uniform ground tiling for Sentinel-1 SLC burst

Burst division into constant ground segment (tiles)

SAR SLC product are defined in the radar geometry on a uniform (slant range distance x azimuth distance) grid. In order to define ground segment (tiles) with a constant size in range direction, it is mandatory to define and adaptative variable number of slant range points per segment.

Denoting \(theta_i\) the incidence angle on the ground at pixel location \(i\), we define the cumulative length as

\[C_0[n] = \Delta s\sum_{i=i_0}^{i_0+n}\dfrac{1}{\sin(\theta_i)}\]

where \(\Delta s\) is the slant range spacing.

The total length of a ground segment defined between pixel \(i_0\) and \(i_N=i_0+N\) writes:

(1)\[ l_b = C_0[N] = \Delta s\sum_{i=i_0}^{i_N}\dfrac{1}{\sin(\theta_i)}\]

In order to divide \(l_b\) into equidistant segments of constant ground length \(l_t\) with possible overlaping length \(l_o\) (\(l_o<l_t\)) we define the ground limits \((s_n, e_n)\) of segment \(n\) as:

(2)\[\begin{split} s_n &=& n(l_t-l_o), n \in [0,1,2,...,N]\\ e_n &=& s_n+l_t\end{split}\]

where \(N\) is the larger possible integer such as \(e_N\le l_b\).

Centering tiles

Defined as in equation (2), the \(N\) segments are not centered over the total length \(l_b\). To center the N segments it is enough to add \(\frac{l_b-e_N}{2}\) to the segment location, i.e.

\[\begin{split}s_c^n &=& n(l_t-l_o)+\frac{l_b-e_N}{2}, n \in [0,1,2,...,N]\\ e_c^n &=& s_c^n+l_t+\frac{l_b-e_N}{2}\end{split}\]

Pixel indexes pertaining to segment \(n\) are thus in \([i^n_{min}, i^n_{max}]\) defined such as:

\[\begin{split}i^n_{min} = \text{larger $i$ such as}\ s_c^n&>&C_0[i]\\ i^n_{max} = \text{smaller $i$ such as}\ e_c^n&<&C_0[i]\end{split}\]

In practice, \(l_b\) is the ground length of a burst (\(l_b\approx\) 80 km), the slant spacing is \(\Delta s\approx\) 2.5 m