## Overview

Image persistence in the IR array occurs whenever a pixel is exposed to light that exceeds more than about half of the full well of a pixel in the array. Persistence can occur within a single visit, as the different exposures in a visit are dithered. Persistence also occurs from observations in a previous visit of completely different fields.

Image persistence is seen in a small, but non-negligible fraction of WFC3/IR exposures. Its properties are discussed in the WFC3 Instrument Handbook in Section 7.9.4. Persistence is primarily a function of the degree to which a pixel is filled (in electrons) and the time since this occurred.

Two examples of persistence are shown below:

The left panel shows an image obtained with WFC3/IR as a parallel from program 11519, Visit 0V.  The primary target was Ton 550 which was observed with COS. The IR exposure is of a nearby field and the image obtained shows a bright diffuse object in the center of the field. About 2 hours earlier, the nearby Sb galaxy NGC 2841 had been observed with WFC3 IR.  The bright diffuse region in the center of the image is a persistence after-image.

The right panel shows an image obtained of the gamma ray burst GRB090423 as part of program 11189, visit H2 .  Several observations of fields containing bright fields from programs 11677 and 11548, visits 19 and AJ,  preceded this observation. The dither pattern used in these sets of observations are clearly visible in the image.  Such obvious examples of persistence are fairly rare in the HST data; using information in the Phase II proposals, STScI scientists attempt to identify observations that are likely to cause this much persistence.  STScI planners inhibit WFC/IR observations for several orbits after observations from these "bad actors", long enough for the afterglow images to fade.  However, while this screening process has improved significantly over time, it is not perfect.

Moreover, it does not deal with the most common cases of persistence, which are far less obvious, a few isolated spots in random locations in the image.

Observers need to consider persistence in planning observations and in analyzing data. Strategies to minimize persistence in planning observations are discussed here.  Tools provided to help observers account for the effects of persistence in analyzing their data are discussed here.

### What causes persistence and what are the characteristics of persistence in the WFC3/IR array?

Persistence is caused by traps that exist in the active regions of diodes that make up the pixels of the detector.  When the diodes are exposed to light, voltage levels within the diode change slightly and allow  free electrons and holes to reach these traps.  When the diode is discharged, the trapped electrons and holes escape the traps slowly over time and cause after images.  The greater the saturation of the detector, the greater the number of traps and the greater the afterglow.  Smith et al. 2008 (Proc. SPIE, 7021, 70210j) has provided a very clear description of the physics of persistence and the effects  in IR arrays.

The characteristics of persistence vary for different devices and device technologies.  The figure below shows the characteristic shape of persistence as observed in a series of darks following an image of Omega Cen which had been deliberately exposed to a level that many stars in the image were saturated.  Here, stimulus is the depth to which individual pixels were exposed.  Note that the persistence is fairly small until the exposure level reaches about half of full well and saturates near full well exposure. The persistence gradually decays with time from the first dark exposure which took place a few minutes after end of the Omega Cen exposure to the last dark which took place about one orbit later.

The next figure shows how persistence decays with time.  The different curves here show the decay for different levels of saturation.  There are 3 curves for each level corresponding to the 3 times this experiment was repeated.  The differences are partially due to the fact that different pixels were illuminated to different levels each time, but may also indicate some intrinsic variability that is not understood.

To good approximation, the persistence decays as a power law with time (with a suggestion that the decay is faster at lower levels of saturation).  For comparison, the dark current is about 0.015 electrons/s.

Based on considerations like those shown above, the WFC3 team has developed a "working model" for persistence in the WFC3/IR array.

$$P_{ij} = N_{ij} \left ( \frac{1}{e^{ \left (x-x_0\right )/\delta x }+1} \right ) \left (\frac{x}{x_0}\right )^\alpha \left ( \frac{t}{1000 s} \right ) ^{-\gamma}$$

Here:

Parameter Description
$$P_{ij}$$ The persistence in the ijth pixel
$$x$$ The maximum depth to which the pixel has been filled
$$t$$ The time since the pixel was filled
$$N_{ij}$$ The position-dependent normalization factor (at 1000 s)
$$x_0$$ The "Fermi energy" definding the midpoint of the region where the persistence is rising rapidly
$$\delta x$$ The "Fermi kT" defining the width of the region where the persistence rises rapidly
$$\alpha$$ The power law index that captures the slow increase in persistence at high saturation levels
$$\gamma$$ The power slope for the decay with time

Using the model and the exposure history, it is possible to estimate the persistence in image.  Tests on individual exposures indicate that it is possible to remove most (about 90%) of the persistence in an image although this requires tuning of the parameters from observation to observation. As is discussed below, we have incorporated this model into software that the WFC3 group is running on all WFC3/IR data.  As a result it is possible for users to obtain an estimate of the amount of persistence in their data.

The original and persistence-subtracted images for the two examples discussed above are shown in the figure above.  Both images are highly stretched and presented as histogram equalized images to show the persistence as clearly as possible.  There is some residual persistence in both images, but clearly the persistence subtracted ones provide a better representation of the celestial objects in both cases.  This is fairly typical of the improvement that can be achieved with our existing model, assuming the parameters are tuned to the individual observation sequence.

LAST UPDATED: 06/17/2019