Chromatic Variation in Distortion (CVD)
Field distortion: Differential plate scale and ZD
Quantitative estimates of the effect
The prime focus corrector of the 2dF telescope top-end is a 4 element corrector charged with not only delivering the un-vignetted 2degree field at the 2dF field plates, but also creating a flat focal plane, with mostly constant plate scale (projected fibre diameters vary between 2.0-2.1 arcsec across the field plate) and without creating large none telecentric angles. Most practicing astronomers care little for much of that previous sentence, but there are subtleties which it contains that have a very real impact on 2dF and AAOmega operations
Does the ADC work correctly?
The first two elements of the prime focus corrector are a prismatic doublet which is actively controlled to act as an Atmospheric Dispersion Corrector (ADC). There have been repeated rumors that there is a problem with the 2dF ADC. While there was an issue in the early days of 2dF, the ADC has been operating correctly for many years now and regular tests indicate that the ADC correctly compensates for atmospheric dispersion.Chromatic Variation in Distortion (CVD)
CVD is a limitation of the design of the 2dF corrector, which was a challenging design for it's time. The practical impact of CVD is an effect similar to atmospheric dispersion, but completely independent of the atmosphere or Zenith Distance. Like atmospheric dispersion, CVD is a differential refraction (with respect to wavelength) effect, but where as the atmospheric component is almost constant across the field, and so can be largely corrected by prismatic optical elements (the ADC), CVD varies strongly across the field (with a radial dependence) and cannot be corrected (in the context of the current 2dF optics).The problem is that the Point Spread Function (PSF) of the prime focus corrector is strongly chromatic and strongly plate position dependent. The effective center of the PSF (in terms of its light weighted position) is NOT a constant as a function of wavelength due to the limits of optical design, for optics the size of those on 2dF, at the time of its construction. This means that the correct position on the field plate at which a fibre should be placed to accept the light from a given target is NOT constant with wavelength. The Configure software has a detailed model for the 2dF corrector and knows where to place fibres to account for this effect, but the user must determine the correct wavelength to use when placing a fibre. Note that in recent versions of Configure, it is possible to specify up to 10 different central wavelengths to use for different subsets of a target list (i.e. one may want to look at RED and BLUE stars using a different central wavelength for each part of the target list).
For a
high resolution study, for example stellar radial velocities at 8600A
via the Calcium triplet, the solution is obvious, one uses the central
wavelength of the observation. However, doing so will mean that
little blue light (perhaps for example at the 4000A Balmer break) would
fall into a fibre placed correctly for 8600A.
For a
low resolution program, the only real option is typically to configure
for the central wavelength and accept some loss of signal at the ends
of ones spectra.
The figure below attempts to demonstrate this effect graphically. This figure has been created using the AAOmega Configure software. The same .fld file was configure 3 times but each time a different configuration wavelength was specified (850, 650 and 525nm here). The .sds file thus created was then investigated and the different 2dF field plate positions that would represent the correct position for each fibre, as a function of configuration wavelength, were extracted.
The plot show the 2dF field plate with Parked fibres (those not used) around the edge of the field plate. Program fibres are shown on the field plate as a black cross with an associated red and blue vector. The cross marks the 650nm configure wavelength position while the vectors show the offset to the 850nm and 525nm positions. As one can see from the plot, 650nm marks the optimum configuration for this wavelength range, so as to loose the least amount of light across the full spectrum (but giving a deficit at both he blue and the red ends). The scale is given by the 1arcsecond circle in lower left corner. The magnitude of the radial displacement is shown in the lower plot. Note that the crosses at ~zero correspond to the guide star fibres which are placed at 5000A for the guide camera in all configurations (the small shifts seen here are due to changes in the effective center of the configuration at the different wavelengths).
The conclusion one reaches is that, for fibres with 2arcsec diameter, the only correct fibre placement when the acquisition of the Red and Blue light is key to a project, is to place the fibre for a central wavelength and accept losses at each end of the wavelength range. An excellent paper on the magnitude of placement errors of this kind is Newman P.R. 2002 PASP 114 918.
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A graphical demonstration of CVD effects in the 2dF prime focus corrector. Note how the effect is most important between 1/2 and 2/3 of the way out towards the edge of the field plate. |
Field distortion: Differential plate scale and ZD
Why you should restrict your range of Hour Angle during an observation
A final effect one must consider is the differential plate scale stretch induced by the atmosphere at high ZD. This is also due to atmospheric refraction, but this time differential with respect to position in the wide field (it is close to monochromatic, to first order). It can only be corrected for fully by moving the fibres on the 2dF field plate to new apparent positions. The atmosphere modifies the true RA/Dec of ones targets to an Apparent observed position. Over a 2degree field of view, this modification has significant variations in magnitude with changes in HA. Whats more, as the Hour Angle changes the size of the modification changes significantly as strong function of field plate position. While the full horror of this effect is a complex shift in apparent position across the field, and depends in detail on where one is pointing on the sky, the effect can (to first order) be considered as three components:- Translation of the field center - taken out by telescope tracking
- Rotation of the field - taken out by the 2dF field plate rotation mechanism
- A differential change in the plate scale - Not correctable
Quantitative estimates of the effect
A series of configurations have been prepared using Configure to demonstrate the effect, and are presented below. These configuration have show the effective "positional error" (note this is not 2dF robot error, but rather an an unavoidable effect of differential atmospheric phenomena) for a 2dF configuration which has been configured for a certain time, and is subsequently observed at a different time.In the plots that follow, we will use 0.5arcsec as our rule-of-thumb for the maximum tolerable positional error due to atmospheric effects, and aim for a mean error below 0.2arcsec. The concerned reader should review the effects of placement errors in more detail, see Newman P.R. 2002 PASP 114 918. When considering these effects, one must also remember that other sources
of error, including the intrinsic accuracy of the positioner; tracking errors, the effects of CVD and errors in the input positions, are likely to contribute at the 0.25" level. When a fibre is away from a it's target by ~1arcsec, one is loosing of the order 50% of the available light.
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Here we see the effect of observing a
field 2 hours away from its configuration time. The fibres
in these -20deg declination field were positioned correctly for a the
field as it would be observed as it transits the meridian. The
Zenith distance during transit for this field would be of the order
10deg. Two hours later the apparent position of the target objects has moved, due to differential atmospheric effects. The upper panel shows the distribution of targets across the field (in units of microns, his plot is in 2dF robot coordinates, with North to the right and East at the top). The vectors have been multiplied by a factor of 800 to make them visible. The circle in the bottom left hand corner indicates the size of a ~2arcsec diameter fibre on the same scale. The lower panel shows the lengths of the vectors in arcsec, i.e. the total error, plotted against radial position in the field. The mean error in this case is 0.15" with a maximum value of about 0.4". A dominant rotational effect is visible, this would be corrected in part by the 2dF field plate rotation mechanism. One might well conclude that it is possible to observe +/- 2hour either side of HA=0, even if plate rotation was not available. |
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Here we see the same plot as above, but
this time with the end of the observation 3hour away from the transit
configuration time. A field plate rotation has been applied in this instance, but we see that the error for many fibre is above the fiducial 0.5arcsec level, even after rotation has been accounted for. |
| This next bit gets a little tricky. But it's important. Most novice 2dF users should probably call their support astronomer about now. |
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One can improve upon the above plot by configiring not for
HA=0, and then letting the field set for three hours, but rather by
configuring for some predefined mid point, which minimizes the errors
in apparant position throughout the exposure. In the plot to the left, the field has been configured for HA=2, but if one was to start observing at HA=0 and observe until HA=3, the maximum error would still be below 0.5arcsec for the full field. Note that this field is at Dec=-20degrees. The situation will be a little different for fields at higher Zenith Distance. |
| Things get really tricky when you want to observe through transit. However this is what one would normaly want to do, and so it must be considered. |
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Once one realises that it is possible to observe over the
range HA=0 -to- +3 hours, then the next question is, "is there a
correct fibre placement which would allow observation from HA=-3 to
HA=+3?". Traditionally one may have used the mid point of the configuration, at HA=0. However this effectively maximizes the positional error, as we saw in the above figures. While the HA=+/-3hour observation results in a complex arrangement of shifts, it is possible to configure the field so as to minimise the overall error for fire placements over the full 6hour integration, provided plate rotation corrections are applied during observations, at least for this Dec=-20degree field. The correct procedure is to configure NOT for the some global midpoint (historically at HA=0), but rather to position each fibre at some exposure-time-weighted midpoint of the range of its individual X and Y plate positions. This last "tour de force" will require a future modification to the Configure software if there is considerable demand for long AAOmega observations. The complex plot to the left demonstrates the ultimate goal. The fibres are positioned at the black crosses, while the magenta, blue, green and red arrows indicate the effective positional errors of the fibres during a 6 hours observation between HA=-3 and HA=+3 for the Dec=-20 field. |
Rob Sharp (rgs@aao.gov.au) & Russell Cannon