I have made a simple simulation of how the 2MASS photometry depends on the size of dead zone between pixels. The number of photo-electrons generated is taken to be the integral of the point spread function (taken to be a Gaussian of full-width at half maximum of FWHM) times the pixel response of the various pixels on which the light impinges. The response of a square pixel of dimension w (unit cell pitch) is taken to be:
where a is the dimension of the dead zone around each pixel. Laboratory measurements suggest that . In addition, there is a dead area at the center of each pixel, a dimple of radius . For computational convenience we describe the dimple as a square dead area of equivalent area to the circular dimple.
The recorded signal will vary according to how the optical image (the Point Spread Function or PSF) is centered relative to the live and dead areas of the pixels. The variation of this alignment for the NSAMP=6 measurements going into a 2MASS observation of a source results in an irreducible photometric variation. The dead area is parameterized in terms of the fractional area in the perimeter that is unresponsive (0, 0.1, 0.2, 0.3). The area of the central dimple is added to the dead area in the perimeter.
The amplitude of the variation depends on the image and pixel sizes, the inoperative fraction of each pixel, and on the sampling scheme. For a source of a given brightness the signal in a single measurement will have a single-sighting dispersion . A calibration factor accounts for the fact that only part of the total pixel area is responsive. Consider how three sampling schemes might improve on this intrinsic dispersion:
Figure 1: The uncertainty in a single sighting (solid lines) and after averaging NSAMP=6 randomly obtained sightings (dashed lines) for 4 values of the dead perimeter area (0,0.1,0.2,0.3) is shown as a function of seeing. The dimple in the center is present in all 4 cases.
I have modeled the 2MASS measurement process in the presence of these effects for a variety of seeing FWHMs and dead area fractions. The Monte Carlo simulation incorporates the description of the dead area surrounding each pixel given above. Two other factors add to the realism of the simulation:
Figure 1 shows the relative uncertainty, , in the brightness of a source seen one time (solid line) for 4 different values of the dead pixel area as a function of the breath of the image (optics plus seeing). The dashed lines show the uncertainties reduced by the factor of . The dead area suggested by the laboratory measurements is denoted by the 0.20 line(*). The figure shows that the single sighting dispersion can be as large as 8% with optics under in conditions of good seeing, FWHM=1.5 . By averaging 6 random sightings, one can improve the photometry to a few percent or better.
Figure 2 shows that the 2MASS sub-pixel sampling scheme is an improvement relative to the random sampling. Under average seeing conditions the dispersion in source brightness %. However, improvements much beyond 1 % are impossible except under poor seeing conditions that would have other deleterious effects.
Figure 2: The uncertainty in a 2MASS observation after averaging NSAMP=6 carefully subsampled sightings for 4 values of the dead perimeter area (0,0.1,0.2,0.3) is shown as a function of seeing. A jitter of 0.1 has been used.
Figure 3 shows the uncertainty for the two sampling schemes, 2MASS and random, as a function of position jitter, . If the jitter is larger than about 0.4 , there is almost no improvement relative to simply combining NSAMP measurements taken at random sub-pixel locations. It should be mentioned that the Read measurements use a very short measurement time, 50 msec. On this timescale, image motion is comparable to the image size; the limiting accuracy of Read will not benefit from the carefully controlled sub-pixel sampling.
Figure 3: The uncertainty in a 2MASS observation after averaging NSAMP=6 carefully subsampled sightings (squares) is shown as a function of telescope jitter. Also shown is the uncertainty obtained from averaging NSAMP random sightings. A seeing of 2 and a dead area of 0.2 has been used.
Figure 2 is consistent with apparently irreducible error seen in the aperture photometry measurements made with the prototype camera. The uncertainty generally reaches a plateau of 1-2% even for bright sources. The M92 data obtained in June 1994 are a special case that may be somewhat worse than average since the sampling on this night of 1.5-2.0 seeing was non-optimum. Near-integral offsets were used in the in-scan direction. Figure 4 shows a simulation made with a step-size of 0.0 in y for different values of the seeing. The predicted dispersion at 1.5-2.0 seeing and a dead area of 0.2-0.3 are consistent with the 2% dispersion seen in these data.
Figure: Similar to Figure 2 but with step in y=0.
Figure 5 shows that the errors in the averaged amplitude measurements follow a Gaussian distribution. A histogram of the amplitude of 5,000 sources measured with 2 seeing and a dead perimeter area of 0.2 shows a Gaussian-like distribution with few outliers.
Figure 5: A histogram of the source amplitudes for seeing of 2 with a dead area of 0.2 shows a compact Gaussian distribution.