Appendix 7. Combined Calibration Scan Images

2. Calibration Scan Image Combination

The 2MASS Combined Calibration Scan Images were assembled from the individual calibration scan images according to the following procedure. Descriptions of each step are given below.

  1. Images from each calibration scan were mapped onto a common spatial grid for each field during pipeline processing.
  2. The registered images were corrected for position offsets.
  3. All registered, corrected images were normalized onto a common photometric scale for each calibration field.
  4. Preliminary combined images and depth-of-coverage maps for each field were constructed by averaging the normalized J, H and Ks images for all north-going and south-going scans separately.
  5. Residual images for each scan were formed by subtracting the corresponding first-pass combined image for the same scan direction.
  6. Scans with image anomalies and high noise levels were identified by examining statistics of the residual images.
  7. Final combined north- and south-going images were constructed for each field by forming the weighted-average of the remaining images, where each scan was weighted by the inverse variance of the sensitivity-adjusted noise computed from the first-pass residual images.
  8. North+south-going combined images were constructed for each field, as well as versions of all images that have pixels covered by less that 30% of the available scans masked off.

In all, 21 FITS format images were produced for each calibration field that can be accessed via the on-line ftp-interface at A7.4. In each of the J, H and Ks 2MASS bands, the images are:

a. Image Registration

To prepare for their eventual combination, a special set of spatially-registered calibration scan images were produced during final 2MASS pipeline data reduction. Unlike the standard calibration Atlas Images, generated for each scan, the special images consisted of single 540´´ × 3600´´ images in each band that were mapped onto a common, predefined pixel grid for each calibration field. [Mention pixel scale - 1"/pix same for all three bands] Aside from their size and the spatial registration, the special image were constructed using the same flux preserving interpolation kernel and pixel rejection that were used for the normal Atlas Images (see IV.3.ii).

During production of the special calibration scan images, two minor problems were introduced that were corrected during later stages of the combination process:

b. Position Correction

Individual calibration scan images contain position offsets relative to the main 2MASS survey because position reconstruction for the calibration data was done using the USNOA-2.0 catalog rather than the Tycho 2 catalog, and because of the cross-scan position offset introduced when remapping the special images. These offsets were corrected simultaneously by first projecting 2MASS PSC source positions into the predefined grid coordinates for each calibration field, computing the positional offsets between the PSC sources and calibration scan extractions made during pipeline processing (IV.3), and computing the average offset in each axis for each scan. These mean offsets were then applied to each special image during the image combination step.

This procedure was intended to remove mean position offsets between calibration scans and the main survey. It did not remove any right ascension or declination offset structure within a given field caused by the USNOA2.0 and Tycho 2 reference catalog differences. Examples of this residual structure can be seen in the plots of position differences between combined calibration scan extracted sources and the 2MASS PSC shown in A7.5. The largest systematic residual differences are seen in the combined calibration scan positions of the 90004 field - the field that has the largest "raw" offsets between calibration and survey scan positions due to the USNOA-2.0 position reconstruction. The large raw offsets caused a significant fraction of the valid matches between the 2MASS PSC and individual calibration scan extractions to be missed, thus biasing the estimate of the correction.

c. Sensitivity Scaling

The intensity of a source registered on images taken at different times at the two 2MASS facilities was not necessarily the same because of differences in the system throughputs and detector quantum efficiencies, and nightly variations in atmospheric transparency. Thus, a star of fixed brightness could produce a different number of integrated digital counts (DN) in the same exposure time, depending on when and where it was observed. For extracted source photometry, these differences were compensated for by the photometric calibration process. When combining images, the pixel intensity values must be scaled to take the system throughput and atmospheric variations into account.

Average differences in detector quantum efficiency and optical system throughput between the two observatory cameras are captured in the instrumental zeropoints, ZPinst. The relative differences in atmospheric transparency are measured explicitly for each calibration scan by the photometric zero point offset, ZPphot (see IV.8). These two factors are used to derive the correction factors that bring images from many different calibration scans to a common intensity scale.

i. Image Correction Scale Factors

Let S(b,h,t) be the multiplicative factor that will adjust the pixel intensities in a calibration scan image in band, b, taken from facility, h (north/south) at time t to a common relative scale. S(b,h,t) can be expressed in terms of a correction factor in units of magnitudes, Kcorr(b,h,t):

S(b,h,t) = 10-Kcorr(b,h,t)/2.5

Kcorr is a linear combination of the "instantaneous" photometric zeropoint offset for the calibration scan, ZPphot, and difference between the instrumental zeropoint appropriate for that scan and some fiducial value, dZPinst:

Kcorr(b,h,t) = ZPphot(b,h,t) + dZPinst(b,h,t)

Because the instrumental zeropoints were defined, such that the photometric zeropoints would have a mean value of ~0 mag over the life of the Survey, the measured value of ZPphot(b,h,t) for any calibration scan gives the relative differential atmospheric throughput. If the "instantaneous" photometric zeropoint offset for a scan is used (the columns [jhk]_zp_ap in the Calibration Scan Information Table), no airmass-dependent extinction term need be applied because these values are derived directly from the mean differences between the true and instrumental magnitudes of the standard stars in each scan and not the nightly extinction-corrected zeropoint offset fits.

We define the fiducial instrumental sensitivities to be those of the northern camera at the start of the survey. Therefore, the relative differences in instrumental zeropoints are given by:

dZPinst(b,h,t) = ZPinst(b,h,t) - ZPinst(b,n,<8/3/99)

where ZPinst(b,n,<8/3/99) is the instrumental zero point in band b for the northern 2MASS camera for survey dates before 1999 Aug 3 UT (survey day 886), when the northern H-band array was replaced.

The instrumental zeropoint values for each band in each camera are given in IV.8a, Table 1. Using those values, dZPinst for each band in each camera is:

Table 1 - Instrumental Zero Point Magnitude Differences
Band North
(before 8/3/1999)
(after 8/3/1999)

Thus, the values of Kcorr(b,h,t) in terms of the instantaneous photometric zero point offsets for each scan are:

Table 2 - Atlas Image Sensitivity Correction Factors in Magnitudes
Band North
(before 8/3/1999)
(after 8/3/1999)

Histograms of the correction factors, Kcorr in each scan for each scan at each observatory are shown in Figure 1. Note that the effective sensitivity varies by up to 30-40% among data for a given band.

Because the sensitivity of all images were normalized to the same photometric scale, the photometric zero points of all J, all H and all Ks images are all the same, and are equal to the mean Read_2 instrumental zero point magnitudes of the northern 2MASS system before 1999 August 3 UT given in Table 1 of IV.8.a. These values, carried in the MAGZP keyword of the combined image headers are: MAGZP(J) = 20.93, MAGZP(H) = 20.67, and MAGZP(Ks) = 20.03.

Figure 1 - Histograms of the sensitivity scaling factors applied to each calibration scan image.

d. Image Combination and Residual Images

The registered, position-corrected and sensitivity normalized images for each calibration field were combined by forming the weighted average of the pixel intensities. 2MASS calibration observations consisted of six independent scans of a calibration field made in alternating north and south directions, with a 5" easterly RA displacement between scans. For each field, the north-going and south-going scans were first combined separately to facilitate identification of image artifacts such as latent images. To provide the deepest possible images, simple averages of the north- and south-going combined images were also produced.

i. Preliminary combination

Image combination was conducted in two steps. In the first step, all available north- and south-going position-corrected, normalized images for each field were averaged together using equal weighting for pixels all scans. The first-pass combined images were used to construct residual images for each scan that were the differences between the individual corrected, scaled images and the first-pass combined image of the appropriate direction. The residual images were used to identify and reject scans that contained artifacts and/or exhibited abnormally high noise levels, and to determine scan weighting values, as described below.

ii. Final combination

The second-pass/final calibration scan images were constructed by forming the weighted-average of the position-corrected, normalized images for each field that did not contain artifacts or high noise levels. Pixel intensities were weighted in the second-pass combination by the inverse variance of the noise level measured in the corresponding residual image. All pixels in a given image were weighted by the same factor.

e. Image Anomaly Identification

Because a small percentage of the calibration scan images contain high signal-to-noise ratio (SNR) artifacts that could persist into the combined images, an automated procedure was developed to identify anomalies so that the "offending" scans could be "quarantined" and excluded from the final combinations (see II.4b for a general discussion of 2MASS image anomalies).

Anomaly identification was based on examination of the noise levels measured in the residual images for each scan. Residual image noise was estimated by histograming the non-blank pixels, and computing the noise as one-half the distance between the 15.87% and the 84.13% quantiles of the histogram. Figures 2-7 show examples of the noise statistics measured from the residual images of the 90272 calibration field. Each pair of plots show the residual image noise plotted as a function of the background level for the scan, and a histogram of the residual noise levels of all scans. Noise values are plotted in units of digital numbers (DN) and are not corrected for zero point scaling, which results in multi-modality vs. background. The residual noise is well behaved as a function of background for all but a few percent of the scans in which the residuals are anomalously high.

Figure 2 - Noise in the J-band residual images of all scans of the 90272 calibration field plotted as a function of the mean image background level. Figure 3 - Histogram of noise values in the J-band residual images of all scans of the 90272 calibration field.
Figure 4 - Same as Figure 2 but for H band. Figure 5 - Same as Figure 3 but for H band.
Figure 6 - Same as Figure 2 but for Ks band. Figure 7 - Same as Figure 3 but for Ks band.

Outliers in the residual image noise vs. background plots are caused by the presence of bright structure in the residual images that result from anything that causes individual images to differ from the long-term average. These can include artifacts such as meteor trails, geosynchronous satellite streaks, insects (on the camera windows!), as well as transient structure in the image backgrounds due to severe atmospheric OH airglow emission or uncorrected image frame biases (see Figures 8-14). An artifact of SNR=sqrt(nscans) in an individual scan will result in a SNR=1 residual when nscans images are combined. A filtering routine was developed that examined the residual images for connected pixels over a SNR=50 threshold. Scans with identified anomalies covering more than 40 pixels were "quarantined" and excluded from the final image combination.

The initial version of the filtering process also quarantined an excessive number of scans with poor seeing, due to the "halos" left around brighter stars in the residual images (see Figure 14). This problem was reduced to an acceptable level by subtracting the initial image combinations once again from the residual images, which removed most of the bright star residual signature for scans with poorer seeing, but left other transient artifacts for identification. This effectively eliminated the problem for all but the highest source-density fields, such as 90547. In that field, on the order of 10% of the scans with the poorest seeing were removed. However, this additional loss in the final combination is not significant because the sensitivity in high density fields is severely limited by confusion noise. For most fields, less than 1% of the scans were removed because of poor seeing.

In addition to scans with identified artifacts and poor seeing, 5% of the scans with the highest noise levels were excluded from each field during final combination. This was done to remove extraordinarily noisy scans with severe background or electronics noise problems. Since these scans usually have spatially non-uniform noise, as illustrated in Figure 8, they are not easily dealt with by noise weighting and would not contribute useful data in most cases.

Examples of assorted anomalies identified in the residual scan images are shown in Figures 8-14.

Figure 8 - Comparison of two J-band residual images of the same calibration field. (left) Scan with uncorrected electronic bias structure. (right) Normal scan. Noise levels (in DN) are marked on images. Figure 9 - (left to right). First-pass combined north-going J-band image of 90009 calibration field showing a residual meteor trail; image of offending scan containing meteor trail; residual image of scan containing meteor trail; residual image of scan with large position reconstruction error.

3-color ((J+H+Ks) residual images of scans with identified artifacts
Figure 10 - Lady bug walking on the camera window. Figure 11 - Bright, unremoved meteor streak. Figure 12 - Geosynchronous satellite trail. Figure 13 - High noise scan with severe OH airglow emission. Figure 14 - Bright star residuals in scan with poor seeing.

f. Depth-of-Coverage

Because of the 5´´ RA stepping during calibration observations, and because of small telescope pointing errors, all calibration scans did not cover precisely the same region on the sky. As a result, the depth-of-coverage in the combined calibration images varies particularly towards the the east and west edges of the images.

Depth-of-coverage maps are provided for all of the J, H and Ks north-going and south-going combined images for each field. These maps are in FITS image format where the pixel values give an integer count of the number of image frames that contributed to the combined image. The frame count gives a more precise pixel coverage value than the number of scans pixels from one or more frames within a scan may have been blanked due to cosmic rays, meteor trails, bad pixels or other transients. Divide the number coverage maps pixel values by six to obtain the approximate number of scans contributing to each pixel. Depth-of-coverage maps were constructed from the preliminary combined images, not the final combinations. Consequently, the relative pixel counts will be correct, but the absolute values may slightly overestimate the total frame count.

In general, the loss of coverage due to scan cross-stepping and telescope pointing differences results in about 10-15% of the possible area of the calibration fields. Figures 15 and 16 show the cumulative coverage histograms for the north- and south-going combined images of the 90272 calibration field, respectively. The roll-off in coverage near the field edges can be seen in the 90272 field north-going coverage map shown in false color in Figure 17. The color mapping is linear in that image, ranging from one frame to a maximum of 6280. Approximately 900 scans were combined for this image, so most of the image has a depth of 6x900=5400 frames (shown in light red). The horizontal stripes with deeper coverage correspond to regions where there can sometimes be seven overlapping frames in a scan because the scan step size was slightly less than 1/6 of the focal plan width.

The background noise levels in the combined images scale approximately as the inverse square-root of the number of input frames. Consequently, the relative noise rises significantly at the east and west image edges. Because non-uniform background noise levels often cause difficulty with noise-threshold source detection algorithms, versions of the north- and south-going and north+south combined images are provided that have pixels covered by less than 30% of the available frames masked off.

Figure 15 - Cumulative area coverage distribution for the combined north-going images of the 90272 calibration field. J-band coverages is shown in blue, H-band in green and Ks band in red. Figure 16 - Same as Figure 15 but for the south-going scans of the 90272 calibration field. Figure 17 - False-color image showing part of the depth-of-coverage map for the north-going combined image of the 90272 calibration field. The color map is linear with a range shown in the annotated color wedge.

[Last Updated: 2006 October 9; by E. Kopan and R. Cutri]

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