The Hapke Model

Contents:

• Overview of Hapke’s Bidirectional Reflectance Theory
  • Core Concepts
  • General Form of the Hapke Equation
  • Applications
• Legendre Polynomials in Hapke Phase Function Expansion
  • The Legendre Expansion
  • Hapke’s Formulation for Anisotropic Scattering
  • Significance
• Chandrasekhar’s H-Functions
  • Definition and Significance
  • Properties
  • Approximations and Usage in Hapke’s Model
  • Computation
• Particle Phase Functions in Hapke Modeling
  • Common Phase Function Models
  • Role in Hapke Model
• Macroscopic Roughness Correction in Hapke Modeling
  • The Roughness Parameter \(\bar{\theta}\)
  • Conceptual Basis of the Correction
  • Implementation in refmod.hapke.roughness
  • Impact on Reflectance
• The IMSA (Isotropic Multiple Scattering Approximation) Model
  • IMSA Reflectance Equation
  • Key Features
• The AMSA (Anisotropic Multiple Scattering Approximation) Model
  • AMSA Reflectance Equation
  • Derivative Function