NIRSpec Instrument Model Calibration Status
The NIRSpec instrument model describes the light path through the instrument from the sky to the detector. The final version of the instrument model was fit using in-flight commissioning data in addition to ground-based pre-launch data. An overview of the instrument model calibration methodology is presented in this article.
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The NIRSpec instrument model describes the light path through the instrument from the sky to the detector (Dorner et al. 2016). It consists of 3 parts: the FORE optics, the spectrograph, and the grating wheel assembly (GWA) calibration. Figure 1 presents a schematic of the instrument model parts. Because of its complexity especially in the MOS mode (which has ∼ 250,000 individual shutters), calibrating the wavelength and astrometric solutions using a static method for each shutter and disperser is impossible. In addition, the GWA, which is the centerpiece of the internal light path, has limited angular positioning repeatability. This means that whenever the GWA returns to the same grating, it does so with a slightly different position, causing the spectra on the detector to shift by small amounts, both in the dispersion and cross-dispersion direction. As a consequence, the parametric model of the instrument became one of the core elements of the spectral and spatial calibration strategy of NIRSpec.
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The purpose of the model is to describe the light path through the instrument from sky to the detector and vice versa. It is composed of coordinate transforms and geometrical parameters. And it splits into 3 main parts: spectrograph model describing the path between the MSA and the detector, grating wheel sensor calibration, and astrometric calibration (© Lützgendorf et al. (2022)).
The NIRSpec instrument model consists of a collection of coordinate transforms between the various optical planes illustrated in Figure 1 (OTE, FORE, COL, CAM, IFU-FORE, IFU-POST), each represented by a paraxial transformation (rotation, magnification, and offset) and a 5th-degree 2-D polynomial representing the local distortions. The model also relies on a set of geometrical parameters that capture the physical properties of key optical elements (MSA, IFU slicer, GWA and FPA), for example, the locations of the individual quadrants in the microshutter assembly (MSA) plane, the precise orientation of the dispersers in the GWA, or the location and orientation of the detectors in the FPA.
The final version of the instrument model was fit using in-flight commissioning data obtained as part of the 6-month long NIRSpec commissioning campaign between December 25, 2021 and July 15, 2022. In addition, data taken during various ground campaigns as well as simulations were used to obtain absolute wavelength calibration of the internal lamps. In total, over 900 free parameters were fit in the process (see Figure 2).
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The different parts of the model are highlighted in the corresponding colors as in Figure 1. The total number of parameters fit in commissioning is >900. This table is published in Lützgendorf et al. (2022).
Calibration of the spectrograph model
The spectrograph (or internal) portion of the NIRSpec instrument model describes the light path from the MSA plane to the detector and back. It can be calibrated on the ground and in space by using the NIRSpec internal calibration lamps and is described in detail in Lützgendorf et al. (2022).
All residuals remain within 0.1 pixel RMS, which should be compared with the maximum acceptable standard deviation (derived from the NIRSpec calibration error budget) of 1/10 of a resolution element (0.2 pixels). The residuals for all modes meet this requirement with a substantial margin (a factor of two). The detailed residuals are listed in the following table. Coordinate i is the spectral direction and j is the spatial direction.
Table 1. Residuals of the optimized model forward projection from MSA to FPA per grating
| Grating | i mean + RMS | j mean + RMS | median absolute |
|---|---|---|---|
| G140H | 0.011 ± 0.063 | 0.000 ± 0.022 | 0.054 ± 0.041 |
| G140M | 0.001 ± 0.096 | 0.003 ± 0.033 | 0.066 ± 0.077 |
| G235H | 0.002 ± 0.102 | 0.011 ± 0.054 | 0.096 ± 0.066 |
| G235M | 0.000 ± 0.062 | 0.003 ± 0.021 | 0.054 ± 0.036 |
| G395H | 0.001 ± 0.089 | 0.003 ± 0.022 | 0.071 ± 0.057 |
| G395M | −0.001 ± 0.072 | 0.003 ± 0.018 | 0.061 ± 0.042 |
| PRISM | −0.004 ± 0.087 | 0.000 ± 0.022 | 0.076 ± 0.048 |
MIRROR | 0.001 ± 0.012 | 0.003 ± 0.015 | 0.017 ± 0.009 |
Table note: Here, i is the coordinate in detector dispersion direction, and j is the spatial direction.
Monitoring the spectrograph model throughout the mission lifetime
In a stable orbit and without further vibrations and temperature changes, the model should remain stable over time. However, this has never been tested and, therefore, there are monitoring programs executed for each Cycle. These programs contain a subset of the internal lamp exposures to validate the accuracy of the model. From the completed Cycle 1 program, no substantial changes can be observed and all parameters are within NIRSpec calibration error budget.
If there is reason to assume a substantial change to the model, contingency plans will be explored and the model likely to be re-fit.
Calibration of the grating wheel sensor model
Much of the following content is a summary and excerpt from Alves de Oliveira et al. (2022).
The GWA components are located in the pupil plane of the instrument, dispersing or redirecting the beam to the camera that focuses it onto the focal plane assembly. The optical alignment of the wheel at instrument level, and that of the optical elements with respect to each other, ensures maximum throughput and minimum stray light and minimizes any image displacement in the instrument's field of view. However, the ball bearing mechanism limits the mechanical angular reproducibility of the wheel, resulting in a bore sight shift of the selected optical element every time the wheel is moved. Additionally, any remaining tilt of the bearing axis with respect to the bearing range will also cause a deviation of the beam path (known as "wobbling"). Combined, these effects produce a displacement of the beam redirected from the optical element on the focal plane in both the spatial and spectral direction, impacting the position of the dispersed or redirected beam on the focal plane. This effect impacts not only the analysis of science data, but also the instrument operations.
To overcome limitations in the accuracy to which the grating wheel can be positioned, 2 position sensors are used to measure the tip/tilt pointing error of each selected GWA optical element every time the wheel is moved. The calibration of a given sensor is then derived by establishing the linear relation between the telemetry reading from the sensor and the derived location of the wheel for the corresponding angle (see Figure 3).
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This example shows the calibration for the mirror. The color bar represents the temperature of the grating wheel for each exposure as measured by a dedicated sensor. delta_theta_x, delta_theta_y are the relative change in GWA angle in x and y-direction based on its GWA_XTIL, GWA_YTIL sensor reading. This figure was published in Alves de Oliveira et al. (2022).
The RMS of the residuals of the linear calibration provides an estimate of the accuracy of the sensor calibration method presented here. For all optical elements and sensor readings, the behavior of the sensors has remained extremely stable from the ground to the in-orbit performances, and the calibration between the sensor readings and the derived GWA angular displacement is shown to be well represented by a linear relation.
Monitoring the grating wheel tilt sensor calibration
Similar to the spectrograph model, a detected monitoring program per Cycle is executed to track the sensor calibration on a monthly basis. A detailed analysis is still pending but preliminary results suggest that the calibration is stable.
Astrometric calibration
The last step in calibrating the NIRSpec instrument model is the astrometric calibration or FORE optics fit. The FORE transform can be measured from images of the sky, but it should be kept in mind that the optical path from the sky to the MSA plane includes the OTE optics. In order to obtain these fits, 2 imaging mode exposures of the JWST astrometric reference field in the Large Magellanic Cloud (LMC) through the ALLOPEN shutter configuration were taken for each filter (see Figure 4).
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Color image of the LMC astrometric field viewed through the open shutters on the NIRSpec detector. Image taken from Lützgendorf et al. (2022).
On average, each filter had about 5,000 stars used for the fit. The JWST Telescopes team used observations from FGS1 and FGS2, obtained in parallel mode, to determine the most accurate pointing and roll angle information for each of the NIRSpec calibration exposures. This was important, as the uncertainty in pointing and roll would have been absorbed in the NIRSpec model fit, thus resulting in an incorrect model for any other pointing on the sky.
Residuals for all filters range between 0.1–0.25 pixel RMS. This is slightly larger than expected from simulations (<0.1). The bars of the shutters and the crowding in the field make the centroiding process challenging. It is therefore assumed that the larger uncertainties mainly originate from the uncertainty in the centroiding, rather than from the accuracy of the model. Several tests were performed to confirm this.
IFU SIAF update
After commissioning it was determined that the IFU SIAF had an offset of 211 mas almost perpendicular to the image slicer. NIRSpec cannot take images through the IFU aperture without the image slicer being in the optical path, and this did not allow to directly obtain an image similar to the astrometric calibration of the rest of the MSA plane. To properly calibrate the SIAF, including the IFU aperture location on sky, dispersed data were used to reconstruct a white light image (Obs. 6 of PID 1120) and, in conjunction with an MSA verification image, the offset in the IFU SIAF was corrected. On July 24, 2023 the new SIAF was activated, and the latest NIRSpec instrument model (v.7.3.1) went into operations.
References
Alves de Oliveira, C., Lützgendorf, N., Zeidler, P., et al., 2022 Proc. SPIE, 12180, 121803S (arXiv:2208.05354)
In-flight performance and calibration of the grating wheel assembly sensors (NIRSpec/JWST)
Dorner, B., Giardino, G., Ferruit, P. et al. 2016, A&A, 592, A113
A model-based approach to the spatial and spectra calibration of NIRSpec onboard JWST.
Lützgendorf, N., Giardino, G., Alves de Oliveira, C., et al. 2022, Proc. SPIE, 12180, 121800Y (arXiv:2208.05355)
Astrometric and wavelength calibration of the NIRSpec instrument during commissioning using a model-based approach