Extension of the Standard Visibility Function to Intervals of One Millimicron by Third-Difference Osculatory Interpolation*

Deane B. Judd

doi:10.1364/JOSA.21.000267

Journal of the Optical Society of America
Vol. 21,
Issue 5,
pp. 267-275
(1931)
•https://doi.org/10.1364/JOSA.21.000267

Extension of the Standard Visibility Function to Intervals of One Millimicron by Third-Difference Osculatory Interpolation

Deane B. Judd

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Deane B. Judd, "Extension of the Standard Visibility Function to Intervals of One Millimicron by Third-Difference Osculatory Interpolation*," J. Opt. Soc. Am. 21, 267-275 (1931)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The two empiric representations (Tyndall-Gibson and Walsh) of the visibility of radiant energy yield curves which fail to pass exactly through the values at every 10 mμ adopted as standard; hence, they can not serve as means of obtaining interpolated values. By the method of osculatory interpolation the visibility function is represented as a series of parabolas of the third degree which join at the specified values so as to have a common first derivative at the junction point. The discontinuities in derivatives of higher order which exist at the junction points are sufficiently small to be of no consequence.

Full Article | PDF Article

More Like This

Interpolation of the O. S. A. “Excitation” Data by the Fifth-Difference Osculatory Formula1

Deane B. Judd
J. Opt. Soc. Am. 21(9) 531-540 (1931)

Comparison of Wright’s Data on Equivalent Color Stimuli with the O. S. A. Data*

Deane B. Judd
J. Opt. Soc. Am. 21(11) 699-728 (1931)

Spectrophotometry at the Bureau of Standards1

K. S. Gibson
J. Opt. Soc. Am. 21(9) 564-587 (1931)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (1)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (3)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

λ in mμ	V_λ	Δ₁V_λ	Δ₂V_λ	Δ₃V_λ
540	0.954	+0.041	−0.041	−0.002
550	.995	.000	−.043
560	.995	−.043
570	.952

λ in mμ	V_λ	∇₁V_λ	∇₂V_λ	∇₃V_λ
570	0.952	+0.043	−0.043	+0.002
560	.995	.000	−.041
550	.995	−.041
540	.954

λ-λ₀	K₁	K₂	K₃
1	+1.1	+0.055	−0.0045
2	+1.2	+.120	−.0160
3	+1.3	+.195	−.0315
4	+1.4	+.280	−.0480
5	+1.5	+.375	−.0625
6	+1.6	+.480	−.0720
7	+1.7	+.595	−.0735
8	+1.8	+.720	−.0640
9	+1.9	+.855	−.0405

λ in mμ	+0.041 K₁	−0.041 K₂	−0.002 K₃	V_λ
551	+0.045100	−0.002255	+0.000009	0.996854
552	+.049200	−.004920	+.000032	.998312
553	+.053300	−.007995	+.000063	.999368
554	+.057400	−.011480	+.000096	1.000016
555	+.061500	−.015375	+.000125	1.000250
556	+.065600	−.019680	+.000144	1.000064
557	+.069700	−.024395	+.000147	.999452
558	+.073800	−.029520	+.000128	.998408
559	+.077900	−.035055	+.000081	.996926

Check by ascending differences: From Table 2 we write: $V_{λ} = 0.952 + 0.43 {K_{1}}^{'} - 0.43 {K_{2}}^{'} + 0.002 {K_{3}}^{'}$
The coefficients, K₁′, K₂′ and K₃′, may be found in Table 3 by reading the values of the coefficients, K₁, K₂ and K₃, for 10−λ+λ₀.

λ in mμ	+0.043 K₁′	−0.043 K₂′	+0.002 K₃′	V_λ
551	+0.081700	−0.036765	−0.000081	0.996854
552	+.077400	−.030960	−.000128	.998312
553	+.073100	−.025585	−.000147	.999368
554	+.068800	−.020640	−.000144	1.000016
555	+.064500	−.016125	−.000125	1.000250
556	+.060200	−.012040	−.000096	1.000064
557	+.055900	−.008385	−.000063	.999452
558	+.051600	−.005160	−.000032	.998408
559	+.047300	−.002365	−.000009	.996926

λ in mμ	V_λ
380	0.00004
1	.000045
2	.000049
3	.000054
4	.000059
5	.000064
6	.000071
7	.000080
8	.000090
9	.000104
390	.00012
1	.000138
2	.000155
3	0.000173
4	.000193
5	.000215
6	.000241
7	.000272
8	.000308
9	.000350
400	.0004
1	.00045
2	.00049
3	.00054
4	.00059
5	.00064
6	0.00071
7	.00080
8	.00090
9	.00104
410	.0012
1	.00138
2	.00156
3	.00174
4	.00195
5	.00218
6	.00244
7	.00274
8	.00310
9	.00352
420	0.0040
1	.00455
2	.00515
3	.00581
4	.00651
5	.00726
6	.00806
7	.00889
8	.00976
9	.01066
430	.0116
1	.01257
2	.01358
3	0.01463
4	.01571
5	.01684
6	.01800
7	.01920
8	.02043
9	.02170
440	.023
1	.0243
2	.0257
3	.0270
4	.0284
5	.0298
6	.0313
7	.0329
8	.0345
9	.0362
450	.038
1	.0399
2	.0418
3	.0438
4	.0459
5	.0480
6	.0502
7	.0525
8	.0549
9	.0574
460	.060
1	.0627
2	.0654
3	.0681
4	.0709
5	.0739
6	.0769
7	.0802
8	.0836
9	.0872
470	.091
1	.0950
2	.0992
3	.1035
4	.1080
5	0.1126
6	.1175
7	.1225
8	.1278
9	.1333
480	.139
1	.1448
2	.1507
3	.1567
4	.1629
5	.1693
6	.1761
7	.1833
8	.1909
9	.1991
490	.208
1	.2173
2	.2270
3	.2371
4	.2476
5	.2586
6	.2701
7	.2823
8	.2951
9	.3087
500	.323
1	.3382
2	.3544
3	.3714
4	.3890
5	.4073
6	.4259
7	.4450
8	.4642
9	.4836
510	.503
1	.5229
2	.5436
3	.5648
4	.5865
5	.6082
6	.6299
7	0.6511
8	.6717
9	.6914
520	.710
1	.7277
2	.7449
3	.7615
4	.7776
5	.7932
6	.8082
7	.8225
8	.8363
9	.8495
530	.862
1	.8739
2	.8851
3	.8956
4	.9056
5	.9149
6	.9238
7	.9320
8	.9398
9	.9471
540	.954
1	.9604
2	.9661
3	.9713
4	.9760
5	.9803
6	.9840
7	.9873
8	.9902
9	.9928
550	.995
1	.9969
2	.9983
3	.9994
4	1.0000
5	1.0002
6	1.0001
7	.9995
8	.9984
9	.9969
560	0.995
1	.9926
2	.9898
3	.9865
4	.9828
5	.9786
6	.9741
7	.9691
8	.9638
9	.9581
570	.952
1	.9455
2	.9386
3	.9312
4	.9235
5	.9154
6	.9069
7	.8981
8	.8890
9	.8796
580	.870
1	.8600
2	.8496
3	.8388
4	.8277
5	.8163
6	.8046
7	.7928
8	.7809
9	.7690
590	.757
1	.7449
2	.7327
3	.7202
4	.7076
5	.6949
6	.6822
7	.6694
8	.6565
9	.6437
600	.631
1	.6182
2	0.6054
3	.5926
4	.5797
5	.5668
6	.5539
7	.5410
8	.5282
9	.5156
610	.503
1	.4905
2	.4781
3	.4658
4	.4535
5	.4412
6	.4291
7	.4170
8	.4049
9	.3929
620	.381
1	.3690
2	.3570
3	.3449
4	.3329
5	.3210
6	.3092
7	.2977
8	.2864
9	.2755
630	.265
1	.2548
2	.2450
3	.2354
4	.2261
5	.2170
6	.2082
7	.1996
8	.1912
9	.1830
640	.175
1	.1672
2	.1596
3	.1523
4	0.1452
5	.1382
6	.1316
7	.1251
8	.1188
9	.1128
650	.107
1	.1014
2	.0961
3	.0910
4	.0862
5	.0816
6	.0771
7	.0729
8	.0688
9	.0648
660	.061
1	.0574
2	.0539
3	.0506
4	.0475
5	.0446
6	.0418
7	.0391
8	.0366
9	.0343
670	.032
1	.0299
2	.0280
3	.0263
4	.0247
5	.0232
6	.0219
7	.0206
8	.0194
9	.0182
680	.017
1	.01585
2	.01477
3	.01376
4	.01281
5	.01192
6	0.01108
7	.01030
8	.00956
9	.00886
690	.0082
1	.00759
2	.00705
3	.00656
4	.00612
5	.00572
6	.00536
7	.00503
8	.00471
9	.00440
700	.0041
1	.00381
2	.00355
3	.00332
4	.00310
5	.00291
6	.00273
7	.00256
8	.00241
9	.00225
710	.0021
1	.001954
2	.001821
3	.001699
4	.001587
5	.001483
6	.001387
7	.001297
8	.001212
9	.001130
720	.00105
1	.000975
2	.000907
3	.000845
4	.000788
5	.000736
6	.000688
7	.000644
8	0.000601
9	.000560
730	.00052
1	.000482
2	.000447
3	.000415
4	.000387
5	.000360
6	.000335
7	.000313
8	.000291
9	.000270
740	.00025
1	.000231
2	.000214
3	.000198
4	.000185
5	.000172
6	.000160
7	.000149
8	.000139
9	.000130
750	.00012
1	.000111
2	.000103
3	.000096
4	.000090
5	.000084
6	.000078
7	.000074
8	.000069
9	.000064
760	.00006
1	.000056
2	.000052
3	.000048
4	.000045
5	.000042
6	.000039
7	.000037
8	.000035
9	.000032
770	.00003

Abstract

Cited By

Figures (1)

Tables (5)

Equations (3)

Journal of the Optical Society of America