The Hapke Model in Excel: Simplified reflectance modeling for lunar remote sensing. (2010)

Undergraduates: Daven Quinn, Jeff Gillis-Davis, Paul Lucey (University of Hawaii)

Faculty Advisor: Drew Coleman
Department: Geology

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This project simplifies Hapke radiative transfer modeling, demonstrating how planetary surfaces can be modeled using open and understandable methods. The Hapke model provides a method for determining surface composition, mineralogy, and particle size from reflectance data of planetary surfaces. In order to improve the accuracy of these compositional estimates, it is desirable to obtain accurate optical constants.

Optical constants, or complex indices of refraction, are a fundamental property of materials that are independent of particle size and shape. They can be combined to derive the spectra of mixtures of materials, which can provide an accurate model for compositional variation in mixtures such as the lunar regolith.

Direct measurement of optical constants is often infeasible. Materials often have optical defects, prohibiting direct derivation of absorption coefficients. Hapke modeling includes a method to find optical constants from the reflectance of powders of known composition and particle size. For this project, the reflectance properties of high-titanium lunar-composition glasses were measured, and Hapke model calculations were coded into an Excel spreadsheet.

In the past, the computation of optical constants has required expensive numerical analysis packages with steep learning curves. Though Excel has limited accuracy, it can produce acceptable approximations of optical constants. This method is useful for illustrative and educational purposes.