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4. Performance
4.1 Limiting Magnitude Estimates
Plot to estimate Limiting Magnitudes and exposure times in J, H and K bands
for CANICA at the 2.1-m telescope of the OAGH. The top panel displays
the Signal-Noice-Ratio (SNR) as a function of magnitude expected for a
single or multiple exposures with a total integration time of 240 seconds.
On the Right hand side axis, errors on the estimated magnitudes are given.
In the bottom panel, total exposure time required to reach a SNR=10 (i.e.
m_err=0.10 mag) is plotted as a function of magnitude. In both panels,
K-band limits were calculated for two values of sky values (Normal=350 counts/s
and Good=200 counts/sec). The limititing magnitudes (SNR=10) for total exposure
time of 240 secs are J=17.5, H=17.2, K=16.0+/-0.2. These values could be
bettered to J=19.0, H=18.8, K=17.6+/-0.2 if the exposure time is 1 Hour.
These calculations are based on the following characteristics of the
detector/instrument: Readout noise = 15 electrons (6 counts), dark=0.02/sec,
pixel scale=0.32 arcsec/pixel, pixels/star=55.0, seeing: 2.0 airmass: 1.20.
The values below correspond to the March 2003 run.
| Filter | Zeropoint | sky/sec |
sky [mag/arcsec²] |
| J | 20.25 |
20 | 14.5 |
| H | 20.50 |
60 | 13.6 |
| K | 20.00 |
350 | 11.2 |
| K | 20.00 |
200 | 12.0 |
The intrinsic photometric error with CANICA is found to be around
0.05 magnitude at best, and can reach 0.20 if proper care is not taken in
chosing the aperture.
So there is no gain in observing to get SNR > 20. The observations
are background limited, and hence SNR improves as SQRT(Texp).
In otherwords, to go down deeper by 1 magnitude, the exposure
time should be increased by a factor of 6.
Zeropoints for Oct12/13 2003 (after aluminization of the
Mirror)
| Filter | Zeropoint | sky/sec |
sky [mag/arcsec²] |
| J | 20.70 |
30 | 14.5 |
| H | 20.79 |
130 | 13.0 |
| K | 20.43 |
350 | 11.6 |
So zeropints are roughly 0.35 magnitude fainter, implying a gain of 40%
in exposure time.
4.2 Observed Errors on Magnitudes and Repeatability
Stellar fields are normally observed by a sequence wherein stars are moved from
one quadrant to another. These observations are used to estimate zeropoints
and errors and repeatability of magnitudes. The method followed is described,
using the K-band observations of AS37 field on Oct 13/14.
The observations were repeated 11 times in the sequence, each of exposure
10 sec. Magnitudes of 12 stars on each of these frames were measured (m_K)
to assess the repeatabilty of the magnitudes. In addition magnitudes
were measured in a combined frame ().
The brightest two stars in the field are standards. The zeropoint is
obtained using the brightest star (AS37-0), and is used to transform
the instrumental magnitudes of other stars.
4.2.1 Chosing the right radius
The most important task in extracting stellar magnitudes is fixing the
smallest radius, which includes almost the entire flux from stars.
The task becomes difficult for fainter stars, as the errors in the sky
estimation can introduce large errors in the magnitude. The figure below
illustrates growth profiles for 5 stars, spanning magnitude range of 5 mag
(K=8.6 to 13.6). The curves are normalized such that at a radius of 10 pixels
(3.2 arcsec), magnitude is zero. The flux outside this radius is only
3% for the brightest two stars (solid and dashed lines respectively).
Assuming that all the stars have similar Point Spread Function (PSF),
the flux outside a radius of 10 pixel should be 3% for even the fainter stars.
Thus for all the stars, magnitudes are measured at radius=10 pixel, and then
0.03 magnitude is subtracted to get the final magnitudes.
Repeatability of the magnitude measurements can be checked by comparing
the
magnitudes of the same star in different frames of a sequence.
In the following figure, the top panels show this as a function
of radius distance from the center of chip (left) and magnitude (right).
The middle left panel shows the magnitude in the combined frame, and the
bottom panels show the magnitude differential from the growth curve for
each star as a function of radius distance from the center of chip
(left)
and magnitude (right). In the middle right panel, magnitude errors based
on
the noise statistics are plotted as a function of magnitude.
From this figure, it can be concluded that:
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