Testing adaptive optics for ALMA The Messenger The outburst of V1647 Orionis FLAMES survey of massive stars ESO users feedback campaign No. 131 – March 2008 –March 131 No. Telescopes and Instrumentation Advanced Calibration Techniques for Astronomical Spectrographs Paul Bristow1 One way to ensure that the engineering Most of the computations involve rotation Florian Kerber1 data propagates from instrument build ing matrices to represent the change of ori- Michael R. Rosa 2,3 to operations is to capture all the engi- entation of the optical ray at the surfaces neering information in a physical model- of the components. For example, the based description of the instrument. matrix representation of the order m 1 ESO This model accompanies the instrument transformation performed by an echelle 2 Space Telescope European throughout its life cycle and is used to grating with constant sE at off-blaze Coordinating Facility, ESO drive the science data reduction pipeline. angle q, operates on a 4D vector with 3 Affiliated to the Science Operations and In our concept the model is combined components (l, x, y, z) representing a ray Data Systems Division, Science Depart- with validated physical data of the instru- of wavelength l. Here q and sE are ment, European Space Agency mental components and calibration refer- amongst the physical model parameters ence data. for this instrument. ESO’s Calibration and Model Support Hence there is a complete set of param- Group is involved in a variety of activi- Implementation and application of an eters that describe the passage of a ties related to the calibration and physi- instrument physical model photon through the spectrograph. These cal description of instruments, with the pa rameters are physical quantities (an- objective of supporting the reduction Our approach comprises an instrument- gles, distances, temperatures, etc.) and of science data and facilitating opera- specific model kernel and associated describe the actual status of compo- tions. Here we describe the construc- software to optimise the model parame- nents. They can always be adjusted to tion, optimisation and application to sci- ters and to apply the model’s predictive match the observed behaviour of the entific data reduction of physical in- power to the calibration of science data. instrument or to predict the effects of tilt- strument models. Such models have ing/modifying a component. For exam - been implemented for the HST STIS ple, adjusting the camera focal length will spectrograph and form an integral part Model kernel change the scale on the detector. of the data reduction pipelines for CRIRES and X-shooter. These models First of all a streamlined model of the dis- are supported by validated physical persive optics, that enables a rapid eval- Optimisation data of the instrumental components uation of where any photon entering the and calibration reference data. instrument arrives on the detector array, The model parameter set can be opti- is constructed. Though based upon the mised to reflect the performance of opti cal design, it is no substitute for the the operational instrument with suitable The life cycle of an instrument can be fully-fledged optical (e.g. Zemax/Code V) calibration data, in a similar way that a described as follows: models developed by the designers. polynomial dispersion solution would be Clearly this model kernel is specific to fit. The difference is that the parameters 1. Science Requirements each instrument, but the following optimised here have physical meaning 2. Optical Design (Code V/Zemax) sub-components and associated param- and represent the actual configuration of 3. Engineering Expertise eters are typical: the instrument. There are essentially two – Entrance slit and collimator scenarios in which one needs to perform 4. Testing and Commissioning – Relative position and orientation of the optimisation. 5. Operation and Data Flow the slit 6. Calibration of Instrument – Focal length of collimator Before the instrument is actually built, the 7. Scientific Data and Archive – Pre-disperser (e.g. Prism) only parameters available are those from – Orientation of entrance surface the instrument design. Inevitably, once Experience shows that it is difficult to – Orientation of exit surface the instrument has been built, it will differ ensure that the know-how and expertise – Temperature from the design predictions, so it is nec- that went into designing and building – Refractive index as a function of essary to establish the true values. This the instrument (steps 1–3) is brought to wavelength and temperature may also be the case after a major main- full use in the instrument calibration and – Main disperser (e.g. reflection grating) tenance intervention, upgrade to the scientific operations (steps 6 and 7). – Orientation instrument or even an earthquake, result- – Grating constant ing in a physical change in the instru- A case in point is the wavelength calibra- – Camera and detector array ment. In this situation a comprehensive tion, in which well-understood physics is – Focal length of focusing optics and uniform set of robustly identified employed to design a spectrograph with – Orientation of detectors calibration features from dedicated cali- an optimal format while during operations – Relative positions of detectors bration exposures is required. The core the dispersion solution is then derived – Dimensions of pixel grid model function is then iteratively called over and over again in a purely empirical for the identified calibration wavelengths manner by, for example, fitting polynomi- We follow the prescription of Ballester and and the results of each iteration are com- als to a sparse calibration line spectrum. Rosa (1997) in constructing this model. pared with the centroids for these wave- 2 The Messenger 131 – March 2008 lengths as measured in the calibration Optical materials data Initial ‘first guess’ data. We employ the Taygeta (Carter 2001) e.g. prism refractive configuration file implementation of the Simulated Anneal- index (T, λ) ing technique to continually adjust, in a statistically sound manner, all of the mod - el parameters until the best match be - Simulated annealing tween predicted and measured centroids Spectral atlas for is found. Figure 1 is a schematic repre- calibration source, Physical model sentation of this procedure. e.g. high quality Th-Ar kernel hollow cathode data In the case of an instrument such as CRIRES which has multiple modes de - Output fined by the orientations of optical com- Matched ponents (and therefore by parameters Predicted centroids in the physical model), we are able to Measured feature of spectral features optimise the parameter set for multiple centroids in detector in detector pixel modes simultaneously by assigning a pixel coordinates coordinates unique value to each of the changing from calibration parameters on the basis of all data col- source exposure lected for the corresponding mode. We can then characterise the parameters associated with the moving components Compare lists and that determine the mode. compute metric that describes how well Most spectrographs have some moving they match components that allow selection of a given wavelength range. Since there are physical limits to the repeatability and accuracy of these mechanisms, it is use- ful to be able to fine tune the model to Satisfactory No Change configuration match the performance of the instrument match? at the time of a given observation. More- over, even without human intervention, instruments develop malfunctions such Yes Simulated annealing as a drift in wavelength zero points that are not well understood initially. Other affects such as thermal or gravitational flexure occur at some level during rou- Optimised tine operations and also subtly affect the parameter exact details of the instrument optics. In configuration such cases it is clear that there must be some deviation from the initial param- can choose to optimise more parameters Figure 1: Schematic representation of the optimi- eter calibration that was done with data when more data points are available. sation process for instrument physical models. acquired in the absence of these effects (or in the presence of another alignment We have recently achieved the full auto- (see “Optimising Calibration Systems” of these effects). mation of this process for CRIRES. The below) in order to avoid the possibility of procedure is illustrated by Figure 2. First false matches. The significant offset For these reasons we have developed the the model is used to trace the locus on between the red crosses and the corre- capability to re-optimise specific parame- the detector of a given entrance slit posi- sponding features identified in the data ters, using either automatically identified tion. A 1D spectrum is then extracted (magenta circles) is due to a shift in spec- wavelength features in contemporaneous from a Th-Ar hollow cathode lamp (HCL) tral format that has occurred in CRIRES calibration exposures or wavelength full slit exposure along this locus and between the acquisition of the calibration standards specified by users (e.g. known bright features are identified. Using the data used to determine the baseline sky lines seen in science exposures). baseline physical model parameter con- model parameter configuration and the These are used in a similar way to that figuration, we predict the positions of epoch of this data. Hence known wave- depicted in Figure 1, except that only the wavelength features along