Notes about the flat-field correction of
1. Image features that need a correction by a
flat-field routine:
The
flat-field correction of
The
small-scale structures are introduced by the spatial inhomogeneity
of the channel plate response and the non-linearity of the analog-to-digital
converters of the detector electronics. Another small-scale structure which may
be present in
Inhomogeneities of the microchannel plate response are due to
the hexagonal pattern of the microfiber bundles and
the relative orientation of these bundles in a stack of three microchannel plates. Depending on this relative
orientation, a complex Moiré pattern of the response is produced, which is very
distinct in the A-Detector but much less pronounced in the B-Detector. If a
clear hexagonal (“chicken wire”) pattern is visible in the image, it is
produced by the lowest channel plate (the one which is closest to the anode).
The smaller structures are produced by the superposition of the fiber bundles of the three plates.
In addition
to these patterns there may be dead pores in one of the channel plates, which
lead to dark spots in the image. Depending on which of the plates has the dead
pore determines the size of the dark spot. Because of the spreading of the
charge, when transferred from one plate to the next, more pores are blacked-out
in the succeeding plate and, thus the dark spot is larger when it is in the
first plate (the one farthest from the anode).
The
non-linearity of the analog-to-digital-converter
(ADC) introduces a difference of 19% in the response between two succeeding
rows of the image. This can be seen in the very distinctive alternating
response of the odd and even rows of the image (along the spatial direction).
The ADC non-linearity causes that the count rate in one row is about 9.5%
higher than average, while in the adjacent row it is 9.5% lower than average,
thus making on average a 19% difference between the rows. In the following, we
will call this the “Odd-Even-pattern”.
Note that
this pattern only exists in the rows of the image, not in the columns where it
has been avoided internally by the detector electronics using a technique
called "dithering". This effect, which is present in both detectors,
is also effectively averaged out if an even number of binning is applied along
the slit direction.
2. Producing flat-field correction data
There is no
flat-field illumination of
In order to produce a quasi flat
illumination of the detectors during the operational phase of
The other
method to determine the “fixed pattern” of the detectors can be employed when a
large enough data set can be used to extract from the average of all images, in
a similar way as above, the small-scale features introduced by the detector. In
general, this average of the images is not as deep an exposure as the “normal”
flat-field exposure of three hours in the Lyman continuum, but its one certain
advantage is that it is as close in time as possible to the actual observations
to which it will be applied. This may be useful in particular cases, because
not all of the “fixed patterns” are really fixed in time.
3. Changes of the fixed pattern with time
It had been
found very early in 1996, by comparing several flat-field correction arrays of
detector A, that the flat-field pattern of the detectors are not constant with
time. This can be found by correlating different flat-field array data. The
correlation can be maximised by a shift of the flat-field pattern, which is
mostly less than one pixel (in X and Y direction), but can amount to several
pixels between different flat-fields.
There may
be several reasons for this shift of the "fixed" pattern: One reason
lies in the scrubbing of channel plates and the resulting gain loss of the
lowest of the three channel plates. Since the channels are inclined with
respect to the anode, the gain loss causes a shift of the charge cloud which is
located on the anode by the position encoding. The gain loss has always been
partly compensated when the high voltage has been raised after a gain calibration
has been done. But the high voltage change may have a distortion effect on the
electrical field between the channel plate and the anode. It may also have an
effect on the position encoding if it affects the dielectric constant in the
delay lines. Both may lead to a shift of the image pattern. Therefore, new
flat-field images have been acquired regularly – roughly every month – after
the high-voltage setting had been newly adjusted during a gain calibration.
Later, when the observations of the solar disk have been reduced to save
lifetime of the detectors, the period between flat-field acquisitions has been
increased.
Since the
gain loss occurs more or less constantly during usage of the detector and the
compensation can only be done stepwise, there is generally a shift between the
data and the flat-field pattern. But in general the shift of the flat-field
pattern is not uniform. A uniform scrubbing of the detector cannot be achieved,
and therefore a differential (, or local) scrubbing, which is due to the
non-uniform illumination of the detector during its use, results in a shift
pattern that is not uniform: depending on which part of the detector area has
been used more, the shift is higher in these areas.
In
addition, as mentioned above, the “fixed pattern” results from a superposition
of the pattern of each channel plate. The scrubbing, however, takes place
mostly in the lowest cannel plate (the one closest to the anode), from which
the largest amount of charge has been drawn. Thus it may be possible that
features arising from different channel plates may suffer a different
displacement in the image. However, this intricacy may be difficult to detect,
since the differences are probably much smaller than one pixel.
There is,
however, a very strong fixed pattern in the flat-field data that never changes.
It is the nonlinearity of the detector ADC in the position encoding
electronics, which causes the difference of responsivity
of odd and even rows. This odd-even pattern is always present along the slit
direction, and it has been found to be very stable throughout the time of all
flat-field images we have.
4. Alternatives for the flat-field application
The general
flat-field routine SUM_FLAT-FIELD.PRO corrects all fixed pattern by multiplication
of the flat-field correction array. It does not take into account any changes
of the fixed pattern with time. Thus it corrects perfectly the odd-even pattern
and much of the other channel plate non-uniformities. By selecting the flat
field array dated closest to the date of observation, the shift between the
flat-field data and the corrected data can be minimised. This is the simplest
approach, and for most purposes the results are sufficient.
To improve
the flat-field correction, the shift of the fixed pattern must be taken into
account. A rude way to achieve this would be to determine an average shift by,
e. g., a cross-correlation between the flat-field array and the data and then
to apply a shifted flat-field array to the data. This, however, disregards the
fact that the odd-even pattern is not shifted, and this results in an
under-corrected odd-even pattern (, unless the shift is exactly an odd number
of integral pixels in the spatial direction).
If a shift
of the flat-field pattern shall be taken into account, the odd-even pattern
must be corrected first. For this purpose we have extracted the odd-even
pattern from the flat-field raw data and produced new flat-field arrays, which
have the odd-even pattern removed. This was done in the following way: For the
A and B detector separately, the average odd-even pattern was determined from
the row-sums of all flat-field exposure raw images available. From the row-sums
the odd-even pattern was extracted by subtraction of the two-pixel average. Since
the pattern is a non-linearity of the ADC, it must be the same all along the
slit. Thus, the average along the row-sum was taken to determine a single value
for the upper and lower deviation, respectively, from the average. These two
values were taken to construct an artificial image array of the odd-even
pattern of 1024 by 360 pixels. This array can then be used to remove the
odd-even pattern from images by multiplication (in the same way as the usual
flat-field function). It has also been applied to all the flat field raw
images, in order to remove from them the odd-even pattern and to produce the
new flat-field correction arrays without odd-even pattern.
In order to
apply the shifted flat-field correction to
Udo
Schühle, schuehle@mps.mpg.de
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