# Radiometric Comparison within the Sentinel-1 SAR Constellation over a Wide Backscatter Range
## 2 Materials and Methods
### Deriving Radar Backscatter from Distributed and Point Targets  
Point targets (like corner reflectors) usually produce a strong reflection which originates from a dominant scatterer within the observed resolution cell. In contrast, a distributed target consists of a large number of randomly distributed scatterers within a resolution cell. Each scatterer contributes with a random phase leading to variability in the magnitude even for the same target type in different resolution cells. Statistically, distributed targets like forests, grassland, or ice areas show specific mean radar backscattering coefficients which depend on observation parameters like radar wavelength, incidence angle, and target type [25].  
The radar brightness \(\beta^{0}\) of a SAR image pixel is calculated by the following formula [26; 27]:  
\[\beta^{0}=\frac{|DN_{i}|^{2}}{A_{dn}^{2}\cdot K} \tag{1}\]  
\(DN_{i}\) is the digital number of the complex image pixel at location \(i\), \(A_{dn}\) is the pixel scaling, and \(K\) is the absolute calibration factor. For estimating the radar brightness of a distributed target, all values regarding the target area are averaged in linear scale and then converted to logarithmic scale \(\beta^{0}\) [dB] = \(10\cdot\log 10(\beta^{0})\).  
The noise level has to be considered for deriving a precise radar brightness, in particular for low backscattering targets with low SNRs. This is usually done by subtracting the mean noise floor (\(P_{noise}\)) from the observed backscatter data according to Equation (2). For the subtraction step, both values (image radar backscatter and scaled noise floor) have to be converted to linear scale; the result is then converted back to logarithmic scale afterwards.  
\[\beta^{0}_{noise\ considered} = \frac{|DN_{i}|^{2}}{A_{dn}^{2}\cdot K}-P_{noise} \tag{2}\]  
For estimating the noise floor, usually specific noise pulses are applied. Nevertheless, deriving a precise and reasonable noise level is a challenging task which requires a deep knowledge about functionality and operating modes of the used SAR processor [28]. It should be noted that the noise floor is not constant over time and consists of several components of different origins including thermal receiver, background, quantization, and oscillator noise. Although the thermal noise is known to be the dominant component, the impact of background noise arising from the Earth surface is also not negligible. A noise floor difference of about 0.8 dB was derived for S-1B between different observation areas (sea and land) [29]. The Sentinel-1 noise floor is further investigated in a few publications by analyzing very low backscatter data [30; 31]. In particular for the EW mode, it was shown that the originally derived noise level annotated within the SAR products was not estimated precisely enough by the former SAR processor version, especially for EW1. As a consequence, the noise estimation procedures were improved [32], leading to an updated version of the SAR processor in early 2019.  
In order to estimate the absolute radiometric accuracy of a SAR system, the RCS values of reference targets are derived from SAR images and compared with the nominal RCS of these targets. This nominal RCS is either known from theory (e.g., for trihedral corner reflectors) or precisely derived from measurements (e.g., for transponders) [33; 34]. The RCS of a point target is estimated from a SAR image by analyzing its impulse response function by taking into account the following subtasks:  
* the impulse response is interpolated to a subpixel resolution,
* the integrated pixel method is used which considers the cumulated power related to the target response (see [35; 36]),
* the background clutter is properly estimated and subtracted.  
The RCS is finally estimated from the SAR image using the integrated image power \(I_{P}\) of the impulse response multiplied with the pixel area \(P_{A}\) and divided by the absolute calibration factor \(K\)[37].  
\[RCS=\frac{I_{P}\cdot P_{A}}{K} \tag{3}\]