Error Propagation in the X-shooter Pipeline
X-shooter will be the first of the second generation VLT instruments. It is a medium resolution spectrograph covering a spectral range of 300–2500nm in a single exposure. It will be delivered to Paranal in 2008.
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University of Amsterdam, Postbus 19268, 1000 GG Amsterdam, The Netherlands; [email protected] APC/UMR 7164, Paris, France GEPI, Observatoire de Paris-Meudon, France ESO, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany
Abstract. X-shooter will be the first of the second generation VLT instruments. It is a medium resolution spectrograph covering a spectral range of 300–2500 nm in a single exposure. It will be delivered to Paranal in 2008. The pipeline will perform full error propagation from raw data through to fully reduced science products. This chapter gives a brief overview of the motivations, complications and solutions found during its development.
1 Motivations The goal of providing full error propagation throughout the pipeline was originally introduced during the definition of the scientific requirements for the instrument. The main motivation for this requirement was to enable the development of a fully accurate optimal extraction routine based on those of Horne [1] and Marsh [2], which require the variance of the data as an input to the algorithm. It is also expected that providing the variance map of the data in the final science products will give scientists an extremely useful tool in the further analysis of the data. Another use of the error data is in the quality control process. The pipeline will enable observers to calculate a quick-look signal to noise spectrum from a completed observation. Also, QC parameters, used by the observatory to monitor the instrument health, are a natural product of the error propagation process.
2 Calculations and Data Formats All the error calculations are based on the classical approach of assuming all errors are randomly distributed, giving the standard error formula for x = f (u, v, ...) of: 2 2 ∂x ∂x ∂x ∂x + ... (1) + s2v + 2suv sx = s2u ∂u ∂v ∂u ∂v
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Where the first two terms in the square-root are the variance of the variables and the third term is the covariance. The data format used within the pipeline carries information on both the variance and quality of all pixels. This format is based upon that proposed by the Euro3D group [3], but simplified to flat Fits image planes, as X-shooter does not require the complex spatial information of the full Euro 3D format. Each output file contains 3 extensions: – The data extension: a 32-bit floating point image containing the result of a pipeline calculation. – The statistical error extension: a 32-bit floating point image containing the result of the error calculation. – The quality extension: a 32-bit integer image, which is used to provide 32 boolean flags for defining bad pixels.
3 The Problem of Covariance As can be seen in Fig. 1, the spectral format of X-shooter is highly distorted, the orders are curved, and the spectral lines have a varying amount of tilt within the orders. This means it is impossible to resample the data using a simple linear kernel, which would preserve the noise statistics. Instead we will have to use a more complex resampling method, which will int
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