Convert hyperspectral exposure image to reflectance

[czender]

This is a draft algorithm to retrieve spectral reflectance based on my understanding of the (possibly soon-to-be) available inputs. Suggestions and correction welcome (the more specific, the better). For simplicity, the algorithm description currently omits the time dimension. It is implicit in all quantities below except rfl_wht.

NOTE: proposal below has been migrated to documentation which supports Latex for ease of reading.
https://terraref.gitbooks.io/terraref-documentation/content/hyperspectral_data.html But the commenting isn't that great,

So please comment below on this issue, or propose changes to the algorithm text as a pull request: https://github.com/terraref/documentation/blob/master/hyperspectral_data.md

---

Inputs and Outputs

syntax: Variable(dimensions) [units]
$$$
% Someone please make LaTeX typeset this...
I_p(\lambda,y,x) = F_{\lambda}(\lambda) R_p(\lambda) C(\lambda)
$$$

Inputs: Required known or measured inputs:**

1. uint16 xps_img(wavelength,y,x) [xps] =Exposure from experiment image (i.e., plants) (known, VNIR, SWIR sensors)
2. uint16 xps_wht(wavelength,x) [xps] =Exposure from white reference sheet/panel (measured by VNIR, SWIR sampling period? location?)
3. float32 rfl_wht(wavelength) [fraction] =Reflectance of white reference (factory calibration) (assume time-constant?)
4. float32 flx_dwn(wavelength) [W m-2 um-1] =Downwelling spectral irradiance (measured by environmental sensor. units?)

Intermediate derived quantities:

1. float32 cst_cnv(wavelength) [xps/(W m-2 um-1)] =Proportionality constant between reflected spectral flux and Exposure (derived)
2. float32 flx_upw(wavelength) [W m-2 um-1] =Upwelling spectral flux (derived. and possibly measured for closure?)

Outputs

1. float32 rfl_img(wavelength,y,x) [fraction] =Reflectance of image (i.e., plants)

Proposed Algorithm to retrieve reflectance from measurements:

1. Assume image exposure linear with incident spectral flux, this implies
   • xps_wht=flx_dwn*rfl_wht*cst_cnv
2. Derive proportionality constant from calibration:
   • cst_cnv=xps_wht/(flx_dwn*rfl_wht)
3. Assume proportionality constant for calibration sheet and plant image are identical, this implies
   • xps_img=flx_dwn*rfl_img*cst_cnv
4. Derive plant reflectance from exposure
   • rfl_img=xps_img/(flx_dwn*cst_cnv)
5. (Optional) Derive upwelling spectral flux from reflectance and compare it to measured upwelling spectral flux (if available) for closure/validation
   • flx_upw=flx_dwn*rfl_img
6. (Optional) Apply PAR-sensor SRF to downwelling irradiance, integrate, compare to measured PAR for closure (integration would require detailed information or assumptions about bandpass of each spectral channel).
7. More?

Before implementing this, I would like feedback and/or sign-off by @dlebauer @nfahlgren @max-zilla @pless @solmazhajmohammadi and @LTBen.

Next steps

More assumptions, input measurements, and/or more sophisticated algorithms would incorporate these additional sources of information:

1. BRDF (angular reflectance properties) of plant/leaves
2. 3D orientation of reflective surfaces (plant/leaves)
3. BRDF (angular reflectance) of calibration sheet
4. Direct/diffuse partitioning of downwelling flux

Notes

• Units of exposure are vague. Exposure is similar to a photon counter modulated by the spectral response function (SRF) of the sensor. The units are denoted [xps] and range from [0..2^16-1] = [0..65535].
• add QAQC tests for sensitivity and saturation in each band
• cross validate with other sensors with know spectral response functions.
• NB: Three required inputs (xps_wht, rfl_wht, flx_dwn) are not ready to use. Their location, units, and/or sampling intervals are unknown. Only xps_img is ready. Please tell me how to get the other three in the notes below. (@LTBen, @markus-radermacher-lemnatec)

[dlebauer]

@ashiklom added some comments to the documentation https://terraref.gitbooks.io/terraref-documentation/content/hyperspectral_data.html

but the commenting system doesn't work well so I am pasting them here:

What are x and y here?

OK, I'm assuming that x and y correspond to pixels...

indeed, this appears to be the case here. Not to be confused with the fact that we are using an x,y coordinate system with units of meters east and north of the SW corner of the gantry (see terraref/documentation#7 and terraref/documentation#9).

why does the white reference only have an x dimension? If there is some averaging taking place, that's a good opportunity for calculating the uncertainty in the reflectance calibration.

"Wavelength" should be defined more precisely, if possible. Is this the wavelength of peak reflectance? Or the midpoint of the bandwidth? What are the bandwidths? This is also related to the optical point about spectral response functions (SRFs) -- unless we know what these are, I personally think wavelength should be treated as an effectively ordinal variable that should only be used in across-instrument comparisons (as well as comparisons with radiative transfer models) with caution.

Related to above -- I think step 6 is critical to using this data in a radiative transfer modeling context. I would actually suggest making it mandatory and, if SRFs are not available, to add a detailed flag to the data describing exactly the assumptions made in reporting "reflectance" at a given "wavelength" (e.g. assume Gaussian SRF with reported bandwidth indicating full-width half-maximum).

[czender]

Good questions. x and y are currently pixels. when the transformation is available from pixel to geographic horizontal dimension we may change from x,y to lat,lon or some other system like the gantry x,y.

White reference in theory only has a wavelength dimension but in practice the one snapshot (called whiteReference) I know of is dimensioned wavelength by x. it's as if the camera scanned only one line.

Currently "wavelength" is the wavelength associated with each channel in the .bil image file. Would welcome higher resolution SRFs and/or bandpasses.

[TinoDornbusch]

Who of you is expert in hyperspectral analysis? My current idea is to do the dark reference measurement before each scan and have the white target mounted on the gantry, such that one part (~10%) of the image is always "white".
Any other ideas on that?

[czender]

Glad to know there is a dark reference available too. I can modify the calibration algorithm to account for that.

[pless]

My understanding of the headwall VNIR sensor is that the sensor has a grid
of pixels. The x-axis of the grid of pixels are all the same, but as you
move up the sensor, the y-axis of the pixels are sensitive to difference
frequencies. The "lens" of the camera may not look like this, but you can
think of it as a slit that is capturing the world one row at a time.

This slit is rotated in order for the hyperspectral camera to see a whole
image
Alternatively the slit can be used the scan the hyperspectral camera over
the ground.

The meta-data for one of the VNIR data captures on 4/7 has fields:

  "current Setting Startpos": "-70",

  "current Setting Stoppos": "70"

(although it also says "use rotating mirror": 0).

However this particular bit of data was captured, the reason that there is
one row of white-balance is that the sensor has one pixel for each
(wavelength, x)

the "y" coordinate relates to either how far the sensor has rotated and
translated as the data is captured.

On Thu, Apr 28, 2016 at 10:04 AM, Charlie Zender notifications@github.com
wrote:

Glad to know there is a dark reference available too. I can modify the
calibration algorithm to account for that.

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#88 (comment)

[TinoDornbusch]

In Scanning mode the mirror is always at position 0 and does not move. Therefore you have the entry "use rotating mirror":0.

[markus-radermacher-lemnatec]

Danke für die Klarstellung, du hast genau recht, die Start/Stop Einstellungen sind irrrelevant, wenn der Spiegel nicht benutzt wird.
-Markus

[rmgarnett]

I think that last comment was meant to be a private email, but I'll translate:

Thank you for the clarification. You're exactly right. The start/stop settings are irrelevant if the mirror is not being used.