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Data Reduction
During the five hours of observation the camera performed flawlessly,
recording images in a continuous mode at a rate of 30 frames per second,
for a total of more than half a million broad-band images. Table 1
summarizes the most relevant observations made during the flight. The
table does not include the calibration measurements, like the flat fields
for the different filters. The actual dataset is more extensive, since the
camera was also continuously recording while optimizing the telescope
focus, movin the field-of-view from one position to another across the
Sun, and while waiting for the pointing and the camera temperature to
stabilize. For example, most of the time needed to record a single
full-disk mosaic of 10 tiles is actually spent waiting for the system to
optimally stabilize itself before taking the actual science images.
Data Reduction Steps
The main steps of the data reduction are:
1) Construction of a flat field;
2) Individually flat field the single frames;
3) Co-align the frames to be averaged, then co-add
them to obtain mosaic tiles;
4) Stitch together the averaged tiles to form a
full-disk mosaic; and
5) Determine the
limb-darkening function and remove it from the full disk mosaic to obtain a
map of the photospheric contrast. Dark current corrections are not
required because of the particular way the camera operates and delivers the
raw images. The raw frames are basically the difference between images
recorded with the detector looking at the actual scene (the Sun) and
looking at the chopper blade (used as baseline reference), thus having the
detector offsets already automatically removed. Foukal and Libonate (2001)
or Bernasconi et al. (2004) provide more details on the camera operation.
Probably this is the most critical step of the entire process.
During the flight we recorded several hundred images at Sun center with the
telescope far from focus. These images are used to create the flat field.
Defocusing the telescope has the effect to remove all the solar surface
features from an averaged image. However, because of the relatively large
field-of-view of the detector, the limb darkening is still present causing
a considerable intensity variation from the center to the edges of the
frame. This residual limb darkening effect is not straightforward to
remove, but we have developed an iterative procedure that allows us to
exactly determine the amount of limb-darkening still present in the
averaged flat field.
The procedure takes the advantage of the fact that the mosaic tiles have
a fairly large overlap with each other. If the flat field is correct then
the regions where tiles overlap, which actually correspond to completely
different parts of the frame, should have the same intensity: First, we
compute a preliminary flat field without limb-darkening correction, by
averaging 300 frames taken at disk center with the telescope out of focus.
Then we proceed with Steps 2 and 3 of the data reduction procedure: flat
fielding of all the individual frames composing a mosaic; co-alignment and
averaging of the frames of the same mosaic tile. Finally, after
determining the exact tile positions in the mosaic (Step 4), we compute the
difference of all the overlaps, pixel by pixel, and add them up to obtain
the sum of all the residuals ΔO. Ideally, the resulting value of
ΔO should
be zero. Values different from zero are due to detector noise, differences
in the actual image because the overlapping tiles have been recorded at
different times, and finally by the incorrect estimation of the flat field
residual limb darkening. We minimize ΔO with an iterative minimization
algorithm. The flat field image is divided by a mathematical model of the
limb darkening described by a third degree polynomial with three free
parameters (it is an expansion of the two degrees polynomial from Allen,
2000):
(1)LD(μ) = 1 + (μ − 1)
⋅ u + (μ2 − 1) ⋅ v +
(μ3 − 1) ⋅ z ,
where μ = cos(θ) is the distance from the Sun center and u,
v, and z are
free parameters. Three additional free parameters are necessary: the
coordinates x and y of the center of LD function with respect
to the flat field image, and the radius r of the Sun. Then we
proceed to re-compute ΔO by repeating the Steps 2, 3, and 4. The
entire process is repeated with different parameters u, v, z, x, y,
and r until the smallest value for ΔO is reached.
Each single frame needs to be individually corrected for pixel-to-pixel
gain differences before co-adding them together. Dark current corrections
are not necessary since each image delivered by the camera is already the
difference between two consecutive frames (scene minus chopper blade).
To reduce the noise level, each individual tile is obtained by averaging
of 60 individual frames taken at the same location. Each image needs to be
co-registered with respect to each other, before co-adding them. We
achieved co-registration of the order of 0.1 pixels or better by cross
correlating edge-enhanced individual frames.
To cover the entire solar disk it is necessary to record images (tiles) at 10 different locations. The
mosaic is built by finding the exact overlap between tiles. The
pointing information recorded by the on board-computer when each tile was
taken is used as first guess. However this can be off by up to 15 arcsec
(about 5 pixels). For a precise overlapping of the tiles we use the same
method as in Step 2.
Here is a finished mosaic.
This represents the first image of the Sun ever obtained with an instrument
with flat sensitivity from 0.28 to 2.6 μm. The image spatial resolution
is about 5.6 arcsec, limited by the pixel size of 2.8 arcsec.
To determine the actual irradiance contrast of the features in the solar
photosphere, the limb darkening function (LD) needs to be removed from the
mosaic. This is done by fitting the same model of the limb-darkening as in
Equation (1) to the actual fill-disk mosaic.
Here you can see the
same mosaic as above but with the
disk intensity divided by the limb darkening function with parameters: u = 0.718,
v = − 0.106,
z = 0.019.
The actual shape of LD can be seen here. Some
large-scale artifacts and some seams between tiles can be still seen, but
this is because the image has been heavily contrast enhanced to better
highlight the faculae and enhanced network. The contrast amplitude of these
artifacts is smaller than 0.3%, which is well below our sensitivity
requirement of 1% for faculae and enhanced network.
