Determine incidence angle modifier (IAM) for direct irradiance using the Schlick approximation to the Fresnel equations.

The Schlick approximation was proposed in 1 as a computationally efficient alternative to computing the Fresnel factor in computer graphics contexts. This implementation is a normalized form of the equation in 1 so that it can be used as a PV IAM model. Unlike other IAM models, this model has no ability to describe different reflection profiles.

In PV contexts, the Schlick approximation has been used as an analytically integrable alternative to the Fresnel equations for estimating IAM for diffuse irradiance 2 (see schlick_diffuse()).


aoi (numeric) – The angle of incidence (AOI) between the module normal vector and the sun-beam vector. Angles of nan will result in nan. [degrees]


iam (numeric) – The incident angle modifier.



Schlick, C. An inexpensive BRDF model for physically-based rendering. Computer graphics forum 13 (1994).


Xie, Y., M. Sengupta, A. Habte, A. Andreas, “The ‘Fresnel Equations’ for Diffuse radiation on Inclined photovoltaic Surfaces (FEDIS)”, Renewable and Sustainable Energy Reviews, vol. 161, 112362. June 2022. DOI: 10.1016/j.rser.2022.112362