WFCAM Linearity

1. From dome flat sequences
2. From sequences of observations of star fields
3. From comparisons with 2MASS data

1. Dome Flat Sequences

March 2005

We make the assumption that the data is linear, then fit a model

d_i = A + B t_i

100 { d_i - ( A + B t_i ) } / d_i

Figure 1: The left hand plot shows median counts (d_i) against exposure time (t_i. Overlaid are the linear fits described in the text. On the Right hand side we plot the percentage deviation from the fit, i.e the non-linearity. On both plots the chips are colour coded (#1:Black, #2:Red, #3:Green, #4: Blue).

We see no evidence for non-linearity at the >1% level. The fluctuations in counts at the bright end appear correlated between the chips. This is better illustrated in Figure 2 (below), which shows that the background illumination was almost certainly varying during the exposure sequence.

Figure 2: Percentage deviation from linearity as a function of exposure time for all four detectors (colours as in Figure 1.

May 2006

Figure 3: J-band background counts per second measured with 2 sec exposures over the duration of the dome flat sequence.

To account for the varying background, we made a simple linear fit to the background rate versus MJD. The counts in each exposure in the dome sequence were corrected to account for the varying illumination. The corrected counts versus exposure are plooted below. We applied the same analysis as above, and the results are shown below in the right hand panel.

Figure 4: The left hand plot shows median counts (d_i) against exposure time (t_i. Overlaid are the linear fits described in the text. On the Right hand side we plot the percentage deviation from the fit, i.e the non-linearity. On both plots the chips are colour coded (#1:Black, #2:Red, #3:Green, #4: Blue).

Again, we find no evidence for significant non-linearity. WFCAM has been constrained to be linear to <=1% by these measurements over almost the entire range. The only significant deviations are where the counts reach the >30,000 level - i.e. we are approaching saturation

Short vs Long exposures

Figure N: A slice through columns 1501 - 1600 for a flatfield image on detector#4 is shown to illustrate the variation in sensitivity across the detector.

For a perfectly linear detector, then the ratio will be unity. If there is non-linearity then this will result in a slope across the ratio image correlated with the sensitivity. The figure below suggests that there may be a very small effect.

Figure N: A slice through columns 1501 - 1600 for a 12 second flatfield image divided by a 4 second flatfield image (and normalized to the maximum), again on detector#4.

The direction of the effect suggets that an increases in brightness leads to a reduction in the measured counts with respect to an expected linear relation. The magnitude of the effect is around 1.5%.

Comparison with 2MASS

The CASU pipeline calibration is based on 2MASS. Colour equations for each filter were derived from data taken in 05A (see the commissioning report). The 2MASS magnitude is first converted into the WFCAM system using these colour terms.

Then for each field we then derive the photometric zeropoint as the median of:

ZP = m(2MASS) + { 2.5 x log10(counts/sec) }

over all stars on all four detectors. The Zeropoint is corrected for extinction assuming a default value (0.05 mags/airmass for each filter).

Figure 4 shows m(WFCAM)-m(2MASS) for the J, H and K filters. The data comprise repeat observations made on photometric nights of 7 standard fields. These observations were spread throughout semesters 05A and 05B. The plots include data from all four detectors.

Figure 1: Delta magnitude (WFCAM-2MASS) versus peak counts for point sources. Data from standard star observations in 05A and 05B from photometric nights.

The same plots for the same data but as a function of magnitude.

Figure 1: Delta magnitude (WFCAM-2MASS) versus magnitude for J, H and K band. Data from standard star observations in 05A and 05B from photometric nights.

We've made a couple of tests to see if there are other dependencies in the effect. The first plot is delta magnitude versus colour to look for any residual colour terms.

Another question was asked. Could the effect be caused by over/underestimation of the background for bright sources? We examine the difference between the per-source background counts (the local background) measured from a 64x64 pixel box, and the median frame for the background. There is no trend in delta(magnitude) with background. The following plot is (local-median) background against source peak counts for the J-band. The J-background level varies between about 300 and 1000 counts/pixel in a 10 second exposure (depending principally on lunar phase/proximity and time of night). The variation in background across the frame is typically significantly less than 1%. The peak counts can also seen to be entirely independent of the background estimate, and we see no evidence that there is a star brightness dependent under- or over-subtraction.

Figure 1: Delta magnitude (WFCAM-2MASS) versus delta sky level (local minus frame median) for point sources. Data from standard star observations taken throughout 05A and 05B on photometric nights.

Conclusions

1. Further dome sequences will be measured and repeated to (a) mitigate against non-constant illumination and (b) to investigate other filters.
2. We will investigate whether there is any correlation between linearity and incident count-rate ( c.f. NICMOS).

Update New dome sequences and stnadard star measurements were obtained on 26th May 2006. These data are now in Cambridge and will be processed shortly.