Data simulator for the HERMES instrument

Data simulator for the HERMES instrument Michael Goodwin*, Scott Smedley, Stuart Barnes^, Tony Farrell, Sam Barden Anglo-Australian Observatory, PO Box 296, Epping NSW 1710, Australia ABSTRACT The HERMES instrument is a high resolution multi-object fiber-fed spectrograph (R~30,000) in development for the Anglo-Australian Telescope (AAT), covering the wavelength range (370-1000 nm). Given the sophistication of HERMES we have developed an end-to-end data simulator that accurately models the predicted detector images. The data simulator encompasses all aspects of the transmission and optical aberrations of the light path: from the science object, through the atmosphere, telescope, fibers, spectrograph and finally the camera detectors. The simulator uses optical information derived from ZEMAX software that has been processed and verified using MATLAB software. The simulator is sufficiently flexible to model other fiber spectrographs. In addition to helping validate the instrument design, the resulting simulated images will be used to develop the required data reduction software. In this paper, we present the simulator overview, requirements, specifications, system model, verification and simulation results. Keywords: HERMES, high-resolution fiber spectrograph, multi-object, data simulator, instrument model, AAT 1. INTRODUCTION The HERMES (High Efficiency and Resolution Multi-Element Spectrograph) instrument[1, 2] is a future high resolution multi-object fiber-fed spectrograph optimized for the primary science of Galactic Archaeology[3] (GA) to be commissioned for the Anglo-Australian Telescope (AAT). The HERMES instrument specifications include a moderate resolution (R~30,000) and high resolution (R~50,000) modes, high multiplex (392 science fibers), high efficiency Volume Phase Holographic[4] (VPH) grating. Four science cameras (4kx4k CCDs) cover the important spectral windows in the wavelength range from 370-1000 nm. The CAD drawing and optical schematic are shown in Figure 1. (a) 3-D mechanical layout (b) 2-D optical layout (rotated 180 degree counter-clockwise in reference to (a)) Figure 1: Schematics of the HERMES instrument. The HERMES Data Simulator (HDS) provides the ability simulate detector images from all four channels allowing early performance verification of the instrument. *mgoodwin@aao.gov.au; phone +61-2-9372-4851; fax +61-2-9372-4860; www.aao.gov.au ^current address: Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Ground-based and Airborne Instrumentation for Astronomy III, edited by Ian S. McLean, Suzanne K. Ramsay, Hideki Takami, Proc. of SPIE Vol. 7735, 77357U 2010 SPIE CCC code: 0277-786X/10/$18 doi: 10.1117/12.856773 Proc. of SPIE Vol. 7735 77357U-1

The HERMES project[5] is funded by the Commonwealth of Australia through an agreement between the Department of Education, Science and Training (DEST) and Astronomy Australia Ltd. (AAL) as an initiative of the Australian Government being conducted as part of the National Collaborative Research Infrastructure Strategy (NCRIS). The HERMES instrument will interface to the existing two-degree field system[6] (2dF) and optical fiber positioner instrumentation of the AAT. The instrument will provide scientific data (kinematics and abundances of ~1,000,000 stars) that will help unravel the complex formation history of the Milk Way Galaxy, with first light planned in 2012[5]. In the following sections of this paper, we report on our end-to-end data simulator that accurately generates synthetic detector images to support the development of the HERMES instrument. 2. OVERVIEW For the purpose of early performance and design verification of HERMES, it was found useful to develop an end-to-end instrument data simulator. The HERMES Data Simulator (HDS) is a command-line interface (CLI) software tool that generates synthetic detector images of each of the four cameras (spectrograph channels) for use by the engineers, instrument scientists and astronomers. The goal of the HDS is that the simulated images are indistinguishable or closely represent that expected from the commissioned HERMES instrument. The HDS system overview diagram is shown in Figure 2. The HDS is sufficiently flexible to simulate other fiber-fed spectrographs by specifying the specific instrument Model Data. The HDS is beneficial to the instrument design for the following reasons: development of the data reduction software input into calibration procedures understanding the design early identification of system level problems ensuring design requirements are met further design optimization and improvements quality by testing continuously throughout the development process detailed science and design verifications Note that simulation tools have been developed previously for other complex astronomical spectrographs. An example is the ESO simulation tool[7] for the second-generation integral-field spectrograph in development for the Very Large Telescope (VLT) or known as the Multi Unit Spectroscopic Explorer (MUSE) instrument (first light 2012). 3. REQUIREMENTS The primary challenge for the HDS is to implement a simulation tool that generates synthetic detector images to support development of the HERMES instrument. A possible solution is the requirement to use a model-based approach having the following general advantages[8]: (i) innovation: explore unique features and cost-effective design trade-offs with rapid design iterations (ii) quality: prevent errors reaching the physical implementation (iii) cost: reduce need for expensive physical prototypes and testing (iv) time: get it right the first time and an accelerated development process Proc. of SPIE Vol. 7735 77357U-2

Figure 2: System overview of the HDS Given the model-based design approach, the high-level requirements of the HDS are: model is linked to the HERMES requirements and specifications details added to the model from specific domains to refine the model (e.g. optical, mechanical, science) intellectual property and engineering data is reused from existing designs simulation of detector readouts for design iterations, optimization and verification against requirements simulation of potential spectrograph image ghosts and scattering flexibility to model other fiber-based spectrographs (e.g. AAOmega[9]) command-line interface for desktop simulation tool for use by astronomers, instrument scientists and engineers Generally, commercial software usually lacks the flexibility needed for the full end-to-end simulation of a complex instrument such as HERMES. In most cases the level of control of the computations in the commercial software is insufficient as well as lacking a suitable interface to be used by a wide range of users, including engineers and astronomers. For these reasons, the HDS is implemented as a custom-built CLI simulation tool coded in C++ that can be compiled under the Linux platform. The simulation tool is encapsulated by a scripted interface providing the necessary flexibility and efficiency to achieve the end-user requirements. However, commercial software is advantageously used to generate the optical aberration and distortion model sub-component that is extracted from the output of the optical raytrace software package called ZEMAX. The optical distortions by ZEMAX and additional components (such as efficiency curves and synthetic spectra) are further processed and verified using the commercial mathematical modeling software package called MATLAB. This facilitated prototyping in a high-level language and interactive environment. 4. SPECIFICATIONS The specifications of the HDS are derived from the requirements outlined in Section 3 and are summarized in Table 1. The specifications are divided into four main components that approximately follow the light path: (i) science object; (ii) atmosphere; (iii) telescope and (iv) instrument. The instrument component is further divided into logical sub-components describing the fiber optics, instrument calibration and efficiency, cameras and detectors. Proc. of SPIE Vol. 7735 77357U-3

Table 1: Specifications for the HERMES data simulator. SPECIFICATION Science Object Atmosphere Telescope DETAILS The science object model spectra are derived from A library of high resolution synthetic stellar spectra from 300nm to 1.8μm with solar and alpha-enhanced composition by P. Coelho et. al [10]. The normalized spectra are scaled by the specified blackbody temperature and flux calibrate to V=0 (A0V star), and then truncated 350-1000nm. The spectral resolution being 0.02Å and flux units of erg sec -1 cm -2 Å -1. Parameter space for science object spectra: Effective temperatures 4750 T eff 6000 K in steps of 250 K Surface gravities log g = 1.5, 2.0, 3.0, 4.0, 4.5 Metallicities [Fe/H] = 2.5, 1.0, 0.5, 0.0, 0.2 Apparent magnitude [user] m V < 17 The sky background is modeled as reflected solar spectra from the Moon with approximate surface brightness 21.5 to 18 mag/arcsec 2. Sky background depends Moon s phase, zenith distance of the Moon, zenith distance of the sky position, the angular separation of the Moon and sky position and the local extinction. The values are derived from A model of the brightness of the moonlight by K. Krisciunas and B. Schaefer[11]. The solar spectra model parameters approximated with T eff =5750, log g = 4.5 and [Fe/H] = 0.0. The background spectra flux is then a function of the fiber angular area on the sky. The sky emission is modeled based on the Osterbrock sky spectrum[12] derived from observations with the HIRES echelle spectrograph on the Keck I telescope. The wavelength coverage is from 400-900 nm range with resolving power about 37,000[12]. The model uses a default scale factor 2*10-17 to convert to units ergs/s/cm 2 /Å to provide reasonable correspondence with the UVES fluxcalibrated, high-resolution, high-snr atlas of optical and near-ir sky emission[13]. The atmospheric spectrum (sum of the sky emission and the sky background) is added to science object and then multiplied by the atmospheric efficiency response. Parameter space for atmospheric model: Sky background [user] 21.5 to 18 (mag/arcsec 2 ); Sky emission [user] 2*10-17 Efficiency response [user] default efficiency response incorporating transmission and astronomical seeing as a function of wavelength Specifies the Anglo-Australian-Telescope (AAT) and the 2dF corrector optics. Parameter space for telescope model: Mirror diameter [user] 3.8 m Proc. of SPIE Vol. 7735 77357U-4

Instrument - Fiber Optics Instrument - Calibration & Efficiency Instrument - Cameras Instrument - Detector Central obstruction Efficiency response [user] 1.5 m [user] default efficiency response of telescope mirrors and corrector optics as a function of wavelength Specifies the fiber optic parameters such as the fiber efficiency response, fiber layout, fiber diameter, fiber mapping to object spectra and number of fibers. Specifies the HERMES instrument efficiency responses and calibration lamps. The calibration arc lamp data for wavelength calibration is taken from two sources. The first source is taken from the 2dF data reduction software[14] (2dFdr) consisting a variety of line lists from a variety of lamps. The second source, a selection of ThAr lines for UVES compiled by M. Murphy et. al[15]. The calibration lamp data for flat fielding calibration is theoretical blackbody curve of T=3000K to model a Quartz lamp. Efficiency response models each four channels: (i) instrument fore optics specified as multiple efficiency profiles representing various fore optics (i.e. pre- VPH grating) components of the spectrograph. e.g. slit relay, collimator, beamsplitter, fold mirror, etc; (ii) Efficiency profiles for the 0T transmission, 1T transmission, 1R reflection and anti-reflective coating of the VPH grating (for image ghosting calculations); Parameter space for instrument efficiency and calibration model: Calibration lamps [user] arc (ThAr, ), flat (quartz) Efficiency response [user] default efficiency response of instrument fore optics, VPH gratings for each of the four channels. Specifies the optical aberration and distortion configuration for the particular camera (four spectrograph channels) as well as parameters for the simulation of the spectrograph ghosting and scattering. Also specified is the efficiency profile for the camera. The camera is the (post-vph grating) spectrograph optics (not the detector). Specifies the detector properties such as the bias, bias width, image window, read noise, dark current, ADU gain, bad pixels, pixel size, pixel variance, charge transfer efficiency, cosmic ray intensity, cosmic ray rates and QE response. 5. SYSTEM MODEL 5.1 Overview The HDS system model abstracts the physical design of the HERMES instrument. This is achieved by translating the HDS requirements and specifications into suitable model components with an underlying data flow. The diagram of the model components are shown in Figure 3 (a) and the data flow in Figure 3 (b). Proc. of SPIE Vol. 7735 77357U-5

A key advantage of the HDS system model is the flexibility to model other fiber-fed spectrographs by the specification of the relevant input Model Data and User Parameters in Figure 3 (b). This has been demonstrated with the simulation and verification of detector images for the AAOmega fiber-fed spectrograph documented in Section 6. (a) Model components (b) Data flow Figure 3: Diagrams summarizing the HDS system model. 5.2 Model components The model components are shown in Figure 3 (a). The components are approximately grouped in related subcomponents that track the light path starting from the science object and ending at the instrument detector. The specifications of the components are described in Section 4. The components of the system model supports flexibility for two model approaches: (i) first principles and (ii) data driven. The first principle model approach to model components uses an understanding of the system s physics to derive a mathematical representation[8]. An example of the first principle model is the case for the science object that uses synthetic model stellar spectra of sufficient resolution and wavelength coverage. Another example is the physical model of the instrument optics using a ray-trace software analysis package. The first principle model provides an insight into the underlying behavior of the components and allows broad parameter sweeps. The disadvantages of the first principle model are that some components cannot be easily modeled or producing such a model is time consuming. However, the data driven model approach to components uses actual test data and measurements[8]. An example of the data driven model are the sky emission lines sub-component of the atmosphere component. The sky emission lines are based on Osterbrock sky spectrum[12] derived from observations on the HIRES echelle spectrograph on the Keck I telescope. The data driven model can model components fast and accurate. The disadvantage is that the data driven model requires actual data (perhaps noise corrupted). An example of using the data driven model at a later stage is replacing the theoretical efficiencies of the VPH gratings and camera optics with actual test data taken in the laboratory. Example output of the science object and atmosphere model components are shown in Figure 4. Proc. of SPIE Vol. 7735 77357U-6

5 x 10-9 4250_20_m05p00.ms.fits 4.5 x 10-15 Sky Background+Emission 4.5 4 4 3.5 3.5 3 Flux (erg/s/cm 2 /A) 3 2.5 2 1.5 Flux (erg/s/cm 2 /A) 2.5 2 1.5 1 1 0.5 0 3000 4000 5000 6000 7000 8000 9000 10000 Angstroms 0.5 0-0.5 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 Angstroms (a) Synthetic stellar spectra (full wavelength) with plot resolution insufficient to show absorption lines, (b) Sky background plus sky emission lines V=18.5 mag/arcsec 2 (bright conditions) Figure 4: Example plots of (a) the science object s model synthetic stellar spectra (Arcturus V=-0.04) and (b) the atmosphere s component sky background and emission spectra model. The instrument optical distortions and image aberrations are represented as grids at the detector and are shown in Figure 5. The distortion grid shown in Figure 5 (a) is interpolated in the spatial direction (y-direction) for fiber-slit positions (1 to 400) and then in the wavelength direction (x-direction). From the interpolated results, each fiber-slit position has a set of cubic polynomials to model the tramline position of the spectra on the detector. The geometrical images aberration grid shown in Figure 5 (b) is used to perform grid convolutions on tramlines to model a spatial-variant PSF. 5.3 Data flow The data flow process is shown in Figure 3 (b). An important input to the simulator tool is the Model Data that characterizes a particular instrument configuration providing flexibility to model other instruments. The optical ray-trace software package called ZEMAX is used to model the optical aberrations and distortions of the instrument physical optics. Each spectrograph channel (grating and camera optics) is model as a separate ZEMAX design file. The mathematical modeling software package called MATLAB is used to efficiently invoke ZEMAX commands to extract the necessary optical aberrations and distortions using the MZDDE[16] Toolbox for MATLAB. The extracted optical distortions and additional components (such as efficiency curves and synthetic spectra) are further processed and verified using MATLAB. The processed output forms a collection of files that describe the Model Data which is loaded by the simulation tool. The Model Data needs only to be calculated once per instrument configuration. The MATLAB model also has the ability to generate basic detector images to verify the simulation tool output. The User Parameters are described in the specifications of Section 4 and control the behavior of the various model components of Figure 3 (a) providing flexibility to meet the different end-user requirements of the simulation tool. The simulation tool implements the methodology specified by the system model. The magnitude-scaled science object spectra undergo contamination by the addition of the atmospheric spectra and the subsequent multiplication by a set of efficiency profiles representing each model component. The resulting spectra at the detector is then exposure-scaled and then undergoes correct sampling (binning) and quantization process to conserve energy from the continuous-space of the spectra into the discrete-space of the pixel-detector. The position of the object spectra on the detector (tramline impulse response) are specified as cubic polynomials that characterize the distortion. For each fiber-slit position (1 to 400), there are two polynomials that provide (i) the object spectra s detector y-position (mm) from detector x-position (mm) coordinates and (ii) the detector wavelength value (microns) from detector x-position (mm) coordinates. The detector x-y coordinates is a simple mapping of the physical spatial sizes of the discrete pixels with a coordinate origin (0, 0) mapped to the detector center. Proc. of SPIE Vol. 7735 77357U-7

The object tramline impulse responses are then blurred by convolution of the spatial-variant point spread function (PSF), or the geometrical image (aberration) of the fiber-slit object (circle). The spatial-variant convolution is approximated by performing a number of smaller spatial-invariant convolutions in a grid configuration (nearest neighbor). Each grid segment region uses a fixed geometrical image as the PSF computed at the central spatial and wavelength grid values. (a) ZEMAX chief-ray distortion grid 11x10 (units mm) (b) ZEMAX geometrical images aberration grid 11x10 (c) Example fitting a cubic polynomial (red line) and linear interpolation (dotted) to ZEMAX chief ray locations (circle) for the distortion grid. The high resolution ZEMAX chief ray calculations (crosses) match the cubic polynomial better than 0.03 microns (detector pixel scale 15 microns). (d) Example ZEMAX geometrical image that is 10x over-sampled compared to detector pixel spatial scale showing a high level of aberration as occurring on the edge detector. The aberrationfree image should be a circle (fiber image). Figure 5: The instrument optical distortions and image aberrations grid calculated using ZEMAX and MATLAB software. The grid represents spatial (vertical) and wavelength (horizontal) values sampled for 11 fibers (total 400 fibers) linearly spaced across the HERMES detector (blue channel) computed for (a) the chief-ray distortion map and (b) the corresponding geometrical images aberrations map. The distortion grid (a) is interpolated and characterized by cubic polynomials (see example (c)) to specify all 400 fiber tramline positions on the detector. Proc. of SPIE Vol. 7735 77357U-8

The final steps of the data flow include modeling object photon noise (shot noise), detector bias, detector noise (e.g. dark, read and pattern), detector defects (e.g. hot pixels, bad columns, fringing) and contaminants (cosmic rays). The final result is a representation of the imaged object spectra as would be expected from a real-life implementation of the fiber-fed spectrograph instrument. A similar procedure is followed to generate calibration detector images. The flat-field calibration images are calculated using source spectra of a continuous theoretical blackbody quartz lamp. The arc-field calibration images are calculated using source spectra of discrete line lists from arc-lamps, such as thorium argon. 6. VERIFICATION The verification process involves a number of different test procedures to ensure that the simulation tool is outputting valid data that complies with the requirements and specifications. The set of tests involve verifying (i) the simulation tool output against the MATLAB model; (ii) the MATLAB model output against actual AAOmega observational data; (iii) the simulation tool output reduced with 2dFdr software. These tests are necessary to validate the simulation tool implementation and accuracy to replicate real instrument data. In this section, we examine the fiber tramline positions. In Figure 6, a simulated detector image for the AAOmega spectrograph (blue channel 580V grating) showing five tramline spectra for the bottom and top sections of the detector are compared to the predicted MATLAB model. The simulated detector image shown in Figure 6 has been processed with 2dFdr data reduction software to remove background. The simulated detector image shown in Figure 6 is an object field based on synthetic spectra having a model T eff =4750K, log g = 1.5 and [Fe/H] = 2.5 with brightness m V =14 and exposure of 1800 seconds, air mass 1.2 (median seeing). From Figure 6, it can be noted that the position of the fiber tramlines found with 2dFdr data reduction software are in excellent agreement with the MATLAB model, showing a y-offset position bias of approx. 0.25 of a pixel. This qualitatively verifies that the simulation tool correctly implements the MATLAB model for fiber tramline positions. Verification of the MATLAB model fiber positions against a real AAOmega spectrograph data are shown in Figure 7. (a) Tramline spectra for fibers 2 to 6 (bottom of detector) (b) Tramline spectra for fibers 396 to 400 (top of detector) Figure 6: Verification of the simulation detector image (object field) with MATLAB model for the case of AAOmega spectrograph (blue channel with 580V grating configuration). The horizontal axis denotes the pixel location from short (371 nm) to long (585 nm) wavelengths. The MATLAB model tramlines are denoted as solid black lines. The tramlines found by processing the simulated detector image with 2dFdr software are denoted as dotted black lines. A y-position bias of ~0.25 of a pixel is observed in the bottom (+ve bias) and top (-ve bias) sections of the detector, zero bias in middle section (not shown). Proc. of SPIE Vol. 7735 77357U-9

fibre ID= 399 4070 4060 4050 4040 0 500 1000 1500 2000 fibre ID= 201 2060 2050 2040 2030 0 500 1000 1500 2000 fibre ID= 1 30 20 10 0 0 500 1000 1500 2000 Figure 7: Verification of the MATLAB model tramline position (solid red line) against an actual flat-field detector image of AAOmega spectrograph (580V grating) processed with 2dFdr reduction software (dashed blue line). The MATLAB model can be fitted to real AAOmega data (dashed line) by applying an offset, scale and a rotation. From Figure 7, it is apparent that the predicted MATLAB model tramline positions are not aligned with the corresponding fiber positions on the flat-field detector image of the AAOmega spectrograph (580V grating). However, the MATLAB model can be fitted (mean error ~0.34 pixels) to real data (dashed line) with a simple transform parameters: y-offset=5.45 pixels; scale factor =0.9936; rotation=-0.1656 degrees (i.e. clockwise). Note that from Figure 7 (and noting above transform parameters) the shape of the fiber tramline distortion profiles is preserved between the model and actual instrument - indicative of a reasonable initial model. The differences between model and instrument are currently being investigated and might be due to unforeseen optical tolerances or mechanical alignments not included in the corresponding ZEMAX optical model. These results are useful to incorporate as a scenario for the HERMES model. 7. SIMULATION RESULTS An example of a set of simulated detector images for the HERMES blue channel (R~30,000, λ~478nm) are shown in Figure 8. The detector image for the object field shown in Figure 8 simulates an exposure time of 1800s using slitlet #40 (fibers 391-400) assigned synthetic stellar spectra having T eff =4750K and brightness m v =12.5 and slitlet #39 (fibers 381-390) assigned spectra T eff =4250K and brightness m v =15.0. The brighter object spectra have signal-to-noise ratio > 50. The total simulation time to generate each detector image on a standard laptop is in the vicinity of several minutes with the bulk processing time consumed with performing the grid convolution. The scriptable command-line interface provides the flexibility and relative ease-of-use by the technical members of the HERMES project team. From Figure 8, the division of slitlets #39 and #40 (each with 10 fibers) is clearly evident in the flat-field calibration image. The arcfield calibration image shows the scarcity and saturation of the wavelength lines (FeAr). The object-field detector image shows how the dynamic range in object brightness and spectral types affect the astronomical observations. It is clear from the simulation tool data products, as shown in Figure 8, are very useful in the development and testing of the data reduction software and verification of the various science programs for the HERMES instrument. Proc. of SPIE Vol. 7735 77357U-10

Figure 8: Section of the simulated detector images (flat, arc and object fields) for the HERMES blue channel (R~30,000, λ~478nm) each showing fibers 381 (lower) to 400 (upper) covering only 25% of the detector wavelength (horizontal). 8. CONCLUSIONS AND FUTURE WORK The HERMES data simulator is an end-to-end simulator to generate synthetic detector images to assist in the early development of the HERMES instrument (planned first-light in 2012). In this paper, we have described the data simulator in reference to the requirements, specifications, system model, verification testing and simulation results. We have shown the flexibility of the data simulator to be configured to simulate other fiber-fed spectrographs, such as the AAOmega spectrograph. We have described the system model and how the simulation tool uses configuration data derived from a detailed ZEMAX optical model with further processing and verification using MATLAB. Early verification tests indicate that the simulation tool is generating valid detector images when compared against the MATLAB model and AAOmega spectrograph data. The simulation tool is currently producing detector images for the blue channel of the HERMES and AAOmega spectrographs. Further work includes further verification testing, particularly more analysis with the 2dFdr data reduction software; ghosting and scattering analysis; generating the configuration data for all four channels of the HERMES instrument; and science case analysis by the Project Scientist. Proc. of SPIE Vol. 7735 77357U-11

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