An atmospheric dispersion corrector for FEROS
Table of Content
IntroductionAtmospheric differential refraction
Basic Principles
A short summary of ADC concepts
The effect on FEROS
Progress
References
Other ADC designs
Commissioning
Introduction
An ADC for FEROS is being designed, to be operative starting from ESO period 72. This page is intended as a repository of relevant info, and eventually collect the progress reports.
Basic Principles
The atmosphere acts lik a prism, diffracting the incoming starlight. The magnitude of the effect depends on the zenith distance of the source, and it is greater at greater zenith distances. During a long exposure, the light from sources in a given field will go through different airmasses, depending both on their position and the exposure time. This is a wellknown effect, which is illustrated in the three graphs below, taken from Donnelly et al. (1989). The graphs show the paths of stars in a 60x60 arcmin field, during an integration from 3 hr to +3 hr HA, and for different declinations of a field supposedly observed from the Lick observatory (latitude = +37:20).DEC=10 
DEC=+20 
DEC=+80 



This effect is important for MOS spectroscopy, since slitlets should be
rearranged during the exposure (continuously or at fixed intervals),
in order to keep the source within the slit.
Moreover, the refraction index n of the atmosphere depends on
the wavelength, so each point in the graph would really be a small
spectrum perpendicular to the horizon. And again, the spectrum is wider
at larger zenith distances. The following graph shows how n
varies vs. wavelength, for dry air, at sea level (P=1013.25 hPa), and 0
C temperature. The refraction index is then larger at shorter
wavelengths. At different pressures
and temperatures, n1 is proportional to P/T, so at
higher
altitudes (lower pressures) the refraction index is lower. Of course,
the
index increases if the temperature decreases. Finally, the presence of
water
vapour (higher humidity ) decreases the refraction index.
(n1) x 10^{6 } vs.
wavelength [nm] 

One can get an idea of the magnitude of the effect by computing the
differential refraction between rays of light at the two extremes of
the
desired spectral range. According to Smart (1931), the differential
refraction
is given by
dR = R(lambda)R(ref) = 206264.80625 * [ n(lambda)  n(ref) ] *
tan (Z)
where Z is the zenith distance, and the refraction index n depends
on the water vapour content (i.e. relative humidity), the temperature,
and the pressure. It is computed as explained here. The graph on the
left below
shows dR vs. wavelength, for several zenith distances, and taking the
reference
wavelength at 500 nm. Several dR curves are overplotted, each computed
for
different values of humidity, temperature and pressure. In particular
the
parameters were selected in ranges typical of La Silla: relative
humidity between 0% and 100%, temperature between 0 C and 20 C, and
pressure between 765 and 775 hPa. The changes with respect to an
average value are then small.
dR vs lambda, for La Silla 
dR vs. lambda for wide range
of parameters 


The graph on the right has been obtained after letting P and T vary in larger intervals, namely T between 10 C and 30 C, and P between 750 and 800 hPa. One sees that the differential refraction increases if P or H increase, and it decreases if T increases. The larger effect is that of pressure.
The blue and red image of a star can thus be several arcsec away, so e.g. for MOS spectroscopy, the slitlets should also be continuously rotated along the parallactic angle during the exposure.
In the case of FEROS, we have a fixed circular slit of 1.8 arcsec, so we cannot overcome the chromatism of the atmosphere. Moreover, we are guiding on a star far from the position of the target, so keeping the guide star centered does not automatically ensure that the target is centered as well (particularly at high airmasses and for long exposure times). In order to keep the impact of the atmosphere low, one should then
 center the image of the target at ca. 400 nm, so the displacement of the 300 nm and 1000 nm images will be simmetric out of the slit. If one is interested in a small wavelength range, center the image at a suitable wavelength;
 keep the exposure times short, in particular at high airmasses, and recenter the target and reacquire the guide star each time.
The figure below shows the relative positions of the images of a target, at 350nm, 500nm, and 920nm, at different zenith distances. The circle represents the 1.8 arcsec fiber entrance, and the spots have a diameter of 1 arcsec. The simulation has been done for H=30% (corresponding to a vapour pressure of 3.7 hPa), P=775 hPa, and T = 10 C. The differential refraction is computed with respect to a reference wavelength of 450 nm. The purpose of the ADC for FEROS is then to compensate this effect, for both the object and sky fibers. The ADC will then not compensate the atmosphere across the whole field of WFI (and tracker chip), so it will not eliminate the problem of guiding away from the target.
Atmospheric chromatic
differential refraction at different airmasses 

A short summary of ADC concepts
[This is a short summary of several works by Wynne, see references]In order to counterbalance the atmospheric dispersion, the immediate idea is that to use a prism. However a simple prism would deviate light away from the optical axis. So one uses an Amici prism, i.e. two prisms cemented together such that they appear like an optical element with parallel external surfaces. The two prisms have the same angle but different refraction indices, such that light of an intermediate wavelength is undeviated, while longer and shorter wavelengths are deviated to compensate the atmospheric dispersion. In order to be able to tune the device for different atmospheric dispersions (i.e. airmasses), one splits the job between two such doublets, each giving half of the required dispersion (see next figure). If one wants to correct a more limited range of zenith distances, one double prism could be enough. The two doublets must be free to rotate independently, so when they are in opposite orientations they give null dispersion, while they give maximum dispersion when their orientation is the same. An optical oil can be used to fill the space between the two discs.

In a converging beam, such a device gives both planeparallel aberrations and prismatic aberrations. The prismatic aberrations can be reduced by choosing special glasses, and by putting the ADC as far away from the focal plane as possible.
That is because, if the difference in dispersion between the two glasses is larger, then the prism angles can be smaller, yielding smaller aberrations. And if the refraction index is the same at some mean wavelength, there is no prismatic aberrations at that wavelength, and there are only chromatic aberrations for the rest of the wavelengths. The typical choice is glass of type UBK7 for the lowdispersion prisms, and LLF6 for the hight dispersion prism, both made by Schott. (see also the glass properties below). Of course, one must choose glasses with good transmission in nearUV.
Moreover, the ADC must give an angular dispersion a_{2}=Fa_{1}/D, if a_{1 }is the angular dispersion of the atmosphere and D is the prism dimension. Thus if the ADC is far from the focal plane (larger D), then it has to give a smaller angular dispersion, requiring a smaller angle, and thus giving smaller aberrations. However, a larger prism must also be made thicker, in order to avoid deformation, so that increases the planeparallel aberrations.
Indeed, the best compromise is reached when the position of the ADC makes the planeparallel aberrations dominate. Since the largest planeparallel aberration is the chromatic difference of focus, it can be corrected by giving a small curvature to the two doublets, and arranging the prisms such that glasses of different type alternate.
Such "achromatized ADC of planesurfaced Amici prisms could probably be used at a focal ratio of up to f/8" (Wynne 1993). See next figure.

The two doublets must be oriented such that the dispersion is orthogonal to the horizon and opposite to that of the atmosphere. The two doublets are then first rotated one relative to each other, with a rotation depending on the zenith distance of the object, and taking into account that the dispersion is proportional to the sine of the rotation angle. The direction orthogonal to the horizon is called parallactic angle. The figure below (left panel) shows the parallactic angle vs. hour angle for La Silla. It has been computed for a series of declinations, from 80 to +40. After the target is ca. 1hr off the meridian, the change of parallactic angle with hour angle is almost constant, so the ADC should be given an almost constant rotation speed. The graph on the right shows the rate of change of the parallactic angle. As expected, it shows that close to the meridian one reaches very high speeds (up to several hundred degrees per hour), especially for declinations slightly smaller or larger than the observatory's latitude. However, in those cases the zenith distance is small, and so there is no need for the ADC. After ca. 2 hr off the meridian, the speeds settle to small values, less than 20 deg/hr, and with a small dependence on the hour angle.
Parallactic angle vs. hour
angle for La Silla 



The effect on FEROS
On February 8, 2003, I took several spectra of a few spectrophotometric standards, following them from ca. 2hr before the meridian, through the meridian. The efficiencies were computed using the pipeline, which corrects the spectra for atmospheric extinction. Finally, the efficiency at a given airmass was divided by that at the meridian. Unfortunately, there are no spectrophotometric standards that pass through the zenith at La Silla, and are bright enough for FEROS. The best object was HR4468, which reaches a low airmass at the meridian. Below I then show the result for HR4468, which I followed until it was only 3 min away from meridian, when the airmass was 1.06. Spectra of 10min exposure time were taken continuously. The right graph shows the ratio of the spectra vs. wavelength, while the left graph shows the expectation based on Donnelly et al. (see references). The simulations show that at high airmesses, one loses flux in the blue and red, compared to the reference wavelength. Donnelly et al. "centered" the 500 nm image on the fiber, so at that wavelength they have the minimum flux loss.The right graph shows the real data. Each curve is labeled with the DIMM seeing, the airmass, the peak efficiency, and the image id. Most curves look like the simulations (solid curves), but two of the curves are steeper (dashed), and one has the peak at a wavelength redder than the FEROS limit.
The solid curves show that the image was centered somewhere below 500 nm, and I interpret the dashed and dotted curves as due to the image centered bluer than 400 nm or redder than ca. 900 nm. One possible interpretation of these deviating curves is the effect of differential atmospheric refraction between the guide star and the target, so the target slowly drifts out of the fiber even if the guide star appears centered (see above).
Simulation of loss of flux due
to ADR (Donnelly et al.) 
Loss of flux in FEROS spectra,
due to ADR 


There is some dependence of the centering wavelength with the seeing. The maxima of the curves are identified in red in the graph above, and their wavelength is plotted vs. the FWHM in the next graph (excluding the curve centered to the far red). The white dots represent the two dashed curves. It looks like that when the seeing gets worse, redder wavelengths are centered in the fiber.

Progress
February 2003
First conceptual design:Alain Gilliotte, 18 Feb 2003: "New ADC mode", Tech.Rep. LSOTREESO75441005 (1.0)
Alain Gilliotte, 5 May 2003: "New ADC mode", Tech.Rep. LSOTREESO75441005 (2.0)
Meeting of August 7, 2003
Alain Gilliotte, 4 September 2003: "Final ADC Design", Tech.Rep. LSOTREESO75441005 (3.0) <2>Software
The following program computes the parallactic angle, given the HA and
DEC of the object. Usage: pangle HA DEC. Returns HA, DEC, parallactic
angle, angle speed in deg/hr, for La Silla. If no arguments are given,
or the values are outside the permitted ranges, it will ask for more
input.
pangle.c
References
These is a selection of papers on the subject (all PS.gz files)
Szeto et al. (ADC for
Gemini MOS)
Arribas et al. 1999
(integral field spectroscopy without ADC)
Cuby et al. (how to large
field MOS without ADC)
Donnelly et al. 1989
(implication of atmosphere for fiberfed spectroscopy)
Filippenko 1982 (one of the classics)
Fluks & The 1992
(detailed modelling of effect of atmosphere and slit)
Livengood et al 1999
(refraction in the IR)
Malyuto & Meinel 2000
Some theory in MPE pages
Newman 2002 (positioning errors
in fiber spectrographs)
Stone 2002 (computing
color differential refraction)
Stone 1996 (computing
atmospheric refraction)
Wynne 1984 (ADC in a converging
beam)
Wynne 1986 (ADC for prime
focus, like f/2.5)
Wynne 1993 (A new concept
for ADC, and a good historical intro)
Wynne 1996 (ADC in
the IR)
Wynne 1997 (ADC and AO)
Wynne
& Worswick 1986 (ADC for Cassegrain focus)
Wynne
& Worswick 1988 (ADC for PF)
Schott documents
Abbe diagram of Schott glassesGlass properties pocket catalog
Glass properties catalog
Other ADC designs/projects
p>For convenience I mirror here a few web pages of other ADC projects.ADC for Keck LRIS (1)
ADC for Keck LRIS (2)
Univ. Illinois SIS (UnISIS)
Subaru PF ADC (made by CANON)
ADC for gMOS (Gemini)
ADC for CTIO 4m