# JWST ETC Residual Flat Field Errors

The JWST ETC includes pixel-to-pixel noise due to an imperfectly corrected flat field. This noise source is often mitigated by dithering. Since the ETC currently does not model dithers, except in a limited sense for a few special cases, such as coronagraphy and IFU spectroscopy, the absence of dithers will limit the sensitivity for very deep (>10,000 s) imaging observations and will also limit the signal-to-noise ratio that can be achieved for bright sources.

Users should be aware that the issues presented in this article are now fixed in the ETC v1.2.2 release and beyond. Specifically, the "number of exposures" in the ETC are interpreted as "number of dithers", and will decrease the residual flat field error by $\sqrt{n_{\rm exp}}$. Conversely, multiple integrations will not decrease the residual flat field error. This way it is possible to investigate the effect of dithering on the predicted SNR.

In its error model, the ETC includes an error term that models residual flat-field errors. For a typical observation, each exposure will be divided by a pixel flat field, which is intended to normalize the relative response (quantum efficiency) of each pixel. However, the flat field is an imperfect measurement itself, and consequently, there will always be some residual pixel-to-pixel response variation, even after division by the flat field. In the absence of dithers, where the pointing of the telescope is the same for multiple exposures, the light from a source will occupy the same pixels on the detector for each exposure. In this case, the presence of a residual flat field error may eventually limit the depth of an observation. JWST detectors are required to have flat fields with pixel-to-pixel variations <10%. In the ETC, the residual flat field error, after flat-field correction, is typically assumed to be in the range of 0.1 to 1.0%. Currently, the ETC only models dithers in a very limited sense, and may, therefore, underestimate the sensitivity of very deep observations.

# Effects of the residual flat field error on deep observations

As a rule of thumb, observers dependent on total exposure times in excess of ~10,000 seconds for broad-band imaging (and somewhat longer for most spectroscopy modes) should be aware of the effects of residual flat field errors. In the limit of extremely long total exposure times, in the absence of dithers, all observations will eventually be limited by the residual flat field error. The practical effect is that ETC calculations will have a "noise floor", beyond which observations with increasing numbers of exposures no longer increase the signal-to-noise ratio by $\sqrt{n_{\rm exp}}$. This is true both for faint and bright sources. Further, in the case of faint sources, background-limited observations (i.e. with high background levels compared to the source) are particularly susceptible to residual flat-field errors. That, for instance, means that narrow band filters will take longer to be limited by the flat-field error, and spectroscopy is similarly less affected.

# Effects of the residual flat-field error on observations of bright sources

Another effect of the residual flat-field error is that there is a limit on how high the signal-to-noise ratio will get for bright sources. The signal-to-noise ceiling will depend on the flat-field error assumed for each instrument, as well as the number of pixels the signal is spread over. For most modes, observations of point sources will be limited to signal-to-noise ratios of a few 100. Note that time series observations (e.g., of exoplanet transits) are immune to this, as they rely on relative measurements on the same pixels.

# But my observation will have lots of dithers. What should I do?

The ETC currently presents a scenario for deep observations that is likely somewhat conservative, and essentially assumes that the observer does not dither, except in a few cases where dithers are implemented for other reasons (specifically IFUs and coronagraphy). However, most observing programs will naturally include significant numbers of dithers. The basic effect of dithers will be to decrease the flat-field noise by $\sqrt{n_{dither}}$, as long as the dither is larger than 1 pixel. While the ETC does not provide an explicit way to include this effect, it is easy to include it in the following way:

1. Create an ETC calculation for a single dither. Note that a single dither may include both multiple integrations and multiple exposures, provided that the telescope does not change pointing between exposures.
2. Note the signal-to-noise (SNR) ratio for a single dither reported by the ETC.
3. Determine the number of dithers $n_{dither}$ for which the telescope offsets to a new pointing, either from APT, or using the dither table relevant for the instrument and mode.
4. Scale the single-dither SNR with $\sqrt{n_{dither}}$ to determine the final sensitivity: $SNR_{total} = SNR_{dither} * \sqrt{n_{dither}}$
5. To estimate the relative effect of the flat-field error, create a new ETC calculation for the total exposure time by assuming the dithers are regular ETC exposures.

Note that scaling with the number of dithers in this way may be optimistic; the ultimate performance is likely bounded by the ETC prediction and the scaling described above.

# The special case of NIRSpec MSA

Observers using the multi-shutter array (MSA) with NIRSpec should be aware that the residual flat-field error is significantly worse than for other modes, as the flat fields for the many individual shutters are necessarily of lower quality than what can be done (e.g., by imaging). In this case, it is not expected that the noise floor can be improved using the above method, and it is recommended that the ETC $n_{exp}$ parameter is used to predict NIRSpec MSA performance also for long total exposure times.

Published 23 Jan 2018 09 Oct 2019 Updated for ETC v1.5.05 Nov 2018Updated for ETC v1.314 Mar 2018 Warning added to reflect changes in the ETC v1.2.2 patch release in regards to the residual flat field err