Grism-based Spectrograph Modeling¶

Version:	0.8 of 16/06/21, 17:33
Author:	Yannick Copin <y.copin@ipnl.in2p3.fr>

Abstract: This module initially implemented the spectrograph optical model used for the TIGER-like integral field spectrograph (e.g. SAURON [Bacon01] and SNIFS [Lantz04]) data-reduction pipeline, and first presented in [Copin00]. It provides a flexible chromatic mapping between the input focal plane and the output detector plane, based on an effective simplified ray-tracing model of the key optical elements defining the spectrograph (collimator, prism, grating, camera), described by a restricted number of physically-motivated distortion parameters.

Optical modeling¶

The model only handles the geometrical part of the light propagation through the spectrograph, i.e. provides a mapping between a wavelength and a position in the entrance focal plane to a position in the detector plane (at the output focal plane). It is therefore assumed all the PSF and scattered light effects (related to focus, axial chromatic aberrations, diffusion, etc.) are modeled independently.

Optical elements¶

The spectrogrism.Spectrograph model includes optical elements between the input focal plane and the output detector plane:

an optional spectrogrism.Telescope, which converts a direction in the sky into a position in the focal plane;
a spectrogrism.Collimator, which converts a position (in the focal plane) into a direction;
a spectrogrism.Grism (an association of a spectrogrism.Prism and a spectrogrism.Grating), which converts a direction into another direction depending on wavelength and dispersion order;
a spectrogrism.Camera, which converts a direction into a position (in the detector plane);
a spectrogrism.Detector, which actually project positions onto the translated and rotated detector.

Both spectrogrism.Collimator and spectrogrism.Camera include geometric quadratic radial distortion and lateral colors (transverse chromatic aberrations). spectrogrism.Prism includes 3D-tilts.

Figure: Modeling of 5×5 sources in the detector plane at 10 individual wavelengths, using the SNIFS-R optical configuration. Orders -1 (very top), 0 (undispersed), 1 (middle) and 2 (bottom) are represented. The size of the symbol somehow encodes the blaze function of the spectrograph.

Positions and directions¶

A 2D-position \((x, y)\) is encoded in complex number \(x + jy = r\,\exp(j\varphi)\).
A 2D-direction \((\theta, \phi)\) – where \(\theta\) is the angle between the optical axis \(Oz\) and the propagation direction, and \(\phi\) the phase in the transverse plane \((Oxy)\) – is encoded in complex number \(\tan(\theta)\,\exp(j\phi)\).
A 3D-direction is encoded by the coordinates of the unit-vector \((x, y, z)\).

Distortions¶

A distortion.StructuredGrid is a structured grid of (complex) 2D-positions, with plotting and distortion-adjustment facilities.
distortion.GeometricDistortion implements the full Brown-Conrady (achromatic) distortion model, including radial and tangential components of arbitrary orders.
distortion.ChromaticDistortion is a minimal lateral-color distortion implementation.

Near Infrared Spectrometer and Photometer (NISP)¶

Zemax simulations¶

The spectrogrism optical model is used to simulate the Near Infrared Spectrometer and Photometer (NISP) of EUCLID, mimicking full sky-to-detector Zemax spectroscopic and photometric simulations for a nominal NISP configuration (courtesy J. Zoubian).

Figure: Zemax sky-to-detector multi-order simulation of 17×17 sources in the detector plane at 13 individual wavelengths (outlined symbols) and minimally 1st-order-adjusted optical model using nominal NISP parameters (filled symbols), along with associated 0th- and 2nd-order predictions.

Questions regarding the current Zemax simulation:

input y-coordinates are offset by +0.85 deg
output y-coordinates are not centered: (dx, dy) = (+0.7, 179.8) mm, corresponding to (+0.7, -4.2) mm for centered y-coordinates
input position (+0.4, +1.25) is missing the 1.85 µm wavelength

NISP optical design¶

The NISP optical design is presented in [Grupp12] and updated in [Grupp14] (see Fig. 1).

Fig. 1 The EUCLID f#20 to f#10 relay system including filter and grating position (from [Grupp12]).

It consists of:

an f/20 1.2 m diameter Korsch type three mirror telescope in off-axis configuration
the Corrector Lens assembly CoLA (fused silica)
depending on the observing mode:

photometric mode (NISP-P):

a filter with mildly powered spherical entrance surface and flat exit surface (fused silica)

spectroscopic mode (NISP-S):

a grism with mildly powered spherical entrance surface and binary optic (curved line) grating exit surface (fused silica)

These intrinsically static elements are placed in filter/grism wheels with limited position repeatibility.
the Camera Lens assembly CaLA (CaF2/S-FTM16/S-FTM16), providing an f/10 beam.
16 2k×2k IR detectors

The objective of this work is to assess the possibility to model in an effective way the NISP-S optical scheme in order to be able to predict multi-order spectrum locations from photometric catalogs.