191001, page BEI.HTM; the home TUB web site opens in a new window:
http://130.149.60.45/~farbmetrik/
or use another home TUB web site with a copy of this information:
http://farbe.li.tu-berlin.de/

For this page without additional image information, see
BE in English, BG in German.
For this page with additional image information (internet speed > 1MB/s recommended), see
BEI in English, BGI in German.

For the preceding page without additional image information, see
AE in English, AG in German, AF in French, AS in Spanish, AI in Italian, AN in Norwegian.
For the preceding page with additional image information, see
AEI in English, AGI in German, AFI in French, ASI in Spanish, AII in Italian, ANI in Norwegian.

For the next page without additional image information, see
CE in English, CG in German.
For the next page with additional image information, see
CEI in English, CGI in German.

Figures and data are in the folders BEXX (colour series B, E=English, XX=00 to 99).

Introduction: Development of a device independent visual RGB* colour space for colour vision and image technology
See also the booklet of K. Richter (2015, 80 pages, 2,5 MB) Colour, Colour Vision and Elementary Colours in Colour Information Technology
ES15.PDF

For the application of "antichromatic Ostwald optimal colours"
download the following two reports. The following two alternative links are in the standard MLA format. If the first link to a CIE web site is not working then the second link may be used for the download from an archive server. .

Thorstein Seim, Reportership Report CIE R1-47, Hue angles of elementary colours, 2009, see (35 pages),
[http://files.cie.co.at/526.pdf]._Internet Archive_.[ http://web.archive.org/web/20160304130704/http://files.cie.co.at/526.pdf].

Thorstein Seim, Reportership Report CIE R1-57, Border between Blackish and Luminous Colours, 2013, see (23 pages),
[ http://files.cie.co.at/716_CIE%20R1-57%20Report%20Jul-13%20v.2.pdf]._Internet Archive_.[ http://web.archive.org/web/20150413002133/http://files.cie.co.at/716_CIE%20R1-57%20Report%20Jul-13%20v.2.pdf].

Technical general information about the dominant wavelength and the und chromaticity diagrams
In the following diagrams many dominant wavelength of equal dominant wavelength (equal hue) are shown. The achromatic chromaticity of different illuminants is connected with the chromaticity of different wavelength of the three colour vision deficiencies (PDT), of the maximum sensitivities of three cones (LMS), and the four elementary hues (Re, Ye, Ge, and Be). It is the goal to combine these colorimetric data in a colour vision model. Only one natural illuminant with a correlated Colour temperature CCT near 5000 K (D50, P50), and which appears neither bluish nor yellowish and in addition neither greenish nor reddish seems useful for the intended development of a device independent RGB* colour space for many applications.

For the three observers Protanops (P), Deuteranops (D), and Tritanops (T) with the three colour vision deficiencies (PDT) the confusion lines to the wavelength of these deficiencies PM (700nm), DL (505c,E) and TS (400nm) are shown. The lines are given by the connection of the chromaticity of the three wavelength and the achromatic chromaticity of D50 Similar the wavelength of the maximum cone sensitivities Lm (Long, 570nm), Mm (Medium, 540nm), and Sm (Short, 450nm) are included, compare CIE 170-2:2016. In addition the wavelength of the four elementary hues Re (700nm), Ye (575nm), Ge (520nm), Be (475nm) are shown. They define the CIELAB hue angles hab 26, 92, 162, and 272 degree of the Reportership Report CIE R1-47:2009. All the wavelength, which are for Red near the purple connection line in the chromaticity diagram, are approximately independent of the eight illuminants. Some additional wavelength may be defined by the cut points of two of the three cone sensitivities.

For eight Planck (P) illuminants with correlated colour temperatures CCT between 6000 K (P60) and 2500 K (P25), and six CIE illuminants D65, D50, P40, A00 (A), E00 (E), C00 (C), and P00 (relative amount of quanta for equal energy), and Q00 (necessary energy for equal amount of quanta). at least 12 lines are shown between the above wavelength and the achromatic chromaticity:
1. in the standard CIE (x,y) chromaticity diagram,
2. in seven chromaticity diagrams (ai, bi) (i=0 to 6),
3. in seven chromatic value diagrams (Ai, Bi) (i=0 to 6),
4. in seven chroma diagrams (A*i, B*i) (i=0 to 6).
The chromatic value diagrams (Ai, Bi), and the chroma diagrams (A*i, B*i) have the same hue angles compared to the chromaticity diagrams (ai, bi).

Technical general information about Ostwald optimal colours
The Ostwald optimal colours of a colour half with two complementary wavelength are shown in the 24 folders BE16 to BE39.
The 12 folders BE16 to BE27 are used for the eight Planck illumimants P60 to P25.
The 12 folders BE28 to BE39 are used for the six CIE illumimants D65 to C, and for P00. and Q00.
Optimal colours are special colours of rectangle reflection, see one example:
ME99/ME990-1N.PDF
The Ostwald-optimal colours are special optimal colours. The two wavelength limits are complementary for a given illuminant, see one example:
ME99/ME990-2N.PDF
An further example is the elementary Green Ge with the dominant wavelength 520 nm (of equal hue) and the two complementary wavelength limits 470 nm and 570 nm. These wavelength are approximately valid for the natural achromatic illuminants D50, P50, P45, and P00.

A natural achromatic illuminant appears neither bluish nor yellowish and in addition neither reddish nor greenish. The correlated colour temperature is approximately in the CCT range 4500 K to 5000 K. Therefore the CIE standard illuminant D50 is a natural achromatic illuminant. As alternate natural achromatic illuminants the illuminants P45 (4500 K), P50 (5000 K), or P00 (relative amount of quanta for equal energy, near 5000 K) may be used.

Munsell colours and Ostwald optimal colours in different diagrams
It is approximately valid for the CIE illuminants C, and the Munsell colours of Chroma C=2 and Value V=1, 2, 5, (with CIE Y values between Y=2 and Y=90):
1. The chromaticity diagrams (ai, bi) (i=0 and 6) form ellipsis of different size in the folders BG10 and BG13.
2. The chromatic value diagrams (Ai, Bi) (i=0 and 6) form circles of different size in the folders BG11 and BG14.
3. The chroma diagrams (A*i, B*i) (i=0 and 6), form circles of equal size in the folders BG12 and BG15.

It is approximately valid for the four natural illuminants D50, P45, P50 und P00 and the Ostwald colours of a colour half (with CIE Y values between Y=5 and Y=90):
1. The chromaticity diagrams (ai, bi) (i=1) form a very different output (factor >10) in the folders BE16 and BE28.
2. The chromatic value diagrams (Ai, Bi) (i=1) form approximately circles of equal size in the folders BE20 and BE32.< 3. The chroma value diagrams (A*i, B*i) (i=1), form different outputs (factor <5) in the folders BE24 and BE36.

The CIE data XYZ are used for the calculation of the chromaticities (ai, bi), the chromatic values (Ai, Bi) (i= and the chroma data (a*, b*) of CIELAB, see the colorimetric formulae in
ME98/ME980-7N.PDF und
ME98/ME981-7N.PDF.

Result for the colorimetric description of Munsell and Ostwald colours with CIE Y values between Y=2 and Y=90:

1. For the CIE illuminant C (C00) the diagrams (Ai, Bi) and (A*i, B*i) (i=0 to 6) may be most useful for the descripti colour scaling experiments of the Munsell colour order system. For examples see page 6/8 (illuminant C) of BE14/BE14L0NP.PDF and page 6/8 (illuminant C) of BE15/BE15L0NP.PDF.< For all Munsell colours of Munsell Chroma=2 the colorimetric chroma C*ab is aproximately equal for i=6 and the range 2<Y<90 (all Munsell Value steps) according to the last output.

2. The diagrams (Ai, Bi) and (A*i, B*i) (i=1) for CIE illuminant D50 (5000K) or P45 (4500K) appear most useful for the the Ostwald optimal colours of a colour half. The illuminants D50 and P45 are producing the approximately natural achromatic colours.

For examples see page 2/8 (illuminant D50) of BE32/BE32L0NP.PDF or see page 4/8 (illuminant P45) of BE20/BE20L0NP.PDF.

For all Ostwald colours the colorimetric chromatic values Cab are approximately equal for i=1 within the range 8<Y<90.

Remark: The colorimetric chromatic values and the chroma of i=1 and i=6 are based on the confusion lines of the colour defective observers Deuteranop (D) and Tritanop (T).

Folder and Title: All colour series with increasing numbers without plots

Image technology data. Change of 256 integer to dec and hex data
Constant contrast step GgK=2,4. Change of integer rgb-data between 0 and 255.
BE00: gPk: 0_0, rx: 0_0, gx: 0_0, bx: 0_255, 4 pages, 152 KB.
BE01: gPk: 0_0, rx: 0_0, gx: 0_255, bx: 0_255, 1024 pages, 37 MB.
BE02: gPk: 0_0, rx: 0_255, gx: 0_0, bx: 0_255, 1024 pages, 37 MB.

Image technology data. Change of 256 integer to dec and hex data
Change of contrast step between GgK=2,4 and 1,2. Change of integer rgb-data between 0 and 255.
BE03: gPk: 0_7, rx: 0_0, gx: 0_0, bx: 0_255, 32 pages, 1,2 MB.
BE04: gPk: 0_7, rx: 0_0, gx: 0_255, bx: 0_255, 8192 pages, 299 MB.
BE05: gPk: 0_7, rx: 0_255, gx: 0_0, bx: 0_255, 8192 pages, 299 MB.

Image technology data. Change of 256 integer to dec and hex data
Constant contrast step GgK=2,4. Change of 256 integer to 'integer and index data.
BE06: gPk: 0_0, rx: 0_0, gx: 0_0, bx: 0_255:32, 4 pages, 100 KB.
BE07: gPk: 0_0, rx: 0_255, gx: 0_255, bx: 0_255:32, 1024 pages, 25 MB.

Image technology data. Change of 256 integer to dec and hex data
Change of contrast step between GgK=2,4 and 1,2. Change of 256 integer to 'integer and index data.
BE08: gPk: 0_7, rx: 0_0, gx: 0_0, bx: 0_255:32, 32 pages, 795 KB.
BE09: gPk: 0_0, rx: 0_255, gx: 0_255, bx: 0_255:32, 8192 pages, 25 MB.

Munsell colours of equal Chroma C=2 and equal Value V=1, 2, 5, 8, and 9
for eigth Planck illuminants P60, P55, P50, P45, P40, P35, P30, and P25,
see page 4 of 8 for the illuminant P45 (CCT = 4500 K).
Allways the CIE chromaticity diagram (x, y) and seven chromaticity diagrams (ai, bi) (i=0 and 6) are on the (left ) side.
BE10: Munsell colours in the CIE chromaticity diagram (x, y) and seven chromaticity diagrams (ai, bi) (i=0 to 6) (right).
BE11: Munsell colours in the CIE chromaticity diagram (x, y) and in seven chromatic values diagrams (Ai, Bi) (i=0 to 6) (right).
BE12: Munsell colours in the CIE chromaticity diagram (x, y) and in seven chroma diagrams (A*i, B*i) (i=0 to 6) (right).

Munsell colours of equal Chroma C=2 and equal Value V=1, 2, 5, 8, and 9
for eight CIE illuminants D65, D50, P40, A00 (A), E00 (E), C00 (C),
P00 (relative amount of quantums for equal energy), and Q00 (necessary energy fo equal amount of quanta), see page 5 of 8 for the CIE illuminant C.
Allways the CIE chromaticity diagram (x, y) and seven chromaticity diagrams (ai, bi) (i=0 and 6) are on the (left ) side.
BE13: Munsell colours in the CIE chromaticity diagram (x, y) and seven chromaticity diagrams (ai, bi) (i=0 to 6) (right).
BE14: Munsell colours in the CIE chromaticity diagram (x, y) and in seven chromatic values diagrams (Ai, Bi) (i=0 to 6) (right).
BE15: Munsell colours in the CIE chromaticity diagram (x, y) and in seven chroma diagrams (A*i, B*i) (i=0 to 6) (right).

Ostwald optimal colours of a colour half with complementary wavelength limits
for eight Planck illuminants P60 to P25 with the correlated colour temperatures CCT 6000 K to 2500 K, see page 4 of 8 for the Planck illuminant P45 (CCT 4500 K).

CIE data XYZ and xyz (left) and these colours in the CIE chromaticity diagram (x, y) and the chromaticity diagrams (ai, bi) (i=0 to 6).
BE16: Yw=100, Ym=520-770.
BE17: Yw=88,6, Ym=520-770.

CIE data XYZ10 and xyz10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and the chromaticity diagrams (ai10, bi10) (i=0 to 6).
BE18: Yw10=100, Ym10=520-770.
BE19: Yw10=88,6, Ym10=520-770.

Chromatic values YABC and chromaticity a, b (left) and these colours in the CIE chromaticity diagram (x, y) and the chromatic value diagram (Ai, Bi) (i=0 to 6).
BE20: Yw=100, Ym=520-770.
BE21: Yw=88,6, Ym=520-770.

Chromatic values YABC10 and chromaticity a10, b10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and the chromatic value diagrams (Ai10, Bi10) (i=0 to 6).
BE22: Yw10=100, Ym10=520-770.
BE23: Yw10=88,6, Ym10=520-770.

CIELAB data LabC* and cube root chromaticities a', b' (left) and these colours in the CIE chromaticity diagram (x, y) and the chroma diagram (A*i, B*i) (i=0 bis 6).
BE24: Yw=100, Ym=520-770.
BE25: Yw=88,6, Ym=520-770.

CIE data LabC*10 cube root chromaticities a'10, b'10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and he chroma diagram (A*i10, B*i10) (i=0 bis 6).
BE26: Yw10=100, Ym10=520-770.
BE27: Yw10=88,6, Ym10=520-770.

Ostwald optimal colours of a colour half with complementary wavelength limits
for eight CIE illuminants D65, D50, P40, A00 (A), E00 (E), C00 (C), P00 (relative amount of quantums for equal energy), and Q00 (necessary energy for equal amount of quanta), see page 5 of 8 for the CIE illuminant C.

CIE data XYZ and xyz (left) and these colours in the CIE chromaticity diagram (x, y) and the chromaticity diagrams (ai, bi) (i=0 to 6).
BE28: Yw=100, Ym=520-770.
BE29: Yw=88,6, Ym=520-770.

CIE data XYZ10 and xyz10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and the chromaticity diagrams (ai10, bi10) (i=0 to 6).
BE30: Yw10=100, Ym10=520-770.
BE31: Yw10=88,6, Ym10=520-770.

Chromatic values YABC and chromaticity a, b (left) and these colours in the CIE chromaticity diagram (x, y) and the chromatic value diagram (Ai, Bi) (i=0 to 6).
BE32: Yw=100, Ym=520-770.
BE33: Yw=88,6, Ym=520-770.

Chromatic values YABC10 and chromaticity a10, b10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and chromatic value diagram (Ai10, Bi10) (i=0 to 6).
BE34: Yw10=100, Ym10=520-770.
BE35: Yw10=88,6, Ym10=520-770.

CIELAB data LabC* and cube root chromaticities a', b' (left) and these colours in the CIE chromaticity diagram (x, y) and the chroma diagram (A*i, B*i) (i=0 bis 6).
BE36: Yw=100, Ym=520-770.
BE37: Yw=88,6, Ym=520-770.

CIE data LabC*10 and cube root chromaticities a'10, b'10 (left) and these colours in the CIE chromaticity diagram (x10, y10) and the chroma diagrams (A*i10, B*i10) (i=0 to 6).
BE38: Yw10=100, Ym10=520-770.
BE39: Yw10=88,6, Ym10=520-770.

Cone sensitivities and excitation, and spectral tristimulus values
for eight CIE illuminants D65, D50, P40, A00 (A), E00 (E), C00 (C),
P00 (relative amount of quanta for equal energy),
and Q00 (necessary energy for equal quanta),
and for eight illuminants P60, P55, P50, P45, P40, P35, P30, P25 (6000K to 2500K).

CIE 1931 02-degree colorimetry.
BE40: for 8 Dxx illuminants.
BE41: for 8 Pxx illuminants.

CIE 1964 10-degree colorimetry.
BE42: for 8 Dxx illuminants.
BE43: for 8 Pxx illuminants.

CIE-LMS F02-degree colorimetry (start with XYZ data).
BE44: for 8 Dxx illuminants.
BE45: for 8 Pxx illuminants.

CIE-LMS F10-degree colorimetry (start with XYZ data).
BE46: for 8 Dxx illuminants.
BE47: for 8 Pxx illuminants.

LMS-CIE F02-degree colorimetry (start with LMS data).
BE48: for 8 Dxx illuminants.
BE49: for 8 Pxx illuminants.

LMS-CIE F10-degree colorimetry (start with LMS data).
BE50: for 8 Dxx illuminants.
BE51: for 8 Pxx illuminants.

LMS-R17M1 model colorimetry (start with LMS data).
BE52: for 8 Dxx illuminants.
BE53: for 8 Pxx illuminants.

LMS-R17M2 model colorimetry (start with LMS data).
BE54: for 8 Dxx illuminants.
BE55: for 8 Pxx illuminants.

LMS-R17M3 model colorimetry (start with LMS data).
BE56: for 8 Dxx illuminants.
BE57: for 8 Pxx illuminants.

LMS-R17M4 model colorimetry (start with LMS data).
BE58: for 8 Dxx illuminants.
BE59: for 8 Pxx illuminants.

HPE-LMS-CIE colorimetry and approximation with model colorimetry LMS-R17Mx (x=1,2,3,4).
Colorimetry CIE_1931 with Hunt-Pointer-Estevez (HPE) transformation
to LMS-values and approximation with LMS-R17Mx.
BE60: for illuminant E00; linear data.
BE61: for illuminants E00 and P00; logarithmic data.
BE62: for illuminants E00 and P00; linear data.
BE63: for illuminants E00 and P00; logarithmic data.
BE64: for illuminant E00; logarithmic data and in colour.
BE65: for illuminant E00; linear data and in colour.

Munsell colours of Chroma C=2 and Value V=1, 2, 5, 8, and 9
for the Munsell experimental chromaticity (x, y)Mex = (0,3100, 0,3244); This chromaticity is near the chromaticity of illuminant C;
CIE chromaticity diagram (x, y), seven chromatic values diagrams (Ai, Bi) (i=0 to 6) (left)
and seven chroma diagrams (A*i, B*i) (i=0 to 6) (right).
BE66: CIE 2 degree observer.

Achromatic colorimetric data for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
and Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
contrast K=25:1 (Yw=90, Yz=90/5=18, Yn=90/25=3,6);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79;
smaller file size compared to BE86 and BE87.
BE67: for CIE 2 degree observer.
BE68: for CIE 10 degree observer.

Notes: The series BE69 to BE85 use the wavelength-30-dataset "440, 470, 510, 540, 570, 600nm".
The series EE69 to EE93 use the wavelength-25-dataset "420, 445, 470, 495, 520, 545, 570, 595, 620nm".

Colorimetry of Ostwald optimal colours for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
or Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
Kontrast K=25:1 (Yw=90, Yz=90/5=18, Yn=90/25=3,6);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79;
CIE 2 or 10 degree observer; shorter file size compared to BE88 to BE92.
BE69: CIE standard illuminant D65, CIE 2 degree observer, Yw=90.
BE70: 8 illuminants Pxx, CIE 2 degree observer.
BE71: 8 illuminants Dxx, CIE 2 degree observer.
BE72: 8 illuminants Pxx, CIE 10 degree observer.
BE73: 8 illuminants Dxx, CIE 10 degree observer.

Relative elementary colour vision by the colour vision model LMS_R17Mx (x=1,2,3,4)
Model cone sensitivities and excitations, and spectral tristimulus values
for threshold values ta=0,00 and ta=0,01.
BE74 log [sensitivities and excitations] LMS_R17Mx (x=1,2,3,4) and log [threshold] with 520 to 620nm.
BE75 log [sensitivities and excitations] LMS_R17Mx (x=1,2,3,4) and log [threshold] with 545 to 595nm.
BE76 log [sensitivities LMS (PDT)] and log [threshold].
BE77 log [sensitivities LMS (PDT)] and log [threshold].
BE78 log [sensitivities LMS (PDT)] and log [threshold].
BE79 lin [sensitivities LMS (PDT)] and lin [threshold].
BE80 log [sensitivities LMS (PDT)] and log [threshold].
BE81 lin [sensitivities LMS (PDT)] and lin [threshold].
BE82 log [sensitivities LMS (PDT)] and log [threshold].
BE83 lin [sensitivities LMS (PDT)] and lin [threshold].
BE84 log [sensitivities LMS (PDT)] and log [threshold].
BE85 lin [sensitivities LMS (PDT)] and lin [threshold].

Achromatic colorimetric data for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
and Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
contrast K=25:1 (Yw=90, Yz=90/5=18, Yn=90/25=3,6);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79;
larger file size compared to BE67 and BE68.
BE86: for CIE 2 degree observer.
BE87: for CIE 10 degree observer.

Colorimetry of Ostwald optimal colours for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
or Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
Kontrast K=25:1 (Yw=90, Yz=90/5=18, Yn=90/25=3,6);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79;
larger file size compared to BE69 to BE73.
BE88: CIE standard illuminant D65, CIE 2 degree observer, Yw=90.
BE89: 8 illuminants Pxx, CIE 2 degree observer.
BE90: 8 illuminants Dxx, CIE 2 degree observer.
BE91: 8 illuminants Pxx, CIE 10 degree observer.
BE92: 8 illuminants Dxx, CIE 10 degree observer.

Achromatic colorimetric data for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
and Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
contrast K>256:1 (Yw=100, Yz<7=100/16, Yn=0,0<100/256=0,4);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79.
BE93: for CIE 2 degree observer..
BE94: for CIE 10 degree observer..

Colorimetry of Ostwald optimal colours for 16 illuminants Pxx (P60, P55, P50, P45, P40, P35, P30, P25)
or Dxx (D65, D50, P45, A00, E00, C00, P00, Q00)
contrast K>256:1 (Yw=100, Yz<7=100/16, Yn=0,0<100/256=0,4);
4 colour spaces CIEXYZ, YAB_77, CIELAB, LABHNU1_79;
CIE 2 or CIE 10 degree observer.
BE95: CIE standard illuminant D65, CIE 2 degree observer, Yw=100.
BE96: 8 illuminants Pxx, CIE 2 degree observer.
BE97: 8 illuminants Dxx, CIE 2 degree observer.
BE98: 8 illuminants Pxx, CIE 10 degree observer.
BE99: 8 illuminants Dxx, CIE 10 degree observer.

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