ACKNOWLEDGMENTS.

Technical aspects of the CCD imaging equipmentwere arranged in collaboration with a S. Souza at Williams College. We are indebted to the Santa Barbara Instrument Group for the loan of theST 2000XM CCD camera used to image the eclipse.

CALIBRATION NOTES

Subsequent to the initialweb posting regarding these data, the individual 40ms integrationCCD frames taken on the flight deck gyro platform of QF 2901 with an SBIGST2000XM CCD, have been instrumentally calibrated.  Each of the frameshad subtracted from them a dark/bias reference frame (made from a mediancombination of 25 dark/bias frames taken on the aircraft just prior tothe eclipse imaging sequence), and were fat fielded as well (see Post Processingfor a note on flat fielding). A wide-field image mosaic created from thecalibrated offset pointed frames (as previously discussed) and is shownhere in several forms.

NOTE: ALL images on or linked from this page areproduced at 1/4 the original pixilization to facilitate web-based display. The original CCD matrix BEFORE enlarging the image composite by combiningoffset pointed fields (see above) was 1600x1200 pixels.  Any discussionrelated to "pixels" here is in the 1/4-size (1/16 array) resampled pixelspace unless otherwise noted.

IMAGE DEPTH and RADIAL EXTENT

How deep did we go?  This is illustratedin a linear display of the final wide-field mosaic in a linear displaystretch to show the full radial extent of the corona.  In this hardstretch at the bottom of the dynamic range, little information is conveyedabout the structure within the corona.

We imaged the corona to a distance of at least6 Solar radii from the heliocenter (see the radial profile below). Indeed, at an even harder stretch than shown above, one can still see decliningisophotes at the edge of the mosaiced field. At such a hard stretch theMoon appears.  At this extreme level of displayed surface brightnessthe limb of the Moon would be diffused by scattered light.  As a visualizationaid, the inset dark circle is a mask which is 2% larger than the apparent(mean) lunar angular diameter.  During the imaging sequence, fromwhich this image mosaic/composite was made, the Moon was moving acrossthe sun, so this mask fully contains its displaced position with respectto the Sun over that time.  In instrumental units, this image is displayedat a stretch from 0 to 100 counts, where the median surface brightnessof the inner corona immediately adjacent to the occulted photosphere wasmeasured at 100,000 counts.

LINEAR DISPLAYS

It is impossible to capture the full extent ofthe dynamic range of the solar corona recorded on the QF2901 flight deckCCD imager in a single linear image display image display.  Indeedabout 10 are needed given the appx. 1/4% stepped intensity display depths(per channel) on most computer monitors.  Indeed, about 10 imagesare needed, as shown in the QuickTime movie,prepared earlier with the data still in uncalibrated form.

DISPLAY TRANSFORMATIONS &RADIAL SURFACE BRIGHTNESS ("GRADIENT") FILTERING

An effective way to collapse the dynamic displayrange is to  perform a non-linear numerical transformation on thedata.  In doing so, however, as the image contrast in any given radialzone (which declines outward from the Sun) is also collapsed.  Hence,in any given radial zone the structural features in the corona are notas apparent as in a linear display specifically optimized in display stretchfor the surface brightness of that zone.  To mitigate this (to variousdegrees) one can subtract the underlying radial brightness profile of thecorona before displaying the image, which then improves the image contrastfor features such as coronal streamers, holes, etc.  Most image editingprograms, such as Photoshop, provide "features" for "radial gradient" masking. However, one cannot specify the quantitative form of the radial mask, andif not properly matched to the data themselves, zonal artifacts are introduces. Additionally, but subjectively, radial gradient masking is often done withtoo heavy a hand, which results in a corona with very star image contrastsin its internal features, which for esthetics (rather than photometric)purposes is often displeasing.

A proper radial gradient filter should be madefrom the data themselves.  I do this by computing the median radialsurface brightness profile, in 1 pixel wide annular zones, and then verymodestly smoothing the profile (with a 2 pixel boxcar) to reduce the effectof any anomalously bright or dark zones due to uncompensated pixel defects. In the case of the above image, here is the radial surface brightness profile,expressed as a median per-pixel intensity with respect to a median pixelthe brightest circum-solar zone in a log (base 10) plot:

As you can see we imaged the corona very well(at high S/N) out to a distance of 300 (1/4 size resampled) image pixels. The angular radius of the Sun is appx. 45 image pixels (hence agreeingwith the earlier statement "we imaged the corona to a distance of at least6 Solar radii from the heliocenter".  The sharp drop-off beyond theR ~ 300 pixel region is where the data become both photon starved and fieldsize constrained.

In subtracting a MEDIAN radial profile one musttake care not to locally oversubtract.  With this data set subtractingmore than 30% of the profile intensity begins to "dig holes" in the imagewhere it is brightest - in the inner corona adjacent to the lunar limb(you can see the rising power in the surface  brightness profile atsmall radii near the limb).  Being very conservative, so that no negativeresiduals arise at any radial zones, images were produces subtracting 20%of the profile.  These are shown, first, in square root displays.

SQUARE ROOT DISPLAYS

Displaying the square root of the data, after20% radial profile subtraction, allow showing most of the coronal dynamicrange in only three images as illustrated below:
 

Note the extent and structure of the coronal streamersbeyond the region, in each display, beyond where the display is saturated. The vertical and horizontal lines are artifacts of imperfect flat-fieldingin combining the image data taken with different field pointings. The flat-field illumination source used to ascertain the inter-pixel CCDresponse may not have been intrinsically uniform (see Flat Field discussion),which makes photometric calibration at the lowest signal levels difficult(if not impossible).  The brighter diffuse arc, are below the sunand to right at about 3 solar radii from the heliocenter, is an artifactdue to an afocal image ghost, likely from a multiple reflection off theaircraft window.

LOGARITHMIC DISPLAYS

To further collapse the radial dynamic range inthe image display a logarithmic transformation can be applied. (Here Iuse log base 10, which makes it easy to keep track of transformed intensities,but any logarithmic base can be used as desired).  Such a displaywill result in a slightly contrast in specific radial zones, but does indeedshow the global structure of the corona at a glance.

To he image above is displayed over [3.8] dexafter subtracting 20% of the radial brightness profile - a dynamic rangeof appx 6,300.  Contrasts "improvements" can be had at the expenseof saturating he display in the center, clipping the extent of the coronaat large radii, or introducing a small level of negative residuals by amodest oversubtraction of the radial surface brightness profile.

CONTRAST ENHANCEMENT

Moderate contrast improvement over most of theradial range, at the expense of the introduction of some quantization noiseat large distance, may be had by taking the product of the above two transformations,and displaying the product itself in a logarithmic stretch.  For thesedata, first subtraction a 30% profile is warranted (and supported by thedata) as it results in only a very small local region of oversubtraction- which sharp eyed observers will see as a few "extra" dark pixels in thefollowing image just at the bottom of the 2% oversized lunar mask:

FLAT-FIELD ERRORS,  IMAGEMOSAICS, and SPATIAL FILTERING

The above image mosaic is not "seamless". This is primarily a result of residual photometric errors in the attemptedflat-field compensation. The flat field calibration frames (from whicha calibration reference file was made and applied to the individual eclipseimages) were obtained prior to shipment of the equipment to Australia/Antarcticaby Steve Souza (Williams College).  While these frames taken withthe optical system (lens and filter) in place  and exposed on a uniformlyilluminated target, these were not sky flats, and hence not at infinity. Examination of the flatted image data obtained from the eclipse, at differentfield pointings, indicates residual large-scale (global) flat-field errors.These are likely due to focus-dependent vignetting in the optical system,pointing-dependent diffuse stray light scattered/reflected from the aircraftwindow, or a combination of both.  Empirical corrections to the differentialflat-field errors were assessed from the image-overlap areas in the ensembleof offset-pointed target frames.  These corrections were then appliedto the image mosaic which, for the most part, removed the differentialflat-field errors.  These errors, before correction, are most severeon frame boundaries both because of detector edge defects, and very differentS/N across over-lap boundaries because of the small number of frames. Corrections to rows and columns along the boundaries themselves, worksbest by assessing the needed corrections after performing a mild gradient-edgeenhancement to the images.  This process (subtracting a fraction ofthe local median about every pixel) is similar to "unsharp masking". Whenproperly controlled this process also spatially filters the image to bringout higher spatial frequency information in the corona, but at the modestexpense of accentuating the pixel-to-pixel noise in the low S/N regionsof the image.  The result, with some subjectivity in tuning parameters,is shown below, and except for some further subjectivity in how to presentthe data (contrast, spatial filter bandwidth, dynamic range clipping, etc.)this is very likely about the "best" which can be obtained from these data(and, it makes a pretty nice picture!):

Two notes:

1) This above flat-field error compensation processworked very well in an intra-field and inter-frame sense (as the imageabove demonstrates).  Bringing frame 11_04 (lower left) under control was much more difficult, and uncompensated systematic can still be seen- though at a very low level.

2) The surface brightness excess in the regionof the previously noted afocal image ghost (at 3 R(sun) to the lower right)was assessed in comparison to the median surface brightness at the sameradial zones, excluding this contaminated sector.  This excess wasthen "removed" (by intensity scaled subtraction) from each pixel whoseintensity exceeded by 3-sigma the azimuthal median at the same radius. The intensity subtracted was the fraction of the intensity at that pointin 3-sigma excess.  This, too, is imperfect, but is a marked improvement.

NOTE: ALL images here are produced at 1/4 theoriginal pixilization to facilitate web-based display.  The originalCCD matrix BEFORE enlarging the image composite by combining offset pointedfields (see above) was 1600x1200 pixels.  Any discussion related to"pixels" here is in the 1/4-size (1/16 array) resampled pixel space unlessotherwise noted.

SOHO/LASCO L2, QF 2901 &SOHO/EIT

The LASCO (Large Angle Spectrometric coronagraph)L2 Coronagraph, and the EIT (Extreme-Ultraviolet Imaging Telescope) onNASA'sSOHO spacecraft were imaging the solar corona and photosphere,respectively, at times very close (and during) the eclipse.  Our QF2901 Flight Deck imager, during totality, covered an inner radial regionwhich cannot be reached by this space-based facility.  An image compositeof outer corona with SOHO/LASCO L2, mid and inner corona from QF 2901,and the photosphere with SOHO/EIT, all nearly contemporaneous, is shownbelow.

The LASCO C2 image was prepared (by the SOHO project)independently from the QF 2901 image, and was provided in non-quantitativeform (as a JPEG file) with its brightest regions hard-stretched to white,and with a linearity transfer which differs from the QF 2901 processedimage.  Hence, the "boundary" between the two images appears somewhatdiscontinuous in local intensity and in their radial brightness gradients,but is presented in this form to illustrate the morphology of the coronalstructures from the photosphere outward.  With the actual LASCO C2data, which we are requesting, we should be able to re-present this equitablyfor both data sets.  In addition, because there is a region of overlapin the LASCO C2 and QF 2901 imagery, we should be able to cross-calibratethe two data sets and obtain an absolute radiometric calibration (subjectto filter band transfer uncertainties) of the entire corona.  Staytuned.

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