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

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

It deals with an updated recommendation concerning the Adoption of ERCS as radiometric measurement quantity for SAR Images

https://www.loomio.org/d/QPIwuD4R/adopting-equivalent-radar-cross-section-ercs-as-the-radiometric-measurement-quantity-for-sar-images

Without touching the core idea of the ERCS concept we have drafted this updated proposal for a CEOS recommendation:

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**Manfred Zink** started a proposal
Wed 31 Aug 2016

# Adopt ERCS (update) Closed Thu 8 Sep 2016

The pixel intensity in a SAR image results from the convolution of the complex target reflectivity function with the complex SAR system impulse response function.

Up to now, radiometric calibration was based on reference point targets whose radar cross section (RCS) was precisely known at boresight and at the SAR center frequency. The existing approach neglects two problems:

- Due to the convolution, the pixel intensity results from an “averaging” over frequency (range) and angle (azimuth).
- The pixel intensity does not only depend on amplitude (i.e., RCS), but also on the phase response of the target. Two targets with identical RCS may appear differently bright in a SAR image.

With modern high-resolution and high-accuracy SAR systems these problems become more severe and have to be considered during radiometric calibration. Instead of the reference target RCS, an “average” of the complex-valued (amplitude and phase) target response over the system bandwidth and angular range of the synthetic aperture has to be used. It is proposed to call this measurement quantity equivalent radar cross section (ERCS).

**Reformulated recommendation:**

Calibration of SAR systems and annotation of SAR products shall use the equivalent radar cross section (ERCS).

Agree - 3 |

Abstain - 3 |

Disagree - 3 |

Block - 3 |

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Manfred Zink
Wed 31 Aug 2016

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evert attema
Wed 31 Aug 2016

Hi Manfred,

This proposal sounds better than the previous attempt. However I worry about your statement about "averaging".

I propose to refer to an equivalent ideal isotropic point target and to take care of the deviation from ideal by convolution.

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**
evert attema
**
Wed 31 Aug 2016

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"?

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**
Björn Döring (DLR)
**
Thu 1 Sep 2016

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.

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Björn Döring (DLR)
Thu 1 Sep 2016

The new proposal captures the core idea: Distinguish RCS from what we actually measure.

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**
evert attema
**
Thu 1 Sep 2016

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.

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Björn Döring (DLR)
**
Mon 5 Sep 2016

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.

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**
evert attema
**
Tue 6 Sep 2016

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.

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Björn Döring (DLR)
**
Wed 7 Sep 2016

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).

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evert attema
Wed 7 Sep 2016

To end this story in a positive way I will support your proposal with the recommendation to find a better word for the new quantity and let the world know about the proposed new SAR calibration algorithm. Piece of cake for DLR/ESA.

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**
evert attema
**
Wed 7 Sep 2016

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?)

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Björn Döring (DLR)
**
Thu 8 Sep 2016

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!

evert attema· Wed 31 Aug 2016The system limited the amount of words in the above. Perhaps we could talk about this is some detail..............