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.
where 
.
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.
.
.
significantly less than the dispersion relative to a random sampling (2).
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:
and dispersion
.
in x and 
in
y (measured in pixels). A jitter of 
is added to account for
image motion and random telescope motion between steps. As the jitter gets large, the
effect of the sub-sampling pattern approaches a simple randomization.
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.