IV. 2MASS Data Processing
3. Atlas Image Generation
The reduced "Read 2-Read 1" frames for each 6°-long scan were spatially registered and combined into a series of 8.53´×17.07´ (512×1024 pixel, 1´´ per pixel) Atlas Images. The Atlas Images represent the coaddition of all six overlapping frames as described below. The images were centered on the cross-scan coverage, and adjacent images within a scan overlap in declination by 54´´. The J, H, and Ks band images were produced separately, but were registered onto a common astrometric grid to facilitate three-color investigations. Atlas Images are written in FITS format, and contain both the astrometric solution for the image in the J2000 coordinate system and the nightly calibrated photometric zeropoints within the FITS header (keyword "MAGZP").
The Atlas Images were produced by first spatially registering the dark-subtracted, flattened, and sky-offset subtracted Read_2-Read_1 frames relative to each other, using the estimated positions of point sources in the frames (cf. IV.6). These frames were placed on the output Atlas Image coordinate grid one at a time, using a flux preserving interpolation kernel (see below). An example of a portion of a single frame along with the corresponding section of the combined Atlas Image is shown in Figure 1. Camera pixels which had poor responsivities, were excessively noisy, or were affected by transient effects, such as meteor trails, satellite tracks, or cosmic rays (as identified by unconfirmed single frame detections), were masked off in the frames prior to the interpolation procedure. The background level of each frame was adjusted to match that of those frames already combined into the image by computing the differences at each point in the sky in the overlap region between the incoming frame and the previously-combined frames, and removing the median of differences from the incoming frame. This process produces seamless images, except in cases where the background levels vary rapidly with time due to clouds, atmospheric OH emission, or severe optical effects from extremely bright objects (such as Pegasi). The final output Atlas Image represents for most pixels the average of six such interpolated, background-adjusted frames. Because some pixels were masked, and there is some margin in the frame overlap, any one pixel in the Atlas Image may represent the average of anywhere from zero to seven frames. Output pixels consisting of zero frames are set to floating point NaN (not a number) value in the Atlas Images. This includes pixels along the image edges. Zero coverage pixels in the compressed Quicklook Images were set to an integer value of zero. Coverage maps were also produced for each image.
Each scan was processed in this way in a continuous 6 degree strip, the output images were written in 512×1024 pixel format with 54 pixel overlap as a convenience. Since the background adjustment made to produce seamless images can cause the absolute background level to diverge from that in the single frames, the background in each image was offset by a constant so that the background reported will reflect the total photon flux to facilitate Poisson noise calculations with standard photometry packages. With the exception of this additive constant, the images are identical in the in-scan overlapped portions. The cross-scan overlap in the images comes from coverage overlap in separate scans, and is therefore not identical.
Certain additional operations were performed on the instrumentally corrected frames prior to interpolation:
Pixels affected by transient effects from meteor trails, satellite tracks, and cosmic rays were identified using unconfirmed single frame detections (solos) and masked off prior to interpolation and image estimation. For each unconfirmed single frame detection brighter than magnitude 15.0, 14.5, or 14.0 in J, H, or Ks respectively, an area 5 arcseconds in radius was masked off in the offending frame. In addition, linear patterns were identified in the solo detections and blanked from one edge of the frame to the other. Because meteor trails usually resulted in an intermittent line of detections, this was an effective way to remove them. Candidate streaks were identified when a line had:
over a minimum length of 20 arcsec. The candidate with the highest count was identified as a streak, and the process continued with the remaining solos until no more streaks could be identified meeting the criteria in that frame.
For each identified streak, a line was blanked completely across the frame with a width computed as follows:
width = 6*(count/8)(in pixels)
which results in a minimum blanking width of 6 camera pixels (12 arcsec). Because slow moving meteors and satellites sometimes appear in 3 or more frames, streaks identified in more than 2 frames were only blanked across their identified length. This may have resulted in incomplete blanking in some cases, but avoided excessive reduction in coverage near slow moving transient objects.
Many hot pixels identified as anomalous and were masked off during the frame flattening procedures. Remaining intermittent hot pixels and cosmic rays producing solos were masked in the above procedure. A few hot pixels survived these filters and produced false sources (see I.6b).
A bias reset decay artifact was identified in the Northern camera J and H band electronics that introduced a background bias which decayed across the lines in each detector quadrant and varied from frame to frame. This bias was removed using the lower quartiles for each line in each frame, and comparing them spatially. A robust offset and slope across the quadrants were computed for each frame to minimize the residuals between the frames in their spatially registered quartiles. This computed bias was removed from the frames and then the frame background was adjusted to match that of those frames already combined into the image by computing the differences at each point in the sky in the overlap region between the incoming frame and the previously-combined frames, and removing the median of differences from the incoming frame. This process did not disturb true sky structure that was constant between frames, but successfully removed most of the bias reset electrical artifact. Some residual of this problem may sometimes be decerned in the images due to the simplicity of the model.
The ideal image coaddition represents the best possible estimate of flux on the sky. Based on well-understood principles from density estimation (e.g., Density Estimation, B.W. Silverman 1986), we smooth our square pixels to remove bias, but not so much that we introduce a large variance from the original images. The optimal smoothing balances these two sources of error.
To derive a smoothing formula, we make the minimum knowledge assumption that a photon hits any point on the pixel with equal probability. We convolve our pixels with a Gaussian smoothing formula and adjust the smoothing length h to give optimal results.
Let be the smoothing
kernel. This smoothing kernel is then integrated over the camera pixel to
yield an estimate of the flux at points (x,y) for a particular pixel:
where (xj,yj) is the center of the jth pixel with linear scale L=2´´. For convenience, we choose a Gaussian for the smoothing kernel K, which immediately yields:
The coadded flux estimate for npix pixels with value m is:
Given an Atlas Image pixel of side length l and center at (x,y), the contribution from the frame pixel j follows by integrating Eq. III.3.b.2:
The mean integrated squared error,
where is the estimate and f is the true flux density, is a standard measure for selecting the optimal smoothing length. Of course, we do not know the true f, but by taking the expectation of MISE, we can evaluate the first two terms from the data. Based on point sources, the optimal value for h=0.1. An empirical selection based on the pipeline performance on extended sources suggests h=0.35. Because the run of MISE for point sources slowly increases for values larger than the optimal, h=0.35 is still nearly optimal for point sources, and this value is adopted (see Figure 2).
A ~20:1 lossy-compressed version the Atlas Images has also been generated using the hcompress algorithm to facilitate fast retrieval, finding charts and visual inspection of the near-infrared sky. These are known as the 2MASS "Quicklook" Images. The low order bits are lost in this compression scheme, so these images should not be used to make quantitative brightness measurements. However, all position information is retained in the "Quicklook" Images.
|Figure 2: Gaussian kernel with h=0.35 convolved over pixel
with active linear size|
L=1.0. The mesh diagram shows the contribution of the flux in the pixel centered
about the origin at arbitrary point (x,y).
[Last updated: 2006 October 10, by R. Cutri, E. Kopan and M. Weinberg.]
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