J. P. McFadden, F. S. Mozer, J. Vernetti, and I. Sircar
Space Sciences Laboratory, University
of California, Berkeley
The report by Frank and Sigwarth (1997a) of atmospheric holes with similar occurrence rates in both the Polar and DE-1 data is unexpected if the source is instrumental since the DE-1 and Polar experiments are quite different. The DE Imager (Frank et al., 1981) consisted of optics and filters, followed by a photomultiplier tube, pre-amplifier, one-shot-discriminator, and counter. The DE Imager's field-of-view (0.29o) scanned as the spacecraft spun, with a moveable mirror in the optics section changing the view by one pixel with each spin. Although the absence of the expected altitude dependence strongly argues that the DE observations of atmospheric holes must be artifacts (see Dessler 1991, and references therein), a clear instrumental source for the anomalous pixels (both dark and bright, in comparable numbers) has not as yet been identified.
The Polar VIS (Frank et al., 1995)
and UVI (Torr et al., 1995) imagers consist of optics and filters followed
by an image intensifier, which provides ~105 photon gain, and additional
optics to focus the photons onto a charge coupled device (CCD). These imagers
produce a 256 x 256 pixel image (200 x 228 for UVI) with a few tens of
seconds resolution. Unlike the DE data, which were overwhelmingly (>99%)
single-pixel events, both of the Polar imagers observe clusters of dark
pixels. The occurrence rate of large dark pixel clusters is higher than
expected for an ideal imager with no image blurring measuring a uniform
dayglow region of the Earth. Below we demonstrate that the high rate of
dark pixel clusters is inherent to both of the Polar instrument designs
and is caused by properties of the image intensifier and the optics that
focus the image onto the CCD.
Both the VIS and UVI imagers focus photons onto the front of an image intensifier. The image intensifier consists of a chevron microchannel plate (MCP) pair followed by a ~1.3 mm gap and a phosphor screen. The MCPs are biased with ~1.8 kV and act as an electron multiplier, producing ~5,000 electrons per photoelectron at the front of the MCP. These electrons are accelerated by a ~5 kV potential to the phosphor screen, where they generate ~20 photons per electron. Of the ~105 photons generated in the phosphor, only a small fraction (~600) are focused onto the CCD. The CCD has a ~16% efficiency, generating ~100 electrons. 100 electrons is the digitization threshold of the CCD readout discriminator, so a single photoelectron produced at the front of the MCPs produces about one digital count in these instruments.
The image intensifier introduces two main sources of variations in the image on the CCD. The first is the finite size of the electron cloud that strikes the phosphor screen, which in turn produces a finite sized light pulse onto the CCD, blurring the image. This blurring contributes to the pixel point spread function of the instrument (the size a point source appears on the image plane), and produces correlations in adjacent pixels. This blurring can be estimated from known properties of the intensifier and MCPs (Wiza, 1979). For a mean MCP secondary electron energy of ~1-2 eV, accelerating potential of 5 kV, and gap between MCPs and phosphor screen of ~1.3 mm, one obtains the "spreading width" of the electron cloud on the phosphor screen equal to 4(1eV/5000eV)1/2(1.3mm) ~ 0.07 mm. Owing to the finite MCP pore size (0.010 mm), spacing (0.012 mm), and the chevron configuration which nominally produces a 3 microchannel cascade at the MCP exit, the charge cloud is spread to ~0.08 mm. For a usable MCP width of ~18 mm (corresponding to 256 pixels), spreading produces a light pulse whose average width is about one CCD pixel width. This is consistent with the measured modulation transfer function of the image intensifier (Frank et al., 1995).
The second prominent source of image variation created by the image intensifier comes from the pulse height distribution from the MCPs. Although a chevron pair is used in the image intensifier, the MCPs are run in low- gain mode with a low bias voltage that does not saturate the microchannels. This is required to prevent large charge pulses (>105 electrons) from exiting the MCPs, which would lead to CCD saturation at nominal count rates. When run in low-gain mode, MCPs have an exponential pulse-height-distribution (Wiza, 1979). This exponential distribution of charge pulses gives an exponential distribution of light pulses at the CCD, which increases the random variation in pixel intensities across a uniformly illuminated image.
A third important source of image variation is penetrating radiation passing through the CCD, which produces large, localized counts in the image. The removal of these pixels using the algorithm prescribed by Frank and Sigwarth (see Mozer et al., 1998) introduces additional errors and smoothing. The effect of penetrating radiation can be significant, increasing the rate of dark pixel clusters by a factor of 2 to >20.
Five additional sources of image variations can be identified between the intensifier and CCD readout. First, a fraction of the photons emitted by the phosphor screen travel parallel to the surface and scatter, broadening the light pulse. Second, imperfections in the optics, between the phosphor screen and CCD, introduce blurring. Third, random variations are added to the image by statistical variations in the number of electrons produced in the CCD for identical MCP cascades and by noise in the CCD digitization, typically 20 +/-10 digital counts for VIS. Fourth, data compression before transmission to the ground introduces additional errors. Fifth, gain variations across the image intensifier produce image distortion. For the VIS imager, these additional sources of variations are believed to be relatively small and are neglected in the VIS simulation described below. The fifth source of error is discussed at the end of the paper.
The UVI imager uses fiber optics
to focus the photons onto the CCD. The individual fibers are about 0.7
CCD pixels wide, and a light pulse at the image intensifier will fall onto
~7 fibers. The combined effects of the finite MCP charge cloud and fiber
optics should cause the UVI spreading width to increase to ~1.5 pixels.
This is consistent with the measured pixel point spread function of UVI
(G. Parks, private communication).
In order to calculate the effect of the image intensifier on the images, we constructed a computer program to generate images and test them for dark pixel clusters. The program uses random-number generators to generate "x" and "y" coordinates on the image plane and light-pulse amplitudes for individual events, where an event is defined as an MCP cascade. Each event produces a finite, integer number of "electrons" deposited onto a 256 x 256 grid array. A variety of charge-pulse-spreading width shapes (delta function, cos2, triangle, box) and sizes (0 to 2 pixels, FWHM) can be selected. Charge-pulse amplitudes can either be fixed at 100 electrons (for testing) or randomly generated as an exponential whose average is 100. The number of events per image is typically chosen between 3x106 and 3x107, which are typical of the VIS and UVI images. Once the image is formed, the individual pixel counts are divided by 100 and converted to an integer digital count to reflect the CCD digitization and readout.
Images can be processed to determine variations in the pixel intensity across the image and to identify clusters of dark pixels. Figure 1a shows the distribution of pixel intensities for an image generated with a fixed 100 electron amplitude per event and a delta function spreading width. This simulation includes no effects of image blurring or MCP exponential pulse amplitude and should produce a distribution with Poisson statistics. (We use the term Poisson statistics to refer to images generated from equal-amplitude, randomly-located events with no correlation between pixels.) As expected, the pixel intensities are "normally" distributed (Gaussian) with a standard deviation equal to the square root of the mean. This simulation is used primarily as a test of the code.
To determine the number of dark pixel clusters in images, we choose the algorithm used by Frank and Sigwarth (1997a) to identify dark pixel clusters. For each pixel in the array, a 32 pixel set that forms the border of a 9x9 pixel array centered on the pixel is used to determine a local mean and local standard deviation. Each pixel is then assigned a "sigma" given by the variation of that pixel's digital count from the local mean, divided by the local standard deviation. An arbitrary cutoff (typically -2.0 in the Frank and Sigwarth papers) is used to define dark pixels, and clusters of dark pixels are then identified in the data. Any dark pixel that is adjacent to another dark pixel is part of the same cluster. The curves in Figure 1b show the distribution of dark pixel clusters for sigma cutoffs of -2.5, -2.0 and -1.5, averaged over 100 images generated with fixed amplitude and zero spreading width, as in Figure 1a. It is clear from this figure that dark pixel clusters appear even in a perfect instrument, although at a much lower rate than observed by the VIS and UVI imagers.
We now perform the simulation using the exponential distribution of pulse amplitudes and a triangle shaped spreading width with a 1 pixel FWHM, which approximates the VIS sensor. Figure 2a shows the distribution of pixel intensities for a single image. Comparing Figures 1a and 2a, one sees the VIS simulated distribution is slightly narrower (standard deviation = 7.7) than the distribution with Poisson statistics (standard deviation = 9.9). Figure 2b shows the distribution of dark pixel clusters averaged over 100 images for the same sigma cutoffs as Figure 1b. The properties of the image intensifier generates an enhanced tail of dark pixel clusters, even though the distribution of pixel intensities is narrower.
Frank and Sigwarth (1997a) argue that the distribution of pixel intensities across a VIS image is a normal distribution, implying Poisson statistics are applicable and that instrumental effects are not generating the dark pixel clusters. Figure 2a shows that the distribution of pixel intensities over a simulated image is a normal distribution, even though adjacent pixels are correlated due to the pixel sized spreading width in the image intensifier. As shown later in this paper, it is this correlation of adjacent pixels that creates the enhanced dark pixel clusters.
In order to determine if these instrumental dark pixel clusters can explain the observed VIS data, we analyzed 700 images on June 1, 1997, between 7:24 and 19:32 UT (5 noisy images thrown out at 10:51-10:56). These images were taken outside the radiation belts at altitudes >25000 km. Images had contamination by penetrating radiation (cosmic rays) removed using an algorithm provided by Frank and Sigwarth and described by Mozer et al. (1998). Dark pixels within the dayglow were identified and the distributions of dark pixel clusters were normalized by the number of dayglow pixels in the images. Figure 3 shows the distributions (solid curves) for sigma cutoffs of -2.5 (diamonds) and -2.0 (squares). The figure also shows the distribution of dark pixel clusters determined from 100 simulated images (dotted curves) for the VIS parameters used in Figure 2. The VIS dark pixel distributions are nearly the same as the simulated distributions. Since the slope of the semi-log curves is primarily a function of the spreading width of the light pulse on the CCD, a small increase from 1 pixel to about 1.1 pixels would bring the curves into nearly perfect agreement.
The dashed curves in Figure 3 are included to demonstrate that the Frank and Sigwarth algorithm for removing contamination by penetrating radiation increases the number of dark pixel clusters. These curves were formed by replacing about 6% of the pixels in simulated images with local means, as specified in the Frank and Sigwarth algorithm (for details see Mozer et al., 1998). The locations of replaced pixels were identical to those replaced in 100 of the VIS images (14:25 - 16:05 UT). As seen from the figure, a replacement of ~6% of the pixels creates a factor of ~2 enhancement in the tail of the dark cluster distribution. The algorithm actually replaces more pixels within the dayglow (~12%) than outside the dayglow (~4.5%) which enhances the VIS dark pixel cluster distribution within dayglow by a factor of ~4. Within the radiation belts, more than 65% of the pixels may be replaced and the number of dark pixel clusters can be enhanced by a factor >20.
As a further comparison with the simulation, we used 120 days (4-97 through 7-97) worth of "-2.0 sigma atmospheric holes" identified by Frank and Sigwarth in the Iowa catalog (see Mozer et al., 1998). These data were produced by the VIS principal investigator and were obtained from an Iowa web site on January 31, 1998. They are the only data in this paper to come from this web site and they are fully consistent with the distributions of Figure 3, which were obtained from one day of raw VIS data provided by Frank and Sigwarth. The atmospheric holes were binned into 5000 km altitude ranges and a distribution of dark pixel clusters for each altitude range is plotted as colored curves in Figure 4. Atmospheric holes in the catalog are only identified when they appear in the dayglow, so proper scaling of these curves requires knowledge of the number of dayglow pixels in each image. Since these data are not provided in the catalog, a factor of x5 scaling was used to make the catalog data consistent with the 700 VIS images plotted in Figure 3. Curves between 15,000 km and 25,000 km are enhanced because Polar was in the radiation belts and the penetrating particle contamination increases the dark pixel cluster rates as discussed above. Note that the dark pixel cluster (or atmospheric hole) event rates are nearly independent of altitude for the other curves, with a small increase at lower altitudes, as one would expect, since the fractional dayglow should increase with decreasing altitude. However, as pointed out by Mozer et al. (1998), if atmospheric holes were produced by occulting objects at low altitudes then these curves should be a strong function of altitude since the number of dark pixels in a cluster should be inversely proportional to the altitude squared. The black curve shows the simulation results for a -2.0 sigma cutoff, which agrees quite well with the VIS dark pixel cluster event rates.
A second simulation was performed to compare with the dark pixel cluster rate determined for the UVI imager. The pixel point spread function of the UVI imager is ~1.5 pixels FWHM (Parks, private communication), and a triangle shaped spreading width with 1.5 pixel FWHM was used. In order to compare the simulation with Parks et al. (1997), we incorporated the Parks algorithm for identifying dark pixel clusters. This algorithm uses a 21 x 21 pixel array centered on each pixel to determine the local mean and local standard deviation. 100 images were generated and the average distribution of dark pixel clusters were determined for sigma cutoffs of -1.5 and -2.0. Figure 5 is a comparison of the simulation (dashed curves) and the UVI measured dark pixel cluster distribution (solid curve) from Parks et al., 1997. The UVI data were scaled up by x4 to bring the y-axis intercepts into agreement. Scaling is required due to the smaller UVI pixel map, incomplete dayglow in the images, and nonuniformities in the UVI images, as seen in Figure 1 of Parks et al. (1997). Simulations have shown that strong gradients in image intensifier gain can reduce the dark pixel rates. The figure shows that the simulation can reproduce the dark pixel cluster distribution observed by UVI.
It is interesting to note that the total rate of dark pixel clusters is a strong function of both the number of pixels and the minimum standard deviation used to identify a dark pixel. A change from -2.0 to -2.5 standard deviations for the definition of a dark pixel causes a factor of ~10 change in occurrence rate of 5 pixel clusters (Figure 2b). Similarly, changing the minimum number of pixels from 5 to 6 in the definition of an "atmospheric hole" will also change the occurrence rate by a factor of ~3. Since these two parameters are arbitrarily changed in various papers by Frank and Sigwarth (1997a, 1997b), similarities in the occurrence rates between the DE-1 imager and Polar are not significant.
It is instructive to separately examine the effects of the finite spreading width and exponential distribution of light-pulse amplitudes. Images created with exponential light-pulse amplitudes and delta-function spreading width show a broader distribution (standard deviation=13.7) of pixel intensities than the distribution with Poisson statistics (standard deviation=9.9) in Figure 1a. However, the distribution of dark pixel clusters for both sets of images is about the same. The exponential light-pulse amplitude distribution creates more variations across the image, but the Frank and Sigwarth algorithm identifies about the same number of dark pixel clusters because the local standard deviations also increase.
If a fixed pulse amplitude (100 electron) and a triangular shaped spreading width (1 pixel FWHM) are used, one obtains a much narrower distribution (standard deviation=5.5) of pixel intensities than the distribution in Figure 1a. The spreading width reduces variations across the image, effectively smoothing the image. However, the number of dark pixel clusters is much larger than in Figure 1b, and is nearly identical to the VIS simulated cluster distribution in Figure 2b. Thus, the MCP exponential charge-pulse amplitudes have little effect on dark pixel cluster distributions. The spreading width is the dominant term that contributes to the enhanced dark pixel clusters, producing local correlations and smoothing of the image that results in the enhanced dark pixel clusters identified by the Frank and Sigwarth algorithm.
Recently, L. Paxton (APL, private
communication) has shown that dark pixel clusters in the Iowa catalog are
not uniformly distributed but are concentrated in particular regions of
the CCD pixel plane. We observed similar concentrations of dark pixels
for the June 1, 1997 raw data. This implies that the VIS image intensifier
does not have uniform gain and further suggests that the source of dark
pixel clusters is instrumental. We simulated 2% and 5% variations in image
intensifier gain over sinusoidal periods of 10 and 40 pixels and found
that the dark pixel clusters are strongly grouped in local gain minima,
as expected. However, the distribution of dark pixel clusters remained
essentially unchanged from Figure 2b, indicating small non-uniformities
in the image intensifier gain do not affect the comparisons in Figures
3, 4, and 5.
The VIS and UVI imagers on the
Polar spacecraft both produce enhanced distributions of dark pixel clusters.
Frank and Sigwarth (1997a, 1997b) interpret these as evidence for small-comet
bombardment of the upper atmosphere. A computer simulation of the response
of the VIS and UVI imagers shows that the enhanced rate of dark pixel clusters
can be explained as instrumental. The primary instrumental source is the
image intensifier, which creates finite sized light pulses on the CCD image
plane that effectively smooths the image and produces local correlations
between adjacent pixels. In addition, the agreement between the DE-1 and
Polar atmospheric hole rates is shown to be artificial and results from
arbitrarily chosen constants in the Frank and Sigwarth algorithms. The
instrumental effects fully explain the distributions of dark pixel clusters
in both instruments without the need for invoking geophysical phenomena.
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Frank, L. A. and J. B. Sigwarth, Simultaneous observations of transient decreases of Earth's far-ultraviolet dayglow with two cameras, Geophys. Res. Lett., 24, 2427, 1997b.
Mozer, F. S., J. P. McFadden, I. Sircar, J. Vernetti, Small comet "atmospheric holes" are instrument noise, Geophys. Res. Lett., in press, 1998
Parks, G, M. Brittnacher, L. J. Chen, R. Elsen, M. McCarthy, G. Germany, and J. Spann, Does the UVI on Polar detect cosmic snowballs?, Geophys. Res. Lett., 24, 3109, 1997.
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Figure 1. 1a shows the distribution of pixel intensities for a simulated image with Poisson statistics. 1b shows the distribution of dark pixel clusters for 100 simulated images with Poisson statistics using the Frank and Sigwarth algorithm to identify dark pixels.
Figure 2. 2a shows the distribution of pixel intensities for a simulated VIS image. 2b shows the distribution of dark pixel clusters for 100 simulated VIS images using the Frank and Sigwarth algorithm to identify dark pixels. Although the distribution in 2a is narrower than 1a, 2b has a much larger dark pixel cluster rate than 1b.
Figure 3. The solid curves are the dark pixel cluster distribution for 700 VIS images on June 1, 1997, at altitudes >25000 km, for sigma cutoffs of -2.0 (squares) and -2.5 (diamonds). The dotted curves are the dark pixel cluster distribution determined from a simulation of the VIS image intensifier using a triangular spreading width of 1 pixel FWHM. The dashed curves use the same simulation as the dotted curves but include a simulated penetrating radiation removal algorithm that mimics the Frank and Sigwarth algorithm applied to the raw VIS images.
Figure 4. The colored curves show the dark pixel cluster distribution for various altitudes determined from 120 days of "atmospheric holes" in the Iowa catalog (see Mozer et al., 1998). The black curve shows that the simulated dark pixel cluster distribution agrees relatively well even without precise corrections for average dayglow per image. The curves between 15000 and 25000 km have enhanced dark pixel clusters because the spacecraft is within the radiation belts.
Figure
5. The solid curves are the dark pixel cluster distribution given in
Figure 2 of Parks et al. (1997) for sigma of -2.0 (squares) and -1.5 (triangles).
The dashed curves are the simulated dark pixel cluster distributions for
a triangular spreading width of 1.5 FWHM. The Parks data were scaled up
by x4 to bring the y-intercepts into agreement and the simulations used
the Parks algorithm to define dark pixel clusters. The figure shows that
the simulation accurately reproduces the observed dark pixel cluster distribution.
J. P. McFadden, F. S. Mozer, J. Vernetti, I. Sircar, Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450. (e-mail: mcfadden@ssl.berkeley.edu)
(Received April 17, 1998; revised July 16, 1998; accepted July 27, 1998)
