Related Experiment Video
Updated: Jun 22, 2026

Scattering And Absorption of Light in Planetary Regoliths
Published on: July 1, 2019
A family of approximations spanning the Born and Rytov scattering series
Abstract:
A new hybrid scattering series is derived that incorporates as special cases both the Born and Rytov scattering series, and includes a parameter so that the behavior can be continuously varied between the two series. The parameter enables the error to be shifted between the Born and Rytov error terms to improve accuracy. The linearized hybrid approximation is derived as well as its condition of validity. Higher order terms of the hybrid series are also found. Also included is the integral equation that defines the exact solution to the forward scattering problem as well as its Fréchet derivative, which is used for the solution of inverse multiple scattering problems. Finally, the linearized hybrid approximation is demonstrated by simulations of inverse scattering off of uniform circular cylinders, where it is shown that the hybrid approximation achieves smaller error than either the Born or Rytov approximations alone.
Related Concept Videos
Convergence of Fourier Series
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
Linear Approximations
Linearization and Approximation
Alternating Series and Absolute Convergence
The Born-Haber Cycle
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
