Wed 17 Aug 2016 8:08AM

Adopting Equivalent Radar Cross Section (ERCS) as the Radiometric Measurement Quantity for SAR Images

BD( Björn Döring (DLR) Public Seen by 347

This thread is hosted by the SAR Subgroup of the CEOS Working Group on Calibration and Validation.

Problems with the Current Definition

Since the conception of the synthetic aperture radar (SAR) principle, radar cross section (RCS) has always been considered as the radiometric measurement quantity for SAR images (i.e. the quantity which allows to distinguish different gray scale values in a typical SAR image). The definition has certainly enjoyed great success in the last decades. With the advent of modern, high-resolution and high-accuracy SAR systems, several fundamental problems became apparent though:

  • RCS is defined as a ratio of powers (scattered vs. incident power), signal phase has no influence. The pixel intensity in a SAR image, on the other hand, depends on magnitude and phase. The consequence is that two different SAR point targets with identical RCSs may appear differently bright in a SAR image (due to the phase response) despite all calibration efforts. Stated differently: A SAR instrument simply does not measure RCS.
  • In general, the RCS of point and distributed targets is angular and frequency dependent. For most older and some current systems, the relevant angular and spectral ranges are small and the backscatter can be approximated to be constant within the relevant spectral and angular range (think: metallic sphere). However, this approximation is flawed for modern high-resolution and high-accuracy SAR systems, where the angular and spectral dependence must be considered.

    An important special case are calibration point targets like trihedral corner reflectors and transponders, which decisively do not look like ideal spheres (with a flat angular and spectral response). To achieve comparable radiometric measurement results across SAR missions and calibration point targets, the angular and spectral dependence must be considered.

The purpose of this Loomio thread is to discuss and prepare a CEOS SAR recommendation for a better definition of the radiometric measurement quantity, which eliminates the problems listed above.

Proposed Definition

For radiometric SAR measurements, the current definition Radar cross section (RCS) shall be substituted with the definition of equivalent radar cross section (ERCS).

The proposed ERCS definition is:

> The equivalent radar cross section (ERCS) shall be equal to the radar cross section of a perfectly conducting sphere which would result in an equivalent pixel intensity if the sphere were to replace the measured target.


  • Sound definition, which is applicable for low-resolution and high-resolution SAR systems alike
  • Adoption of concepts which proved successful in other fields of metrology:
    • Black body ↔ metal sphere
    • Standardized photometric scales in stellar photometry ↔ Standardized SAR passbands
  • Traceable radiometric calibration becomes possible, therefore also:
    • Applications in legal metrology (important for commercial customers)
    • Mis-calibrations between systems can be avoided (consider Sentinel-1A/B, RADARSAT-2, RCM-1/2/3)
    • Research results become reproducible across SAR missions

What Changes?

  • Use the new ERCS definition in requirement specifications for upcoming SAR missions (so that the definition can be used in measurement uncertainty analyses).
  • Calibration targets must be calibrated to a known ERCS (before: RCS). This means that the angular and frequency dependent RCS of a calibration point target (typically a transponder or a trihedral corner reflector) must be measured, and its ERCS must be computed (e.g. with a point-target SAR simulator, see Resources below).
  • In the future: Discuss adoption of standardized passbands (i.e., standardized apodization functions).


The discussion and the result of the voting on this Loomio thread is indicative only. The Loomio platform is intended to facilitate opinion building outside and in preparation of the yearly CEOS SAR Workshops. Official recommendations are only ever passed at the summary session of a CEOS SAR Workshop.


  • CEOS draft recommendation on ERCS (2015).
  • CEOS presentations on ERCS: 2015, 2014, 2013.
  • Björn J. Döring and Marco Schwerdt: The Radiometric Measurement Quantity for SAR Images. IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 12, Dec. 2013. Links: 1, 2.
  • Björn J. Döring, Marco Schwerdt: The SAR Passband Problem: Analytical Model and Possible Practical Solutions. IEEE Transactions on Geoscience and Remote Sensing (2015). Links: 1, 2.
  • Björn J. Döring, Philipp Looser, Matthias Jirousek, and Marco Schwerdt: Reference Target Correction Based on Point Target SAR Simulation. IEEE Transactions on Geoscience and Remote Sensing, vol. 50, no. 3, 2012. Links: 1, 2.

Poll Created Wed 17 Aug 2016 8:09AM

Adopt ERCS Closed Thu 8 Sep 2016 9:01PM

For radiometric SAR measurements, the current definition radar cross section (RCS) shall be substituted with the definition of equivalent radar cross section (ERCS).

The proposed ERCS definition is:

> The equivalent radar cross section (ERCS) shall be equal to the radar cross section of a perfectly conducting sphere which would result in an equivalent pixel intensity if the sphere were to replace the measured target.


Results Option % of points Voters
Agree 66.7% 2 BD( MZ
Abstain 0.0% 0  
Disagree 33.3% 1 EA
Block 0.0% 0  

3 of 15 people have voted (20%)


evert attema
Fri 19 Aug 2016 9:44PM

I have concerns about the applicability of a metal sphere as a theoretical reference. Doesn't work for small spheres. Just stick to current reference of isotropic scatterer (sigma 4 PI/lambda squared) and add phase equal to 0 deg.


evert attema
Fri 19 Aug 2016 10:02PM

I have concerns about the applicability of a metal sphere as a theoretical reference. Doesn't work for small spheres. Just stick to current reference of isotropic scatterer (sigma = lambda squared/4PI) and add phase equal to 0 deg.


evert attema Fri 19 Aug 2016 10:15PM

Never trust equations proposed by retired scientists...
By the way, as many of the CEOS working group members should remember, the current rcs reference is traceable to ISO standards using the ESA transponders, a distance measurement (m) and a measurement of the diameter of a metal (perfectly conducting) plate (m).


Aloke K Mathur Sat 20 Aug 2016 4:21PM

Characterization of the RCS for larger CRs is most desirable requirement sppecially for CRs used in CAMPAIGN mode.


evert attema Sun 21 Aug 2016 9:34AM

Fully agree. For actual calibration targets that have only approximately the characteristics of a theoretical isotropic point target the deviations in terms of the angular, spectral and polarimetric - amplitude and phase - responses have to be taken into account for a successful calibration.


Björn Döring (DLR) Mon 22 Aug 2016 5:30PM

Thanks for your comments, @evertattema !

(1) Metallic Sphere

You are correct: The analogy of the "perfect target" (flat frequency and angular response) being like a metallic sphere is only an analogy which breaks down for lower frequencies (or smaller spheres). Alternatively, we can indeed talk about the actual properties that this theoretical "black body" of SAR radiometry should have.

Just to provide the reasoning for introducing this ideal metallic sphere in the first place: It nicely summarizes the properties through a single object which is rather easy to think about. If we adopt ERCS and then perform a radiometric measurement, we actually ask: "What is the size of an equivalent ideal target (this idealized metallic sphere) which would result in the same backscatter intensity after processing?"

The "ideal metallic sphere" cannot exist in practice, but neither can a "black body" (a body which absorbs all radiation). Nevertheless, the concept of a "black body" has helped to concisely describe its properties and is valuable during analysis. The "ideal metallic sphere" could play an identical role in SAR.

(2) Transponder Calibration

The problem with current reference target calibrations (including the ESA transponders) is, as you say, that they are calibrated with respect to a reference RCS. We argue though that we actually do not measure RCS in SAR, but something like an "averaged RCS" (which on top depends on phase, unlike RCS), and that quantity we call ERCS. We therefore have calibration targets which are traceably calibrated to one measurement quantity, but we are actually measuring a different quantity. In the future, we should rather calibrate our targets with respect to a reference ERCS.

It is correct though that one may expect numerical values which are sufficiently close to each other if the reference target has a rather flat frequency response and if the relative bandwidth of the SAR system is narrow.


evert attema Tue 23 Aug 2016 6:47AM

Thanks for your further explanation. CEOS is the place to let the experts decide. I believe I understand the concept. Personally I do not see the need for ercs and I find the concept confusing the issue. In my opinion we have a perfect 'active' equivalent of a black body; the isotropic point target. SAR measures the complex echo of the 'target' that could be presented in a processed data product as sigma_0 or beta_0 and phase. What else do we need?


Björn Döring (DLR) Wed 24 Aug 2016 7:01AM

I think we agree on the basic concept. We would like our targets to be
"ideal isotropic scatterers" (with no frequency dependence). With the
concept of ERCS we now want to resolve the mismatch between this ideal
target and real-world targets like the often used trihedral corner
reflectors (see the attached annotated slide from the 2013 talk).

I think we all agree that real-world targets (corner reflectors,
transponders, but also urban areas, fields, snow, etc.) in general do
not resemble ideal targets. At the moment we have some ambiguity of
how to deal with the imperfections of real-world targets (including
calibration targets). If ESA and DLR both use corner reflectors for
the calibration of Sentinel-1, for instance, we expect the measurement
results to be compatible. Yet we have not defined which RCS within the
100 MHz bandwidth we want to refer to, or how to take an
average. Without being more precise here, we cannot guarantee that the
calibrations result in compatible radiometric measurement results.

The ideal behind ERCS is now to define this link, and push for
everybody using the same link in the future.


evert attema Thu 25 Aug 2016 8:07AM

I am afraid I do not agree with the concept. Firstly even the theoretical isotropic point target has a (mild) frequency dependence (sigma=lambda-squared/4PI). This follows from EM theory.
Secondly I recommend as before to introduce in the calibration algorithm a correction function that takes into account the deviation of a selected reference target from the theoretical isotropic point target. Not very difficult to do. The correction will be specific for each used reference target and does not need international agreements. With this correction any software will give identical results.
Finally I recomnend that CEOS recommends as in the past to have operators distribute calibrated date such that the user community at large does not have to worry about the above. A new concept confuses the issue.


Björn Döring (DLR) Thu 25 Aug 2016 5:29PM

May I answer with some questions?

  • Which correction function should people use? (One way is described in the listed paper Reference Target Correction Based on Point Target SAR Simulation.). The procedure should certainly be the same so that different calibration teams arrive at compatible results, or not?

  • Would you agree that we do not actually measure RCS? (phase and averaging play a role)

    Then how can we use reference targets whose RCS we know, but not the quantity value we are actually measuring?

Otherwise, I agree with your first point (an actual sphere has a frequency dependence), and it may be a good idea to reformulate this part of the proposal to avoid confusion with the aforementioned "theoretical sphere". Also, of course data should only be distributed calibrated, but the point here lies one step before: Different calibration bodies/teams using different but traceable references should arrive at the same calibration results, which is currently not ensured.


evert attema Thu 25 Aug 2016 6:25PM

You have lost me with your statement about measuring rcs. The digital counts 'we measure' represent amplitude and phase of a radar echo. These counts can be related to various quantities related to the observed scene or target (e.g. rcs, sigma_0, polarimetric parameters) by means of data calibration. This process, if done properly, yields information related to the target only not the measuring system. In my experience this is a complicated job that required system knowledge and it is not something 'people' can do. ESA is in the Sentinel-1B commissioning phase and the above is demonstrated as we speak. The international commissioning team discovered many little details but gets in the end consistent results. I am not as pessimistic as you appears to be about the ability to resolve the calibration problem but indeed it needs a dedicated effort by experts. Perhaps a joined paper after the commissioning about the calibration process would be an idea.


Björn Döring (DLR) Tue 30 Aug 2016 4:04PM

Sorry for not being able to express myself any clearer... Let me respond foremost to your first remark because it is at the core of the discussion in this thread. You said:

The digital counts 'we measure' represent amplitude and phase of a radar echo. These counts can be related to various quantities related to the observed scene or target (e.g. rcs, sigma_0, polarimetric parameters) by means of data calibration."

I agree with the first sentence, but not the second. We do not actually measure RCS (or sigma_0 or similar quantities for distributed targets, which are simply RCS normalized by a reference area). This can be seen both from the principal equations (RCS vs. the SAR system equation, see attached image), but also by thinking about some examples:

  • The calibration approach should work for any kind of SAR system, from low to high resolution. To take an extreme example: Consider an ultra wide band high-resolution SAR system with a relative bandwidth exceeding 100 % (airborne systems already exist). Now the RCS of any (distributed or point) target is in general frequency dependent. When we consider e.g. the backscatter of snow over a bandwidth of 10 GHz around a center frequency of 10 GHz, the backscatter varies by several dB (see exemplary plot on slide 6 in the ERCS CEOS presentation from 2015). Which RCS should be reported after calibration? In the SAR image, the spectral information is always reduced to a single value.

  • Furthermore, this value actually depends on the SAR system as well. First, if we shift the center frequency, the measured "averaged" RCS (= ERCS) will change (again because of the general frequency dependence of the RCS). Second, if we modify our processor (mostly the type of apodization filter for improved side-lobe suppression), the measured "averaged" RCS (= ERCS) will change as well. This is all expected, but has not yet been considered for radiometric calibration.

  • Besides the problem of "averaging" over frequency and angle, we also have the problem of phase. Our measurement result (after SAR processing) depends on the phase response (phase over frequency) of our target. Two targets with identical RCS (the phase response is not considered) may appear differently bright in a SAR image despite all calibration efforts, so we really do not measure RCS. Examples of targets with potentially identical RCSs but different phase responses are calibration transponders or moving targets, resulting in "smeared" impulse responses in the SAR image.

So to sum up, in SAR we have always measured something else than RCS (we call it ERCS), and there is no problem at all. The problem only starts to surface if we now tie our radiometric calibration targets to RCS, although our measurement quantity is not RCS. We need to agree on a way for going from RCS to ERCS so that radiometric calibrations give compatible results in all cases.


evert attema Wed 31 Aug 2016 12:12PM

Dear Björn,
Our interesting discussion appears to go into a direction where the same message gets repeated in different wordings and I am afraid that it becomes a bit boring for the internet community at large.
I propose that we summarise our points of view and that the matter is further discussed in an appropriate forum such as CEOS.
It appears to me that we agree on the following:
What "we measure" with SAR is a complex response function involving amplitude and phase.
What we try to do is the characterise the measuring system (the SAR) in such a way that SAR processors can calibrate the response to produce calibrated products for the user community for example sigma_0 in the case of incoherent scattering by distributed targets. Ideally sigma_0 data products are independent of the SAR being used. In reality this goal cannot be reached due to target complexities such as partial coherence and wavelength dependence. However current SARs in orbit reach amazing calibration accuracies in the order of 0.1 dB. In terms of target phase response it is a similar story. By applying phase corrections very nice coherence values are achieved even with interferometry involving different sensors.
Where we may disagree is the use of the RCS concept. My position is the following:
Even before my time the RCS concept has been introduce to express a power ratio in terms of a surface measure (m squared). I found this concept in combination with the theoretical isotropic point target very useful particularly in addressing audiences without in-depth knowledge of EM theory and without a solid mathematical background.
However in the calibration business reference targets can only be an approximation of an ideal point target. Personally I am not a great fan of corner reflectors for radiometric calibration although they are great for phase calibration and achieving localisation accuracy.
In my opinion dedicated transponders are better for high accuracy but these devices have to be designed for a particular SAR and would obviously not work with all SARs. Their characteristics in terms of – amplitude & phase - angular response and frequency dependence have to be determined in detail to support amplitude and phase calibration. Transponder designs try to match the characteristics of a theoretical point target to simplify the corrections required within the operational angular and frequency range.
I agree with your statement that “we do not measure RCS” see above.
Where I disagree in the discussion is the way forward you propose to define an ERCS as a relation between the peak pixel intensity and the reference target. I may not interpret this properly but that is what your proposed definition says.
As you know we use for calibration purposes not the peak intensity but the integrated response of the reference target in the SAR image (scaled to sigma_0 or beta_0). I cannot help thinking that the proposal for an ERCS is a smoke screen that sweeps the full details of the SAR response (your equation) under the carpet. I believe that if “we do not measure RCS” we would not “measure your ERCS” either.
I found our public debate interesting and I am looking forward to the results of the discussion in the CEOS working group.


Björn Döring (DLR) Wed 31 Aug 2016 2:21PM

Thanks for your nice summary and your contribution to the discussion, Evert! It will help in reshaping the proposal. I am happy that we agree on the "we do not measure RCS" part though!


Manfred Zink Wed 31 Aug 2016 3:07PM

After a physical discussion between Björn and myself taking this discussion into account we drafted an updated proposal for which we opened a new thread: