The APO 3.5-m Guider Report
- Jeff Morgan
- Astronomy
- University of
Washington
- Seattle, WA
- April 1998
I. Outline and links to sections of this
report
- II. User oriented information
An overview of the guider performance
Guider software of interest
Guider web page
Grabbing a guider image
Guider focusing
III. Engineering data on the guider performance
Overview
Atmospheric turbulence limitations
Guiding on/off tests
Simultaneous guider and SPIcam
tests
Past reports of guider performance and comments
on guider requirements
Searches for correlations between guide
errors and other parameters
Twilight tracking tests
The temporal characteristics of the
tracking errors
IV. Summary
General comments
Past attempts to improve guider
performance
Guider standard star field
V. References
List of references
II. User oriented information
An overview of the guider performance
The first section of this report is geared to inform
a normal user of the telescope about the general capabilities of the
3.5m guider. We also present information on routines which will allow
a user to make better use of the guider data and to monitor its
operation.
The guider hardware consists of a Grade 1 thinned,
backside illuminated MPP SITe CCD with 24 µm pixels in a
1024x1024 format. This camera was choosen for its high sensitivity,
complete lack of image defects, and its large pixels. Without
binning, the telescope optics produce an image scale of 0.14
arcseconds/pixel on the guider. The imager is cooled by a two stage
TEC. The hot side of the TEC is liquid cooled by an ethylene
glycol/water solution. The radiator, pump, and air reservoir for the
liquid cooling system are mounted in the instrument rotator along
with the guide camera and its filter mechanism. Fans and ducting are
included to vent the heat from the radiator out of the rotator box
into the ambient air of the dome. The liquid cooling system is
necessary owing to the large physical size of the CCD. The choice to
mount the cooling system inside the rotator box was made because this
was felt to be a better option than attempting to run liquid lines
through the rotator cable wrap. The cooling system is sufficient to
keep the CCD at -25 C at all times, which is its current temperature
setpoint. The CCD utilizes a Photometrics PXL controller. The gain on
the camera is 10.5 ± 0.1 electrons/ADU and the read noise is
22.5 ± 0.2 electrons. The readout rate of the camera is fairly
rapid at 200 kHz, resulting in a total readout time of about 3
seconds for a full, unbinned frame.
The guider hardware includes a focus mechanism which
is independent of the normal telescope focus and a 7 position filter
wheel. The operation of the focus and filter mechanisms is described
in the
TCC
documentation found in the normal APO web
pages (see the GCamera documentation). We will not duplicate that
here. The APO web pages also contain information on the
filters which are available for the guide camera.
However, it is worthwhile mentioning here some
information on the units of the guider focus mechanism and how this
is related to the normal telescope focus. Movement of the telescope
focal plane is related to movement of the secondary by the
equation
(1)
where 
is the induced axial motion
of the telescope focal plane, 
is the motion of
the secondary mirror, and 
is the ratio of the
telescope focal length to the focal length of the primary mirror. For
the APO 3.5-m we have 
which means that equation
(1) reduces to 
. Equation (1) implies that
as the distance between the secondary and the primary is increased,
the telescope focal plane moves in toward the tertiary. Owing to some
mechanical changes to the guider focus mechanism when the new guide
camera was installed, the units of the guider focus have been
inverted. The controller software has not been changed to reflect
this fact. As a result, increasing values of
the guider focus correspond to motion of the focal plane toward the
tertiary. The software expects units of
microns for the guider focus mechanism. Experience with science
instruments has shown that focus changes smaller than 25 µm
produce neglible changes in the measured stellar profiles. Equation
(1) shows that an equivalent motion for the guider focus is
approximately 850 µm. Focus motions smaller than this are not
normally useful because they produce changes in the stellar profile
smaller than the typical noise of the stellar width
measurements.
We have measured the par-focal behavior of the guider
with respect to SPIcam's focus. At 90 degree intervals of the rotator
angle (starting with a rotator mount position of 257 degrees), we
found the best focus position of SPIcam by movements of the
secondary. At the same time, after focusing SPIcam we focused the
guider by means of the guider mechanism focus. As a final check
against possible temporal drifts of the focus throughout the duration
of the focus measurements, at the end of this procedure we repeated
the focal measurements at the original starting rotator mount
position. As expected, the on-axis focus for SPIcam varied by less
than 50 µm. The reproducibility of the first and last SPIcam
focus measurements were within 20 µm, which is typical of the
noise level of the focus measurements. At the same time, we measured
the following best focus positions for the guider:
|
Rotator Angle
|
Guider Focus
|
Focal Difference
|
|
257
|
47096
|
0
|
|
347
|
47945
|
850
|
|
74
|
48395
|
1299
|
|
160
|
46578
|
518
|
|
247
|
47578
|
482
|
There is at most a slight drift of guider focus as a
function of rotator mount position. 180 degrees from the beginning
focus, at a rotator mount position of 74 degrees, a focus difference
of 1299 µm was seen in the guider focal position compared with
the original measurement at a rotator mount position of 257 degrees.
This difference is small enough compared to the noise that its
reality is in doubt. The average focal position for the guider when
using SPIcam is therefore at 47518 ± 710. This should be the
current instrument block setting for the SPIcam guider focus
position.
We have measured the guider throughput using several
Landolt standards. In a one second exposure through the R filter, a
15th magnitude star produces 956 ± 15 ADUs on the camera. With
the gain quoted above, this is equivalent to 10038 ± 157
electrons/sec. This means that with a one second exposure through the
R filter, a 21.6 magnitude star will produce one read-noise worth of
electrons on the detector. A more realistic detection limit for the
guider can be estimated as follows. With 1 arcsecond seeing and 3x3
binning, a stellar profile covers approximately 9 binned pixels. If
we require at least 3 times the read-noise in each pixel to define a
minimum stellar detection, we are requiring a minimum flux of 608
electrons for the detection of a star. This definition of a minimum
stellar detection and the throughput given above imply that in 1
second through the R filter we can detect a star of 18.0 magnitude.
The brightness limit for practical guiding is much more difficult to
define because it depends on many more variables, such as background
variations and the sensitivity of the fitting routines to noise. We
discuss this issue below.
We have also used stellar measurements to
characterize the 1% ND filter which is currently in use in the
guider's filter wheel. By comparing the measured flux of several
stars through the R filter and the R filter + 1% ND filter stack, we
conclude that the 1% ND filter has an average transmission of 1.55
± 0.04 % over the R bandpass.
The telescope is currently capable of keeping objects
centered to within an error circle with a 1-
radius of 0.24 ± 0.1 arcseconds anywhere in
the sky with one notable exception. Near the zenith, this performance
will degrade. We have only one measurement of how fast this behavior
degrades as you approach zenith. Users are advised that tracking
within 6 degrees of zenith will produce significant degradation.
Within 6 degrees deviations of up to 0.75 arcseconds are caused by
the inability of the rotator to keep up with the sidereal motions. We
also know that there are times when or places on the sky where the
behavior of the guider appears to improve to give a 1-
error circle of approximately 0.10 arcseconds.
We currently do not know the causes nor the systematics of these
variations. We will return to this topic in section III of this
report.
The guider camera sensitivity is sufficient to make
guiding feasible nearly anywhere in the sky without worrying about
preparing finding charts for guide stars ahead of time. We have been
able to guide on stars as dim as 18.9th magnitude using 20 second
guider exposures. A star this dim with moderately poor seeing
(approximately. 1.5 arcseconds) produces a profile with a peak of
about 40 ADUs above the background on the guide camera. This profile
was successfully identified by the star finder software and the error
circle of guider centroids did not significantly increase compared to
the distributions obtained with stars 10 and 100 times brighter. From
star counts near the galactic pole, we estimate that there should
almost always be a star brighter than 19th magnitude in the field of
view of the guider at all times.
For moderately bright stars (< 15th magnitude),
the guider software is not very sensitive to the background
conditions. Tests of the guiding at twilight show that a sky
background as large as 3 times the peak guide star intensity has
little or no effect on the guiding. Details of this test are shown in
section III of this report.
(return to outline)
Guider software of
interest
The guider keeps a ring-buffer of its 20 most-current
images stored on
tycho.apo.nmsu.edu in
the directory
/export/images/guider
under the names gImg**.fits where "**" runs from 01 to 20. As the
names imply, these are stored as FITS images. The most recent image
can be determined by reading the file "last.image" which is found in
the same directory. In this directory you will also find a null file
called "gImg.ready". When this file is present in the guider images
directory you may safely open and read "last.image" or any FITS file
present. When it is absent you should not attempt to open these
files. GImg.ready will disappear from the guider images directory
only momentarily while the guider Mac writes out a new file. In this
way a user can tell when its OK to transfer files between systems.
There are three facilities that users should be aware
of which make the guider easier to use. Two of these scripts allow
the user to see the data that comes from the guider and the third
script allows a user an easy way to focus the guider.
(return to outline)
Guider web page
We have Eric Deutsch to thank for the authorship of
this routine. The guider web page routine converts the FITS images to
GIFs and then displays them on a web page. This allows almost real
time display of the guider images. There is an inherent lag of
approximately 30 seconds between the display and the acquisition of
the most recent image. To use this facility connect to:
http://www.astro.washington.edu/deutsch-bin/latestguiderimage
This page should be self-explanatory. The page is set
to reload every 20 seconds by default, although the reload time can
be adjusted from the page itself. Note that the processing system is
not on all the time; if the field "Guider Auto-Fetcher" is OFF,
please ask the Observing Specialist to turn it on for you (via the
cloudcam interface). Questions/problems/suggestions about this
display system (but not about the guider itself) may be sent to
deutsch@astro.washington.edu.
Eric has also put together a second application which
plots up parts of the guider data stream as it comes out to the TCC.
This application is written in IDL and therefore will require this
commercial software if you want to run it. In addition to the most
current guider image, this application includes a plot of the X and Y
differences between guider centroids as a function of time, a plot of
the FWHM of the guider stellar profiles as a function of time, and a
plot of the integrated stellar intensities as a function of time. As
an added convenience, this application also displays the latest cloud
monitor image. If you are interested in running this application on
your home machine, you are encouraged to contact Eric at the address
given above. The primary weakness of this application is that it does
not allow you to do stretches of the guider image, nor can you do any
quantitative analysis of the guider data. These needs are addressed
by the next routine.
(return to outline)
Grabbing a guider
image
The next facility comes to us from Al Diercks, but
don't blame him if things don't work. I have hacked his code to
remove a security bug that the original code contained. It is an IRAF
script which grabs a guider image and displays it in an IRAF display
window. This is useful when one needs to make quantitative use of a
guider image. The routine is called glg
which,I believe, stands for "get last guider
(image)". Al is a concise fellow! The guts of this routine requires
that you have a "Perl" interpreter on your local machine. Perl stands
for "Practical Extraction and Report Language". It is a script
processing language which runs on any Unix machine. You can find a
copy of Perl and a description of it at the following site:
http://www.cis.ufl.edu/perl/
All users, please note that an original version of
this routine exists which attempts to retrieve the guider images
directly from the guider Macintosh rather than from tycho.
This technique has a strong tendency to crash
the guider, especially if rapid guider
exposures are being made. Please make sure that you have the current
version of this routine! Any copy of glg.cl and gsnag.pl which do not
have the version labeled in the first three lines of the routine, or
any copy earlier than version 2.0 should be discarded.
If you wish to install a copy of this, then proceed
as follows:
- Obtain a copy of the files
glg.cl and
gsnag.pl from
tycho.apo.nmsu.edu
in the directory
/export/catalogs/apotop/visitor1/iraf/zmisc.
We'll assume here that you have placed these files in a directory
called /home/user.
- In your IRAF login.cl file add the lines:
- task glg=/home/user/glg.cl
- task $gsnap="$/home/user/gsnap.pl $(1) $(2)
$(3)"
- After logging into IRAF type
- set passwd = ******
- where ****** is the visitor1 password on
tycho. If you don't know this password, then you will need to
contact someone at the site. You will only have to enter this
password once per IRAF session. Please do not put the "set
passwd" line in your login.cl! Doing this represents a
significant security breach for tycho!
- Type
glg to see the
latest guider image. Note that the routine glg will leave you in
the routine "imexam" with the guider image loaded.
(return to outline)
Guider focusing
The third routine is an mcnode script called
gfocus5.tcl. As its
name implies, this is a TCL script which will run in an mcnode
window. Tcl stands for "Tool Command Language". It is a script
processing language similar to Perl. A copy of this routine is kept
in the home directory of the visitor1 account on tycho. You must have
an mcnode window open to use gfocus5.tcl. After opening an mcnode
window on your home machine, follow these directions to use
gfocus5:
- In your mcnode window type "source gfocus5.tcl"
to load the script.
- You may then run the script with the following
mcnode command:
- gfocus5 itime mode mid inc
- where:
- itime = guider
exposure times for focus frames (default = 10 seconds)
- mode = t or g = type
of focus (default = g). t will do a telescope focus (i.e. moving
the secondary). g will do a guider mech focus (ie. no secondary
motion)
- mid = middle focus
position (default = current focus position). This will be the
focus position at the middle of the range searched in the focus
sweep that is taken.
- inc = increments to
use for focus position (default = 50 for telescope focus, 1000 for
guider focus). As mentioned earlier (see equation (1)), a minimum
sensible guider focus increment is approximately 850.
As an example of a call to this routine, if you
wanted to take 10 second exposures, moving the guider mechanism focus
2000 µm between each exposure, centered around a focus position
of 48000 µm, then the call to this routine would be: gfocus5 10
g 48000 2000.
As with any TCL procedure, all of the command
parameters are position specific. You may
default any of the command parameters.
However, once a parameter is defaulted, all of the following
parameters must also be defaulted. This routine takes five guider
images and measures the widths of the stellar profiles in each image.
It then does a least-squares fit to a second-order polynomial to this
data. If the polynomial has a minimum within 2 * inc of the middle
focus position, then the routine sets the telescope to this position.
Otherwise, it returns the focus to the starting position. The routine
will fail gracefully if it is unable to find your star in each of the
five images taken. Note that the default behavior of this routine is
to use the guider focus mechanism rather than telescope secondary
motions. For more detail on the behavior of this routine, see the
comments documented at the beginning of the script. In the same
folder, there is also a routine called
gfocus3.tcl. This
routine is called with the same parameters as gfocus5.tcl. It is
faster in that it fits the polynomial to the data from 3 images. In
general, I recommend the use of gfocus5.
(return to outline)
III. Engineering data on the guider
performance
Overview
The goals of this section of the report are
four-fold. First, we will discuss the theoretical limitations to
guiding and a few results that have been obtained from others. Then,
we would like to convince the reader that the signal and position
sensitivity of the current guider are not limiting factors. Third, we
wish to show that we need to be doing a better job if ever we want to
take advantage of sub-arcsecond conditions at the site. And finally,
we will conclude this section by discussing our attempts to
understand what are the root sources of the tracking errors that we
currently experience when guiding.
(return to outline)
Atmospheric turbulence
limitations
There are several things that can become the
fundamental limitations to guiding accuracy. Poisson errors of the
photon flux can create inaccurate centroid positions for very dim
guide stars. But, it can be easily be shown that we are not typically
limited by this effect with the current 3.5-m guiding. The easiest
way to observe this is to measure the guiding errors as a function of
guide star intensities. These errors will decrease with the square
root of the integration time. We see no such effect in the current
guider errors.
Atmospheric turbulence represents another fundamental
limitation to guiding. Turbulence is the root cause of telescopic
"seeing". It is common to relate FWHM measurements of seeing to the
Fried parameter, 
, effectively the phase coherence length through
the atmosphere. For long exposure images (anything greater than a few
tens of milliseconds) on telescopes greater than a very modest size
(approximately 5" in diameter) its relationship to telescopic seeing
is well known and is roughly given by the relationship:
(2)
where 
is the 1-sigma seeing in radians and 
is the wavelength of light observed (Roddier,
1981). Often, the factor of 1.27 in equation (2) is dropped owing to
the approximate nature of the relationship. We will follow that
convention here. The relationship between the seeing in FWHM units
and in sigma units is given by the relationship 2.35 * = FWHM.
Image motion caused by turbulence is a more complex phenomena which
depends on many atmospheric conditions. Despite its complexity, we
can estimate the effects of turbulence on the image motions based on
known average atmospheric conditions and theory.
Martin (1987) describes how to calculate the image
motions caused by atmospheric turbulence given knowledge of several
key atmospheric parameters. The phenomenon depends on the seeing
(
), telescope diameter (
), wind speed (
), wavelength of light observed (
), thickness of the turbulent layer one looks
through (
), exposure integration time (
), and direction with respect to the wind in
which you measure the image motion (
). In his article Martin shows calculations
appropriate to a small aperture telescope which did not include the
effects of a finite thickness of the upper atmosphere layer of
turbulence. I include here the extension of those calculations
appropriate to the 3.5-m telescope. I also include here the effects
of the finite thickness of the upper atmospheric turbulent layer.
This is necessary when large (greater than about 4" diameter)
aperture telescopes are considered because the effects become
dominant under these conditions.
Following Martin, for given atmospheric conditions
and telescope size the variance of image motion caused by turbulence
is a function of the exposure time in which it is measured and the
direction on the image plane in which it is measured. It decreases
with exposure time and it decreases if the image motion is measured
in the direction of the wind. With the convention that 
= 0 is the direction of the wind, the variance
of image motion in
arcseconds2 is
given by
(3)
where 
is the first order Bessel function and 
and 
are dimensionless
spatial frequencies corresponding to the outer and inner scale
lengths of turbulence in the atmosphere. Their relation to the outer
and inner scale lengths of turbulence are given by the
equations
(4)
Here 
and 
are the inner and outer scale lengths.
Hufnagel (1978) gives an excellent discussion of
important atmospheric parameters which affect turbulence and the
range of variation that can be expected to be seen in them. The inner
scale length is the dimension at which turbulent motions dissipate
into frictional heating of the atmosphere. Typically this length is
on the order of 1 cm and is small enough that its effect on the
calculations can usually be ignored. The outer scale length is the
upper size limit to turbulent eddies. Its size depends considerably
on the environment the turbulent layer is found in.
In the context of image motions the equations given
by Roddier (1981) and Hufnagel (1978) indicate a very important thing
about atmospheric turbulence (Cf. 6-28 and 6-29 in Hufnagel). Image
motion is affected more strongly by turbulence near the ground than
it is by upper atmospheric turbulence. The opposite is true for
scintillation! It is often noted in the literature that Hufnagel
shows that the largest contribution to turbulence comes from a shear
layer near the top of the tropopause where average wind velocities
are around 27 m/sec and the outer scale length varies between 10-100
m, independent of observing location. For scintillation, this is an
important simplification, but it is not appropriate to apply these
conditions to image motion owing to its sensitivity to ground layer
turbulence. However, both Hufnagel and Roddier point out that even in
ground layers turbulence has been shown to be confined to shear
regions which have scale lengths which vary from 100-200m. In
summary, when it comes to image motion, ground wind speeds and outer
scale lengths of 100-200m are approprate to use in equation (4). It
is also likely, but not proven, that outer scale length is a function
of wind speed. Here we will simply assume that these are independent
quantities.
In
Figure
1 I show the image motion calculated by
equation (3) for three different situations. The line marked by
circles shows the 1 standard deviation image motion expected in the
direction perpendicular to the wind vector (
=90) when the outer scale length is 200 m, which
is about the largest expected. The line marked by squares shows the
image motion in the orthogonal direction under the same conditions.
The line marked with diamonds shows the image motion expected if the
outer scale length is near the smallest expected. The abscissa is a
dimensionless parameter that depends on the local wind speed (
), the exposure integration time (
), and the telescope aperture diameter (
).
As can be seen from
Figure
1, theory predicts that image motion will
increase as wind speed decreases. This is perhaps counter-intuitive,
but it is the correct conclusion. It helps to understand that image
motion is driven by the larger scale turbulent features in the
atmosphere. Equation (3) is based on Taylor's "moving screen"
approximation in which it is assumed that the turbulent cells are
essentially stable in size during an exposure and move with the wind
velocity across the telescope field of view. The effect of the wind
motion is to average over the large scale structure in the direction
of the wind, nullifying their effects on the integrated exposure.
This is also why the maximum image motions are predicted to be in the
direction perpendicular to the wind (
=90) rather than in the direction of the wind.
The image motions do not go to zero when the wind velocity is zero
because it is assumed here that the turbulent motions are independent
from the bulk wind velocity.
For a typical ground wind speed of 10 mph (4.47
m/sec) and a 10 second exposure 
. Under these conditions, Figure 1 indicates that the
maximum image motion due to turbulence is about 0.066 arcseconds and
that it should vary by as much as a factor of about 40%, depending on
the direction in the image plane in which it is measured. Under the
best of conditions (smallest value for 
), the maximum image motion measured on the image
could be as small as 0.054 arcseconds. Shorter exposures or differing
wind speeds can cause image motions to rise up to about 0.082
arcseconds. Equation (3) shows that these results depend on 
. Therefore, if the seeing degrades to 2
arcseconds (
m) then the expected image motion
will rise to a maximum of 0.15 arcseconds. From this analysis we can
see that the guider is not usually being limited by atmospheric
turbulence. But, we will see that at times we are reaching this
theoretical limit.
(return to outline)
Guiding on/off tests
Figure
2 shows a sequence of measurements that were
taken where guiding was initially off, turned on, and then again
turned off. Only the x-centroid data are shown, but the y coordinate
had statistically similar behavior. Each 3x3 binned pixel is equal to
0.42 arcseconds. At this time the 1- scatter during guiding was 0.28 pixels, or 0.12
arcseconds. The drift in the telescope during the periods when
guiding was turned off is evident. During time intervals of 20
minutes or greater the telescope drift is often more complicated than
a simple linear motion. This is illustrated by the data shown in the
first 20 minutes of
Figure
1. If the slow telescope drift is removed by
subtracting a polynomial fit to the data, then one finds that the
scatter of the guider centroids is approximately equal to the scatter
seen during guiding. In this case a scatter of 0.15 arcseconds was
measured before and after guiding was turned on. This is not the
lowest scatter which we observed on this night. Data from the same
night shows measurements with a scatter as low as 0.09 arcseconds
during guiding. In all of these guiding-on/guiding-off tests we have
observed that the scatter of the points both before and after guiding
is approximately equal to that observed during guiding. This
indicates that the scatter is not caused by the addition of the
guiding control loop to the telescope software, but is of a more
fundamental nature. The seeing at the time that all of these
measurements were taken was 1.2 arcseconds, which from my earlier
discussion equates to a maximum expected scatter from turbulence of
0.10 arcseconds. From this it is seen that at times we are in fact
approaching the best performance possible out of the guider.
Figure
3 shows the results of two guide-on/guide-off
tests that were taken at nearly the same telescope coordinates. Test
3 was taken at the coordinates: Azimuth=223, Altitude=62, and Rotator
Angle=215. Test 7 was taken 5 hours later using a different star at
the coordinates: Azimuth=225, Altitude=60, and Rotator Angle=219. The
wind conditions differed between the two tests. Test 3 was taken when
the wind velocity was 8 m.p.h. and in a direction which was 29
degrees from the telescope enclosure opening. During test 7 the wind
velocity was higher (14.3 m.p.h.) and directed more closely to the
slit opening (only 13 degrees away).
We will return to the issue of the varying wind
conditions later. Here, I wish to point out the similarities between
these two tests in the telescope drifts during the times when the
guiding was off. Its easy to see in the figure where guiding was
turned on during each test. For test 3, guiding was turned on about
21 minutes after data acquisition started. For test 7 guiding was
turned on about 20 minutes after data acquisition started. In the
x-direction both tests show a steady downward drift with a magnitude
of about 1.5 arcseconds over the guide-off period. The drift in the
y-direction over the same period of time was smaller (about 0.75
arcseconds) and in the upward direction in both tests. Marked on
Figure
3, are the 1-
errors measured during the guide-on portion of
each curve. It can be seen that the tracking errors measured during
both tests were also quite similar.
The guide-off drift at random places in the sky
varies considerably and on time scales as fast as 2 minutes. The
drifts seen in
Figure
1 are good examples of such behavior. By way
of contrast, the shape of the drift curves in Figure 1 are much
different from those seen in
Figure
3 during tests 3 and 7. In general, this is
what has been found, very few of the drift curves look alike. From
the similar shapes of the drift curves seen in Figure 3, I conclude
that the drifts are not random and are primarily a function of
telescope position. This is consistent with the hypothesis that the
drifts come primarily from small scale errors in the telescope
pointing model.
(return to outline)
Simultaneous guider and
SPIcam tests
Figures
4 and
5
show a sample of some of the data which we have analyzed in order to
characterize the guider's performance in terms of its effects on
on-axis imagery with a science instrument. For these observations
SPIcam was mounted on-axis. A star of moderate intensity (peak of 360
ADUs) was found and used for guiding with 20 second exposures.
Simultaneously, 10 second images were taken with SPIcam. Guider
centroid positions were taken from the TCC log and IRAF's "imexam"
was used to compute the centroid positions on the SPIcam exposures.
The mean x and y centroid positions were subtracted from each
centroid and the difference from these means are shown in the
figures. The solid squares show the SPIcam centroid positions and the
open circles show the simultaneously acquired guider centroid
positions. Even though we used shorter exposures on SPIcam, these
data are more sparse than the guider data owing to SPIcam's long read
time.
When the rotator is at an object angle of 0°,
the -x axis on the guider is always aligned towards the West, which
is the direction of stellar motion. North lies in the +y guider axis
direction. The parallactic angle is the direction from North towards
the local zenith. The orientation of the parallactic axis with
respect to the guider axes is illustrated on
Figure
4. Motions of the telescope's altitude axis
always move the image along the parallactic axis. Motions of the
telescope's azimuth axis always move the image perpendicular to the
parallactic axis. While the direction of tracking is always in the -x
direction, the proportion of altitude and azimuth motions that
compose this tracking motion change with the parallactic angle. In
the case of Figures 4 and
5,
the parallactic angle was +22 degrees and most of the tracking
motions were being done by the azimuth axis of the telescope.
The x-axis is also the axis which points in the
direction of the rotator motions. It is important to remember that
the TCC does not actively control the instrument rotator when
guiding. Motions of the field owing to imperfections in the rotator
are degenerate with motions owing to imperfections in the positioning
of the altitude and azimuth axes. Simultaneous observations of
multiple stars are required to break this degeneracy and correct for
rotator errors along with errors in the altitude and azimuth axes.
Requiring that multiple stars be available in the guider field of
view at all times is too restrictive to guarantee guider operations
at all positions in the sky. Because of this, the guiding software
assumes that the rotator is a perfect mechanism and attempts to keep
the guide star stationary on the guide camera by moving only the
altitude and azimuth axes of the telescope.
In
Figures
4 and
5
it can be seen that the image motions on the guider are mirrored by
image motions on SPIcam. For example, when an Easterly excursion is
seen in the guider, an Easterly excursion of similar magnitude is
observed on SPIcam. There are a few notable exception to this. For
example, on Figure 4, the SPIcam centroid at 16.5 minutes into the
measurements differs by 0.4 arcseconds from the corresponding guider
centroid, but for 80% of the points on all similar measurements that
we have made, the agreement is within 0.1 arcsecond or better. The
image excursions on SPIcam are in phase with the guider image
motions. There are no apparent delays between the motions seen on the
two cameras. This mirrored, in-phase behavior I call "common-mode"
motion. It is a strong indication of four things.
First, the common-mode motions show that the errors
observed in the guider are directly related to the errors that will
be present in the science instrument. This means that from guider
data alone we should be able to deduce the effects of tracking errors
on the PSF of the science instrument.
Second, the common-mode motions imply that there are
no problems with the centroiding algorithms nor significant noise
sources which are specific to the guider. The software used to
analyze the SPIcam and guider images are different, the sky
backgrounds and noise levels of the two cameras are very different
and yet the agreement between the SPIcam and guider centroid
positions is good. We have verified that the guider software gives
centroid positions that are in good agreement with other software by
taking raw guider frames and computing the centroids for these frames
with IRAF imexam. We have found the imexam centroids to agree with
the guider code centroids to within 0.02 pixels. This represents
agreement to within 2.8 milliarcseconds, which is two orders of
magnitude smaller than the reported guide errors. Thus, the centroid
software does not appear to be a problem. There currently is 3.3 kHz
noise present in the guider images, but we do not believe that this
noise is a significant contributor to the guide errors. This 3.3 kHz
noise generates fluctuations in the guider images of 7.8±2.5;
ADUs peak-to-peak. This noise level is not significant when compared
with the flux levels obtained with the bright star tests that we
mention above (thousands of ADU in the peak). Since the residuals
that we see are present at the same level even when guiding on bright
stars, we conclude that the 3.3 kHz noise is not a significant
contributor to the current guiding errors. In addition to this, the
common-mode motions imply that at most, errors caused by sky
background or camera noise contribute less than 0.1 arcseconds to the
tracking errors.
Third, the common-mode behavior of the tracking
errors argues that the rotator is not the cause of the tracking
errors that we measure. Errors in the rotator motions will show up
preferentially as differences between the SPIcam x-axis centroids and
the guider x-axis centroids. This is not seen in the data. The
agreement between the x-axis data is as good as that for the y axis.
Rotator errors will also tend to exhibit a phase lag between the
motions seen on the guider and those seen on the science instrument.
No such lag appears in the data.
Fourth, the common-mode behavior is one indication
that variations in the seeing are not the cause of our large scatter
in the centroid positions. The stars observed by SPIcam and the
guider are separated by 0.31 degrees. Their fields of view experience
different seeing variations. Seeing variations would cause
differential motion between the science instrument and the guider.
Common-mode motions are indicative of errors in the telescope
tracking.
The 1-
tracking errors for each
axis are labeled
on Figures
4 and
5.
Since there is no apparent correlation between the x- and y-axis
positions, the total tracking errors are just the quadrature sum of
both the x- and y-axis tracking errors. In the case of Figures 4 and
5, we have a total tracking error of 0.23 arcseconds on the guider.
This represents a contribution of approximately 0.53 arcseconds to
the FWHM seeing.
(return to outline)
Past reports of guider
performance and comments on guider requirements
On the surface, these results appear to be worse than
those quoted from a measurement of guiding performance which was done
back in September 1995 by Al Diercks et al. In 1995, using less
sensitive, poorer quality guide camera made by SpectraSource, Diercks
et al. did similar tests and found an rms deviation of 0.15
arcseconds while guiding. As we pointed out above, we have made
single measurements of the guider performance which have rms
deviations equal to or smaller than those made by Diercks et al. But
the average performance from approximately 16 measurements is worse.
The earlier tests were rather limited in extent (a single run) and
they could easily have been taken at a position or time when the
telescope tracking was above average. Similarly, early tracking tests
on the 3.5-m indicated a best performance of 0.1 arcseconds
peak-to-peak (Figure 10.2 of the
SDSS proposal, volume 1). However, there they
also noted that the data shown was taken from a period when "...the
tracking was particularly smooth." All of these results are
consistent with the viewpoint that the average closed-loop guiding of
the telescope has not changed significantly since the telescope was
built. But past reports of its behavior have been somewhat
optimistic.
It should be noted that the comments above are
focused exclusively on our closed-loop tracking and this behavior is
somewhat different from open-loop tracking and pointing of the
telescope which have seen recent improvements. Although these issues
are not completely seperate, the open-loop tracking errors are
dominated by errors in the pointing model for the telescope whereas
this is not the case for closed-loop tracking.
We need better performance from the guider if we are
to ever make good use of sub-arcsecond seeing conditions at the site.
The current errors are not sufficiently small to eliminate the
telescope tracking from contributing a significant increase in the
widths of stars on the science instrument. Normally the seeing is
reported in units of FWHM of a stellar profile on the science
instrument. The conversion between the FWHM of a Gaussian profile and
the 1-
radius of this same profile is given
by 
. If the seeing is producing stellar
profiles with 1 arcsecond FWHM, this is equivalent to a 
arcseconds. If we assume that the tracking
errors are random, then the seeing profile will add in quadrature
with the tracking errors. For example, if we assume 1 arcsecond
seeing and a 
of 0.24 arcseconds for the tracking
errors while using the guider, then we will have a stellar profiles
with 
arcseconds. This is equivalent to
1.14 arcseconds FWHM. Under these conditions it can arguably be said
that the guider only slightly degrades the stellar profiles. But, in
sub-arcsecond seeing conditions we would have significant
degradation. If the seeing drops to 0.6 arcseconds FWHM, a 0.24
arcsecond tracking error produces a 0.82 arcsecond FWHM stellar
profile. If we assume a goal of only a 20% degradation in the stellar
PSF when the seeing is 0.6 arcseconds, then we require the tracking
errors to be less than 0.17 arcseconds.
There are numerous possible causes for the tracking
errors which we report above. At a fundamental level, we will always
be limited in the accuracy of our guiding by the strength and
stability of the stellar point spread function (PSF). As I implied
above, we do not believe that the errors that we are reporting are
intrinsic to the signal strength of the guide stars themselves
because we get good agreement between simultaneous measurements of
the telescope position made with the guider and with SPIcam. Also,
the errors reported have been shown to be independent of both guide
star brightness. Using 2 and 5 second guider exposures (with peak
guide star fluxes of 300 ADUs) produce results similar to those
obtained with 20 second guider integrations on the same star. In
addition, tests with fainter stars (peak fluxes of only 30 ADUs) give
similar error residuals.
(return to outline)
Searches for correlations
between guide errors and other parameters
We have extensively looked into the possibility of
systematics in the tracking errors that we have observed. There are
no obvious correlations of the tracking errors with position in the
sky, parallactic angle, nor velocity of a particular telescope axis
(including the rotator). Early in the process of collecting guiding
data it appeared that the tracking errors might be correlated with
wind velocity. However, subsequent tests seem to disprove this
hypothesis.
Figure
6 shows a plot of the wind velocity versus
the measured tracking errors. The numbers above each point in Figure
6 show 
, the difference in degrees between
the wind direction and the slit direction. The initial dataset did
not include the points marked with solid circles. If one ignores
these points and the point with the largest tracking error, then a
trend might be indicated in the data. We noticed that the large error
point was initially unique in the data set in the sense that it was
the only point measured while the wind direction was directed
straight into the dome slit. This spurred us to test the wind
correlation hypothesis by taking the data points marked with solid
circles. The new points appear to disprove the hypothesis. The
tracking error curves for the data points with 
and 
have already
been displayed in
Figure
3. Other plots of the tracking errors as a
function of position on the sky (not including the region near the
zenith!), rotator position, azimuth position, altitude position, and
the associated axis velocities show even worse correlations than that
which is seen in Figure 6.
(return to outline)
Twilight tracking
tests
Guiding tests during twilight were done to measure
the sensitivity of the guiding to changes in the background sky
level. A bright star was chosen at a moderate zenith angle and within
1 hour of the meridian in the southern sky. Guiding was turned on and
measurements were taken until significant variations were noticed in
the guider data.
Figure
7 shows the sky background measured on the
guider as twilight approached. The arrow on the figure shows the
point at which the sky level became equal to the peak intensity in
the guide star profile. The brightness increase shows a logarithmic
behavior, perfectly consistent with theoretical expectations (Tyson
and Gal 1993). The sky level had risen to approximately 3 times the
peak stellar intensity before the test was terminated.
Figure
8 shows the x and y guider centroid positions
measured during the period covered in
Figure
7. The 1-
deviations for each
axis are shown on the figure. No evidence for effects of the rising
background level can be seen in the centroid data. The total
dispersion of the data points (
arcseconds) is
lower than our average quoted tracking error, but quite consistent
with tracking errors measured earlier on that same night.
Figure
9 shows the stellar widths as measured by the
guider software during the twilight sky test. The average seeing
during this test was 1.29 arcseconds. The variations in measured FWHM
widths are, for the most part, quite typical of the variations seen
during normal nighttime guiding. But, at the end of the plot,
starting near 56 minutes after starting data acquisition, the effects
of the rising background level can be seen. The onset of errors in
the width determination are quite sudden and catastrophic. The third
to the last point was obtained when the background level was 2.7
times the stellar peak intensity. By the time the second to the last
and last points were obtained, this ratio had risen to 2.9 and 3.0,
respectively.
A similar story is seen in the stellar peak
measurements which are shown in
Figure
10. If the last three measurements in Figure
10 are ignored, the mean stellar peak was measured to be
21163±3376; ADUs. This dispersion represents a 16% fluctuation
in the measured peak values. The integrated intensity was found to be
219164±10698, representing a 5% variation. These are not good
photometric conditions, but they are not unusually bad. It is a well
known phenomenon that seeing deteriorates at the onset of twilight
due to the associated increase in atmospheric turbulence. However,
the results here are more consistent with failure of the fitting
software to handle the large increase in sky background. At about 56
minutes into the data acquisition, the stellar widths begin to rise.
This is what one would expect from deteriorating seeing. But, the
stellar peak intensities and the integrated stellar flux both begin
to drop to levels far below the measured statistical fluctuations.
Since the stellar flux is a constant, the decrease in integrated flux
is a clear sign that the fitting routine began to do a poor job of
estimating the stellar profile at this time.
(return to outline)
The temporal characteristics
of the tracking errors
Finally, we have also investigated the temporal and
statistical characteristics of the tracking errors in an effort to
shed light on their possible causes. Many of the tracking error
measurements do not appear to come from segments of randomly varying
data.
Figure
11 is one example. This is the power spectrum
of the data shown in
Figures
4 and
5.
The x-axis data show a strong peak at 0.00637 cyc/sec (corresponding
to a period of 157 seconds) while very little is seen on the y-axis.
A random distribution will have evenly distributed power at all
frequencies. This power spectrum is reproducible only in a very crude
sense. Just 1 hour prior to when the data of Figure 11 were taken, in
a close part of the sky, a data set taken under identical conditions
shows a spectral peak in the x-axis at 0.0075 cyc/sec (133 seconds),
while again showing almost nothing in the y-axis. In other words, if
two measurements of the power spectrum are made close in time, then
they are similar, but not identical.
The power spectrum of
Figure
12 gives us insight as to the true source of
the long period (approximately 140 seconds) variations and insight
into why this low frequency component seems to be variable in time.
We will show below why we believe that this long period variation is
simply an artifact of the data acquisition while the true noise
source lies at higher frequencies, somewhere above 0.02
cyc/sec.
The total power contained in the low frequency
spectrum of
Figure
11 can be explained quantitatively as the
result of aliasing from higher frequency components. Immediately
after the data of Figure 11 were taken, using the same star with a
higher sampling rate (and shorter guider integration time), the power
spectra of
Figure
12 was measured. Most of the power in the
high frequency spectrum of Figure 12 is contained in harmonic
multiples of the peak seen in the low frequency plot. Marked on
Figure 12 are the locations of the first 13 harmonic multiples of the
peak seen in Figure 11. Most, but not all, of the harmonic multiples
have peaks associated with them. In particular, peaks associated with
the 7:1 and 10:1 multiples are apparently missing. This shows
qualitatively that the power in the low frequency spectrum could be
coming from aliasing of the higher frequency components. But we will
show that the absolute values of the two power spectra are also
consistent with this picture.
To compare the absolute values shown in the two power
spectra you must take into account both the differing sampling rates
as well as the differing averaging. In the first case, 20 second
exposures were taken with a sampling rate of 24.7 seconds. In the
second spectra, 2 second exposures were taken with a sampling rate of
5.5 seconds. The absolute units of FFT power spectra shown are
(arcseconds/sample
time)2. With
differing sample rates, the easiest way to compare the absolute
values of the power spectra is by looking at the standard deviations
of each data set, which are directly related to the integral power in
the power spectrum in the following way. If 
is the standard deviation of a data set and 
its power spectral frequency components,then the
relationship between these is given by:
(5)
where N is the total number of points used to compute
the FFT. It is thus possible to compute the "sigma" that would have
been generated by only a portion of the frequency spectrum by using
only those frequency components in the sum.
The varying exposure times of each data set
correspond to different averages of the input signal. An exposure is
equivalent to multiplying the signal with a boxcar function of the
duration of the exposure, which we will call 
. In Fourier space, this is equivalent to
convolving the input signal by a sinc function of the form:
(6)
where 
is the Fourier frequency
variable in radians/sec. The first zero of this sinc function is
found at 
. Only a few percent of the total
integral of the sinc function is found outside its first zero. We can
therefore approximate the effects of this sinc function as a boxcar
in Fourier space with width 
. In this
approximation we simply assume that the input signal is zero beyond a
frequency of 
cyc/sec. For the case of a 20
second exposure, this corresponds to 0.05 cyc/sec.
We are now prepared to quantitatively compare
Figures
11 and
12.
We will do so by using Figure 12 to predict the amount of power that
we should have measured for the conditions of Figure 11. In the case
of Figure 11 the power spectrum is plotted from 0 to 0.02 cyc/sec,
owing to the sampling rate, but the 20 second exposure times mean
that these measurements are sensitive to variations which extend all
the way out to 0.05 cyc/sec. If we sum the power in Figure 12 from 0
to 0.05 cyc/sec, this gives us an equivalent averaging to the
measurements of Figure 11. Applying this sum in equation (5) yields
an equivalent standard deviation of 0.20 arcseconds. This is in
reasonable agreement with the measured deviation of 0.23 arcseconds
found in Figure 11. A repeat of these two measurements taken later in
the night yielded similar results with the high frequency spectrum
predicting a deviation of 0.22 arcseconds while the actual deviation
measured in the low frequency spectrum was found to be 0.26
arcseconds. In both of the tests the actual low frequency deviation
was approximately 15% higher than the predicted deviation. I believe
these discrepancies are the result of the approximations used above,
but they could also be due to slow temporal variations in the noise
source itself. In either case, I contend that the low frequency power
spectra are quantitatively consistent with a noise source that was
roughly constant in spectral distribution and amplitude over the
whole period it took to measure both low and high frequency spectra
(ie. over approximately 45 minutes time). Small changes can be seen
between the two sets of data. Therefore, over periods of 2 hours (the
time between the starts of these two data sets), noticeable
variations are present.
It is worth noting here that the data of
Figures
11 and
12
are consistent with aliasing in one other way. The low frequency peak
that is so prominent in Figure 11 appears in Figure 12, but with a
much diminished absolute power. In fact, if equation (5) is used to
compare the power in the same frequency intervals, we find a
deviation of 0.23" between 0 and 0.02 cyc/sec in Figure 11, but a
deviation of only 0.056" over the same interval in Figure 12.
The picture that emerges from these spectra is that
the peaks seen in the low frequency power spectra are almost
completely the result of aliased high frequency structure which is
slowly (on a time scale of 2 hr.) changing with time. In fact,
Figure
12 implies that there is almost no
significant power at the lower frequencies. A high frequency
measurement of the guider errors was also made right after we took
the spectrum in which the 0.0075 cyc/sec peak was found. Similar
results were obtained when comparing this low frequency spectrum with
its matched high frequency measurement; i.e. 9 out of 11 of the
harmonic multiples have power spectral peaks associated with them,
the absolute powers of the low and high frequency measurements match
when corrected for variable sampling and averaging, and there is very
little power in the low frequency portion of the high frequency
spectrum. I need to emphasize here that the two high frequency
spectra differ in a way that is consistent with the drifts seen in
the low frequency peaks. In other, words there are no fixed high
frequency peaks in common between the two high frequency
measurements. This made acquiring an understanding of these data sets
particularly difficult!
We conclude from this spectral analysis that the
tracking errors are not random in nature and that noise with temporal
frequencies in the range of 0.02 to 0.05 seconds are what are
contributing the most significant part of the tracking noise in 20
second guider exposures. Unfortunately, we cannot conclude from these
data that the noise is being generated at these frequencies. In fact,
the high frequency spectra show that the noise increases as you
decrease the guider exposure time. The ratio between the short and
long exposure deviations is 1.38. The exposure times here differ by a
factor of 10. Therefore, the noise would appear to vary only weakly
with the exposure time. The measured ratio implies a variation
proportional to 
.
Figure
1 shows that for the right conditions this
might be consistent with turbulence being the source of the noise.
The slowest variation in Figure 1 is proportional to 
, but as was mentioned before, its very hard to
reconcile the absolute values of the errors with this
hypothesis.
It is possible that the noise source has its
fundamental frequency well above what we have measured. From this
analysis we can only say that the noise is being generated at
frequencies above 0.02 Hz. Acquiring further guider data is unlikely
to shed more light on this aspect of the problem because we cannot
acquire the guider data much more quickly than we already have. And,
even if we could, we would soon run into seeing limitations if we
were to sample more rapidly. We also conclude from this analysis that
the frequency spectrum of the noise being generated is not stable
over a long time scale (i.e. for periods longer than approximately 1
hour). However, if we are dealing with only high harmonics of the
true noise source, then its possible that the amount of temporal
drift that we are seeing is consistent with a fairly constant
frequency source of noise. Under these conditions, small frequency
variations of the fundamental cause much larger variations of the
higher harmonics.
(return to outline)
IV. Summary
General comments
My analysis leads me to the conclusion that for
reasonably faint stars (at least down to 13th magnitude) the guider
is producing measurements of the stellar centroids with accuracies
that exceed our current control capabilities. We appear to have a
noise source which is increasing the image motion during guiding by a
factor of about 2 over what we would expect to see from atmospheric
turbulence alone. The noise is not random in nature but it does vary
with time. The noise appears to be introduced into the system at
frequencies above 0.02 cycles/sec. At times the telescope guiding
does appear to meet our needs, but on average it is falling short.
Press et al. (1988, pg. 440) point out that the variance of power
spectra density measurements taken from a single spectrum as we have
done with
Figures
11 and
12
are very large (100%!). This is the main reason for taking any
conclusions based on those spectra with a (large!) grain of salt. The
solution to this is, unfortunately, taking much longer data sets in
order to get multiple measurements of the power spectrum of the
noise. If we continue to measure average noise levels that are around
0.24 arcseconds, then it would be worthwhile to obtain two very long
(>2 hr.) sets of guider data with quick exposure times (5
secconds). Both of these data sets should be taken through similar
ranges of telescope coordinates. This would allow for the spectral
averaging that is necessary to beat down the intrinsic noise levels
in any power spectral analysis.
Atmospheric turbulence fits some of the qualitative
behavior of the noise such as its weak dependence on exposure time.
But, turbulence does not appear to explain magnitude of the errors
observed. Also, turbulence offers no explanation for the non-random
nature of the error signals that we have measured.
We should investigate the possibility that the
telescope servo control is not capable of reliable motions of the
telescope below 0.1 arcseconds and the possibility that there are
round-off errors in the control software.
(return to outline)
Past attempts to improve
performance
It should be pointed out here that in the first week
of January, 1998 a software bug was found and fixed in the TCC code
which deals with the guider control loop. The error was in how the
TCC was computing a running average of the tracking errors that the
guider was providing. At the time, the weighting that was being
applied to in the running average was such that it did not appear
that the error would have much impact on the guide corrections that
were being made. The fix was to remove the code that computed the
running average. At the same time code which enables the user to
control the magnitude of the corrections that the TCC applies was
included. At this time the guide_gain parameter was added. This was
done primarily to enable the guide-on/guide-off tests reported here.
Since this fix was applied, only one night, January 9, 1998, of
appropriate guider data has been acquired and analyzed.
On January 9, 1998 six tracking error measurements
were made. They show an average tracking error of 0.17±0.02
arcseconds, which is consistently below the average tracking error
found from the entire data set. As can be seen in
Figure
6 the dispersion of the tracking errors is
fairly large. So, it is not yet known whether the most recent data
truly indicate improved guider performance. Several nights worth of
data are needed to tell. This data can probably be acquired
"parasitically" by simply waiting for users to use the guider for
long (>1/2 hour), uninterrupted periods of time and then culling
the data from the TCC logs. The night assistants should be forewarned
of the importance of these opportunities and asked to let me know
when such data sets are available.
One last comment should be made concerning the 3.3
kHz noise in the guider images which was noted in section III. Since
the time of the early guider measurements, efforts have been made to
eliminate this noise in the guider. It appears that these efforts
have been successful. Originally, it was thought that putting the
liquid coolant pump to the guider on the telescope UPS power was a
bad idea. It was feared that the pump would contaminate the UPS
power. An isolation transformer was placed in the power line to this
pump and it was put on normal, unconditioned line power. When fans
were added to cool the coolant heat exchanger, the 3.3 kHz noise
increased dramatically. It was noted that these fans were powered
from the same line as the coolant pump. We have since placed the pump
and fans on UPS power. This appears to have decreased the 3.3 kHz
noise back to the original levels by cutting a ground-loop circuit.
The isolation transformer now serves to keep the fan and pump noise
out of the UPS power line. This noise has not been entirely
eliminated, as evidenced by the background noise seen in
Figure
13, which we introduce below.
(return to outline)
Guider standard star
field
In an effort to help monitor the throughput of the
APO 3.5-m telescope, we have measured the R magnitudes of several
stars in the open cluster RNG0188, which is at a declination of
nearly 85 degrees. It is hoped that by periodic monitoring of this
cluster, we can sense the general throughput of the telescope. Owing
to its high declination, this cluster is available for observation at
APO all year. It will always remain at an airmass of about 2.0, which
should simplify corrections for airmass. We present in
Figure
13 a finding chart for the stars measured. In
this figure north is up and east is to the left. The stars in the
field are labeled in order of decreasing brightness. In
Table
1 we give the R magnitudes and coordinates
for each star as seen in Figure 13. The R magnitudes shown in Table 1
are corrected to an airmass of 0. The flux measurements are
uncorrected (ie. the flux measured at 2.05 airmasses) and are given
in ADUs. The R band extinction correction at the time of these
measurements was found to be 0.09 ± 0.01 magnitudes/airmass. The
measurements were taken at an airmass of 2.05. The guider was binned
3x3 and a 10 second exposure was used to acquire the data in Figure
13. Aperture photometry was done using the IRAF routine qphot. The
fluxes quoted come from integrating the sky subtracted flux within an
aperture diameter of 3.8 arcseconds (9 binned pixels). SPIcam was
also used to measure this same field on the same night in the R band.
For stars in Table 1 brighter than 16.0 magnitudes the SPIcam
measurements agreed with the guider measurements to an error of 4%.
For the dimmer stars, the guider measurements quoted here are less
accurate owing to the limited fluxes measured on the guider. This
standard field is centered at the coordinates RA 00:43:57.9 DEC
84:58:05 (1950).
(return to outline)
V. References
List of references
Hufnagel, R.E. 1978 "Propagation through atmospheric
turbulence", The Infrared
Handbook, ed. W.L. Wolfe and G.L. Zissis,
(Washington: U.S. Government Printing Office), p. 6-1, 6-56.
Martin, H.M. 1987 "Image motion as a measure of
seeing quality",
P.A.S.P.,99,
1360-1370.
Press, W.H. et al. 1988
Numerical Recipes in C, The Art of Scientific
Computing, Cambridge University Press.
Roddier, F. 1981 "The effects of atmospheric
turbulence in optical astronomy", Progress in
Optics, XIX, ed. by E. Wolf,
p.281-376.
Tyson, N.D. and Gal, R.R. 1993 "An exposure guide for
taking twilight flatfields with large format CCDs",
Astron. J., 105,
1206-1212.
(return to outline)