Seibert Q. Duntley,
Jacqueline I. Gordon,
John H. Taylor,
Carroll T. White,
Almerian R. Boileau,
John E. Tyler,
Roswell W. Austin,
and James L. Harris
The authors are with the Visibility Laboratory of the Scripps Institution of Oceanography, University of California, San Diego, with the exception of Carroll T. White who is in the U.S. Navy Electronics Laboratory, San Diego, California. USA
Seibert Q. Duntley, Jacqueline I. Gordon, John H. Taylor, Carroll T. White, Almerian R. Boileau, John E. Tyler, Roswell W. Austin, and James L. Harris, "Visibility," Appl. Opt. 3, 549-598 (1964)
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These terrains were measured on the ground by means of a goniophotometer, beneath and during the collection of the data in Sec. VI.
Computed from equations by Duntley (1952) for the lighting condition prevailing for items 1 and 2 in this table.
Data taken with a goniophotometer, 10 October 1956.
Data taken with a photoelectric telephotometer from a helicopter at 300 ft (91.4-m) altitude, mountain forested area near Julian, California, 23 September 1959.
Luminous directional reflectance for terrains 11 through 14 were computed from spectrophotometric data by Krinov (1947) using CLE. Illuminant B. Disparity between data for azimuths 90° and 270° “is explained apparently by the direction of shallow furrows in relation to the sun”, (Krinov–Belkov, 1953, p. 75).
Parentheses indicate estimates based on incomplete spectral data.
Sky condition: clear.
Data taken with a goniophotometer, January 1959.
Table 4.1
Values of Threshold Contrast as Function of Target Diameter for Stimulus Duration of 0.33 seca
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
120.0
0.00763
8.20
0.0158
3.32
0.0320
1.95
0.0650
82.5
0.00785
7.80
0.0163
3.22
0.0331
1.92
0.0670
62.5
0.00810
7.40
0.0168
3.15
0.0341
1.88
0.0690
51.0
0.00835
7.00
0.0174
3.07
0.0352
1.85
0.0710
43.5
0.00860
6.75
0.0179
3.00
0.0362
1.82
0.0735
37.0
0.00890
6.45
0.0184
2.90
0.0373
1.78
0.0760
32.5
0.00915
6.10
0.0191
2.82
0.0384
1.75
0.0780
29.5
0.00940
5.90
0.0196
2.75
0.0396
1.73
0.0800
23.5
0.0100
5.65
0.0202
2.70
0.0404
1.70
0.0830
21.5
0.0103
5.40
0.0208
2.61
0.0422
1.67
0.0855
19.0
0.0107
5.15
0.0216
2.55
0.0436
1.64
0.0883
17.5
0.0110
5.00
0.0222
2.49
0.0450
1.61
0.0910
16.5
0.0113
4.80
0.0229
2.43
0.0464
1.58
0.0940
15.0
0.0117
4.60
0.0236
2.39
0.0478
1.56
0.0965
14.2
0.0120
4.45
0.0243
2.33
0.0492
1.53
0.100
13.2
0.0124
4.30
0.0251
2.29
0.0504
1.51
0.102
12.5
0.0127
4.15
0.0258
2.24
0.0522
1.48
0.106
11.5
0.0132
4.00
0.0267
2.19
0.0541
1.46
0.108
10.8
0.0136
3.90
0.0275
2.15
0.0558
1.44
0.112
10.2
0.0140
3.75
0.0283
2.11
0.0573
1.42
0.116
9.70
0.0144
3.65
0.0292
2.06
0.0592
1.39
0.119
9.10
0.0149
3.50
0.0301
2.03
0.0610
1.38
0.122
8.70
0.0153
3.41
0.0311
1.99
0.0630
1.35
0.127
1.33
0.131
0.945
0.264
0.671
0.530
1.32
0.134
0.930
0.272
0.660
0.550
1.29
0.138
0.920
0.280
0.651
0.565
1.27
0.143
0.905
0.288
0.642
0.583
1.25
0.148
0.890
0.297
0.633
0.600
1.23
0.152
0.880
0.306
0.622
0.620
1.21
0.157
0.865
0.316
0.615
0.635
1.19
0.162
0.855
0.326
0.604
0.660
1.18
0.166
0.840
0.337
0.596
0.680
1.16
0.172
0.830
0.347
0.588
0.700
1.14
0.178
0.815
0.358
0.579
0.720
1.12
0.183
0.805
0.369
0.569
0.745
1.11
0.189
0.790
0.380
0.560
0.770
1.09
0.195
0.780
0.392
0.552
0.795
1.08
0.200
0.765
0.405
0.545
0.815
1.06
0.207
0.759
0.415
0.537
0.840
1.04
0.213
0.745
0.428
0.528
0.870
1.03
0.220
0.735
0.442
0.519
0.900
1.02
0.226
0.725
0.455
0.512
0.925
1.00
0.233
0.713
0.470
0.505
0.950
0.990
0.240
0.701
0.485
0.497
0.985
0.975
0.248
0.692
0.500
0.960
0.256
0.682
0.515
Binocular viewing, foveal fixation, and forced-choice temporal method. Values are averages from large-scale plots of four observers, and hence represent smoothed data.
Table 4.2
Probability Conversion Factors
To obtain detection probability
Multiply value of contrast at P = 0.5 by
0.90
1.50
0.95
1.64
0.99
1.91
Table 4.3
Contrast Correction Factors to Be Applied when Observer Is Deprived of Knowledge of Various Target Propertiesa
Target properties
Correction Factor (↓)
Location ±4° or more
Time of occurrence
Size (3 used)
Duration (3 used)
+
+
+
+
1.00
+
−
+
+
1.40
+
−
+
−
1.60
+
−
−
+
1.50
+
−
−
−
1.45
−
+
+
+
1.31
+, knowledge; −, lack of knowledge. Adapted from Blackwell (1958, 1959).
Table 6.1
Measured and Equivalent Attenuation Lengths, and Ratio of Altitude to Equivalent Attenuation Length
Attenuation length L(z) was recorded continuously as a function of altitude from 6.096 km to 0.305 km during descent of airplane at 305 m per min, with the zero altitude value recorded simultaneously in an instrumented van beneath the flight pattern. These data are shown in Fig. 6.1. Attenuation lengths above 6.096 km are extrapolated, using density ratios calculated from Minzner et al. (1959).
The quantity 1/L(z) is equal to Elterman’s mean attenuation coefficient Ka(h), and the two quantities
and Ka(h) ·h1 may be used interchangeably in Eq. (6.1). See Elterman (1963).
The value of z/L(z) where z = ∞ was calculated from the sea level to space transmittance obtained from measured and extrapolated attenuation length data.
Table 6.2
Sky Luminance B(z, θ, 0°),aUpper Sky, in Azimuth of Sunb
Parenthetical symbols: photometer altitude z, zenith angle θ, and azimuth applicable to table.
Average zenith angle of sun during flight was 41.5°
The tabulated value in ft-L times 3.426 gives the value in cd/m2.
Sky luminances were recorded by airborne equipment during descent, at five altitudes: 20,000, 8500, 7000, 4000, and 1000 ft. Simultaneous records were made in instrumented van. The data for the different azimuths and zenith angles were plotted against altitude and interpolated graphically so that the tabulated values could be read from the graphs.
Extrapolated path luminances for an observer above 20,000 ft may be calculated as the products of 20,000-ft values and appropriate pressure ratio from Table 6.12. This assumes that the character of the aerosol at 20,000 ft and above is unchanged, and that the total number of scattering particles in a vertical path of sight above 20,000 ft is proportional to the pressure.
Sky luminances at zenith angle of 45° were near the sun, exceeded the range of photometer, and hence are not available.
Table 6.3
Skv Luminance B(z, θ, ±45°),a Upper Sky, 45° from Azimuth of Sunb
Parenthetical symbols: photometer altitude z, zenith angle θ, and azimuth applicable to table.
Average zenith angle of sun during flight 41.5°.
In using these tables, it has been found that above 10,000 ft altitude increments of 5000 ft and 10,000 ft are satisfactory.
The tabulated value in ft-L times 3.426 gives the value in cd/m2.
Path luminances from 0 to 20,000 ft altitudes for zenith angles from 95° to 180° were calculated as follows: (1) Path functions for 1000 ft altitude B* (1000,θ,φ) were calculated from flight data and Eq. 10 of Duntley et al. (1957). (2) Path functions for sea level B* (0,θ,φ) were recorded in the van. (3) Path luminances for first 1000 ft altitude
were calculated by means of Eq. 17 of Duntley et al. (1957). (4) Inherent background luminances (groundcover luminances) bB0 (0,θ,φ) were calculated by means of Eq. (6.2). See Eq. 4 of Duntley et al. (1957). (5) Path luminances for other than first 1000-ft altitude were calculated by means of Eq. (6.2).
Path luminances for altitudes above 20,000 ft were extrapolated as follows: (1) Path functions for 20,000 ft B* (20,000,θ,φ) were calculated from flight data and Eq. 10 of Duntley et al. (1957). (2) Path functions above 20,000 ft B* (z,θ,φ) were calculated, in 100-ft increments, in proportion to atmospheric density. (3) Path luminances above 20,000 ft
were calculated by means of Eq. 17 of Duntley et al. (1957).
Table 6.8
Path Luminance
,a Lower Sky, 45° from Azimuth of Sunb
These terrains were measured on the ground by means of a goniophotometer, beneath and during the collection of the data in Sec. VI.
Computed from equations by Duntley (1952) for the lighting condition prevailing for items 1 and 2 in this table.
Data taken with a goniophotometer, 10 October 1956.
Data taken with a photoelectric telephotometer from a helicopter at 300 ft (91.4-m) altitude, mountain forested area near Julian, California, 23 September 1959.
Luminous directional reflectance for terrains 11 through 14 were computed from spectrophotometric data by Krinov (1947) using CLE. Illuminant B. Disparity between data for azimuths 90° and 270° “is explained apparently by the direction of shallow furrows in relation to the sun”, (Krinov–Belkov, 1953, p. 75).
Parentheses indicate estimates based on incomplete spectral data.
Sky condition: clear.
Data taken with a goniophotometer, January 1959.
Table 4.1
Values of Threshold Contrast as Function of Target Diameter for Stimulus Duration of 0.33 seca
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
Target diameter (min of arc)
Threshold contrast
120.0
0.00763
8.20
0.0158
3.32
0.0320
1.95
0.0650
82.5
0.00785
7.80
0.0163
3.22
0.0331
1.92
0.0670
62.5
0.00810
7.40
0.0168
3.15
0.0341
1.88
0.0690
51.0
0.00835
7.00
0.0174
3.07
0.0352
1.85
0.0710
43.5
0.00860
6.75
0.0179
3.00
0.0362
1.82
0.0735
37.0
0.00890
6.45
0.0184
2.90
0.0373
1.78
0.0760
32.5
0.00915
6.10
0.0191
2.82
0.0384
1.75
0.0780
29.5
0.00940
5.90
0.0196
2.75
0.0396
1.73
0.0800
23.5
0.0100
5.65
0.0202
2.70
0.0404
1.70
0.0830
21.5
0.0103
5.40
0.0208
2.61
0.0422
1.67
0.0855
19.0
0.0107
5.15
0.0216
2.55
0.0436
1.64
0.0883
17.5
0.0110
5.00
0.0222
2.49
0.0450
1.61
0.0910
16.5
0.0113
4.80
0.0229
2.43
0.0464
1.58
0.0940
15.0
0.0117
4.60
0.0236
2.39
0.0478
1.56
0.0965
14.2
0.0120
4.45
0.0243
2.33
0.0492
1.53
0.100
13.2
0.0124
4.30
0.0251
2.29
0.0504
1.51
0.102
12.5
0.0127
4.15
0.0258
2.24
0.0522
1.48
0.106
11.5
0.0132
4.00
0.0267
2.19
0.0541
1.46
0.108
10.8
0.0136
3.90
0.0275
2.15
0.0558
1.44
0.112
10.2
0.0140
3.75
0.0283
2.11
0.0573
1.42
0.116
9.70
0.0144
3.65
0.0292
2.06
0.0592
1.39
0.119
9.10
0.0149
3.50
0.0301
2.03
0.0610
1.38
0.122
8.70
0.0153
3.41
0.0311
1.99
0.0630
1.35
0.127
1.33
0.131
0.945
0.264
0.671
0.530
1.32
0.134
0.930
0.272
0.660
0.550
1.29
0.138
0.920
0.280
0.651
0.565
1.27
0.143
0.905
0.288
0.642
0.583
1.25
0.148
0.890
0.297
0.633
0.600
1.23
0.152
0.880
0.306
0.622
0.620
1.21
0.157
0.865
0.316
0.615
0.635
1.19
0.162
0.855
0.326
0.604
0.660
1.18
0.166
0.840
0.337
0.596
0.680
1.16
0.172
0.830
0.347
0.588
0.700
1.14
0.178
0.815
0.358
0.579
0.720
1.12
0.183
0.805
0.369
0.569
0.745
1.11
0.189
0.790
0.380
0.560
0.770
1.09
0.195
0.780
0.392
0.552
0.795
1.08
0.200
0.765
0.405
0.545
0.815
1.06
0.207
0.759
0.415
0.537
0.840
1.04
0.213
0.745
0.428
0.528
0.870
1.03
0.220
0.735
0.442
0.519
0.900
1.02
0.226
0.725
0.455
0.512
0.925
1.00
0.233
0.713
0.470
0.505
0.950
0.990
0.240
0.701
0.485
0.497
0.985
0.975
0.248
0.692
0.500
0.960
0.256
0.682
0.515
Binocular viewing, foveal fixation, and forced-choice temporal method. Values are averages from large-scale plots of four observers, and hence represent smoothed data.
Table 4.2
Probability Conversion Factors
To obtain detection probability
Multiply value of contrast at P = 0.5 by
0.90
1.50
0.95
1.64
0.99
1.91
Table 4.3
Contrast Correction Factors to Be Applied when Observer Is Deprived of Knowledge of Various Target Propertiesa
Target properties
Correction Factor (↓)
Location ±4° or more
Time of occurrence
Size (3 used)
Duration (3 used)
+
+
+
+
1.00
+
−
+
+
1.40
+
−
+
−
1.60
+
−
−
+
1.50
+
−
−
−
1.45
−
+
+
+
1.31
+, knowledge; −, lack of knowledge. Adapted from Blackwell (1958, 1959).
Table 6.1
Measured and Equivalent Attenuation Lengths, and Ratio of Altitude to Equivalent Attenuation Length
Attenuation length L(z) was recorded continuously as a function of altitude from 6.096 km to 0.305 km during descent of airplane at 305 m per min, with the zero altitude value recorded simultaneously in an instrumented van beneath the flight pattern. These data are shown in Fig. 6.1. Attenuation lengths above 6.096 km are extrapolated, using density ratios calculated from Minzner et al. (1959).
The quantity 1/L(z) is equal to Elterman’s mean attenuation coefficient Ka(h), and the two quantities
and Ka(h) ·h1 may be used interchangeably in Eq. (6.1). See Elterman (1963).
The value of z/L(z) where z = ∞ was calculated from the sea level to space transmittance obtained from measured and extrapolated attenuation length data.
Table 6.2
Sky Luminance B(z, θ, 0°),aUpper Sky, in Azimuth of Sunb
Parenthetical symbols: photometer altitude z, zenith angle θ, and azimuth applicable to table.
Average zenith angle of sun during flight was 41.5°
The tabulated value in ft-L times 3.426 gives the value in cd/m2.
Sky luminances were recorded by airborne equipment during descent, at five altitudes: 20,000, 8500, 7000, 4000, and 1000 ft. Simultaneous records were made in instrumented van. The data for the different azimuths and zenith angles were plotted against altitude and interpolated graphically so that the tabulated values could be read from the graphs.
Extrapolated path luminances for an observer above 20,000 ft may be calculated as the products of 20,000-ft values and appropriate pressure ratio from Table 6.12. This assumes that the character of the aerosol at 20,000 ft and above is unchanged, and that the total number of scattering particles in a vertical path of sight above 20,000 ft is proportional to the pressure.
Sky luminances at zenith angle of 45° were near the sun, exceeded the range of photometer, and hence are not available.
Table 6.3
Skv Luminance B(z, θ, ±45°),a Upper Sky, 45° from Azimuth of Sunb
Parenthetical symbols: photometer altitude z, zenith angle θ, and azimuth applicable to table.
Average zenith angle of sun during flight 41.5°.
In using these tables, it has been found that above 10,000 ft altitude increments of 5000 ft and 10,000 ft are satisfactory.
The tabulated value in ft-L times 3.426 gives the value in cd/m2.
Path luminances from 0 to 20,000 ft altitudes for zenith angles from 95° to 180° were calculated as follows: (1) Path functions for 1000 ft altitude B* (1000,θ,φ) were calculated from flight data and Eq. 10 of Duntley et al. (1957). (2) Path functions for sea level B* (0,θ,φ) were recorded in the van. (3) Path luminances for first 1000 ft altitude
were calculated by means of Eq. 17 of Duntley et al. (1957). (4) Inherent background luminances (groundcover luminances) bB0 (0,θ,φ) were calculated by means of Eq. (6.2). See Eq. 4 of Duntley et al. (1957). (5) Path luminances for other than first 1000-ft altitude were calculated by means of Eq. (6.2).
Path luminances for altitudes above 20,000 ft were extrapolated as follows: (1) Path functions for 20,000 ft B* (20,000,θ,φ) were calculated from flight data and Eq. 10 of Duntley et al. (1957). (2) Path functions above 20,000 ft B* (z,θ,φ) were calculated, in 100-ft increments, in proportion to atmospheric density. (3) Path luminances above 20,000 ft
were calculated by means of Eq. 17 of Duntley et al. (1957).
Table 6.8
Path Luminance
,a Lower Sky, 45° from Azimuth of Sunb