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

Dear Evert,

I agree, the interest in the community is currently not very high so I am the more grateful that you have been willing to continue the discussion!

(1) Conversion of Units

You are right. The equation I stated is indeed overly simplified and was just meant to show the "averaging" part of it. In this form the pixel brightness seems to not depend on SAR system transmit power, range distance, antenna gains, noise, or system losses, which are all effects that we see in practice. Often these factors are summarized in a scaling factor, but of course they may be included in the h. In this case, h would have a unit unequal [1], and so would s_out.

(2) Calibration

Yes, I agree with this. I guess the problem here is: Which equation (and which units within) is the "correct" one?

(3) RCS And Calibration of Point Targets

Yes, I agree with all of this. Now how do we go from an imperfect reflectivity (e.g. a transponder) to the "calibrated/corrected" reflectivity? This is one of the problems the "ERCS proposal" is about: To standardize the approach of how we can link the frequency dependent, complex backscatter with the quantity that we see in a SAR image.

Sentinel-1 is a nice example: As you know, both ESA and DLR operate Sentinel-1 transponders. At the moment, it is not defined how we reduce the complex frequency and angular dependent backscatter of each transponder to a single value (we only derive a single value from the SAR image which "summarizes" the complex backscatter over frequency and angle). Wouldn't you agree that (in this case slight) offsets can occur depending on the procedure?

(4) New Definition?

The following is based on my understanding of what you mean by "real problem". Maybe I am heading off in a wrong direction here, so please correct me.

If I properly interpret what you mean by "problem", you said something similar in the previous thread:

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.

If I understand you correctly, the SAR sensor should, after perfect calibration, have no effect on the radiometric measurement result. I do not agree with this. Three examples:

• SAR systems are generally built for different frequency bands, often even integrated on a single platform for multispectral acquisitions. Each frequency band is calibrated. After calibration, various radar targets (forest, snow, even rain clouds, etc.) appear to have different reflectivities at different frequency bands, and this is of course expected (a feature, not a "problem"). The reason for building multispectral systems lies in acquiring additional information.

• In this regard, I like to compare the SAR sensor with colorful (red, green) sunglasses. Depending on which glasses we put on and depending on the color of the object we are looking at, one object appears brighter than another with the one pair of glasses, and the other way around. So to bring it back to SAR: The measurement result indeed depends on the SAR sensor (e.g. its center frequency and bandwidth, but also on the processor). The challenge for calibration is that systems which are nominally identical (e.g. Sentinel-1a, Sentinel-1b, and the upcoming three RCM satellites) should yield comparable measurement results.

• The same idea (the pixel brightness depends on the filter used) also affects astronomical photometry. I believe the following would fit quite nicely for SAR systems as well [source]:

  The methods used to perform photometry depend on the wavelength regime under study. At its most basic, photometry is conducted by gathering light in a telescope, sometimes passing it through specialized photometric optical bandpass filters, and then capturing and recording the light energy with a photosensitive instrument. Standard sets of passbands (called a photometric system) are defined to allow accurate comparison of observations.

  The only difference is that at the moment, we do not have a set of "standard passbands" in SAR (see discussion here).

There are still a couple of issues. Some of which I believe are misunderstandings that we should be albe to resolve quickly others may perhaps require some further work. My proposal is to deal with these outside loomio by email and/or a meeting in-the-flesh (at ESTEC?)

I like the proposal to continue the discussion in either way, and I am all for finding the best and clearest name possible. Thanks again for the discussion!