# 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

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:

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:

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.

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

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