Notes on SAR Interferometry; Ionospheric influence

My student recently defended her thesis on ionospheric influence on SAR interferometry (InSAR). The problem was a possibility of significant ionospheric influence on space-borne InSAR at low frequencies (P-band) used in forest monitoring, for example. Here’s a few musings on the modeling of the problem. Obviously, this post will go to the scientific section…

This will be exercise in my presentation skills… Great possibilities of a free vector graphics program InkScape inspired me to be more “picture oriented…” This post will need several revisions before it’s correct. Don’t take anything written here for granted!

Problem

Consider the following picture: single-satellite configuration

A space-borne SAR makes a range measurement. The pulses will arrive at times and , respectively. Ionosphere induces an extra delay that can be converted to an extra range increment . Note that time and range are related via the constant . Consider a linear approximation

First, let’s suppose that is a slowly varying function. Then,

What happens during the interferometric processing is that the first point is shifted in to time and it is associated with a reference range . That means, the only information about ionospheric influence we have is in the time distance between the two points:

The phase used for interferometry should be

.

…and here comes the task: Suppose we add a second (slave) satellite (see the picture here). What will the calculation of look like? And what about the complete model for hight determination?