# Non-linearity at large ADU¶

Huan's report shows there is large non-linearity at adu range from 3000 - 30000. Juan put together a few exposures for comparing the fitting codes. Here are some results from my analysis. What I noticed is that the non-linearity can be well eliminated by a quadratic term of the exposure time. In the fitting function on the plot, x is exposure time, y is mean count in ADU.

0. Corrected exposure time:

As the quadratic fit can bring the system to linear at large ADU, then I can correct the exposure time so that it fit a linear model. The resulting corrected exposure time - exposure time was plotted below. As you can see, not all CCD share the same trend, which may indicate it is not a shutter issue.

1. extension 1:

2. extension 22:

3. extension 65:

## Possible flux dependence of PSF (Vinu V. & Gary B.)¶

See the document posted on doc-db #6964. In this work we mainly focusing on the dependence of PSF on flux. An independent study of that was also done by Nicolas Regnault. For this exercise we use 22 r-band exposures taken for the star flat study (ObsID = 163540-163561). We check this dependence by plotting the SExtractor parameters FLUX_RAD (which corresponds to the radius of the object that encloses 50% of FLUX_AUTO) vs FLUX_MAX of stars selected based on abs(SPREAD_MODEL) < 0.002, MAG_AUTO and FLUX_RAD. The selection of stars are done CCD by CCD. The result for ObsID=163554 is shown in Figure vv1. The left panel shows the relation between FLUX_RAD and FLUX_MAX. The black dots are the selected stars and red filled circles with error bar shows the average of FLUX_RAD in different bins. The error bar are corresponds to the std. error which is the std. dev / sqrt(N). The green lines are the best fitted lines to each CCD and we take care of both x and y errors while fitting. The line is fitted between the range FLUX_MAX=5000 and FLUX_MAX=25000. We found that there is ~1% change in PSF in this figure. However, this could be due to the particular estimator of half light radius, i.e. FLUX_RAD. Therefore, we measured half-light radius by ourself using total light within an aperture of size 6 pixels. We did not find any noticeable change even when using aperture size of 7 and 8 pixels. The result of our measurement is shown in the right panel of Figure vv1 for ObsID 163554. Even though the dependence of PSF on flux is not so strong as earlier it is not entirely due to the particular estimator in SExtractor. However, to avoid any type of estimator related dependence we use our measurement of half light radius (R50) for the rest of the study.

The difference between the slopes derived from SExtractor parameters and from our parameters are shown in Figure vv2

To reduce the noise of the estimated slopes of the relations we average the slopes of the individual CCDs estimated from all the 22 exposures. In the rest of the discussion we use this average slopes of CCDs over all the 22 exposures. Refer Figure vv3 to see the distribution of slopes estimated from single exposure (green) and from 22 exposures (red). The distribution of average slopes of 22 exposures are much narrower than the one estimated from single exposure. The left panel shows the distribution of slopes of the relation between R50 and FLUX_MAX of ObsId 163554 (green) and distribution of average slopes from 22 exposures (red). The middle and right panels show similar results for x and y second moments (see discussion below)

The dependence of PSF on flux raise the question whether that can be the result of charge transfer efficiency. We, therefore, plot the PSF R50 vs the distance to the serial register, i.e the y-coordinate of the star on the CCD. The results are shown in the left panels of Figure vv4 and Figure vv5 for S and N CCDs respectively. This separation of CCD is done because their serial registers are in the opposite sides of the CCD. We found that the average percentage change of PSF over the y-coordinate is -0.1% and -0.2% for S and N CCDs. The values of the relative change of R50 and average and median values of slopes are also shown in the figure. One of the signatures of the charge transfer efficiency related PSF dependence is that it causes asymmetry in the PSF. We, therefore, measured the second order x and y moments (Mxx and Myy) of these stars and plotted them against the distance to the serial register. The results are shown in the middle and right panels of Figure vv4 and Figure vv5. We found that the average change in Mxx and Myy are -0.7% and 0.3% for S CCDs and -0.4% and -0.1% for N CCDs. During this exercise we noticed that some CCDs show very large dependence of moments (Mxx and Myy) on the distance to the register.

In Figure vv6 we plot spatial distribution of the slopes of R50 and y position (left panel) moments vs y position (middle and right panels) on the 2D image plane. The color represents the values of the slopes. We found that CCDs with large slopes belong to the edges of the images. This is very important result as it implies that the dependence may be related to optics.

Finally, we go back to our original problem of the flux dependent PSF. In Figure vv7 we plot the average dependence of PSF on flux for each CCDs. These averages of each CCDs are measured from 22 observations. The left panel shows the how R50 varies with FLUX_MAX. The average change of R50 is 0.4% between FLUX_MAX=5000 and FLUX_MAX=25000. This is small but should be considered for the weak lensing studies. The middle and right panels we shows the variation of Mxx and Myy with FLUX_MAX. We found that there is no asymmetry in the PSF with flux and both Mxx and Myy varies 0.6% over the specified flux range.

We also, study whether there is any spatial dependence of this relation by plotting the slopes on the 2D image plane. We found that there is not noticeable dependence. This result is shown in Figure vv8