There are several posts on this topic, but none seem to explicitly answer my present confusion.

There is ellipsoid-based gamma0 and terrain-flattened gamma0, and it seems that they are often given with the same symbology despite being different.

ASF provides ALOS/PALSAR RTC data products in gamma0 (correction procedure here). These RTC data include incidence angle maps (I think its the local incidence angle from the DEM used for terrain correction). **What equation can I use to convert these RTC gamma0 values to RTC sigma0 based on the local incidence angle?**

For gamma0 calibrated using the incidence angle relative to the Earth ellipsoid, it seems that sigma0 = gamma0 * cos(θ) based on the relationship of the areas used for normalization when converting from beta0 to gamma0 and sigma0 (e.g., Small 2011).

However, in the 2D diagram below (from TerraSAR-X guide) where θ is the local incidence angle and backscatter coefficients are represented as sides of a triangle, the geometry is such that sigma0 = gamma0 / cos(θ).

So, using the local incidence angle for RTC data, is it:

**(1) sigma0 = gamma0 * cos(θ)**

**or**

**(2) sigma0 = gamma0 / cos(θ)**

Or perhaps something more involved? It seems to depend on whether or not you’re using the local incidence angle and whether or not the backscatter coefficients are already terrain-corrected, but I’m not confident what is appropriate for my case.

Thanks for any help.