# The wavelength calibration of the UVOT Grisms¶

## History of the wavelength calibration¶

From the grism design and ground calibration the dispersion was determined for the centre of the detector. This was further refined post launch and implemented in the Swift UVOT ‘’ftool’’ ‘’uvotimgrism’’ and related calibration files. The anchor for this calibration is the position of the zeroth order peak (which after April 2008 has been derived by an aspect solution using the weak zeroth orders).

The 2009 wavelength calibration, which instead is using an anchor defined in the first order, is valid for the whole detector. The current calibration is that one with some minor improvements. In the following pages some detailed information dates back to 2009. Any updates mostly concern the determination of the accuracy of the anchor which is indicated in the relevant text.

In 2014 some patches on the detector showed lower sensitivity in photometry. Some spectra at medium offset appear to also show these. While this is being investigated, avoid offsets in the Y-axis direction on the detector between about 1 and 3 arcseconds.

in 2016 a drop in the UV grism sensitivity below 1800Å was recognised. Flux calibration source observations were started to check the current correction. The resulting changes to the calibration are discussed at 2017 update of the Flux calibration of the UVOT grisms.

## Calibration approach¶

The wavelength calibration relies on two parts. One is the mapping of the sky position of the target to the grism detector image which is used to define an anchor position at a default wavelength, the other is determining the dispersion in relation to the anchor position.

The anchor position selected in the initial calibration was the peak emission of the zeroth order. The current calibration uses the 2600Å position for the uv grism, and the 4200Å position for the visible grism in the first order. A mapping from the source position in a lenticular filter (i.e., the v,*b*,*u*,*uvw1*,*uvm2*,or uvw2 filters) relative to its boresight to that in the grism image has been determined. Recent observations with the Swift UVOT grism have by default an observation right before or after the grism exposure in one of the lenticular filters to assist in that mapping. Older grism observations can be aspect corrected using the distortion-corrected zeroth orders. Using the corrected World Coordinate System (S) then allows also a determination of the first order anchor position.

The dispersion varies over the detector. Remarkably, in the uv grism the cross-dispersion location of the orders relative to each other depends also on the location of the spectrum on the detector. In the default observing position at the centre of the detector, the second and third order partially overlap with the first order. Unfortunately, in the uv grism the second order is still quite strong compared to the first order, especially in the blue which for spectra from uv-bright sources can cause overlap from 2750A in first order. Away from the centre, near the top of the detector the second order uv section curves away from the first order, and also has a small displacement. This means that for that part of the detector, for sources with known bright emission line spectra, a second order wavelength scale could be determined.

The anchor determination and dispersion calibration accuracy is limited since we are not able to have a dense coverage of the detector with calibration observations. Our approach has been to use the optical model used for the instrument design to aid us in extending the calibration over the whole detector. This “Zemax” model was originally developed for the design of the XMM “OM” instrument, it was used again for the Swift UVOT with only very minor changes to account for the UVOT setup. Since the UVOT operations use each of the two grism also in a socalled “clocked” mode, where the filter wheel positions the grism optics slightly offset from the main optical axis, these were modeled separately.

## Determination of the anchor positions¶

Each grism mode was calibrated in turn. More detailed results can be found in the calibration paper and The CALDB documentation for the wavelength calibration of the UV grism, or in separate pages with links given below.

Considering the spectral resolution (R=75 uv grism;R=100 visible grism), and relatively faint calibration sources needed, the emission lines from Wolf-Rayet spectra were used. The UV grism, nominal mode calibration used mostly spectra taken from WR86, a known long period binary, with good lines going down to 1909A. The UV clocked grism used mostly WR52 which has lines going down even further in the UV. The visible grism calibration used for both modes mainly spectra from the fainter WR121, since the visible grism is too sensitive to use WR52 or WR86.

Initially, the ground calibration of the UV grism was also used as further verification of the in-orbit results. There were no unexpected discrepancies found.

The following steps were found to be needed to determine anchor positions:

• the images of the calibration line spectra were used to measure the position of the lines.
• the anchor position on each image was determined from the position of spectral lines.
• the position of the source in aspect corrected lenticular filter images was determined with respect to the boresight location at the time of observation.
• the boresight location of the anchor on the grism image was determined as well as the mapping from the lenticular filter to the grism image.
• the anchor positions predicted by the zemax model were shifted to align the model to the observations of the boresight.
• first the model was scaled with a simple scale factor to align all anchors to within 20A.
• As a further correction a bispline was determined. The order of the bispline varies with the grism mode.

In a given observation, the actual anchor positions may still show an offset from the calibrated position. We find that the accuracy is about 15Å unless there is drift during the exposure of grism and associated lenticular filter. In a few cases the offsets found are as large as 40Å, so be warned.

If no lenticular filter observation is available and the UVOTGRASPCORR program has been used for finding the world coordinates of the grism image, the the error in the anchor position may be much larger. This larger error seems to be due to some correctible problem. Currently (December 2014) the source of the problem has not been found.

Some sky locations are worse then others for attitude lock, and it is difficult to predict where and when the results will be off. These anchor errors/offsets imply that the whole wavelength scale is shifted.

## Determination of the dispersion¶

How the dispersion changes by position of the spectrum on the detector has been determined by off-setting the calibration spectra so they covered all areas of the detector. The observed dispersion has been used to determine how to scale the “Zemax” model. To determine the dispersion scale factors, the line positions were determined in pixel distances from the anchor, and compared to the model. The scale factor was allowed to slowly vary with detector position.

In the 2009 calibration the model was scaled with a single factor, although the factor was allowed to vary slowly over the detector. That works well for most of the spectrum, but not for the shortest nor for the longest wavelengths. For the UV grism the model is lacking the details below 2100Å of the filter characteristics, while above 4000Å the PSF is assuming a very asymmetric and extended shape, calling into question the definition of the PSF peak. The 2013 version of the uv clocked grism wavecal is using a linear fit in wavelength rather than a fixed scale factor which gives a better dispersion result overall. For the other grism modes a single scale factor was sufficient.

The accuracy of the dispersion, neglecting wholesale offsets due to anchor problems, is about 15Å in the uv grism. It is worst at the low and high wavelengths (< 1900Å, > 4000Å).

## Summary of wavelength accuracy (2014 update)¶

The accuracy of the anchor error depends on the method used to find the anchor position in the grism. If the position was determined using the grism image only, the accuracy is worse. The best accuracy if obtained when the grism exposure was taken combined with a lenticular filter exposure.

Note

In August 2014 we found that the anchor error is nearly twice as large when no lenticular filter observation was included with the grism mode.

for the combination of grism + lenticular filter the accuracies are as follows:

UV grism nominal mode: For 95% of the spectra (2-sigma error) the anchor position will cause an shift in the wave length scale of less than 35Å. The 2-sigma error to the wavelengths due to inaccuracies in the dispersion will be less than 18Å (2000-4500 Å).

UV grism clocked mode: A revision of the wave length calibration was released June 2013 with corrections for the shortest and longest wavelengths. The shift due to misalignment is less than 17A for 95% of the spectra. The error in the wavelengths due to inaccuracies in the dispersion is within 11A below 4500Å, and within 21Å for wavelengths between 4500-6000 Å.

visible grism nominal mode: The 2-sigma error in anchor positions is 30Å in the centre of the detector, 44Å overall. The 2-sigma error in the dispersion is less than 10Å.

visible grism clocked mode: The for 95% of the spectra the error in the anchor position is 44Å. The error in the dispersion less than 14Å.

for the grism without a lenticular filter the accuracies are larger::

UV grism nominal mode: For 95% of the spectra (2-sigma error) the anchor position will cause an shift in the wave length scale of less than 53Å. The 2-sigma error to the wavelengths due to inaccuracies in the dispersion will be less than 15Å (2000-4500 Å).

UV grism clocked mode: The shift due to anchor misalignment is less than 47Å for 95% of the spectra. The error in the wavelengths due to inaccuracies in the dispersion is within 11A below 4500Å, and within 21Å for wavelengths between 4500-6000 Å.

visible grism nominal mode: The 2-sigma error in anchor positions is 88Å. The 2-sigma error in the dispersion is less than 10Å.

visible grism clocked mode: The for 95% of the spectra the error in the anchor position is 118Å. The error in the dispersion less than 16Å.

## The Zemax optical model¶

The Swift UVOT grism calibration uses of the Zemax optical model which was used to design the grisms for the XMM/OM and the Swift/UVOT instruments to supplement calibration observations. We have established that the model is valid and useful in various ways. The model has been compared the pre-launch ground calibration observations, to observations at and away from the boresight of the instrument for the first order and occasionally for the second order or zeroth order data. However, since the Zemax model does not include the fibre taper optics between the MCP and the CCD, small corrections to the model were needed which were derived based on observations of the emission line spectra of WR stars.

The comparison between the original design model and the actual instrument data suggests that the mounting of the grisms was a few degrees rotated away from the design as is evident of the angle of the spectra on the detector. The correction, based on the angles of the grism spectra on the detector in the nominal and clocked modes, is 3.8 ± 0.2 degrees for the UV grism and 2.6 degrees for the V grism. For the computation of the nominal and clocked modes a tilt was applied to the grism assembly model, and an offset for the clocked modes, corresponding to the position angle of the grism in the filterwheel, and the effect of the clocking action respectively. The tilt angles used were 61.2 deg for UV nominal, 54.665 deg for UV clocked, 57.9 deg for the visible nominal, and 50.6 deg for the visible clocked grism.

Those have been the only corrections made to the original zemax grism optical design model. The original model for the UV grism was optimised for the 260nm wavelength in the first order; that for the V grism for 420nm in first order. These have been used (and refered to) as the anchor point of the spectra in the wavelength calibration described here. The spectra of (telescope) on-axis sources give the boresight spectrum where the anchor wavelengths in first order fall near the centre of the detector.

The Zemax model use has limitations, one is caused since the fiber taper part of the detector is not included in the model. The fibre taper results in some image distortion. To some extent this is taken out by using the distortion measured for the lenticular filters. For spectral analysis and its calibration the ‘detector image’ has therefore been used. The detector image is created by applying the distortion correction from the lenticular filter to the raw grism image. However, that process may in turn introduce a small distortion component due to the a possible distortion in the lenticular filters.

## Relation to the 2005-2007 calibration¶

The instrument boresight is known to vary slightly for the different lenticular filters and is not a well-defined location on the detector for a spectrum. The boresight of the grisms in the first calibration was determined as a certain point in the zeroth order, whose location is defined by an algorithm based on the positions zeroth order peak emission for weak sources in the image as implemented in the “UVOTGRASPCORR” “Ftool”. The values for the UVOT grism boresight in the “CALDB” “TELDEF” files are for the zeroth order.

Several limitiations in the first wavelength calibration have been resolved in this calibration.

• The first is, that all first order spectra on the grism image can now be calibrated rather then just those near the default position.
• The second improvement is, that the wavelength scale accuracy has improved by providing a solution valid over the whole detector.
• The third improvement is using the optical model.

Anchor point offset errors cause a wholesale shift of the wavelength scale. Anchor point offsets have different error sources in the two methods. Using a lenticular filter taken in combination with the grism gives error sources in the aspect correction of the lenticular filter less than a pixel, and in the transfer to the grism detector image, which is typically one to three pixels. When using the “UVOTGRASPCORR” tool the error sources are the accuracy with which “UVOTGRASPCORR” determined the attitude, which has also a random error of around 3 pixels, but shows also an unexplained systematic error which seems to depend on the particular star field. One in around twenty images tends to have larger offsets. That can be due to satellite drift during the grism plus lenticular filter observation when attitude lock of the satellite is not good, or failure of “UVOTGRASPCORR” to match the correct zeroth orders to the USNO-B1 catalog source positions.

Some colour dependence may be present in the UVOTGRASPCORR aspect solutions: The zeroth order suffers for the brighter sources from a combination of modulo-8 noise and saturation. The dispersion of the zeroth order is very non-linear with most of the red part of the spectrum on a few pixels, and the blue part in a weak extended tail. Although using only weak sources in the image will preferenctially select the red peaks, some colour dependence may exist in the aspect correction of the grism image.

By using the optical model, scaled to have a best fit to the calibration observations, we obtain the dispersion and anchor position over the detector. The model also provides data on the zeroth, second and third orders. Only the second order has been calibrated for anchor and dispersion. The multi-order data is essential for understanding the spectra, since the second and third order fall generally on top of the longer wavelengths in the first order. A consistent model prediction of the variation of the angle of the spectral orders on the detector is used, though small corrections for curvature of the spectra were not predicted and have been measured from the calibration spectra. Finally, the point spread function of incoming radiation as function of wavelength, order and position is predicted by the model, and the predicted PSFs are useful for these are not nice gaussians, but rather elongated and horse-shoe or donut shaped for the longer wavelengths.

### Relevant Documents¶

• description UVOT instrument: Roming et al. 2005, see also the XMM-OM description: Mason et al. 2001.
• SWIFT-UVOT-CALDB: Swift UVOT Grism Clocking, Alice Breeveld, 19th October 2005, Revision #01, Swift UVOT Calibration Documents Version 06-Apr-2006
• SWIFT-UVOT-CALDB: Teldef Files, Alice Breeveld, 19th October 2005, Revision #01, Swift UVOT Calibration Documents Version 06-Apr-2006