230201 'BNAX' http://farbe.li.tu-berlin.de/BEA_I.HTM or http://color.li.tu-berlin.de/BEA_I.HTM.

For links to the chapter A Colour Image Technology and Colour Management (2019), see
Content list of chapter A: AEA_I in English or AGA_I in German.
Summary of chapter A: AEA_S in English or AGA_S in German.
Example content part AEAI of some available parts AEAI to AEZI: AEAI in English or AGAI in German.
Example images part AEAS of all 26 parts AEAS to AEZS: AEAS in English or AGAS in German.

For links to the chapter B Colour Vision and Colorimetry (2020), see
Content list of chapter B: BEA_I in English or BGA_I in German.
Summary of chapter B: BEA_S in English or BGA_S in German.
Example content part BEAI of some available parts BEAI to BEZI: BEAI in English or BGAI in German.
Example images part BEAS of all 26 parts BEAS to BEZS: BEAS in English or BGAS in German.

For links to the chapter C Colour Spaces, Colour Differences, and Line Elements (2021), see
Content list of chapter C: CEA_I in English or CGA_I in German.
Summary of chapter C: CEA_S in English or CGA_S in German.
Example content part CEAI of some available parts CEAI to CEZI: CEAI in English or CGAI in German.
Example images part CEAS of all 26 parts CEAS to CEZS: CEAS in English or CGAS in German.

For links to the chapter D Colour Appearance, Elementary Colours, and Metrics (2022), see
Content list of chapter D: DEA_I in English or DGA_I in German.
Summary of chapter D: DEA_S in English or DGA_S in German.
Example content part DEAI of some available parts DEAI to DEZI: DEAI in English or DGAI in German.
Example images part DEAS of all 26 parts DEAS to DEZS: DEAS in English or DGAS in German.

For links to the chapter E Colour Metrics, Differences, and Appearance (2023), under work, see
Content list of chapter E: EEA_I in English or EGA_I in German.
Summary of chapter E: EEA_S in English or EGA_S in German.
Example content part EEAI of some available parts EEAI to EEZI: EEAI in English or EGAI in German.
Example images part EEAS of all 26 parts EEAS to EEZS: EEAS in English or EGAS in German.

Project title: Colour and colour vision with Ostwald, device, and elementary colours -
Antagonistic colour-vision model TUBJND and properties for many applications

Chapter B: Colour Vision and Colorimetry (2020), Main part BEA_I

Each chapter includes main parts (I) with information to an image part (S).
There are 26 image parts (S), each with 10 figure pages.
The 10 figure pages (0 to 9) include up to 16 figures, and each figure with up to six formats.

Structure, content, and order of files and figures on the example chapter
Colour Vision and Colorimetry


Figure 1 shows the structure of the web site BE(A..Z)I.HTM und BE(A..Z)S.HTM.
For the download of this figure in the VG-PDF format, see AEX00-5N.PDF.

Structure, content, and order of files and figures on the web site http://farbe.li.tu-berlin.de.


Figure 2 shows the structure, the content, and the order of files and figures on the web site http://farbe.li.tu-berlin.de.
For the download of this figure in the VG-PDF format, see AEX0L0N1.

List of links to the contents of all image parts

Image part BEAS in English or BGAS in German.
Title: Antagonistic colour vision model and applications;
Mixture of spectral colours to optimal colours of Ostwald;
Six chromatic mixture colours as optimal and device colours;
Application chromatic adaptation;
Application adaptation to the visual luminance range

1. Introduction and goals.
2. Antagonistic colour vision model and applications.
3. Model for chromatic adaptation.
4. Model for adaptation to the visual luminance range
beteem white W and black N for the contrast steps
C=2:1, 4:1, 36:1 to 288:1, and seven further steps.
5. Antagonistic colorimetry: linear, logarithmic, or?
for further information and discussion, see BEAI.

go to the image part BEAS to study the 10 image pages and the content.


Image part BEBS in English or BGBS in German.
Title: Eight Planck and Daylight illuminants Pxx and Dxx;
for the calculation of the Ostwald-optimal colours;
complementary optimal colours with antagonistic tristimulues values
X, Y, Z, and Xw-X, Yw-Y, Zw-Z
in the CIE chromaticity diagram (x, y), and other
colorimetric diagrams for the CIE standard illuminants D65 and A

1. Introduction and goals.
2. Relative sprectral radiation of the 8 illuminants Pxx and Dxx.
3. Wavelength ranges of the Ostwald colours for 16 illuminants.
4. Calculations of tristimulues values X, Y, Z, and Xw-X, Yw-Y, Zw-Z, as well as
wavelength limits, dominant and complementary wavelength.
5. Alternative starting wavelength limits compared to the preferred limits.
6. Equal chromatic values for the antagonistic colour pairs
R-C, Y-B und G-M
in the chromatic value diagram (A2, B2),
and comparison with CIELAB chroma.

go to the image part BEBS to study the 10 image pages and the content.


Image part BECS in English or BGCS in German.
Title: Ostwald-optimal colours for the CIE-02-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for complementary optimal colours of antagonistic tristimulues values X, Y, Z, and
Xw-X, Yw-Y, Zw-Z in the CIE chromaticity diagram (x, y);
for four contrast steps C=25:1, 10:1, 4:1, and 2:1

1. Introduction and goals.
2. Location of complementary Ostwald-optimal colours in the CIE (x, y) chromaticity diagram.
2. Approximately equal chromatic values CAB2 for all Ostwald-optimal colours.
3. Decreasing of chromaticity difference between colour and white
for any of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Change of the triangle location in (x, y) to a circular location
in the chromatic value diagrams (A2, B2) for any of the four contrast steps C and discussion.

go to the image part BECS to study the 10 image pages and the content.


Image part BEDS in English or BGDS in German.
Title: Ostwald-optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for complementary optimal colours of antagonistic tristimulues values X10, Y10, Z10, and
Xw10-X10, Yw10-Y10, Zw10-Z10 in the CIE chromaticity diagram (x10, y10);
for four contrast steps C=25:1, 10:1, 4:1, and 2:1

1. Introduction and goals.
2. Location of complementary Ostwald-optimal colours in the CIE (x10, y10) chromaticity diagram.
2. Approximately equal chromatic values CAB2,10 for all Ostwald-optimal colours.
3. Decreasing of chromaticity difference between colour and white
for any of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Change of the triangle location in (x10, y10) to a circular location
in the chromatic value diagrams (A2,10, B2,10) for any of the four contrast steps C and discussion.

go to the image part BEDS to study the 10 image pages and the content.


Image part BEES in English or BGES in German.
Title: Antagonistic model of colour vision for Ostwald colours;
Additive mixture of spectral colours to Ostwald optimal colours

1. Introduction and goals.
2. Additive spectral colour mixture with a colour integrator to the Ostwald-optimal colours.
3. Antagonistic model of colour vision; mixture to grey for D65.
4. Additive colour mixture for four display devices sRGB, WCGa, Offs, and Ostw.
5. Normalized reflections R/0,5 or log[R/0,2] and relations
to the lightness and to antagonistic visual signals.

go to the image part BEES to study the 10 image pages and the content.


Image part BEFS in English or BGFS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BEFS to study the 10 image pages and the content.


Image part BEGS in English or BGGS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each if the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BEGS to study the 10 image pages and the content.


Image part BEHS in English or BGHS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for 3 complementary colour pairs R-C, Y-B, and G-M;
in chromatic value diagrams (A1, B1) and (A2, B2)

1. Introduction and goals.
2. Equal chromatic values in diagrams (A1, B1) and (A2, B2);
3. Equal chromatic values for three complementary colour pairs R-C, Y-B and G-M;
4. Equal change of chromatic values for any of 4 contrast steps C=25:1, 10:1, 4:1, and 2:1.

go to the image part BEHS to study the 10 image pages and the content.


Image part BEIS in English or BGIS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for 3 complementary colour pairs R-C, Y-B, and G-M;
in chromatic value diagrams (A1, B1) and (A2, B2)

1. Introduction and goals.
2. Equal chromatic values in diagrams (A1, B1) and (A2, B2);
3. Equal chromatic values for three complementary colour pairs R-C, Y-B and G-M;
4. Equal change of chromatic values for any of 4 contrast steps C=25:1, 10:1, 4:1, and 2:1.

go to the image part BEIS to study the 10 image pages and the content.


Image part BEJS in English or BGJS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB, Y);
for chromatic values CAB and tristimulus values Y;
diffferent Y-tranfers and Y-scales for four contrast steps C=25:1, 10:1, 4:1, and 2:1

1. Introduction and goals.
2. Approximately equal chromatic value CAB in any hue plane.
3. Equal decreasing of chromatic values CAB
for each of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of the different Y-transfers and Y-scales for the four contrast steps C and discussion.

go to the image part BEJS to study the 10 image pages and the content.


Image part BEKS in English or BGKS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB, Y);
for chromatic values CAB and tristimulus values Y;
diffferent Y-tranfers and Y-scales for four contrast steps C=25:1, 10:1, 4:1, and 2:1

1. Introduction and goals.
2. Approximately equal chromatic value CAB in any hue plane.
3. Equal decreasing of chromatic values CAB for each if the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of different Y-transfers and Y-scales for the four contrast steps C and discussion.

go to the image part BEKS to study the 10 image pages and the content.


Image part BELS in English or BGLS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for 3 complementary colour pairs R-C, Y-B, and G-M;
in chromatic value diagrams (A, B) and (A1, B1)

1. Introduction and goals.
2. Equal chromatic values in diagrams (A, B) and (A1, B1);
3. Equal chromatic values for three complementary colour pairs R-C, Y-B and G-M;
4. Equal change of chromatic values for any of 4 contrast steps C=25:1, 10:1, 4:1, and 2:1.

go to the image part BELS to study the 10 image pages and the content.


Image part BEMS in English or BGMS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for 3 complementary colour pairs R-C, Y-B, and G-M;
in chromatic value diagrams (A, B) and (A1, B1)

1. Introduction and goals.
2. Equal chromatic values in diagrams (A, B) and (A1, B1);
3. Equal chromatic values for three complementary colour pairs R-C, Y-B and G-M;
4. Equal change of chromatic values for any of 4 contrast steps C=25:1, 10:1, 4:1, and 2:1.

go to the image part BEMS to study the 10 image pages and the content.


Image part BENS in English or BGNS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BENS to study the 10 image pages and the content.


Image part BEOS in English or BGOS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each if the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BEOS to study the 10 image pages and the content.


Image part BEPS in English or BGPS in German.
Title: Ostwald optimal colours for the CIE-2-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each of the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BEPS to study the 10 image pages and the content.


Image part BEQS in English or BGQS in German.
Title: Ostwald optimal colours for the CIE-10-degree observer;
for 8 Planck-illuminants Pxx, and for 8 daylight illuminants Dxx;
for two complementary hue planes in diagrams (CAB2, Y);
for chromatic values CAB and tristimulus values Y

1. Introduction and goals.
2. Approximately equal chromatic value CAB2 in any hue plane.
3. Equal decreasing of chromatic values CAB2
for each if the four contrast steps C=25:1, 10:1, 4:1, and 2:1.
4. Reason of Y-transfer for four contrast steps C and discussion.

go to the image part BEQS to study the 10 image pages and the content.


Image part BERS in English or BGRS in German.
Title: Just noticeable colour differences (JNDs) of Ostwald colours;
Hue circles and hue planes of Ostwald colours for 2 contrasts C>288:1 and 2:1

1. Introduction and goals.
2. Just noticeable colour differences (JNDs) of Ostwald colours.
3. Equal JNDs for all antagonistic (complementary) optimal colours
according to Holtsmark and Valberg.
4. Hue circles and hue planes of Ostwald colours
for 8 CIE illuminants and 2 contrasts C>288:1 and 2:1.
5. Relation of the Holtsmark results to the colorimetric line
elements of Schroedinger und Stiles.

go to the image part BERS to study the 10 image pages and the content.


Image part BESS in English or BGSS in German.
Title: Viewing situation of adjacent and separate colours;
Antagonistic colour attributes and scaling of N*, I*, W*, T*, C*, and A*

1. Introduction and goals.
2. Viewing situation of adjacent and separate colours.
3. Colour attributes Blackness N*, whiteness W*, Chromaticness C*,
and the antagonistic attributes I*, T*, and A*.
4. Antagonistic optimal colours of a colour half.
5. Colour vectors of the antagonistic colour vision model and relation with
linear colour values, and linear and nonlinear colour attributes.

go to the image part BESS to study the 10 image pages and the content.


Image part BETS in English or BGTS in German.
Title: Colour line elements for adjacent and separate colours;
Colour difference formulae CIELAB and IECsRGB for scaling,
and LABJNDx and IECsRGBJND for thresholds

1. Introduction and goals.
2. Viewing situation of adjacent and separate colours.
3. Colour-difference formulae for scaling and threshold.
4. CIELAB for separated colours and LABJND for adjacent colours.
5. Differences of colour line elements for scaling and thresholds.

go to the image part BETS to study the 10 image pages and the content.


Image part BEUS in English or BGUS in German.
Title: Ostwald, sRGB and WCGa colours in chromaticity and in chromatic value diagram;
line elements and derivations of achromatic colours for scaling and thresholds

1. Introduction and goals.
2. Ostwald, sRGB, and WCGa colours in the chromaticity diagram (x, y), and in the chromatic value diagram (A2, B2).
3. Simplified colour-difference formulae for scaling and thresholds.
4. Colour difference formulae CIELAB and IECsRGB for scaling,
and LABJNDx and IECsRGBJND for thresholds.
5. Line elements and derivations of achromatic colours for scaling and thresholds.

go to the image part BEUS to study the 10 image pages and the content.


Image part BEVS in English or BGVS in German.
Title: Colour thresholds and line elements in 10 colour spaces
IECsRGBu0 to 9 with additional function data

1. Introduction and goals;
2. Modifications IECsRGBu0 to 9 of the colour space IECsRGB, similar to CIELAB;
3. Corresponding line elements for the experimental contrast Y/(delta Y);
4. Absolute lightness L* (CIE 15) and T* (IEC 61066-2-1 (sRGB)) and relative lightness l* and t*;
5. Logarithmic and linear figures for L*, T*, l* and t*;
6. Logarithmic figures for threshold delta Y, sensitivity (delta Y)/Y, and contrast Y/(delta Y);
7. Parameters of the formula T*=Sn(Y/Yu)^(1/g)-Sd with Yu=18,
for exaample Sn=50, 1/g=1/2,4, Sd=0.

go to the image part BEVS to study the 10 image pages and the content.


Image part BEWS in English or BGWS in German.
Title: Colour thresholds and line elements in 10 colour spaces IECsRGBu0 to 9
1. Introduction and goals;
2. Modifications IECsRGBu0 to 9 of the colour space IECsRGB similar to CIELAB;
3. Corresponding line elements for the experimental contrast Y/(delta Y);
4. Absolute lightness L* (CIE 15) and T* (IEC 61066-2-1 (sRGB)) and relative lightness l* and t*;
5. Logarithmic and linear figures for L*, T*, l* and t*;
6. Logarithmic figures for threshold delta Y, sensitivity (delta Y)/Y, and contrast Y/(delta Y);
7. Parameters of the formula T*=Sn(Y/Yu)^(1/g)-Sd with Yu=18,
for exaample Sn=50, 1/g=1/2,4, Sd=0.

go to the image part BEWS to study the 10 image pages and the content.


Image part BEXS in English or BGXS in German.
Title: Colour thresholds and line elements in 10 colour spaces
CIELABu0 to 9 with additional function data

1. Introduction and goals;
2. Modifications CIELABu0 to 9 of the colour space CIELAB;
3. Corresponding line elements for the experimental contrast Y/(delta Y);
4. Absolute lightness L* (CIE 15) and T* (ISO/CIE 11664-4 (CIELAB)) and relative lightness l* and t*;
5. Logarithmic and linear figures for L*, T*, l* and t*;
6. Logarithmic figures for threshold delta Y, sensitivity (delta Y)/Y, and contrast Y/(delta Y);
7. Parameters of the formula T*=Sn(Y/Yu)^(1/g)-Sd with Yu=18,
for exaample Sn=66, 1/g=1/3,0, Sd=16.

go to the image part BEXS to study the 10 image pages and the content.


Image part BEYS in English or BGYS in German.
Title: Colour thresholds and line elements in 10 colour spaces CIELABu0 to 9
1. Introduction and goals;
2. Modifications CIELABu0 to 9 of the colour space CIELAB;
3. Corresponding line elements for the experimental contrast Y/(delta Y);
4. Absolute lightness L* (CIE 15) and T* (ISO/CIE 11664-4 (CIELAB)) and relative lightness l* and t*;
5. Logarithmic and linear figures for L*, T*, l* and t*;
6. Logarithmic figures for threshold delta Y, sensitivity (delta Y)/Y, and contrast Y/(delta Y);
7. Parameters of the formula T*=Sn(Y/Yu)^(1/g)-Sd with Yu=18,
for exaample Sn=66, 1/g=1/3,0, Sd=16.

go to the image part BEYS to study the 10 image pages and the content.


Image part BEZS in English or BGZS in German.
Title: Colour thresholds and line elements in 10 colour spaces
CIELABn0 to 9 with additional function data

1. Introduction and goals;
2. Modifications CIELABn0 to 9 of the colour space CIELAB;
3. Corresponding line elements for the experimental contrast Y/(delta Y);
4. Absolute lightness L* (CIE 15) and T* (ISO/CIE 11664-4 (CIELAB)) and relative lightness l* and t*;
5. Logarithmic and linear figures for L*, T*, l* and t*;
6. Logarithmic figures for threshold delta Y, sensitivity (delta Y)/Y, and contrast Y/(delta Y);
7. Parameters of the formula T*=Sn(Y/Yn)^(1/g)-Sd with Yn=100,
for example Sn=116, 1/g=1/3,0, Sd=16.

go to the image part BEZS to study the 10 image pages and the content.


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For the start TUB web site (not archive), see
index.html in English, indexDE.html in German.

For the archive information (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.