Diffuse reflectance spectroscopy of particulate systems: a comparative study of discrete models

H. S. Shah; P. R. Desai; M. S. Roy

doi:10.1364/AO.36.003538

Applied Optics
Vol. 36,
Issue 15,
pp. 3538-3546
(1997)
•https://doi.org/10.1364/AO.36.003538

Diffuse reflectance spectroscopy of particulate systems: a comparative study of discrete models

H. S. Shah, P. R. Desai, and M. S. Roy

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H. S. Shah, P. R. Desai, and M. S. Roy, "Diffuse reflectance spectroscopy of particulate systems: a comparative study of discrete models," Appl. Opt. 36, 3538-3546 (1997)

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Abstract

A comparative study of statistical particle model theory of diffuse reflectance has been made. Theories have been applied to six particulate samples having different optical characteristics and average particle sizes that vary from 42 to 106 µm. We made an overall assessment of each theoretical model by determining the CIELAB color difference using experimentally measured and theoretically predicted diffuse reflectance spectra in the visible spectral range. We discuss the performance ratings of the models of other researchers and discovered numerous typographical errors in Fresnel reflection coefficient expressions. We provide the correct versions for these expressions.

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Sample	Range of Particle Size (µm)	Average Particle Size (µm)
WG	15–58	42.6
GYG	90–130	106
GG	90–125	106
FAS	35–75	56
BG	50–75	75
CS	50–90	74

Wavelength (nm)	WG	GYG	GG	FAS	BG	CS
400	0.016	0.076	0.042	0.040	0.237	0.002
420	0.016	0.078	0.044	0.024	0.244	0.003
440	0.016	0.076	0.044	0.022	0.246	0.010
460	0.016	0.072	0.044	0.024	0.239	0.021
480	0.016	0.066	0.044	0.020	0.218	0.029
500	0.017	0.062	0.044	0.016	0.184	0.042
520	0.017	0.058	0.042	0.012	0.154	0.072
540	0.016	0.058	0.040	0.010	0.120	0.122
560	0.016	0.044	0.038	0.008	0.097	0.189
580	0.015	0.038	0.034	0.009	0.072	0.258
600	0.015	0.034	0.030	0.012	0.054	0.316
620	0.015	0.028	0.030	0.016	0.042	0.413
640	0.014	0.024	0.028	0.024	0.042	0.533
660	0.014	0.024	0.030	0.034	0.044	0.671
680	0.015	0.022	0.032	0.044	0.054	0.834
700	0.016	0.018	0.032	0.037	0.065	0.987

Sample	X	Y	Z	ΔE
WG
Experimental	79.935	83.947	89.788	—
Melamed	76.932	80.817	86.637	1.37
Mandelis-1	86.680	87.935	94.167	1.69
Mandelis-2	75.999	79.966	85.928	1.79
GYG
Experimental	70.998	73.880	72.662	—
Melamed	66.403	68.406	66.584	3.02
Mandelis-1	71.427	72.685	70.088	3.85
Mandelis-2	69.050	71.692	71.145	1.27
GG
Experimental	72.558	75.824	80.196	—
Melamed	68.688	71.542	74.581	2.43
Mandelis-1	74.232	77.206	80.190	1.85
Mandelis-2	70.954	74.193	78.014	0.98
FAS
Experimental	80.389	86.071	87.429	—
Melamed	77.783	83.312	83.425	1.45
Mandelis-1	84.406	90.408	90.703	1.99
Mandelis-2	75.799	80.608	83.570	2.91
BG
Experimental	50.672	51.862	38.710	—
Melamed	31.128	31.900	28.227	16.93
Mandelis-1	58.918	58.156	43.787	6.46
Mandelis-2	59.320	59.613	46.401	5.40
CS
Experimental	52.893	59.371	88.495	—
Melamed	40.538	46.820	85.023	12.93
Mandelis-1	42.978	48.877	91.623	14.06
Mandelis-2	45.993	56.030	93.291	12.58

Sample	Range of Particle Size (µm)	Average Particle Size (µm)
WG	15–58	42.6
GYG	90–130	106
GG	90–125	106
FAS	35–75	56
BG	50–75	75
CS	50–90	74

Wavelength (nm)	WG	GYG	GG	FAS	BG	CS
400	0.016	0.076	0.042	0.040	0.237	0.002
420	0.016	0.078	0.044	0.024	0.244	0.003
440	0.016	0.076	0.044	0.022	0.246	0.010
460	0.016	0.072	0.044	0.024	0.239	0.021
480	0.016	0.066	0.044	0.020	0.218	0.029
500	0.017	0.062	0.044	0.016	0.184	0.042
520	0.017	0.058	0.042	0.012	0.154	0.072
540	0.016	0.058	0.040	0.010	0.120	0.122
560	0.016	0.044	0.038	0.008	0.097	0.189
580	0.015	0.038	0.034	0.009	0.072	0.258
600	0.015	0.034	0.030	0.012	0.054	0.316
620	0.015	0.028	0.030	0.016	0.042	0.413
640	0.014	0.024	0.028	0.024	0.042	0.533
660	0.014	0.024	0.030	0.034	0.044	0.671
680	0.015	0.022	0.032	0.044	0.054	0.834
700	0.016	0.018	0.032	0.037	0.065	0.987

Abstract

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Equations (20)

Applied Optics