Precision of Determination of Kubelka and Munk Coefficients from Opaque Colorant Mixtures

D. G. Nickols; S. E. Orchard

doi:10.1364/JOSA.55.000162

Journal of the Optical Society of America
Vol. 55,
Issue 2,
pp. 162-164
(1965)
•https://doi.org/10.1364/JOSA.55.000162

Precision of Determination of Kubelka and Munk Coefficients from Opaque Colorant Mixtures

D. G. Nickols and S. E. Orchard

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D. G. Nickols and S. E. Orchard, "Precision of Determination of Kubelka and Munk Coefficients from Opaque Colorant Mixtures," J. Opt. Soc. Am. 55, 162-164 (1965)

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Abstract

Kubelka and Munk absorption and scattering coefficients for a nonwhite pigment dispersion (tinter) can be obtained from reflectance measurements on opaque samples of a reference white base and two tinter/white mixtures. The precision of the coefficients depends on the strengths of the mixtures, and the conditions for maximum precision have been determined from a theoretical analysis of the errors caused by a constant error in the measurement of absolute reflectance. One sample should consist of tinter without admixture of white, while the other should have reflectances as far as possible between 25% and 75% throughout the spectral range of interest.

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Equations (16)

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R₂	10%	20%	30%	40%	50%	60%	70%	80%	90%

R₁
10%	0	342	472	532	558	563	544	485	332
20%	342	0	161	242	281	292	278	233	142
30%	472	161	0	86	131	150	148	123	74
40%	532	242	86	0	48	71	77	67	41
50%	558	281	131	48	0	26	37	35	22
60%	563	292	150	71	26	0	13	17	12
70%	544	278	148	77	37	13	0	6	5
80%	485	233	123	67	35	17	6	0	2
90%	332	142	74	41	22	12	5	2	0

R₂	2%	4%	6%	8%	10%	12%	14%	16%	18%	20%

R₁
5%	530	143	115	282	394	473	531	575	609	636
10%	747	503	296	130	0	102	182	247	299	342
15%	818	638	475	335	216	118	36	33	90	138
20%	852	706	570	448	342	250	172	106	49	0
25%	872	745	626	517	420	336	262	198	143	95
30%	885	771	662	562	472	392	323	261	208	161
35%	894	787	686	592	507	432	365	306	254	208
40%	900	799	703	613	532	459	394	337	287	242
45%	904	807	714	627	548	477	414	358	309	266
50%	907	813	721	636	558	489	427	372	324	281
55%	909	816	725	640	563	494	433	379	332	290
60%	910	816	725	640	563	494	433	380	333	292
65%	910	815	722	635	557	488	427	374	329	289
70%	909	811	713	624	544	474	414	362	317	278
75%	907	801	698	604	521	451	391	340	297	260
80%	901	784	670	569	485	414	356	307	267	233
85%	888	749	619	511	426	358	303	260	224	194
90%	855	671	521	411	332	273	228	193	165	142
95%	724	468	326	243	189	152	125	105	89	77

R₂	10%	20%	30%	40%	50%	60%	70%	80%	90%

R₁
10%	0	399	705	873	912	851	715	519	278
20%	399	0	396	681	812	805	697	514	278
30%	705	396	0	391	648	730	668	507	277
40%	873	681	391	0	383	601	619	493	275
50%	912	812	648	383	0	371	530	470	272
60%	851	805	730	601	371	0	350	422	267
70%	715	697	668	619	530	350	0	308	254
80%	519	514	507	493	470	422	308	0	215
90%	278	278	277	275	272	267	254	215	0

R₂	2%	4%	6%	8%	10%	12%	14%	16%	18%	20%

R₁
5%	124	42	42	124	206	286	363	436	506	572
10%	325	246	165	83	0	83	165	246	324	399
15%	508	437	363	285	206	124	42	42	124	206
20%	664	603	539	471	399	324	246	165	83	0
25%	790	740	686	629	568	502	433	360	284	205
30%	882	843	800	754	705	651	593	531	465	396
35%	943	913	880	845	806	764	718	669	615	557
40%	976	953	929	902	873	841	806	768	727	681
45%	982	966	948	928	907	884	858	830	799	766
50%	966	954	941	928	912	896	878	858	836	812
55%	930	922	913	903	893	881	869	855	840	823
60%	876	871	865	858	851	844	835	826	816	805
65%	807	804	800	796	791	786	781	775	769	762
70%	724	722	720	717	715	712	708	705	701	697
75%	629	628	626	625	623	622	620	618	616	613
80%	522	522	521	520	519	519	518	517	516	514
85%	405	405	405	404	404	404	403	403	402	402
90%	278	278	278	278	278	278	278	278	278	278
95%	143	143	143	143	143	143	143	143	143	143

R₂	10%	20%	30%	40%	50%	60%	70%	80%	90%

R₁
10%	0	342	472	532	558	563	544	485	332
20%	342	0	161	242	281	292	278	233	142
30%	472	161	0	86	131	150	148	123	74
40%	532	242	86	0	48	71	77	67	41
50%	558	281	131	48	0	26	37	35	22
60%	563	292	150	71	26	0	13	17	12
70%	544	278	148	77	37	13	0	6	5
80%	485	233	123	67	35	17	6	0	2
90%	332	142	74	41	22	12	5	2	0

Abstract

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Tables (4)

Equations (16)

Journal of the Optical Society of America