(Internal) Alaska SAR Facility info: RADARSAT, sigma naught, beta naught
Anonym
The correspondence below is with the Alaska SAR Facility's 'guru' Jason: jason@conan.gi.alaska.edu
may also try Alison at: allison@dino.gi.alaska.edu
ASF's URL: http://www.asf.alaska.edu/index.html
Also, more RADARSAT info available from RSI (RadarSat Int'l) and CDPF (Canadian Data Processing Facility)
RSI: (604) 231-4960, ask for Don
For more technical questions, contact Bill Jeffrey @ CDPF (819) 827-3001
RSI and CDPF are the original source of ALL RadarSat data; all of their data products include a base calibration (antenna corrections and some corrections based on known reflections from the Amazon Basin); further, some of their products apply a instrument-specific LUT correction, which basically just makes the data 'look nice'. It accounts for differential reflection due to incidence angle based on the general surface type (i.e., sea ice, ocean, land). The DNs you read off of one of their tapes is most likely calibrated radar brightness, or 'beta'. To figure out how to calculate Sigma Naught or Beta Naught from these data, see "Extraction of Beta Nought and Sigma Nought from RADARSAT CDPF Products" by Nick Sheperd of Altrix Systems. This paper is included as one chapter of a free document available from RSI on their anonymous FTP site: ftp.rsi.ca, in the CEOS_DFN directory, in a file called RSI_D4.DOC. This FTP site in general has lots of info, but its a little difficult to figure out what's what.
QUESTION 1
> Hi Calibration Guy!
>
> Your Web page is fantastic -- a great resource!
>
> I have a question about raw vs. calibrated RadarSat data. I'm
> not sure if I've sent this e-mail to the correct person or place, but
> any help you could provide would be much appreciated.
>
> When one is working with a final calibrated RadatSat image, what
> are the units of the data? They seem to be some type of scaled value.
> I assume it must me a measure of backscatter energy, is it actually
> 'sigma naught'? Or is the sigma naught the raw data, that is then
> calibrated into the finished product. Also, have you ever heard of
> 'beta naught'? What is this?
>
> Thanks for your help! David
ANSWER 1
(note: Jason is refering to ASF's calibration techinques/programs)
After applying the calibration equation to the image pixel values, you
have floating point values whose units are dB m^2 / m^2 which is Sigma
Naught, or NRCS (Normalized Radar Cross Section). Notice that the
m^2 actually cancel out, so this is
in a way unitless. It is normalized to the area of the ground imaged
for each pixel. In order to do this you have to know the actual orientation
of that little patch of ground to the RADAR. Our processor does not know
this, so we apply a correction for incidence angle assuming the whole
earth is a smooth ellipsoid.
This is okay for ocean or sea ice scenes and flat scenes, but obviously
fails in areas where the topography is not flat. Beta Naught is
referred to as Radar Brightness, and does not correct for the local
incidence angle. The spaceborne radar inherently measured Beta Naught,
not Sigma Naught.
If you don't know, the radar cross section (RCS) is expressed in dB m^2. The
amount of energy returned from a target is measured, and then you can
compute the size of a conducting sphere which would return the same
amount of energy. From this size, you calculate the area in m^2 of
the cross section of the sphere, and this become the RCS value. It's an
odd unit, for sure. Sigma Naught is then the RCS returned, normalized to
the surface area imaged, or dB m^2/m^2.
SAR images processed by the CDPF in Canada produce Beta Naught values
when their calibration equations are applied. Some facilities call their
data Beta Naught in the description, but they divide out the sine of
the flat earth incidence angle anyway. It's a terminology used to remind
us all that we need to know the local incidence angle in order to calculate
Sigma Naught.
Does this help?
-Jason
QUESTION 2
> So, the CDPF more-or-less produces 'uncalibrated' SAR imagry -- where
> the user would have to do the calibration to sigma naught themselves.
ANSWER 2
No, their processor IS calibrated as well, they just output a slightly
different parameter. One could even argue that their product is
technically more correct than ours...
With data from either facility you need to derive local slope information
before you can accurately measure Sigma Naught from a SAR image over
hilly terrain.
SUMMARY
> I just want to be sure I'm understanding the difference between
> Beta and Sigma Naught, so let me summarize what I've got so far:
>
> Raw Beta Naught is Radar Brightness and is inherently the
> quantity measured by the instrument. This raw measurement does not
> correct for the local incidence angle. Does this raw value normalize
> for the area imaged by each pixel? Would its units be (dB m^2/m^2) or
> (dB m^2), or something else?
>
> ASF's Calibrated Sigma Naught, or NRCS, is RCS normalized to the
> surface area imaged by each pixel. Included in this normalization is an
> estimate of the incidence angle, assuming the Earth is a smooth
> ellipsoid.
>
> CDPF's Calibrated Beta Naught are calibrated in that they are
> corrected based on returns from corner reflectors, etc.., but have not
> been corrected for the local incidence angle. Does this data type still
> divide by the area of the pixel (despite not attempting to correct for
> incidence angle)?
>
> Other facilities produce Beta Naught SAR images that HAVE been
> corrected for incidence angle (assuming a flat Earth). So, just knowing
> that the data is called 'Beta Naught' isn't enough info to know whether
> an incidence angle correction has been done. But, Sigma Naught, by
> definition, includes an incidence angle correction.
>
> Assuming the Beta Naught SAR images (whether they include the
> incidence angle correction or not) have normalized for the area imaged
> by each pixel, the units of both Beta and Sigma Naught are (dB m^2/m^2)
> = dB.
>
> Neither calibrated Sigma Naught nor Calibrated Beta Naught have
> accurately accounted for local slope, so beware of quantitative analysis
> of these SAR images in hilly terrain.
>>
SUMMARY RESPONSE
Hmmm, I've been discussing this with Allison and I'm afraid we've become
quite confused ourselves! We can be of no help to you today, we'll have
to take a while to sort this out....
Sigma is the Radar Cross Section in dB m^2 (the equivalent area of sphere...)
Sigma Naught is the RCS per square meter, or dB m^2/m^2 or just dB
We think that Beta (Radar Brightness) is the reflectivity of the surface
or the percentage of energy returned.
We also think that Beta Naught is the normalized Radar Brightness and is
thus unitless (dB.) Our theory is that Beta Naught is normalized to
steradians, because you don't need local geometry in order to derive
Beta Naught.
We're scratching our heads on this Beta question...
In any case, Sigma is the quantity which is useful for characterizing
a surface, but you must have local slope information in order to accurately
derive it. Beta is inherantly what the radar measures, but does not have
much physical meaning without converting it to Sigma.
-Jason
FINAL E_MAIL FROM JASON
I have been working with my developer on modifying our calibration workstation
to ingest CDPF products and so I've had a chance to consider these
differences over the past few weeks.
I found a good reference paper on "extraction of calibration parameters from
CDPF products" if you'd like a copy I can have somebody fax it to you...
Here's my state of understanding:
Beta - Radar brightness in dB m^2
Beta-0 - Radar brightness per unit area in dB m^2/m^2
Sigma - Radar backscatter corrected for local incidence angle dB m^2
Sigma-0 - Sigma per unit area in dB m^2/m^2
Gamma - Unit measured by scatterometer
Gamma-0 - Gamma per unit area
Relations between the three:
beta = sigma/sin(incidence)
gamma = Sigma/cos(incidence)
-Jason