AAOmega, CVD and Atmospheric Distortions:

The Chromatic Variation in Distortion of the 2dF prime focus corrector and the effect of the Earth's atmosphere

The prime focus corrector of the 2dF telescope top-end is essentially a 4-element corrector, incorporating an Atmospheric Distortion Corrector (ADC). It is charged with not only delivering the un-vignetted 2degree field at the 2dF field plates, but also creating a flat focal plane, with nearly constant plate scale (projected fibre diameters vary between 2.0-2.1 arcsec across the field plate) and without creating large non-telecentric angles. The subtleties of this have a very real impact on 2dF and AAOmega operations (Lewis et al., 2002, MNRAS)

Does the Atmospheric Distortion Corrector (ADC) work correctly?

The first two elements of the prime focus corrector are both prismatic doublets, counter-rotated to compensate for atmospheric distortion. The ADC is actively controlled and 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 cutting-edge design for its time. The practical impact of CVD is an effect similar to atmospheric dispersion, but independent of the atmosphere or Zenith Distance. Like atmospheric dispersion, CVD is a differential refraction (with respect to wavelength) effect, but whereas 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 (in a radial direction and with a radial magnitude 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 centre 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 spherical 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 optimum wavelength to use when placing a fibre. Note that in recent versions of Configure, it is possible to specify up to 9 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). This option is described in more detail in the Configure input description.

For a high resolution study, for example stellar radial velocities at 860nm 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 400nm Balmer break) would fall into a fibre placed correctly for 860nm.

For a low resolution program, the best option may be to configure for the central wavelength and accept some loss of signal at the ends of ones spectra.

The figure below demonstrates the predicted strength of this effect graphically. This figure has been created using the AAOmega Configure software. The same .fld file was configured 3 times, each time with a different configuration wavelength (850, 650 and 525nm here). The .sds files thus created were 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 figure shows 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 lose the least amount of light across the full spectrum (but giving a deficit at both the blue and the red ends). The scale is given by the 1 arcsecond circle in the 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 centre of the configuration at the different wavelengths).

A direct demonstration of the actual effect of CVD is shown in Figure 5 of Cannon et al. AAO Newsletter Feb 2008, p26-30. This was created using the 'raster scan' technique on a set of observations of relatively bright stars and finding the centroids of the stellar images. The pattern agrees very well with the predicted effect shown below.

There is more discussion of both the ADC and the dramatic effects of CVD in Cannon et al. AAO Newsletter Feb 2000, p14-15.

The conclusion one reaches is that, for fibres with 2arcsec diameter, the best fibre placement when the acquisition of the Red and Blue light is key to a project, is usually 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.

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 could only be fully corrected for by moving the fibres on the 2dF field plate to new apparent positions. However, this is not practical with 2dF since it would involve re-configuring the entire field.

The atmosphere modifies the true RA/Dec of one's targets to an Apparent observed position. Over a 2degree field of view, this modification has significant variations in magnitude with changes in HA. What is more, as the Hour Angle changes, the size of the modification changes significantly as a strong function of field plate position. While the full effect is 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 centre - 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

The first and second effects are accounted for during observations. However, the differential plate scale change (which contains the remaining complexity of the true distortion in this overview) would require a mechanism that could stretch the solid metal field plates!

The Configure software and the 2dF positioner know about these effects and so fibres can be correctly configured for a particular HA, but as one moves away from this HA the fibre placements become increasingly incorrect. 2dF was designed with a 1 hour reconfiguration (positioning) time so that observations would only need to be performed +/-30mins from the correct HA. In practice most users find +/-1 hour is acceptable for a full 2degree field configuration and +/-2 hours is fine for fields near the zenith. Smaller fields of view are affected to a lesser degree, fields at higher |HA| are affected more quickly due to the larger differential plate scale change encountered.

Quantitative estimates of the effect

A series of configurations have been prepared using Configure to demonstrate the effect, and are presented below. These configurations 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 0.5 arcsec as the maximum tolerable positional error due to atmospheric effects, and aim for a mean error below 0.2 arcsec. 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 arcsec level. Note: when a fibre is away from its target by ~1 arcsec, one is losing ~50% of the available light and the relative losses are greatest in good seeing!

	Here we see the effect of observing a field 2 hours away from its configuration time. The fibres in this Dec = -20deg field were positioned correctly for 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, this 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 ~2 arcsec 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 component would be corrected by the 2dF field plate rotation mechanism. In this case, it is possible to observe +/- 2hour either side of HA=0, even if plate rotation was not available.
	Here we see the same plot as above, but this time with the end of the observation 3 hours away from the transit configuration time. A field plate rotation has been applied in this instance, but we see that the uncorrectable error for many fibres 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.
	One can improve the above plot by configuring 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 apparent 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.
	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, one global time will not be suitable for each fibre. 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 fibre placements over the full 6 hour integration, provided plate rotation corrections are applied during observations, at least for this Dec=-20 degree field. The correct procedure is to configure NOT for the some global mid-point but rather to position each fibre at some exposure-time-weighted mid-point of the range of its individual X and Y plate positions. The complex plot to the left demonstrates this 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 hour observation between HA=-3 and HA=+3 for the Dec=-20 field. The configure software was updated in 2008 to calculate the optimum centroids for all targets given the start time and duration of an exposure. The overall loss of signal is minimised as a result of this change.

Sarah Brough (sb@aao.gov.au) & Russell Cannon

AAO