The system limited the amount of words in the above. Perhaps we could talk about this is some detail..............

Perhaps it may be desirable to review the terminology in your proposal. The ERCS is not really any longer simply a surface with dimension m-squared. I believe the quantity you propose is dimensionless. When I thought about a (better) term it occurred to me that you used a better term yourself in the proposal: "complex target reflectivity function". Perhaps "complex target (back) scattering function" would be an option and "complex bi-static scattering function" for bi-static geometries. How about TSF for "target scattering function"?

The ERCS as proposed has the same unit as RCS: m².

Yes, calling it "complex target (back-)scattering function" is an option. What we need to define though is how a reference TSF should look like, and the proposal was to let it have a flat frequency and phase response. It is the same with length: First we define that we want to call our measurement unit "meter", and then we define what we understand when we say "1 m". According to the idea: A target (arbitrary TSF) which has an ERCS (or any other new name) of 1 m² (in a certain bistatic configuration, where monostatic is just a special case) has a backscatter which is equivalent to the RCS of target whose target amplitude and phase scattering function (TSF for amplitude and phase) is constant over frequency and phase and whose RCS is 1 m².

In my opinion reference to ERCS and 1 m-squared reference is an unnecessary complication. In my opinion it is desirable to update the proposal once more and recommend to the world of SAR calibrators to use the complex target scattering function (dimensionless) in lieu of simply the RCS.
In practice reference targets (transponders, corner reflectors, etc.) would be deployed after measurement of their actual scattering function. As simply as that.
I cannot help thinking that the concept of ERCS as an "average" is undesirable and that we do not measure ERCS or anything like this but the complex radar echo as the convolution of the complex target reflectivity function with the complex SAR system impulse response function.

In my opinion, converting the measurement quantity to a dimensionless quantity (unit [1]) is certainly not an option.

• What is calibration? The BIPM defines calibration as:

  Operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties (of the calibrated instrument or secondary standard) and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication.

  The key here is measurement standards. How do we ensure that different measurement standards (expressed by "complex target scattering function (dimensionless)") all have a defined relationship to each other if we do not base the description of their properties on (SI) units? How do you express that transponder 1 scatters more than transponder 2? Which of them is the "absolute" reference if you have 100 transponders? This is what we have SI units for so that we can relate measurement results back to well known national and international standards (in our case: meter).

• The reason for the current measurement quantity [m²] is the radar equation. How would you propose to "remove" m² from the radar equation?

• Furthermore, "removing/normalizing" the unit is a much bigger change than what was proposed before. The idea around the ERCS concept is to adapt what we have to resolve the remaining ambiguities, but to leave as much as possible as it is.

Dear Björn,

I admire your tenacity on this issue but as stated before I wonder if our interest in the subject is still shared by the international community. However within reason I will keep responding to your comments.

1) Conversion of units..
I do not propose any conversion. I just assumed that in your own equation "what a SAR measures" the complex function s_out is a complex ratio and dimensionless - Am I right?

2) Calibration
The definition you quoted is a lot longer than the original CEOS definition but I see no contradiction. In terms of your own equation calibration is the process of defining the system transfer function h(x,y) by measuring the function s_out with known input expressed by your function S(x,y). In operation the known function h(x,y) then is used to derive information from unknown targets.

3) RCS and the radar equation
Here again I am not proposing any change with respect to the current definitions. RCS is a very useful parameter that expresses a power ratio in terms of a surface. Except for hypothetical isotropic (point) targets RCS is a function of aspect angle and wavelength. Furthermore the information on phase response (or location of scattering phase center) is missing and has to be added for a complete definition of the function S(x,y) in your equation. I guess we agree on all of this.
In practical situations it is therefore not sufficient to characterize a reference target (corner reflector, transponder) by only RCS at bore-sight and center frequency. Obviously this characterization (calibrating the calibrator) has to be with respect to traceable standards such as the procedure followed currently for Sentinel-1 transponders.

4) New definitions?
The reason I do not support the ERCS proposal is that an average RCS over aspect angle and frequency does not solve the problem. Still different SARs (in terms of bandwidth and aspect angle range) will have different ERCS dependent on the sensor. In my opinion the concept ERCS sweeps the real problem under the carpet.