Absolute Reflectances from Reflectometer Readings

W. F. Sullivan

doi:10.1364/AO.10.001550

Applied Optics
Vol. 10,
Issue 7,
pp. 1550-1558
(1971)
•https://doi.org/10.1364/AO.10.001550

Absolute Reflectances from Reflectometer Readings

W. F. Sullivan

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
W. F. Sullivan, "Absolute Reflectances from Reflectometer Readings," Appl. Opt. 10, 1550-1558 (1971)

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

Abstract

Equations have been derived that allow differences in reflectometer readings of the same sample with various reflectometers to be minimized by placing all reflectances on an absolute basis. For pigmented vehicle films the Fresnel reflectances and transmittances at the air–vehicle interface can be calculated for an arbitrary incident angular light distribution. The form of the reflected and transmitted angular distributions can also be calculated. The equations have been used to determine absolute reflectances of titanium dioxide pigmented films from meter readings of two reflectometers—the General Electric Recording and the Colormaster.

Full Article | PDF Article

More Like This

Absolute Reflectances from Reflectometer Readings

A. C. Little
Appl. Opt. 10(12) 2779-2780 (1971)

Reflected Shadow Method for the Study of Constrained Zones in Cracked Plates

P. S. Theocaris
Appl. Opt. 10(10) 2240-2247 (1971)

Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere

C. M. Sonnenschein and F. A. Horrigan
Appl. Opt. 10(7) 1600-1604 (1971)

Previous Article Next Article

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 (5)

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 (4)

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 (47)

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

θ_I (deg)	θ_t (deg)	F(θ_i)	F(θ_r)	F(θ_t)
0	0′	0	0	0
1	40′	0.03490	0.06139	0.05026
2	1°20′	0.06976	0.00279	1.0045
3	2°0′	0.10453	0.00417	0.15054
4	2°40′	0.13917	0.00555	0.20060
5	3°20′	0.17365	0.00092	0.25043
6	4°0′	0.20791	0.00827	0.29999
7	4°40′	0.24192	0.00961	0.34941
8	5°19′	0.27564	0.01109	0.39952
9	5°59′	0.30902	0.01235	0.44830
10	6°39′	0.34202	0.01366	0.49600
11	7°18′	0.37461	0.01508	0.54555
12	7°58′	0.40674	0.01628	0.59303
13	8°37′	0.43837	0.01762	0.64105
14	9°17′	0.46997	0.01878	0.68149
15	9°56′	0.50000	0.02006	0.73430
16	10°35′	0.52992	0.02129	0.78060
17	11°14′	0.55919	0.02249	0.82616
18	11°53′	0.58779	0.02365	0.87107
19	12°32′	0.61566	0.02477	0.91521
20	13°11′	0.64279	0.02584	0.95863
21	13°49′	0.66913	0.02703	1.0022
22	14°28′	0.69466	0.02800	1.0439
23	15°6′	0.71934	0.02910	1.0858
24	15°44′	0.74314	0.03014	1.1268
25	16°22′	0.76604	0.03114	1.1668
26	17°0′	0.78801	0.03203	1.2059
27	17°37′	0.80902	0.03313	1.2450
28	18°14′	0.82904	0.03413	1.2830
29	18°51′	0.84805	0.03508	1.3196
30	19°29′	0.86603	0.03584	1.3547
31	20°5′	0.88295	0.03685	1.3904
32	20°4′	0.89979	0.03780	1.4034
33	21°17′	0.91355	0.03872	1.4583
34	21°53′	0.92718	0.03959	1.4905
35	22°29′	0.93969	0.04043	1.5214
36	23 °4′	0.95106	0.04137	1.5513
37	23°39′	0.46126	0.04228	1.5812
38	24°14′	0.97030	0.04315	1.6092
39	24°48′	0.97815	0.04913	1.6369
40	25°22′	0.98481	0.04508	1.6631
41	25°56′	0.99027	0.04602	1.0879
42	26°29′	0.99452	0.04706	1.7122
43	27°31′	0.99756	0.04799	1.7341
44	27°35′	0.99939	0.04914	1.7565
45	28°7′	1.0000	0.05029	1.7774
46	28°39′	0.99939	0.05145	1.7960
47	29°11′	0.99756	0.05261	1.8143
48	29°42′	0.99452	0.05489	1.8295
49	30°12′	0.99027	0.05537	1.8478
50	30°43′	0.98481	0.05673	1.8615
51	31°12′	0.97815	0.05835	1.8755
52	31°41′	0.97030	0.06001	1.8889
53	32°10′	0.96126	0.06172	1.8980
54	32°38′	0.95106	0.06358	1.9075
55	33 °6′	0.93969	0.06531	1.9151
56	33°33′	0.92718	0.06761	1.9217
57	34°0′	0.91355	0.06976	1.9263
58	34°26′	0.89879	0.07211	1.9297
59	34°51′	0.88295	0.07462	1.9320
60	35°16′	0.86603	0.07721	1.9320
61	35°40′	0.84805	0.07920	1.9326
62	36°41′	0.82904	0.08282	1.9269
63	36°26′	0.80902	0.08592	1.9225
64	36°49′	0.78801	0.08901	1.9145
65	37°10′	0.76604	0.09233	1.9057
66	37°31′	0.74314	0.09570	1.8939
67	37°51′	0.71934	0.09919	1.8800
68	38°11′	0.69466	0.10270	1.8629
69	38°29′	0.66913	0.10634	1.8442
70	38°39′	0.64279	0.11048	1.8287
71	39°5′	0.61566	0.11350	1.7955
72	39°21′	0.58779	0.11703	1.7669
73	39°36′	0.55919	0.12315	1.7342
74	39°51′	0.52992	0.12611	1.6872
75	40°5′	0.50000	0.12633	1.6561
76	40°18′	0.46947	0.12968	1.6069
77	40°31′	0.43837	0.13103	1.5577
78	40°42′	0.40674	0.13243	1.5003
79	40°52′	0.37461	0.13309	1.4360
80	41°2′	0.34202	0.13050	1.3783
81	41°11′	0.30902	0.13090	1.2849
82	41°19′	0.27564	0.12938	1.1838
83	41°26′	0.24912	0.12298	1.1639
84	41°32′	0.20791	0.11618	0.98530
85	41°37′	0.17365	0.10646	0.86450
86	41°41′	0.13917	0.09458	0.71611
87	41°44′	0.10453	0.07678	0.59360
88	41°47′	0.06961	0.05698	0.40474
89	41°48′	0.03490	0.03020	0.21545
90	41°49′	0	0	0

θ_i (deg)	θ_t (deg)	F(θ_i)	F(θ_r)	F(θ_t)	θ_i (deg)	θ_t (deg)	F(θ_i)	F(θ_r)	F(θ_t)	θ_i (deg)	F(θ_i)	F(θ_r)
0	0	0	0	0	31	50°35′	0.88295	0.05184	0.41043	61	0.84805	0.84805
1	1°30′	0.03490	0.00139	0.02233	32	52°39′	0.89879	0.05696	0.40145	62	0.82904	0.82904
2	3°0′	0.00976	0.00278	0.04462	33	54°47′	0.91355	0.06309	0.38983	63	0.80902	0.80902
3	4°30′	0.10453	0.00416	0.06684	34	57°1′	0.92718	0.07091	0.37483	64	0.78801	0.78801
4	6°0′	0.13917	0.00553	0.08891	35	59°21′	0.93869	0.08088	0.35633	65	0.76604	0.76604
5	7°31′	0.17365	0.00696	0.11052	36	61°51′	0.95106	0.09414	0.33312	66	0.74314	0.74314
6	9°1′	0.20791	0.00829	0.13221	37	64°28′	0.96126	0.11175	0.30578	67	0.71934	0.71934
7	10°31′	0.24192	0.00960	0.15365	38	67°26′	0.97030	0.13789	0.27026	68	0.69466	0.69466
8	12°3′	0.27564	0.01098	0.17423	39	70°44′	0.97815	0.17676	0.22033	69	0.66913	0.66913
9	13°39′	0.30902	0.01235	0.19471	40	74°37′	0.98481	0.24151	0.17159	70	0.64279	0.64279
10	15°6′	0.34202	0.01371	0.21455	41	79°46′	0.99027	0.37610	0.09636	71	0.61566	0.61566
11	16°38′	0.37461	0.01503	0.23395	42	90°0′	0.99452	0.99452	0	72	0.58779	0.58779
12	18°10′	0.40674	0.01631	0.25290	43		0.99756	0.99756		73	0.55919	0.55919
13	19°43′	0.43837	0.01762	0.27104	44		0.99939	0.99939		74	0.52992	0.52992
14	21°17′	0.46947	0.01791	0.28902	45		1.00000	1.00000		75	0.50000	0.50000
15	22°51′	0.50000	0.02025	0.30505	46		0.99939	0.99939		76	0.46947	0.46947
16	29°25′	0.52922	0.02149	0.32114	47		0.99756	0.99756		77	0.43837	0.43837
17	26°1′	0.55919	0.02284	0.33595	48		0.99452	0.99452		78	0.40674	0.40674
18	27°37′	0.58779	0.02418	0.35004	49		0.99027	0.99027		79	0.37461	0.37461
19	29°41′	0.61506	0.02584	0.36252	50		0.98481	0.98481		80	0.34202	0.34202
20	31°0′	0.64279	0.02733	0.37280	51		0.97815	0.97815		81	0.30902	0.30902
21	32°32′	0.66913	0.02837	0.38558	52		0.97030	0.97030		82	0.27564	0.27564
22	34°11′	0.69466	0.02966	0.39559	53		0.96126	0.96126		83	0.24912	0.24912
23	35°53′	0.71934	0.03154	0.40355	54		0.95106	0.95106		84	0.20791	0.20791
24	37°36′	0.74313	0.03289	0.41061	55		0.93969	0.93969		85	0.17365	0.17365
25	39°20′	0.76604	0.03466	0.41618	56		0.92718	0.92718		86	0.13917	0.13917
26	41°7′	0.78801	0.03668	0.41981	57		0.91355	0.91355		87	0.10453	0.10453
27	42°55′	0.80902	0.03888	0.42202	58		0.89879	0.89879		88	0.06961	0.06961
28	44°46′	0.82904	0.04142	0.42220	59		0.88295	0.88295		89	0.03490	0.03490
29	46°39′	0.84805	0.04433	0.42055	60		0.86603	0.86603		90	0	0
30	48°35′	0.86603	0.04808	0.41058

λ(nm)	R_sa⁽^a⁾¹²	R_sa⁽^a⁾¹³	R_sa⁽^a⁾¹⁴	R_sa⁽^a⁾
400	0.965	0.962	0.957	0.964
450	0.972	0.969		0.971
500	0.975	0.973		0.974
550	0.977	0.975	0.972	0.976
600	0.976	0.975		0.976
650	0.974	0.975		0.974
700	0.971	0.972	0.972	0.972

G. E. recording spectrometer (550 nm)			Colormaster (green filter)

M_pv^a	R_pv^(a)	R_pv⁽^v⁾	M_pv	R_pv^(a)	R_pv⁽^v⁾
23.3	0.227	0.376	19.45	0.236	0.377
46.0	0.449	0.649	42.00	0.451	0.645
65.5	0.639	0.805	62.68	0.649	0.809
97.9	0.956	0.981	95.70	0.964	0.985
98.9	0.965	0.985	96.90	0.976	0.989

θ_I (deg)	θ_t (deg)	F(θ_i)	F(θ_r)	F(θ_t)
0	0′	0	0	0
1	40′	0.03490	0.06139	0.05026
2	1°20′	0.06976	0.00279	1.0045
3	2°0′	0.10453	0.00417	0.15054
4	2°40′	0.13917	0.00555	0.20060
5	3°20′	0.17365	0.00092	0.25043
6	4°0′	0.20791	0.00827	0.29999
7	4°40′	0.24192	0.00961	0.34941
8	5°19′	0.27564	0.01109	0.39952
9	5°59′	0.30902	0.01235	0.44830
10	6°39′	0.34202	0.01366	0.49600
11	7°18′	0.37461	0.01508	0.54555
12	7°58′	0.40674	0.01628	0.59303
13	8°37′	0.43837	0.01762	0.64105
14	9°17′	0.46997	0.01878	0.68149
15	9°56′	0.50000	0.02006	0.73430
16	10°35′	0.52992	0.02129	0.78060
17	11°14′	0.55919	0.02249	0.82616
18	11°53′	0.58779	0.02365	0.87107
19	12°32′	0.61566	0.02477	0.91521
20	13°11′	0.64279	0.02584	0.95863
21	13°49′	0.66913	0.02703	1.0022
22	14°28′	0.69466	0.02800	1.0439
23	15°6′	0.71934	0.02910	1.0858
24	15°44′	0.74314	0.03014	1.1268
25	16°22′	0.76604	0.03114	1.1668
26	17°0′	0.78801	0.03203	1.2059
27	17°37′	0.80902	0.03313	1.2450
28	18°14′	0.82904	0.03413	1.2830
29	18°51′	0.84805	0.03508	1.3196
30	19°29′	0.86603	0.03584	1.3547
31	20°5′	0.88295	0.03685	1.3904
32	20°4′	0.89979	0.03780	1.4034
33	21°17′	0.91355	0.03872	1.4583
34	21°53′	0.92718	0.03959	1.4905
35	22°29′	0.93969	0.04043	1.5214
36	23 °4′	0.95106	0.04137	1.5513
37	23°39′	0.46126	0.04228	1.5812
38	24°14′	0.97030	0.04315	1.6092
39	24°48′	0.97815	0.04913	1.6369
40	25°22′	0.98481	0.04508	1.6631
41	25°56′	0.99027	0.04602	1.0879
42	26°29′	0.99452	0.04706	1.7122
43	27°31′	0.99756	0.04799	1.7341
44	27°35′	0.99939	0.04914	1.7565
45	28°7′	1.0000	0.05029	1.7774
46	28°39′	0.99939	0.05145	1.7960
47	29°11′	0.99756	0.05261	1.8143
48	29°42′	0.99452	0.05489	1.8295
49	30°12′	0.99027	0.05537	1.8478
50	30°43′	0.98481	0.05673	1.8615
51	31°12′	0.97815	0.05835	1.8755
52	31°41′	0.97030	0.06001	1.8889
53	32°10′	0.96126	0.06172	1.8980
54	32°38′	0.95106	0.06358	1.9075
55	33 °6′	0.93969	0.06531	1.9151
56	33°33′	0.92718	0.06761	1.9217
57	34°0′	0.91355	0.06976	1.9263
58	34°26′	0.89879	0.07211	1.9297
59	34°51′	0.88295	0.07462	1.9320
60	35°16′	0.86603	0.07721	1.9320
61	35°40′	0.84805	0.07920	1.9326
62	36°41′	0.82904	0.08282	1.9269
63	36°26′	0.80902	0.08592	1.9225
64	36°49′	0.78801	0.08901	1.9145
65	37°10′	0.76604	0.09233	1.9057
66	37°31′	0.74314	0.09570	1.8939
67	37°51′	0.71934	0.09919	1.8800
68	38°11′	0.69466	0.10270	1.8629
69	38°29′	0.66913	0.10634	1.8442
70	38°39′	0.64279	0.11048	1.8287
71	39°5′	0.61566	0.11350	1.7955
72	39°21′	0.58779	0.11703	1.7669
73	39°36′	0.55919	0.12315	1.7342
74	39°51′	0.52992	0.12611	1.6872
75	40°5′	0.50000	0.12633	1.6561
76	40°18′	0.46947	0.12968	1.6069
77	40°31′	0.43837	0.13103	1.5577
78	40°42′	0.40674	0.13243	1.5003
79	40°52′	0.37461	0.13309	1.4360
80	41°2′	0.34202	0.13050	1.3783
81	41°11′	0.30902	0.13090	1.2849
82	41°19′	0.27564	0.12938	1.1838
83	41°26′	0.24912	0.12298	1.1639
84	41°32′	0.20791	0.11618	0.98530
85	41°37′	0.17365	0.10646	0.86450
86	41°41′	0.13917	0.09458	0.71611
87	41°44′	0.10453	0.07678	0.59360
88	41°47′	0.06961	0.05698	0.40474
89	41°48′	0.03490	0.03020	0.21545
90	41°49′	0	0	0

Abstract

Cited By

Figures (5)

Tables (4)

Equations (47)

Applied Optics