## Overview

New encircled energy (EE) corrections were calculated for two filters,  F275W and F814W, by correcting for time sensitivity changes of the detector before combining the Point Spread Functions from each image.

Values derived for UVIS1 and UVIS2 are in very good agreement with each other and with the 2009 EE vaues (see figure below). Following these results, EE values for the other ultra-violet filters were also changed by ~1% and EE for wavelengths larger than 7,500 A were changed by ~0.5%  to be in close agreement with the F814W EE values.

Chip-dependent, filter-based EE fractions were derived from aperture photometry of three white dwarf standards G191B2B, GD153 and GD71 (plus the G star P330E) and spliced to the 2009 in-flight models at r=35 pixels (1.4 arcsec).

## UVIS EE Tables

ASCII (CSV) tables for UVIS1 and UVIS2.

• Row 1: header information, Row 2-: EE fractions by wavelength

• Column 1: Wavelength (Angstroms), Column 2-end: Aperture radius in arcseconds

UVIS 1

UVIS 2

## Recommendation

For photometry with aperture radii <10 pixels and targets placed in the upper-left corner of Amp A (e.g. UVIS1-C512A-SUB, UVIS1-C1K1A-SUB), we recommend using the UVIS1 EE fractions, since the PSF in this quadrant is slightly out of focus compared to the rest of the UVIS focal plane. For all other cases we recommend using the UVIS2 EE fractions.

## Prior Calibration

After WFC3's installation in 2009, deep observations in F275W and F625W were obtained in 5 positions across the UVIS array, and these were used to revise the pre-flight EE. EE fractions for all remaining filters were interpolated from the revised 2009 optical model (ISR 2009-38).
[The 2009 EE tables are available here.]

The 2016 chip-dependent EE fractions were derived from filter-based aperture photometry, spliced to the 2009 models at r=35 pixels (1.4 arcsec) and are consistent with the 2009 model EE fractions for all but a few filters.  The uncertainty in the EE curves at the infinite aperture is ~0.5%.

Generally, fewer than 8 observations were obtained per narrow band filter, and for some apertures there are only 2.  Therefore the filter based encircled energy values for these filters have larger uncertainties than EE values for the broad band filters.   The figure below shows the filter-based EE fractions at 10 pixels for all full frame filters for UVIS1 (green) and UVIS2 (red ), as well as the original pre-flight EE model values (black) and the in-flight revised model EE fractions (blue).

F200LP  has an extremely broad bandwidth ~6000 Å centered at ~4885 Å.  F953N has 8 images in UVIS1 but only 2 images in UVIS2. Thus its EE is highly uncertain, and users may wish to adopt the UVIS1 EE values instead. Consult Table 6 in ISR 2016-03 to compare the number of input frames used to create the filter-based EE curves.

## Examples

For drizzled images, or flat-fielded images multiplied by the pixel area map (i.e. FLT*PAM), the mean signal in a circular aperture of radius r is:

$$Flux = \frac{F_r \cdot PHOTFLAM}{EE(r)}$$

Where Fr is the signal within aperture r in electrons per second, EE(r) is the encircled energy fraction at radius r, PHOTFLAM is the inverse sensitivity at the infinite aperture, whose default value is PHTFLAM1.

The equivalent calculation using magnitudes is:

$$m=m_i + 2.5\times \log{\left (EE(r)\right)} + ZP$$

where mi is the instrumental magnitude, mi = -2.5*log(Fr), ZP is the PHOTFLAM equivalent in magnitude units from ISR 2017-14 Table 2, and EE(r) is as above.

For example, aperture photometry using a *drz.fits image, for radius r = 3 pixels of a star on the UVIS1 CCD with the F606W filter yields F= 950 e-/s.

The inverse sensitivity of F606W is PHTFLAM1 = 1.13745E-19 erg·s-1·cm-2·Å-1 /(e-/s). The encircled energy at r = 3 pixels is

EE(r=3) = 0.742 (UVIS1)

In physical units:

Flux = 950 * 1.13745E-19  /  0.742=  1.4563E-16 erg·s-1·cm-2·Å-1

In VEGAMAG:

m = -2.5*log(950) + 26.014 + 2.5*log(0.742) = 18.246 mag

NOTE: Photometry at r<8 pixels relative to r=10 pixels varies with position and depends strongly on the telescope focus and breathing. At r=3 pixels, the variation is between 4% -10% (see ISR 2013-11).

LAST UPDATED: 11/05/2020