2MASS Seeing and Image Shape Statistics for the First 6 Months of Mt. Hopkins Operations

Introduction

Some of the other factors that will impact the 2MASS sensitivity and accuracy include sky and telescope background levels (see  Gizis 1997 2MASS Background Levels Over Time) , atmospheric transmission and telescope and camera stability, etc. 2MASS Quality Assurance will assign quality levels to each survey scan by comparing statistical measures of these factors to empirically determined thresholds relating these factors to achieved point and extended source sensitivity and reliability.   Scan data not meeting minimum thresholds will be assigned low or failed quality levels that will result in reobservation.

As part of the effort to understand the affect of atmospheric seeing (and other factors that degrade image quality) on survey performance, I have compiled image size and shape statistics for all processed 2MASS scans acquired between the dates of 21 May and 19 December 1997.  Data from 125 days and a total of 7470 scans are included in this analysis. The majority of scans processed to date are calibration data, but at least 10% are survey scans. Image size and shape are standard quality assurance output diagnostics from the 2MAPPS system for all scan data.
 

Results

• Image size is characterized by the seeing shape parameter derived by the SEEMAN subsystem. The shape is the product, alpha*beta, where alpha and beta are the parameters of a modified exponential fit to a large number of stars in each scan. See the SEEMAN Subsystem Design Specification document for more detail.  The  Quality  Assurance output for each scan processed by 2MAPPS reports the average seeing shape and its dispersion.
• The measured image full-width at half maximum intensity (FWHM) is related to the seeing shape (sh) via the approximate relation:
FWHM(arcseconds) = 3.13*sh - 0.46

This relationship was measured from PROPHOT point-spread function (psf) images derived from scan data. Figure 1 shows the measured FWHM as a function of seeing shape for a series of actual J (blue), H (green) and K_s (red) psf's used in the 2MAPPS system. Note that the relationship is independent of wavelength, as should be the case. The minimum practical limit for seeing shape is ~0.90-0.95 (FWHM=2.4"-2.5") because of the raw camera pixel size.

Figure 1 - Measured PROPHOT psf FWHM(") as a function of average seeing shape.

 

• Figure 2 shows the average seeing shape measured for all processed scans as a function of running survey day number (Day 1 = 970301, Day 82 = 970521). In this figure, and all following, J data are encoded in blue, H data in green and K_s data in red.  The large gaps in the middle of the plots correspond to the poor weather encountered in July and the August shutdown for the summer monsoons.  Note that seeing shape data were not available for some processed scan data from mid-July.

Figure 2 - Average J, H and Ks seeing shapes for all processed scans plotted versus running survey day number.

 

• The accuracy with which SEEMAN can estimate seeing during a scan is limited by the degree to which seeing varies during the scan. For moderately high star density regions, SEEMAN will attempt to characterize image size in each coadd image (approximately every 12 frames, or so). However, in CAL scans, the seeing is estimated only once for the scan. In Figure 3 is shown the relationship between measured average seeing shape and the shape uncertainty for all scans. Larger seeing shapes tend toward higher measurement errors, indicating that when the seeing is poor, it is also highly variable. However, there are also large dispersions for relatively small shapes, suggesting that rapid seeing variations can and do occur for any absolute seeing.

Figure 3 - Seeing shape measurement uncertainty plotted as a function of seeing shape, for J, H and K_s

 

• Figure 4 shows histograms of the J, H and K_s seeing shape distributions over the first six months of Mt. Hopkins observations. Note the steep drop-off in shape below 1.0 caused by the pixel limitation of the survey cameras. The fairly rapid decline in the distribution for shapes larger than 1.1  shows that the seeing at the Mt. Hopkins sight is generally very good (at least within our ability to measure it).

Figure 4 - Histograms of seeing shape distributions.

 

• Cumulative seeing shape distributions are shown in Figure 5. The horizontal line in the cumulative distribution marks the 50% point, indicating the median measured seeing shapes for Mt. Hopkins. The modal, median and 90th percentile shape values for the J, H and K_s shape distributions are given in the table below.

 

	J	J	H	H	Ks	Ks
	shape	FWHM(")	shape	FWHM(")	shape	FWHM(")
Mode	1.03	2.8	1.02	2.7	1.04	2.8
Median	1.07	2.9	1.05	2.8	1.06	2.9
90%	1.23	3.4	1.19	3.3	1.20	3.3

 

Figure 5 - Cumulative distributions of measured seeing shapes.


• When the northern 2MASS telescope is run out of focus, the resulting images become elongated due to slight astigmatism. (See http://spider.ipac.caltech.edu/staff/roc/2mass/2d/smear.html for a description of this behavior.) Because the seeing shape is an azimuthally averaged quantity, asymmetric star images can result in a artificially elevated seeing shapes.

The average image symmetry is characterized during processing of each 2MASS calibration and survey scan by measuring the ratio of the cross-scan to in-scan second image moments of composite star images. These composite images are generated by combining individual star images from an entire scan. Values of the second image moment ratio (R2) larger then 1.0 indicate images elongated in the cross-scan (RA) direction, and values less than 1.0 indicate elongation in the in-scan (DEC) direction. Figure 6 shows a time history of R2 measured for all scans as a function of running survey date. Severe elongation occurred in June 1997 because the initial calibration of the auto-focus parameters were made in April and May when temperatures were significantly lower than in June. Better calibration was carried out at the beginning of July and since that time the telescope auto-focus performance has been excellent.

Figure 6 - Measured average image second moment ratios for all processed scans plotted versus running survey day number.

 

• A histogram of logarithm of the second image moment ratios measured for all scans is shown in Figure 7. Note the asymmetry towards smaller values corresponds to preferential image elongation in the in-scan direction, as was prevalent in June. Note also in Figure 7 that the modal values in J, H and K_s are offset slightly. This is a result of the fact that the three channels in the northern camera are not parfocal. A compromise best telescope focus value is generally used. The J and H best-focus positions are similar, and K_s is off slightly.

Figure 7 - Histograms of log second moment ratios for all scans.

 

• Figure 8 shows the relationship between measured seeing shape and the image moment ratios for each band. Note that when the atmospheric seeing is poor, point source images will smear out, effectively smoothing out any image asymmetry.  Therefore, the prominent diagonal trends in the point loci indicate how image asymmetry affects the seeing shape measurements. An offset in moment ratio of +/-0.2 from unity will produce an increase of approximately 0.05 in the shape measurement (~0.2" in FWHM). The effect becomes increasingly non-linear with larger asymmetries.

Figure 8 - Relationship between average second moment ratio (R2) and average seeing shape for all scans.

 

• The cumulative distributions of the logarithm of |image moment ratio|  measured over the first six months of operation are shown in Figure 9.  This quantity shows in a convenient manner the relative +/- offset from a symmetric image (R2=1.0). Currently, moment ratios varying by +/-0.1 from unity are flagged in the Telescope and Instrument health monitoring report. These are ad hoc numbers selected very early on, and are clearly overly conservative. Image moment ratios between 0.9 and 1.1 have been measured for only 55-60% of the scans obtained so far, and are in fact difficult to achieve because of the compromise between best J and K_s focus settings. Quantitative limits will be established by relating point and extended source photometric accuracy and sensitivity to seeing and asymmetry.

Figure 9 - Cumulative second image moment ratio distribution for first six months of operation.