Curvature Model Product

Metadata

Data product name	DpdSirCrvModel
Data product custodian	SIR
Name of the Schema file	euc-sir-CrvModel.xsd
Processing function using the data product	SIR

Proposed for inclusion in EAS/SAS

This product is proposed for inclusion in the SAS: no

This is an internal Data Product.

Data product elements

Header	object of type sys:genericHeader
Data	object of type sir:sirCrvModel
QualityFlags	object of type dqc:sqfPlaceHolder
Parameters	object of type ppr:genericKeyValueParameters

Detailed description of the data product

The sirCrvModel describes the 2D spectra displacements wrt the ideal dispersion direction, which (in case GWA_TILT=0) is perfectly aligned along the pixels grid . The model operates within the SIR rotated layout where the dispersion direction is nearly horizontal, and this direction remains consistent across all detectors (see Optical Model Product description for further details)

Due to optical distortions in real data, spectra are not perfectly aligned along the pixels, they are curved and the description of these curves vary within the Field of View (FOV). The sirCrvModel describes these deviations (in mm) of the spectral trace wrt the theoretical dispersion direction.

Each grism/tilt configuration is independently calibrated and the coefficients of each configuration are store the sirCrvModelOrders structure. The sirCrvModel collects all the sirCrvModelOrders available.

Relevant items of sirCrvModelOrder, are:

• GWATilt: (A in Fig. 34) the grism nominal tilt value (0, +4, -4);

• ExtraTilt: (B in Fig. 34) the extra tilt computed during calibration (not implemented yet);

• SpectraOrder: (C in Fig. 34) the list of sirCrvModelContent, each item contains the geometrical description of a given spectrum order for the current grism (see description below).

Fig. 34 : The DpdSirCrvModel description

SpectraOrder description

For each spectral order, one Chebychev mono dimensional polynomial (of order \(N\)) is used to compute the displacement \(\Delta c\) along the cross dispersion direction, originating from the lambda reference position determinated by the sirOptModel.

(1)\[\Delta c_{[mm]} = \sum_{k=0}^N \alpha_{x,y,k} T_k\left(\Delta d_{[mm]}\right)\]

Fig. 35 The spectra curvature and its description according with the CrvModel

Each spectrum will have its own set of \(\alpha_{x,y,k}\) coefficients because each spectrum will be in a different position in the FOV, i.e. \(\alpha_{x,y,k}\) are not constant across the FOV, they depends on the \(x,y\) position of the spectrum in the FOV.

The SIR Pipeline uses a global model to describe this coefficients variation. The local coefficients \(\alpha\) are obtained by the evaluation of a global 2D Chebychev polynomial

\[\alpha_{x,y,k} = \sum_{i,j} a^{(k)}_{i,j} T_i(x)T_j(y)\]

These \(\textbf{A}^{(k)} := \{ a^{(k)}_{i,j} \}\) matrices are stored in the sirCrvModelContent structure, which contains:

• Order: (D in Fig. 34) the order of the spectrum (1st, 0th, 2nd, …) to describe;

• LocalModelDeg: (E in Fig. 34) the degree of the Local crv model (\(N\) in the equation (1));

• LocalRanges: (F in Fig. 34) the validity domain of the local Chebychev polynomial; this range plays the same rule of the domain variable in numpy.polynomial.chebyshev.Chebyshev definition. (Range extremes are in mm)

• GlobalRanges: (G in Fig. 34) the validity domain (along the 2 directions of the FOV) of the local 2D Chebychev polynomial. Even in the case the range extremes are in mm

• Model: (H in Fig. 34) a list of specificDegreeMatrix, each item of this list contains one \(\textbf{A}^{(k)}\) matrix. If the local polynomial is of degree \(N\), the model will contain \(N+1\) matrices. Each matrix is used to obtain one local coefficient \(\alpha_{x,y,k}\) in a given position (\(x,y\)) of the FOV