Stephen J. Dain and Jeffery K. Hovis, "Recommendations and requirements for the wavelengths in Rayleigh equation anomaloscopes," J. Opt. Soc. Am. A 40, A121-A129 (2023)
DIN 6160:2019 is a technical standard that sets requirements for Rayleigh equation anomaloscopes. Table 1 of the standard contains the limits for centroid wavelengths and spectral half power bandwidths (SHBW). The centroid limits are more restrictive than dominant wavelength recommendations. The SHBW limits have no known evidence base and are inconsistent between colors. The spectral characteristics of three commercial anomaloscopes brands were measured using a telespectroradiometer. Only the oculus instruments complied with DIN 6160 Table 1, but all the anomaloscopes complied with published recommendations. All complied with the DIN 6160 bandwidth requirements. This highlights the need to provide an evidence base for such requirements.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Wavelength of light, which, in some specified respect, has the same property as the heterogeneous beam under consideration.
In the current context, the “specified respect” is taken as the chromaticity in CIE 1931, , but any linear transformation of CIE 1931 will give the same result for the colors concerned.
Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions with the specified achromatic stimulus, matches the color stimulus considered in the CIE 1931 chromaticity diagram.
NOTE: When dealing with fully saturated colors, the chromaticity diagram and achromatic stimulus used does not affect the value of the dominant wavelength.
The various measures applied to the red color of Nagel Model I are
illustrated in Fig. 1.
Table 2.
Peak, Center, Centroid, and Dominant Wavelengths of the Nagel Model II as a Function of Setting Calculated from Published Spectral Data [10]
Setting
Deuteranomaly
Normal
Protanomaly
Red-Green Setting
18
41
62
Green
Peak
537
538
537
Centre
535.8
536.4
537.2
Centroid
535.8
536.4
536.9
Equivalent
536.3
536.9
537.5
Yellow Setting
22
17
13
Yellow
Peak
590
590
590
Centre
589.4
589.4
589.5
Centroid
589.5
589.5
589.5
Equivalent
589.4
589.4
589.4
Red-Green Setting
18
41
62
Red
Peak
664
666
668
Centre
666.2
667.8
668.8
Centroid
666.2
667.8
668.8
Equivalent
664.6
665.9
666.8
Table 3.
Recommendations on the Wavelengths for a Rayleigh Equation and the Requirements of DIN
Chromaticity Differences () Corresponding to Wavelength Tolerances for the Red, Green, and Yellow Lightsa
Bandwidth
2
3
4
5
6
7
15
16
17
20
21
22
to 830 nm
Green
−
0.011
0.014
0.017
0.021
0.024
0.011
0.015
0.019
0.023
0.027
0.011
0.015
0.018
0.022
0.025
Yellow
−
0.014
0.022
0.015
0.022
0.015
0.022
Red
−
0.002
0.013
0.014
0.015
0.020
0.022
0.023
0.002
0.009
Note: Bold entries represent the equivalent of applying the color difference represented by the DIN 6160 ${\pm}\;{3}\;{\rm nm}$ in the yellow to the red and green. Underlined values represent the equivalent of applying the equivalent color difference to the $\pm {2}\;{\rm nm}$ in the yellow.
Table 5.
Details of the Anomaloscopes Measured, Their Location, and Operating Principle
Location
Type
Principle
School of Optometry and Vision
Nagel Model I Older style
Direct vision Amici prism
Science, University of New South
Oculus Heidelberg I
LEDs and interference filters
Wales (UNSW Clinic)
Neitz
Interference filters and incandescent source
UNSW Clinic and UNSW Optics & Radiometry Laboratory (ORLAB)
Oculus HMC (two)
LEDs and interference filters
Department of Optometry and Vision Science, University of Melbourne (U Melb)
Neitz OT-II
LEDs and interference filters
Oculus HMC
LEDs and interference filters
Australian College of Optometry, Melbourne (ACO)
Nagel Model I Newer style
Direct vision Amici prism
University of Washington (U Wash)
Nagel Model I Newer style,
Direct vision Amici prism
Table 6.
Measurements of Nine Anomaloscopes’ Peak, Center, Centroid, and Equivalent Wavelength and SHBWa
Nagel Model I Older Style
Nagel Model I Newer Style
UNSW Clinic
ACO
U Wash
Color
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
545
585
659
551
594
664
545
587
660
Centre
544.3
583.3
656.9
549.7
594.2
667.4
545.0
584.8
659.1
Centroid
544.4
584.7
656.9
549.7
593.8
664.9
545.0
584.9
659.1
Equivalent
544.4
584.7
654.9
549.5
593.3
663.9
545.1
584.8
656.7
Shorter half power
−3.8
−3.7
−8.0
−2.8
3.7
−7.2
−3.4
−7.1
−7.9
Longer half power
2.5
2.5
6.1
3.2
4.1
8.6
3.3
2.7
6.1
Spectral half power bandwidth (longer–shorter)
6.2
6.3
14.1
6.0
7.8
15.9
6.7
9.8
14.0
Oculus Heidelberg I
Oculus Heidelberg HMC
UNSW Clinic
UNSW Clinic
UNSW ORLAB
U Melbourne
Color
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
552
590
660
546
591
665
547
590
665
546
591
665
Centre
550.6
589.3
663.6
548.1
588.3
664.9
548.3
588.0
665.3
547.8
588.3
664.9
Centroid
550.7
590.2
664.5
548.2
589.6
664.7
548.4
589.5
665.1
547.7
589.6
664.7
Equivalent
551.2
589.1
658.6
548.6
589.3
661.1
548.7
589.2
660.4
548.1
589.3
660.4
Shorter half power
−5.5
−5.1
−3.0
−4.4
−6.1
−5.9
−4.5
−4.3
−5.8
−4.0
−6.1
−5.7
Longer half power
5.1
2.3
14.9
7.2
1.4
5.9
7.1
7.2
5.8
6.7
1.4
5.7
Spectral half power bandwidth (longer–shorter)
10.5
7.4
17.9
11.6
7.5
11.8
11.5
11.5
11.6
10.7
7.5
11.4
Neitz OT
Neitz OT-II
UNSW Clinic
U Melbourne
Color
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
551
592
675
546
592
670
Centre
551.3
592.9
675.6
545.4
592.9
669.9
Centroid
551.3
593.0
675.6
547.1
593.0
670.0
Equivalent
551.5
593.0
669.0
546.1
592.7
667.4
Shorter half power
−1.4
−2.2
−3.2
−2.5
−2.1
−3.4
Longer half power
1.7
3.5
4.6
3.6
3.7
3.9
Spectral half power bandwidth (longer–shorter)
3.1
5.7
7.8
6.1
5.7
7.3
Note: Bold entries represent the equivalent of applying the color difference ($\Delta u^\prime v^\prime$) represented by $\pm 3\;{\rm nm}$ in the yellow to the red and green. Similarly, the underlined values represent the equivalent of applying the color difference ($\Delta u^\prime v^\prime$) represented by $\pm 2\;{\rm nm}$ in the yellow.
Table 7.
Summary of Compliance with DIN 6160 Centroid Wavelength Requirements and Published Dominant Wavelength Recommendationsa
Compliance
DIN 6160
Recommendations
Model
Location
Green
Yellow
Red
Green
Yellow
Red
Nagel Model I
UNSW Clinic
✗
✗
✗
✓
✓
ACO
✗
U Wash
✗
✗
✗
Oculus Heidelberg I
UNSW Clinic
Oculus HMC
UNSW Clinic
UNSW ORLAB
U Melb
Neitz OT
UNSW Clinic
✗
✗
Neitz OT-II
U Melb
✗
Note: $\surd$ in the recommendations indicates compliance with the most stringent (hence, all) recommendations for that color; otherwise, the requirement met is indicated.
Tables (7)
Table 1.
Definitions for Characterizing the Wavelength of Narrowband Spectral Distributions
Wavelength of light, which, in some specified respect, has the same property as the heterogeneous beam under consideration.
In the current context, the “specified respect” is taken as the chromaticity in CIE 1931, , but any linear transformation of CIE 1931 will give the same result for the colors concerned.
Wavelength of the monochromatic stimulus that, when additively mixed in suitable proportions with the specified achromatic stimulus, matches the color stimulus considered in the CIE 1931 chromaticity diagram.
NOTE: When dealing with fully saturated colors, the chromaticity diagram and achromatic stimulus used does not affect the value of the dominant wavelength.
The various measures applied to the red color of Nagel Model I are
illustrated in Fig. 1.
Table 2.
Peak, Center, Centroid, and Dominant Wavelengths of the Nagel Model II as a Function of Setting Calculated from Published Spectral Data [10]
Setting
Deuteranomaly
Normal
Protanomaly
Red-Green Setting
18
41
62
Green
Peak
537
538
537
Centre
535.8
536.4
537.2
Centroid
535.8
536.4
536.9
Equivalent
536.3
536.9
537.5
Yellow Setting
22
17
13
Yellow
Peak
590
590
590
Centre
589.4
589.4
589.5
Centroid
589.5
589.5
589.5
Equivalent
589.4
589.4
589.4
Red-Green Setting
18
41
62
Red
Peak
664
666
668
Centre
666.2
667.8
668.8
Centroid
666.2
667.8
668.8
Equivalent
664.6
665.9
666.8
Table 3.
Recommendations on the Wavelengths for a Rayleigh Equation and the Requirements of DIN
Chromaticity Differences () Corresponding to Wavelength Tolerances for the Red, Green, and Yellow Lightsa
Bandwidth
2
3
4
5
6
7
15
16
17
20
21
22
to 830 nm
Green
−
0.011
0.014
0.017
0.021
0.024
0.011
0.015
0.019
0.023
0.027
0.011
0.015
0.018
0.022
0.025
Yellow
−
0.014
0.022
0.015
0.022
0.015
0.022
Red
−
0.002
0.013
0.014
0.015
0.020
0.022
0.023
0.002
0.009
Note: Bold entries represent the equivalent of applying the color difference represented by the DIN 6160 ${\pm}\;{3}\;{\rm nm}$ in the yellow to the red and green. Underlined values represent the equivalent of applying the equivalent color difference to the $\pm {2}\;{\rm nm}$ in the yellow.
Table 5.
Details of the Anomaloscopes Measured, Their Location, and Operating Principle
Location
Type
Principle
School of Optometry and Vision
Nagel Model I Older style
Direct vision Amici prism
Science, University of New South
Oculus Heidelberg I
LEDs and interference filters
Wales (UNSW Clinic)
Neitz
Interference filters and incandescent source
UNSW Clinic and UNSW Optics & Radiometry Laboratory (ORLAB)
Oculus HMC (two)
LEDs and interference filters
Department of Optometry and Vision Science, University of Melbourne (U Melb)
Neitz OT-II
LEDs and interference filters
Oculus HMC
LEDs and interference filters
Australian College of Optometry, Melbourne (ACO)
Nagel Model I Newer style
Direct vision Amici prism
University of Washington (U Wash)
Nagel Model I Newer style,
Direct vision Amici prism
Table 6.
Measurements of Nine Anomaloscopes’ Peak, Center, Centroid, and Equivalent Wavelength and SHBWa
Nagel Model I Older Style
Nagel Model I Newer Style
UNSW Clinic
ACO
U Wash
Color
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
545
585
659
551
594
664
545
587
660
Centre
544.3
583.3
656.9
549.7
594.2
667.4
545.0
584.8
659.1
Centroid
544.4
584.7
656.9
549.7
593.8
664.9
545.0
584.9
659.1
Equivalent
544.4
584.7
654.9
549.5
593.3
663.9
545.1
584.8
656.7
Shorter half power
−3.8
−3.7
−8.0
−2.8
3.7
−7.2
−3.4
−7.1
−7.9
Longer half power
2.5
2.5
6.1
3.2
4.1
8.6
3.3
2.7
6.1
Spectral half power bandwidth (longer–shorter)
6.2
6.3
14.1
6.0
7.8
15.9
6.7
9.8
14.0
Oculus Heidelberg I
Oculus Heidelberg HMC
UNSW Clinic
UNSW Clinic
UNSW ORLAB
U Melbourne
Color
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
552
590
660
546
591
665
547
590
665
546
591
665
Centre
550.6
589.3
663.6
548.1
588.3
664.9
548.3
588.0
665.3
547.8
588.3
664.9
Centroid
550.7
590.2
664.5
548.2
589.6
664.7
548.4
589.5
665.1
547.7
589.6
664.7
Equivalent
551.2
589.1
658.6
548.6
589.3
661.1
548.7
589.2
660.4
548.1
589.3
660.4
Shorter half power
−5.5
−5.1
−3.0
−4.4
−6.1
−5.9
−4.5
−4.3
−5.8
−4.0
−6.1
−5.7
Longer half power
5.1
2.3
14.9
7.2
1.4
5.9
7.1
7.2
5.8
6.7
1.4
5.7
Spectral half power bandwidth (longer–shorter)
10.5
7.4
17.9
11.6
7.5
11.8
11.5
11.5
11.6
10.7
7.5
11.4
Neitz OT
Neitz OT-II
UNSW Clinic
U Melbourne
Color
Green
Yellow
Red
Green
Yellow
Red
Wavelength (nm)
Peak
551
592
675
546
592
670
Centre
551.3
592.9
675.6
545.4
592.9
669.9
Centroid
551.3
593.0
675.6
547.1
593.0
670.0
Equivalent
551.5
593.0
669.0
546.1
592.7
667.4
Shorter half power
−1.4
−2.2
−3.2
−2.5
−2.1
−3.4
Longer half power
1.7
3.5
4.6
3.6
3.7
3.9
Spectral half power bandwidth (longer–shorter)
3.1
5.7
7.8
6.1
5.7
7.3
Note: Bold entries represent the equivalent of applying the color difference ($\Delta u^\prime v^\prime$) represented by $\pm 3\;{\rm nm}$ in the yellow to the red and green. Similarly, the underlined values represent the equivalent of applying the color difference ($\Delta u^\prime v^\prime$) represented by $\pm 2\;{\rm nm}$ in the yellow.
Table 7.
Summary of Compliance with DIN 6160 Centroid Wavelength Requirements and Published Dominant Wavelength Recommendationsa
Compliance
DIN 6160
Recommendations
Model
Location
Green
Yellow
Red
Green
Yellow
Red
Nagel Model I
UNSW Clinic
✗
✗
✗
✓
✓
ACO
✗
U Wash
✗
✗
✗
Oculus Heidelberg I
UNSW Clinic
Oculus HMC
UNSW Clinic
UNSW ORLAB
U Melb
Neitz OT
UNSW Clinic
✗
✗
Neitz OT-II
U Melb
✗
Note: $\surd$ in the recommendations indicates compliance with the most stringent (hence, all) recommendations for that color; otherwise, the requirement met is indicated.