On the Long-Term Evolution of the Sensitivity of the STEREO HI-1 Cameras

Abstract

The Heliospheric Imagers (HI) on the Solar TErrestrial RElations Observatory (STEREO) observe the solar wind and disturbances therein as it propagates from close to the Sun to 1 AU and beyond. In this article we use stellar photometry over much of the mission to date to make a determination of the long-term evolution of the photometric response of the inner (HI-1) cameras. We find very slow degradation rates of the order of 0.1 % per year, similar to those found for HI-2 by Tappin, Eyles and Davies (Solar Phys. 290, 2143, 2015) and significantly slower than rates found for other comparable instruments. We also find that it is necessary to make a small (${\approx}\,1~\%$) revision to the photometric calibration parameters used to convert instrument units into physical units. Finally, we briefly discuss the effects of pointing instabilities on the measurement of stellar count rates.

Appendix: Gain Anomalies

During the early development of the techniques used in this article to determine the degradation rates of the HI-1 cameras, disagreements between some of the methods that we tested suggested that there must be some peculiarities in the evolution of the instrument gains. In this Appendix we briefly summarise the anomalies and their implications for the analyses presented in this article as well as for the use of the HI data for scientific analysis.

In Figure 3 we plot the per-orbit median count rates of each star scaled by the whole-mission median for that star. Two features are immediately apparent:

• i) There was an abrupt drop in the apparent gain of both HI-1 instruments late in the mission. A similar drop (not shown) was also seen in the apparent gain of the HI-2 instruments.

• ii) There were a number of drops in the apparent gain of HI-1B, predominantly before the start of 2009. These drops appear to be quasi-periodic.

Figure 3

The apparent gains of the HI-1 cameras over the course of the mission up to the start of conjunction operations. Each point represents the median value for a single star as it transited the HI-1 field during one orbit. The $\text{pluses}$ and the left axis show the values for HI-1A, the crosses and the right axis those for HI-1B. The vertical dashed lines show the times of the transitions to gyroless operations.

Analysis of the F-coronal signal in the Level-1 images (which have no background subtraction) shows that these gain anomalies do not affect the response to extended sources, only the response to point sources.

1.1 A.1 Spacecraft Attitude Control

The late-mission drops in apparent gain occurred (to the nearest day) at the times at which the attitude-control gyros were switched off (18 September 2013 for STEREO-A, and 7 January 2014 for STEREO-B). After this time, attitude sensing was maintained with the guide telescope and star tracker. During gyroless operation, the pointing stability of the spacecraft (especially in roll) is significantly degraded, from a standard deviation on a timescale of one hour of less than 1 arcsecond to about 1 arcminute with maximum excursions of about 0.1^∘. It should be noted here, however, that this remains well within the mission specification of a roll jitter of better than 3.4 arcminutes on a timescale of 15 to 30 seconds (Driesman, Hynes, and Cancro, 2009).

Before transmission to Earth, the HI-1 science images are $2 \times2$ binned and then 30 (99 for HI-2) separate exposures are summed (Eyles et al., 2009). A cosmic-ray-scrubbing algorithm is applied to each exposure before binning and summing to remove energetic-particle hits (Eyles et al., 2009). This algorithm flags any pixel in an exposure that is more than $5\sigma$ above its value in the previous exposure and replaces it with the value from the previous exposure, i.e.

$$ I_{\mathrm{c}}^{\prime} = \left \{ \textstyle\begin{array}{l@{\quad}l} I_{\mathrm{p}}, & \mbox{where}\ \sqrt{15}\frac{(I_{\mathrm{c}}-I _{\mathrm{p}})}{\sqrt{I_{\mathrm{c}}}} > 5, \\ I_{\mathrm{c}}, & \mbox{elsewhere}, \end{array}\displaystyle \right . $$

(3)

where $I_{\mathrm{c}}$ is the number of counts in a pixel in the current exposure, $I_{\mathrm{p}}$ is the number of counts in the same pixel in the previous exposure, and $I_{\mathrm{c}}^{\prime}$ is the number of counts in the pixel in the corrected exposure. The factor of $\sqrt{15}$ comes from the fact that 1 DN corresponds to 15 photoelectrons (Eyles et al., 2009). The scrubbing is only triggered by increases in counts relative to the previous image because cosmic-ray hits always add counts to the image, therefore $I_{\mathrm{c}}^{ \prime} \le I_{\mathrm{c}}$. Examination of the particle-hit statistics showed that after the change to gyroless attitude control, the number of flagged pixels increased substantially. We therefore conclude that the degraded pointing stability, which can lead to shifts of up to about one image bin near the centre of the image for both HI-1 and HI-2 over the timescale of the image accumulation, is causing the steep flanks of stellar signals in the HI images to be eroded by the particle-scrubbing algorithm.

On 24 February 2016, a new attitude-control algorithm was implemented on STEREO-A, which gives significantly improved pointing stability. Initial tests show that this will probably be sufficient to allow meaningful gain determinations for the post-conjunction phase of the mission, but it will certainly require a longer interval to obtain meaningful numbers than was the case while the gyros were in use. As of the time of writing, there is not a sufficient interval of observations to make a useful determination.

1.2 A.2 HI-1B Movements

The cause of the short-duration drops in the apparent gain in HI-1B is less immediately obvious. However, it was noted that the majority of them occurred close to the times of spacecraft momentum dumps (W.T. Thompson, private communication, 2015). A closer analysis shows that each gain drop generally starts a few days before the dump and continues until a few days after. The gain drop does not correlate well with any measure of the spacecraft pointing or fluctuations thereof. It has also been found (Brown, Bewsher, and Eyles, 2009; Davis et al., 2012) that the HI-1B pointing undergoes sudden shifts of several image bins, which were believed to be caused by dust impacts; in fact the distribution of such shifts was used by Davis et al. (2012) to estimate the dust distribution near 1 AU.

In Figure 4 we show the pointing offsets at the centre of the HI-1B field for the science phase of the mission from 1 April 2007 until the loss of contact with STEREO-B on 1 October 2014. These offsets are calculated by comparing the nominal pointing information in the Level-0 image headers with the corrected pointings in the Level-1 image headers (Brown, Bewsher, and Eyles, 2009). This shows that rather than being a simple movement between two extremes, there is a D-shaped locus of accessible pointings and that the pointing is usually close to the periphery of this. The offset double-D shape is the result of a correction to the STEREO-B roll calibration that was applied on 18 June 2008 (W.T. Thompson, private communication, 2015). This correction resulted in a change of the nominal pointing placed in the Level-0 image headers. A corresponding change in the pointing adjustments at this time is also present in the HI-2B data. The other movements seen in Figure 4 occur in HI-1B alone and so must be related to movements of the HI-1B camera mounting, relative to the rest of the HI-B structure.

Figure 4

Pointing offsets of HI-1B relative to its nominal pointing from 1 April 2007 to 1 October 2014. Each dot represents the pointing offset of a single HI-1B science image. All images within the interval are included. The points well outside the main locus are from images where the pointing determination (Brown, Bewsher, and Eyles, 2009) did not find a satisfactory solution – such images are not processed through to the Level-2 stage and thus are not included in the main analysis presented in this article.

While the times of low apparent gain in HI-1B, like the gyroless data for all imagers, correspond to times of high particle-hit detections, there is also a slow variation of the hit rates around the orbit due to the variation in the number of stars as a function of galactic latitude (see Appendix A.3). Therefore, setting a simple threshold for particle hits per image would either fail to flag some affected images or would exclude some images unnecessarily. To find a proxy for times when the particle scrubbing was causing significant erosion of stellar counts, but handling the slower variations in a meaningful way, we therefore devised the statistic $\Delta$. We define $\Delta$ as

$$ \Delta(P) = \frac{P_{0.75}}{\mathrm{mmm} (P_{0.25},180)} - 1, $$

(4)

where $P$ represents the number of pixels scrubbed in each exposure of an image, $P_{x}$ represents the $x$th fractile of these counts, and $\mathrm{mmm} (P_{x},n)$ represents the background of $P_{x}$ computed using the mmm routine from the SolarSoft DAOPHOT suite from the $n$ images before and after the current image; the ${\pm}\, 180$ image window corresponds to ± five days at the nominal HI-1 image cadence of 40 minutes, and was chosen to give a baseline shorter than the slow variations of recorded particle hits around the orbit, but longer than the typical gain dropouts. This parameter was found to correlate well with times of reduced apparent gain and to be largely insensitive to slow variations of hit rates around the orbit. The value of $\Delta$ also increased very markedly for all of the HI cameras following the switch to gyroless attitude control (although these data are excluded from the analysis in the main body of this article). After some experimentation, we chose to exclude any images where $\Delta$ exceeded 0.15 from use in the analyses presented in this article. This eliminated about 39,000 of 86,500 science images for HI-1B, and about 6000 of 83,000 for HI-1A (the latter are most probably real particle events with short enough timescales to produce a high value of $\Delta$).

To better understand the behaviour of HI-1B across a momentum dump, we present plots of the apparent gain, and of several parameters related to the particle-hit counts and the pointing of HI-1B in Figure 5. In Figure 5a we show the evolution of the apparent gain of HI-1B across the momentum dump; the reduced gain both before and after the actual time of the dump is clearly seen. In Figure 5b we plot the values of $\Delta$ over the same interval, showing how low gain matches times of high particle-hit spread. Figure 5c shows the pointing corrections between the Level-0 and Level-1 images. The large shifts discussed by Brown, Bewsher, and Eyles (2009) correspond to rapid movements across the D-shaped region of accessible pointings, and they appear as the main discontinuities in the pointing corrections in Figure 5c. In addition to these large jumps, there are intervals of smaller fluctuations on timescales shorter than or comparable with the HI-1 image cadence (Figure 5c and d). We found that there was good correlation between these rapid fluctuations in the pointing correction and times of low apparent gain (and high $\Delta$). These times of rapid pointing fluctuation occur preferentially whenever any of the attitude-control reaction wheels were spinning faster than 350 revolutions per second (rps) (Figure 5e), but are they also seen at other times, still mainly when the wheel speed was high. The reduction in the occurrence of these gain drops after the start of 2009 corresponds to an increase in the frequency of momentum dumps so that after this time, the wheels were seldom spun up to 350 rps. We speculate that vibrations from the reaction wheels cause whatever is loose in HI-1B to break free at spin rates above 350 rps. At somewhat lower wheel speeds the same vibrations, while insufficient to initiate wandering, do prevent the assembly from settling after it has been freed by some other cause such as a dust impact.

Figure 5

Example of the depression of HI-1B apparent gain around the momentum dump on 25 September 2007 (day 268). a) The apparent gain of HI-1B. The continuous line is the daily average, the dots are values for individual images, and the vertical dashed line marks the time of the momentum dump. b) The cosmic-ray spread parameter [$\Delta$]. c) The adjustments of pointing made between the Level-0 and Level-1 images in image bins (Brown, Bewsher, and Eyles, 2009). The continuous line is the correction in the image $x$-direction and the dashed line is in the $y$-direction. d) The pointing scatter (defined as the pointing correction for the current image minus a 15-image running median of the correction). The line is a daily median value and the points are the values for each image, also in image bins. e) The speeds of the four STEREO-B reaction wheels (obtained from the STEREO Science Center: stereo-ssc.nascom.nasa.gov/data/moc_sds/behind/data_products/converted_sc_housekeeping/ ), in rps.

1.3 A.3 Orbital Motion

A final consideration is the extent to which the normal drift of the stars across the image plane will trigger false positives in the cosmic-ray-scrubbing procedure. Since there is no record retained of exactly which pixels have been scrubbed, only the total number in each exposure, this can only be estimated by simulation. On most days, one single-exposure $2048 \times2048$ image is transmitted for calibration and instrument-monitoring purposes. These calibration images can potentially be used as the basis for a simulation of the interaction of the apparent stellar motion with the scrubbing algorithm. This was done by generating simulated shifted images from the actual single-exposure images, and then applying the scrubbing algorithm to these image pairs. For this investigation, we took a number of these full-resolution single exposures (specifically those from July and August of 2009, 43 for HI-1A and 42 for HI-1B) and simulated the cosmic-ray scrubbing, and hence its effect on stellar count rates, by using the algorithm:

• i) For each single-exposure image, the previous exposure was simulated by shifting 2.5 or 25.0 arcseconds along the $x$-axis (corresponding to the one-minute exposure cadence during an image accumulation, and the ten-minute gap between the last exposure of one image and the first exposure of the next image, respectively), using the IDL routine INTERPOL to perform a spline interpolation.

• ii) Equation (3) was then used to compute the scrubbed current exposure, with the simulated image serving as the previous exposure.

• iii) The original and scrubbed current images were both binned to a resolution of $1024 \times1024$.

• iv) For all stars brighter than magnitude 9.0 (including those not suitable for normal calibration purposes), the aperture-photometry methods described in Section 2.2 were used to compute the counts.

• v) The ratios of the scrubbed to the unscrubbed integrated stellar counts were then computed.

• vi) Finally, an estimated effect for a normal science image was derived by summing the 25 and 2.5 arcsec scrubbing ratios with weights of 1/30 and 29/30, respectively.

In Figure 6 we show the simulated ratios of scrubbed to unscrubbed count rates, binned in 0.1 magnitude bins. The simulations show a small discrepancy between HI-1A and HI-1B, for which we do not currently have an explanation. Since this is a small adjustment to a small correction, we feel justified in using a single intermediate value to make an estimate of the fractional reduction of count rate due to the effects of orbital motion. A reasonable approximation can be made with three linear relations:

$$ \frac{R_{\text{scrubbed}}}{R_{\text{unscrubbed}}} = \left \{ \textstyle\begin{array}{l} 0.981 + 0.0013 m_{\mathrm{v}} \\ 0.933 + 0.0071 m_{\mathrm{v}} \\ 0.989 \\ \end{array}\displaystyle \right \}\quad \mbox{where}\ \left \{ \textstyle\begin{array}{l} 7.5 \le m_{\mathrm{v}} < 9.0, \\ 5.0 \le m_{\mathrm{v}} < 7.5, \\ m_{\mathrm{v}} < 5.0, \end{array}\displaystyle \right . $$

(5)

this relation is shown as the dashed line in Figure 6. Although this effect appears substantial, the majority of the stars used in the determination of the calibration parameters are towards the faint end of the range (only about 500 of almost 1500 stars used in the calibrations are brighter than magnitude 7.5, and fewer than 50 are brighter than 6.0); therefore the influence is dominated by the first condition in Equation (5), and the resulting adjustment to the calibration parameters is slightly lower than 1 %. Since the scrubbing due to orbital motion is a function only of stellar magnitude, it only affects the photometric calibration parameters and not the evolution rates.

Figure 6

Estimated effect of the cosmic-ray scrubbing on stellar count rates in HI-1 images due to the normal movement of the stars across the CCD. The line with $\text{crosses}$ shows the results for HI-1A, the line with $\text{pluses}$ shows HI-1B. The dashed line shows the estimated correction given in Equation (5).

We also note that the calibration parameters for HI-2 presented by Tappin, Eyles, and Davies (2015) are not materially affected by this effect as i) the movement of the stars across the CCD is about four times slower (in pixels per exposure) because of the larger pixel size of HI-2, ii) only one in 99 exposures has a long gap before it rather than one in 30, and iii) the PSFs for HI-2 (especially HI-2B) are larger than in HI-1 so that the image gradients are smaller. As a result of this, any corrections in HI-2A, even for the brightest stars, are only about 0.2 % (and much lower than that for the majority of stars), while in HI-2B there is no detectable effect. We therefore conclude that there is no need for a revision to the calibration parameters presented by Tappin, Eyles, and Davies (2015).

1.4 A.4 Summary

The effects outlined in this Appendix are described in more detail in a separate article (Tappin, 2017) as they are of considerable importance for the use of HI data for astronomical studies.

We emphasize here that the only influence that these effects have on the primary scientific objectives of the STEREO-HI cameras (the study of structures in the solar wind) is in the determination of the calibration parameters used to convert the observations into physical units. We have taken them into account by

• i) excluding data after the switch to gyroless pointing control,

• ii) excluding times when high values of $\Delta$ indicated HI-1B pointing shifts, and

• iii) applying a simple correction to compensate for the influence of orbital motion.