A, Fig. 4.26-5a

BE830-4A, Fig. 4.26-5b

BE830-8A, Fig. 4.26-5c

Fig. 4.26-5(a, b, c): Sensitivities M (540nm), L (570nm), and O (600nm) on a linear ordinate.

Fig 2f-5a shows a linear ordinate scale for three sensitivities Mo, Lo, and Oo. La is calculated by the logarithmic sum of Mo and Oo.

Fig. 4.26-5b shows the linear differences of Fig. 4.26-5a. For the sensitivity difference Oo(lambda) - La(lambda) a dashed curve in red is used because the sensitivity Oo(lambda) is a calculated sensitivity. Together with similar functions in the blue part around 470 nm (of smaller values?) the hue appearance in the spectral range according to the elementary (e) colours Be, Ge, Ye, and Re can be described.

BE321-1A_1, Fig. 4.26-6a

BE321-2A_1, Fig. 4.26-6b

BE321-3A_1, Fig. 4.26-6c

Fig 2f-6(a, b, c): Peak sensitivities Lm, Mm, Sm , confusion lines of PL, DM, TS observers, and elementary hues.

Fig. 4.26-6a shows the location of the peak sensitivities Lm, Mm, Sm, the confusion lines of PL, DM, TS observers, the elementary hues Be, Ge, Ye, and Re and all

Fig. 4.26-6b and c show the chromatic value of the

The spectral distribution is P(lambda) = lambda/560nm E(lambda), and is called P00 in this paper. With the linear equations given in Fig. 4.62 and 6c the antichromatic

DM100-3N_7, Fig. 4.26-7a

DM101-5N_7, Fig. 4.26-7b

Fig. 4.26-7a, b: Chromatic values A0, B0, C0,AB and chromaticities (a, b) of

The Fig. 4.26-7a shows the chromatic values A0, B0, and the chromaticities (a0, b0) of the

In Fig. 4.26-7b the chromatic value C0,AB is approximately independent of hue and of the Y value for the antichromatic

Results and discussion

The confusion lines TS and PL of the Tritanope (T) and Protanope (P) observers with missing L and S cones connect the achromatic and the chromaticity of 400 nm and 700 nm in Fig. 4.61. The TS line defines a basic chromatic value system (A1, B1), see Fig. 4.63, to produce equal chromatic values for the

Conclusion and development

All

Acknowledgement and remarks

I thank Thorstein Seim (Norway) for many proposals to improve the results on this paper. Most figures of this paper have a code of four letters, for example BE32, see Fig. 7. One can find this figure and many similar ones on a public university server

http://130.149.60.45/~farbmetrik/BE32/index.html or a copy (less actual) on the public server http://farbe.li.tu-berlin.de/BE32/index.html. Both servers include many additional references.

References of section 2f:

[1]

http://color.li.tu-berlin.de/color.

For an english version for the (mobile) display output, see

http:/standards.iso.org/iso/9241/306/ed-2/ES15.PDF.

and according to ISO 9241-306:2018, Annex D,

http:/standards.iso.org/iso/9241/306/ed-2/index.html.

[2] CIE 224:2017.

[3]

[4]

http://farbe.li.tu-berlin.de/buche.html.

[5]

[6]

[7]

For the download of this figure in the VG-PDF format, see

eew51-7n.pdf

The book of

For the download of this figure in the VG-PDF format, see eeu00-1n.pdf.

The

For the download of this figure in the VG-PDF format, see eea10-5n.pdf.

The output as function of the domiant wavelength looks very similar compared to the tristimulus value of cero greyness of the experimental results of

The crosses are the caculated data of the

https://aic-color.org/publications,

go to AIC 1971 to download the above paper of

_________________________

For links to the main chapter E

Content list of chapter E (links and file names use small letters), see

eea_s in English or ega_s in German.

In future the figures and the text may be improved.

Link to the next topic (under work in 2023)

eea_s43 in English or ega_s43 in German.

-------

For the TUB start site (not archive), see

index.html in English, or
indexDE.html in German.

For the TUB archive site (2000-2009) of the BAM server
"www.ps.bam.de" (2000-2018)

about colour test charts, colorimetric calculations, standards,
and publications, see

indexAE.html in English,
indexAG.html in German.

For similar Information of the BAM server "www.ps.bam.de"
from the WBM server (WayBackMachine)

https://web.archive.org/web/20090402212108/http://www.ps.bam.de/index.html