.. _SIRSpectralPSFModel: Spectral PSF Model Product -------------------------- Metadata ______________________ +--------------------------------------------+----------------------------------------------------------------------------------------------+ | Data product name | DpdSirSpectralPsfModel | +--------------------------------------------+----------------------------------------------------------------------------------------------+ | Data product custodian | SIR | +--------------------------------------------+----------------------------------------------------------------------------------------------+ | Name of the Schema file | .. raw:: html | | | | | | `euc-sir-SpectralPsfModel.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:sirSpectralPsfModel | +--------------+----------------------------------------------+ | QualityFlags | object of type dqc:sqfPlaceHolder | +--------------+----------------------------------------------+ | Parameters | object of type ppr:genericKeyValueParameters | +--------------+----------------------------------------------+ Detailed description of the data product ======================================== .. DetailedDescStart The ``sirSpectralPsfModel`` describes the 2D spectrogram width across 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 :ref:`sirOPTModel` description for further details). The :ref:`sirCRVModel` describes the geometric curvature of spectrograms and its variation within the Field of View (FoV); similarly, the ``sirSpectralPsfModel`` describes the chromatic evolution of the cross-dispersion width (in pixels), as well as its variations within the FoV. Each grism/tilt configuration is independently calibrated and the coefficients of each configuration are stored in the ``sirPsfModelOrders`` structure. The ``sirPsfModel`` collects all the ``sirPsfModelOrders`` available. Relevant items of ``sirPsfModelOrder``, are (see :numref:`SIR_PSF_schema_`, and :numref:`SIR_CRV_schema_` for additional details): * ``GWATilt``: the grism nominal tilt value (0, +4, -4); * ``ExtraTilt``: the extra tilt computed during calibration (not implemented yet); * ``SpectraOrder``: the list of ``sirPsfModelContent``, each item contains the geometrical description of a given spectrum order for the current grism (see description below). .. _SIR_PSF_schema_: .. figure:: figures/psf_schema.png :width: 400pt The `DpdSirSpectralPsfModel` description. Cross-dispersion width measurement """""""""""""""""""""""""""""""""" The cross-dispersion width is estimated from (unsaturated) spectrograms of bright stars within the FoV, using a Gaussian-fit of the cross-dispersion profile (actually an erf-fit to account for integration over pixels and minimize sub-sampling issue if any). .. figure:: figures/spectrogram_RGS000+0.png :width: 500pt An RGS000+0 spectrogram, shown in SIR coordinates (pixels). Obviously, along-dispersion axis is horizontal, while cross-dispersion axis is vertical. .. figure:: figures/spectrogram_RGS000+0_xdisp.png :width: 300pt A cross-dispersion profile, and the Gaussian fit used to estimate the cross-dispersion position and width of the spectrogram at given along-dispersion position. SpectraOrder description """""""""""""""""""""""" For each spectrogram and dispersion order, a 1D-Chebychev polynomial expansion (of order :math:`N`) is used to model the cross-dispersion width :math:`\sigma` (in pixel), as a function of the distance :math:`\Delta d` (in mm) from the reference position set by the ``sirOptModel`` (see :numref:`SIR_PSF_trace_`): .. math:: :label: psfmono \sigma \text{[pix]} \approx \sum_{k=0}^N \alpha_{x,y,k} T_k\left(\Delta d \text{[mm]}\right) .. _SIR_PSF_trace_: .. figure:: figures/psf.png :width: 400pt The spectrogram width and its description according with the PsfModel. This is the so-called *local model*. Each spectrogram, probing different positions :math:`(x, y)` in the FoV, has its own set of coefficients :math:`\alpha_{x,y,k=0\ldots N}`. The SIR Pipeline then uses a *global model* to describe the spatial variations of the local coefficients :math:`\alpha` across the FoV, namely a 2D Chebychev polynomial expansion: .. math:: \alpha_{x,y,k} \approx \sum_{i,j} a^{(k)}_{i,j} T_i(x)T_j(y) These :math:`\textbf{A}^{(k)} := \{ a^{(k)}_{i,j} \}` matrices are stored in the ``sirPsfModelContent`` structure, which contains (see :numref:`SIR_PSF_schema_` and :numref:`SIR_CRV_schema_` for additional details): * ``Order``: the order of the spectrum (1st, 0th, 2nd, ...) to be described; * ``LocalModelDeg``: the degree of the Local crv model (:math:`N` in the equation :eq:`psfmono`); * ``LocalRanges``: 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``: 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``: a list of ``specificDegreeMatrix``, each item of this list contains one :math:`\textbf{A}^{(k)}` matrix. If the local polynomial is of degree :math:`N`, the model will contain :math:`N+1` matrices. Each matrix is used to obtain one local coefficient :math:`\alpha_{x,y,k}` in a given position :math:`(x,y)` of the FoV. .. DetailedDescEnd