Estimated optical constants of Gypsum in the regions of weak absorptions:
  Application of scattering theories and comparisons to independent measurements

Ted L. Roush
NASA Ames Research Center, Astrobiology & Space Sciences Division
Planetary Systems Branch, MS 245-3, Moffett Field, CA  94035-1000

Francesca Esposito
INAF, Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131, Napoli, Italy

George R. Rossman
Division of Geological and Planetary Sciences
Califorinia Institute of Technology, Pasadena, CA  91125-2500

Luigi Colangeli
INAF, Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131, Napoli, Italy


Diffuse reflectance spectra of multiple grain size fractions are used to estimate the optical constants of gypsum over the 0.4-15 mm wavelength region.  Two independent scattering theories are used to iteratively determine the imaginary index of refraction from the measured reflectance.  We compare the results of these two with each other, and with imaginary indices of gypsum reported in the literature.  We find that the scattering theory results are more sensitive in the infrared to weak spectral features that are clearly distinguished in the diffuse reflectance spectra.  However, we find the scattering results provide a poor determination of the optical constants in the regions of relatively strong absorptions.  At visible and near-infrared wavelengths we provide a comparison to the results obtained from analysis of the diffuse reflectance to results obtained from direct transmission measurements of gypsum crystals.  We find the imaginary index of refraction determined from scattering theories is systematically less than that obtained from transmission spectra, especially for regions of weak absorption.  We attribute this discrepancy to potential scattering that occurs within the crystals during the transmission measurements.  We combine the resulting real and imaginary indices of refraction with those reported at infrared wavelengths to provide values covering visual, near-, and infrared wavelengths (0.4-333 mm, 25000-30 cm-1).

Gypsum Crystal

Gypsum crystal 2.856 mm thick from Brookville, Saline County, Kansas

Data from the Paper

Figure 1, Imaginary Indices of Refraction                      Click to Save
Aronson et al. [1983] E \\b
Long et al. [1991] E \\a=X
Long et al. [1991] E \\b=Y
Long et al. [1991] E \\c=Z
Long et al. [1991] Average 
This study Pellet
Marzo et al. [2004] KBr pellet
Long et al. [1991] Pellet

Figure 2, Diffuse Reflectance Spectra
RELAB                     <45 µm
RELAB 25 -75 µm
ASTER Medium
ASTER Coarse

Figure 3, Specular Reflectance of Gypsum
This Study                         Pressed Pellet

Figure 4, Transmission Spectra of Four Gypsum Crystals
Gypsum 034 E \\X  
Gypsum 034  E \\Z   
Gypsum 1171 E \\X  
Gypsum 1171 E \\Z  
Gypsum 2856 E \\X 
Gypsum 2856 E \\Z 
Gypsum 14293 E \\X 
Gypsum 14293 E \\Z 

Figure 5, Contour Plot
Shaded Countour Plot     Data        

Figure 6, Calculated Single Scattering Albedo Values
Albedo Values  Data     

Figure 7, Comparison of k-values
Hapke [1993] ASTER data               Data  
Shkuratov et al. [1999] ASTER data               Data  
Shkuratov et al. [1999] RELAB data               Data  
Long et al [1993] average values               Data      

Figure 8, k-values
Shkuratov et al. [1999] ASTER                Data  
Shkuratov et al. [1999] RELAB                Data  
Long et al. [1993] average                Data  

Figure 9, Transmission Spectra of (010) face
full model all Data
modified model all Data
simplified model all Data

Figure 10, Optical Constants of Gypsum Samples
 0.0341 cm, E \\X = ~alpha Data a
 0.0341 cm, E \\Z = ~ gamma Data b
 0.1171 cm, E \\X = ~alpha Data c
 0.1171 cm, E \\Z = ~ gamma Data d
 0.2856 cm, E \\X = ~alpha Data e
 0.2856 cm, E \\Z = ~ gamma Data f
 1.1493 cm, E \\X = ~alpha Data g
 1.1493 cm, E \\Z = ~ gamma Data h
Derived imaginary index, E \\X = ~alpha      see files a-h  
Derived imaginary index, E \\Z = ~ gamma         see files a-h     

Figure 11, Derived Imaginary Indices
 0.0341 cm, E \\X = ~alpha Data
 0.0341 cm, E \\Z = ~ gamma Data
 0.1171 cm, E \\X = ~alpha Data
 0.1171cm, E \\Z = ~ gamma Data
 0.2856 cm, E \\X = ~alpha Data
 0.2856 cm, E \\Z = ~ gamma Data
 1.1439 cm, E \\X = ~alpha Data
 1.1493 cm, E \\Z = ~ gamma Data
Combined imaginary index, E \\X = ~alpha              Data             
Combined imaginary index, E \\Z = ~ gamma  Data

Figure 12, Theoretical values
n-values Infrared    Data   
n-values Vis-NIR   Data  
k-values Infrared   Data  
k-values VIS-NIR   Data  

Figure 13, Average n-values
Hapke theory    Data  
Shkuratov theory Data

Figure 14, Average n-values
Average of all theory     Data  

Figure 15,  Data Comparisons
Imaginary Index, E\\X          Data       
Imaginary Index, E\\Z    Data  
Transmission average Data
Hapke-Shkuratov    Data  
Sub-sampling Transmission    Data  
Sub-sampling Hapke-Shkuratov    Data  

Journal of Geophysical Research 112