Relation between wavefronts and coordinate transforms

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Overview of the NIRSpec instrument

The primary science driver for NIRSpec is the spectroscopy of high-redshift galaxies out to z “ 6 and beyond, where the end of the dark ages and begin of the reionization era is assumed. A second objective is the study of the evolution and assembly of galaxies throughout the ages. Therefore, the instrument has been designed as a multi-object spectrograph with the goal to observe at least 100 objects simultaneously. This capability is offered by a MicroShutter Array (MSA), consisting of four configurable grid masks for individual target selection (Kutyrev et al., 2008), covering a Field Of View (FOV) of at least 9 arcmin2. In addition, NIRSpec harbors an Integral Field Unit (IFU, Closs et al., 2008) with a small FOV to resolve single objects in both spatial and spectral dimensions. And lastly there are five FiXed SLits (FXSL) with different widths for high-contrast long-slit spectroscopy. Especially one of them (SLIT_A_1600) has gained scientific importance, as it offers the spectral analysis of exoplanetary transit events, and thus the characterization of exoplanets.
NIRSpec is sensitive across a spectral range of 0.6 to 5 μm, more than three wavelength octaves, which therefore is divided into three main scientific bands. In each of them, two dedicated gratings provide a spectral resolution of R “ λ{Δλ « 1000 and R « 2700. The complete wavelength span can also be observed with a polished. Only some subsystems employ other materials as Invar and Aluminum.

Optical layout of JWST and NIRSpec

The JWST observatory consists of an Optical Telescope Element (OTE), and an Integrated Science Instrument Module (ISIM). The OTE primary mirror is assembled from 18 partially deployed hexagonal segments. The telescope optics has an effective focal length of 131.4 m and delivers a f {20 beam to the instruments at the curved exit focal surface (OTE Image Plane, OTEIP, see Figure 1.2). The field of view is split up into different regions for the science instruments and the FGS (Figure 1.3). JWST has an off-axis telescope, therefore a master chief ray has been defined serving as reference origin for the FOV coordinates. NIRSpec has a field allocation rotated clockwise by 41.5°, defined by nine field points F1–F9. The spectral direction is tangential to the symmetry axis of the telescope optics.
At the OTEIP, the NIRSpec Field Stop (FS) constrains the observable sky area. The light is then picked up by the two coupling mirrors COM1 and COM2 and guided to the optical bench. The general optical design consists of three major blocks, all employing Three-Mirror Anastigmats (TMAs) (te Plate et al., 2005). Figure 1.4 shows the paraxial representation of the optical train with the different modules and key components. A design drawing of NIRSpec with the light path can be seen in Figure 1.5.
The FORE optics re-images the OTEIP onto the slit plane at the MSA with an adjusted scale, a telecentric beam, and flattened focal surface. The nominal f-number is converted to f {12.5. In the pupil plane, the Filter Wheel Assembly (FWA) is located, carrying the filters listed in Table 1.1. Before reaching the MSA, the light also passes through the Refocusing Mirror Assembly (RMA), which allows the adaption of the focus without displacing the beam laterally.
The COLlimator optics (COL) projects the light from the slits onto the Grating Wheel Assembly (GWA), where a pupil plane is located. The GWA is equipped with eight elements described in Table 1.1 and allows the selection of disperser band and resolution, or mirror for imaging. Finally, the CAMera optics (CAM) focuses the (dispersed) beam onto the two detectors in the Focal Plane Array (FPA) with a f-number of f {5.6.
The IFU entrance aperture is located in the MSA plane, but normally obscured by the MSA magnet arm. IFU and MSA observations are exclusive as their spectra share the detector area, so all shutters have to be closed during IFU operations, and the IFU has to be blocked for MOS exposures. The IFU optics are split into an IFU FORE part, which re-images and -scales the MSA plane onto the slicer, and an IFU POST part, which picks up the 30 image parts, and creates a virtual slit image for each slice at the MSA plane. The rest of the light path is similar to the other observation modes. More details of the optical properties are given by Closs et al. (2008).
For the internal calibration, NIRSpec is equipped with a CAlibration Assembly (CAA), which hosts a series of lamps for different flatfield and spectral calibration illuminations. The beam of the CALibration optics (CAL) is coupled into the nominal NIRSpec path by putting the OPAQUE filter, that also acts as a shutter for external light.
One part of the ground support equipment is the Calibration Light Source (CLS, Bagnasco et al., 2008). This is the primary tool for the absolute radiometric and spectral calibration of NIRSpec during the ground calibration campaigns. It consists of a lightbox with filament lamps and a set of four filter wheels, which carry different attenuators and spectral filters to generate appropriate illuminations for the flatfield and spectral calibration. In addition, there is an Argon emission line source and a laser diode for accurate spectral reference. All the sources are fed into a large integrating sphere, whose exit aperture mimics the JWST pupil. A Field Stop Mask (FSM) can be placed at the NIRSpec entrance for a flatfield illumination, as well as a PinHole Mask (PHM) to calibrate the geometrical distortion. The latter has a grid of small holes (diameters typically ă 8 μm) which create quasi point-like sources in the OTEIP, and also allow the characterization of the polychromatic PSF of the instrument.
In spring 2011, the first NIRSpec flight model (FM1, Figure 1.6) has successfully undergone cryogenic testing and calibration. Due to hardware issues, a second assembly of the components is currently under way (FM2), and will likely be completed towards the end of 2012.

The NIRSpec Instrument Performance Simulator

Early in the development of NIRSpec, the need for an instrument simulator was realized, given the inherent complexity of a multi-object spectrograph, with all other operation modes on top. In the frame of the project, the Centre de Recherche Astrophysique de Lyon (CRAL) has developed the NIRSpec Instrument Performance Simulator (IPS) software (Gnata, 2007; Piquéras et al., 2008, 2010). Its primary functions are to assess the instrument specifications, verify the performance, and do end-to-end simulations of calibration and scientific exposures. Besides, it serves to create realistic input data for processing tools, as the Instrument Quick Look Analysis and Calibration software (IQLAC, Gerssen et al., 2008) or the final NIRSpec data reduction pipeline.
To simulate the propagation of light, the instrument is divided into optical mod-ules, mostly defined by the single TMAs (COM + FORE, COL, CAM, CAL, OTE, IFU FORE, IFU POST), and the functional parts as filters, slits, and dispersers. The IPS uses a novel approach combining Fourier optics for the diffractive effects, geo-metrical coordinate transforms between the key optical planes, and simple efficiency calculations for the radiometry. These elements produce noiseless electron rates as a first main simulation product. The data contains the number of electron per second in each detector pixel, without any photon or readout noise, separate for each disperser order.
In a second stage, the readout process is simulated. All detectors in JWST use a sampling up the ramp-technique, where the signal in each pixel is probed non-destructively during the integration time. In the IPS, the electron rates for each pixel are collapsed over the orders, dark current is applied, and all the noise contributions added (Poisson, readout, etc.). The currently integrated signal is then put into a readout frame, and depending on the parameters, the frames are averaged to groups and written into the readout cube file.
In order to reduce the calculation time of electron rates, the sources are split into three spatial and spectral categories, each of them simulated differently. The spatial types are point sources (spatially unresolved), background sources (spatial variations on scales much larger than the instrument Point Spread Function, PSF), and extended sources (in between). The spectral types are continuum spectra (spectral variations on scales much larger than a resolution element), unresolved emission lines and absorption lines associated with a continuum, and spectrally resolved (in between).
Point sources are always completely Fourier-propagated for each required wave-length. For the other source types, there is a collection of pre-calculated PSFs for the step up to the slit plane, and for the spectrograph from slit to detector. They can be created with a single wavefront error map for the whole module, or with a grid of 3×3 maps covering the relevant fields. From them, the locally vaild PSF is then interpolated. Background sources are projected to the detector, the slit mask is applied, and they are convolved with the spectrograph PSF. Extended sources are similarly processed, but convolved with the PSF at the slit plane before applying the slit mask.
In the case of emission and absorption lines, this is done for the single given wavelength only. With continuum spectra, the spectrograph PSF is collapsed in spectral direction before being interpolated to the local wavelengths. Besides, the sampling along the spectral direction on the detector is reduced to full pixels. The spectrally resolved spectra are always using the full 2D PSF for each oversampled wavelength step on the detector.

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Goal and structure of this thesis

The goal of this thesis is to demonstrate the verification of the IPS, the instrument model and the instrument itself, and show first scientific simulations of NIRSpec observations.
In order to assure correct and accurate simulation results, one has to differentiate between two sources of errors: The intrinsic design of functions and algorithms in the software, and the data used in the instrument model.
The first can be partially checked by simulations with controlled inputs and models, which allow an independent calculation of the expected results. This approach has been taken in the acceptance tests required before the software delivery. However, they may not be sensitive to wrong assumptions in the software design, and effects caused by realistic model data.
The second type of errors can be mitigated by assembling the instrument model from measured and as-built subsystem data where possible. Nevertheless, this is not always feasible, the data may be inaccurate, and the interplay with other model data can cause unforeseen effects. To verify the software functions as well as the models, it is necessary to compare simulations with theoretical results and with real instrument measurements. A first set of them for the NIRSpec FM1 is available from the cryogenic calibration campaign, taken in spring 2011.
The final purpose of the IPS is to provide realistic simulations of in-orbit ob-servations. Naturally, a complex instrument also yields a complex simulator, and to facilitate the scientific application, it is necessary to create a simple way to use external source data. Besides, the IPS outputs are electron rates or raw data cubes, which need to be processed before any scientific analysis.
With the necessary tools and data prepared, it is then possible to produce accurate on-sky simulations, and analyze them easily. This enables a in-depth assessment and verification of NIRSpec’s capabilities for different science cases. Besides, it shows the characteristics and quality of the data that could be expected from the instrument.
This thesis describes the different steps in the model preparation and verification process, along with software tools for science data input and output data processing, and presents first simulations of on-sky observations. The structure is split into the following parts: In chapter 2 we revise two specific IPS algorithms, and in chapter 3 we describe the data of the as-built instrument model. We present two software tools to facilitate the usage of the IPS in chapter 4. In chapter 5 we demonstrate how we verified the instrument model by comparing simulations with calibration data, and finally in chapter 6 we show the simulation and analysis of two scientific observation types: a multi-object scene, assembled from high-redshift galaxies, and exoplanetary transit events.
The work was embedded in the NIRSpec project environment, and makes use of various other existing efforts, most notably the IPS software. For clarity, we repeat essential characteristics of the simulator in chapter 2, in detail the algorithm for coor-dinate transforms in the instrument. Using this concept, we re-implemented the slit tilt effect based on the presented analysis. Also the general algorithm of the Fourier propagation and the coupling with physical parameters was established during the software design, however it had never been verified with the real orientations and the process of stepping through the instrument principal planes. In the end, the corresponding code was fully revised with the new considerations from this thesis.
The assembly of an as-built instrument model described in section 3.2 was largely a team effort, especially as it was part of the deliverable package in the IPS project. However, the work leading to the optical as-built model presented in section 3.3, originates solely from this thesis. It only uses the existing alignment model from Astrium as a starting point, and was done independently of officially required activities.
Finally, the development of the auxiliary software, the verification of the instru-ment model data, and the scientific simulations are fully original work, contributions from collaborators are marked accordingly.
As mentioned in section 1.4, the IPS consists of several modules to model different physical processes (Piquéras et al., 2008). The basic considerations for the design of the algorithms can be found in Gnata (2007). However, some points had not been defined in detail, and other effects were only apparent once realistic simulations were run. Two major issues are the geometrical coordinate transforms, especially the effect of the slit tilt, and the orientation and sampling of wavefront errors and PSFs. We therefore review two simulation elements, the implementation of coordinate transforms in section 2.2, and the Fourier propagation in section 2.3. Independent of these major points, there was always close support of the software development team during the IPS project, for various issues ranging from user interaction, finding and isolating errors in the computations, and testing so far unused functionality.

Table of contents :

1 Introduction 
1.1 The James Webb Space Telescope
1.2 Overview of the NIRSpec instrument
1.3 Optical layout of JWST and NIRSpec
1.4 The NIRSpec Instrument Performance Simulator
1.5 Goal and structure of this thesis
2 IPS software verification 
2.1 Introduction
2.2 Revision of coordinate transforms
2.2.1 General formalism
2.2.2 Derivation of transform parameters
2.2.3 Slit tilt implementation
2.3 Revision of Fourier propagation
2.3.1 General application
2.3.2 Geometrical orientation
2.3.3 Single propagation steps
2.3.4 Implementation for NIRSpec
2.3.5 Sampling of PSFs and wavefront errors
2.3.6 Required sampling for NIRSpec
3 NIRSpec model description 
3.1 Model data overview
3.2 Subsystem and telescope data
3.3 NIRSpec as-built optical model
3.3.1 Motivation
3.3.2 Model description
3.3.3 Model verification and transformation to cold
3.3.4 Relation between wavefronts and coordinate transforms
3.3.5 Data extraction for the IPS model
4 Science software tools 
4.1 Science data interface
4.1.1 Motivation
4.1.2 Object positioning
4.1.3 Object input file types
4.1.4 Object separation criteria
4.1.5 Technical implementation
4.2 Spectrum extraction pipeline
4.2.1 Purpose and scope
4.2.2 Software implementation
4.2.3 Spectrum extraction operations
5 NIRSpec model verification 
5.1 Motivation
5.2 Instrument geometry
5.2.1 Initial data and manual tuning
5.2.2 Model optimization
5.2.3 GWA tilt sensor integration in extraction
5.3 Test of IPS with tuned instrument model
5.4 Calibration Light Source spectra
5.5 Instrument efficiency
5.5.1 Filter transmissions
5.5.2 Grating efficiencies
5.5.3 Overall instrument throughput
5.5.4 IFU throughput
5.6 Limitations of simulations
6 NIRSpec science simulations 
6.1 Multi-object deep field
6.1.1 Introduction
6.1.2 Observation scene creation
6.1.3 Galaxy shapes
6.1.4 Galaxy spectra
6.1.5 Exposure simulation
6.1.6 Spectrum extraction
6.1.7 Results and discussion
6.2 Exoplanetary transits
6.2.1 Introduction
6.2.2 Host star brightness limits
6.2.3 Noise from pointing jitter
6.2.4 Effective integration times
6.2.5 Signals and noise
6.2.6 Simulations of HD189733b
6.2.7 Simulations of GJ1214b
6.2.8 Simulations of an Earth-sized planet in the habitable zone
7 Conclusion and outlook

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