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WAC-ed Moon

Some of the Wide Angle Camera (WAC) views of the lunar surface as taken by NASA's Lunar Reconnaissance Orbiter (LRO) show uncalibrated pixels of data. The images appear as strips of parts of a whole image that look, to all intents and purposes, like a Venetian blind that just don't line up correctly. 
 
In August 2010, however, I was able to understand the effect that was occurring with the WAC images, and this led to successful calibration of the images to look relatively good. The discovery was merely a personal one from an amateur perspective as I well understood that those engineers and scientists working with the LRO camera data knew exactly what was happening all the time. However, as sometimes happens, a large divide can exist between the amateur and professional community, the discovery, it has to said, was well founded without their help or assistance.

Thanks then to:
Jim Mosher using Delphi and Rick Evans using Octave

Thanks also, for their assistance in helping me to understand how the LROC camera operations work, to:
Prof. Mark Robinson of Arizona State University
Principal Investigator with LROC 
School of Earth and Space Exploration
Tempe, AZ

Dr Jeff Anderson of the Astrogeology Science Center
Assistant Science Center Director for Technical Operations
U.S. Geological Survey
Flagstaff, AZ

Fig 1.  On the left side of the image above you can see how the Wide Angel Camera (WAC) onboard LRO takes sequential 'framelet' images of the surfaceduring its orbit. Each framelet is scanned in as data by the WAC and reversed in order, so when an uncalibrated image is viewed, it looks exactly likethe one seen at top right of above image (here, just six framelets, 1 to 6, are shown). A better description of what is required for an uncalibrated image into a calibrated image can be seen in Fig 2 below. Note also that while some of the uncalibrated images have to be rotated by 180 degrees, and then flippedhorizontally afterwards to suit the 1961 IAU cardinal convention (for example, having North at top and East at right as one looks at, say, the Nearside face of the Moon),
not all images appear this way. During periods of its orbit, the orientation viewing axis of LRO has to be rotated because of thermal issues, so recording of images in relation to the above cardinal convention may be correct (also, the direction of orbit affect image recordings). 

Fig 2. The above image shows again just six set of framelets. Each framelet in the original images (but not always) is
14 pixels high, however, if stacked in reverse order in this configuration, features in the image won't exactly match up correctly as
there also has to be an over-lap of 3 pixels as each framelet is laid down (bottom of image).

When the final image has been calibrated, it still doesn't look correct as the field of view of the WAC camera is producing
 a somewhat 'squishy' effect at the side edges similar to a bow-tie configuration. This effect can be removed by
following a formula (below) that takes the particular pixels at the edges and re-positioning them into the correct (and expected) location
in the final image (see Fig 4 below)

The distortion effect has the formula:

Xd = Xc · (1 +k1 · r2 +k2 · r3),

 Yd = Yc · (1+ k1 · r2 + k2 · r3).

Fig 3. The distortion formula used to correct for the 'squishy' effect seen in some calibrated images.

For the visible detector, k is the distortion coefficient with values of k1 = −0.0099, and k2 = −0.00050, Xd and Yd is the distorted position (the actual measured position in x and y), while r is the distance from the optical centre (the difference in samples from the optical centre). If we take the ideal camera as representing 1.0 (that is the observed expected position), then for pixels close to the edge of the WAC photos, the exact location of these pixels are actually closer towards the central region than one would expect. As a result, overlap between framelets in these regions can cause problems with pixel alignment, leading to a type of ‘jitter’ effect of features that don’t exactly match up. Add to that, LRO may at times be flying too fast or too slow (relative to the lunar surface) during an observing run, so gaps in framelets where data wasn’t collected will result for the former, while for the latter overlap will lead to duplicate data. Gross topography over the WAC scene will also cause pixel misalignment.

ig 4. Above image shows the 'bow-tie' effect, the 'squishy' effect and its correction.

The WAC Camera

Fig 4. The Wide Angel Camera (WAC) above is the large baffle-like appendage attached to the main electronics system (the small baffle below it is the UV optic). The WAC measures 14.5 cm x 9.7 cm x 7.6 cm (note penknife as dimension reference), and has a field-of-view (FOV) of approximately 92 degrees. It is a pushframe camera consisting of a multispectral imaging system that is able to collect small multiple, sequential lines of data in one integration, called a framelet, that are then built up as a complete image through the downtrack motion of LRO. Image credit Malin Space Science Systems.

Some samples (just two of hundreds already calibrated)

Some useful references

* Robinson, M. S. et al. (2010). Lunar Reconnaissance Orbiter Camera (LROC) Instrument overview –
http://www.springerlink.com/content/572k747286387261/fulltext.pdf  – Space Science Reviews, Volume 150, Issue 1-4, pp. 81-124, 2010.

* Chin, G. et al. (2007). Lunar Reconnaissance Orbiter Overview: The Instrument Suite and Mission –
http://lro.gsfc.nasa.gov/library/LRO_Space_Science_Paper.pdf  Springer Science and Business Media, Inc. 2007.

* Robonson, M. S. et al. (2005). LROC – Lunar Reconnaissance Orbiter Camera –
http://www.lpi.usra.edu/meetings/lpsc2005/pdf/1576.pdf  Lunar and Planetary Science Conference No. 36, 2005.