NICMOS IntraPixel Sensitivity
Chun Xu and Bahram Mobasher
Space Telescope Science Institute
Introduction
Accurate photometry depends, in part, on the width of the Point
Spread Function (PSF) compared to the pixel size. If the PSF is
much smaller than the pixel size and if there is any sensitivity
variations within a pixel, then the detected flux is dependent on
the positions of the PSF within the pixel. This could lead to
significant uncertainties in photometric accuracy of point-like
sources.
In case of the NICMOS, this effect is negligible for NIC1 and
NIC2, as the PSF core is much broader than their pixel size and
hence, to a large extent, the PSF covers the entire pixel.
However, NIC3 with a pixel size of 0.2 arcsec, could
undersample the PSF at all wavelengths, leading to different
total fluxes for a given star at various dither positions. The
purpose of this study is to characterize the nature of this effect
and to correct it. We analyzed data from both Cycle 7 (pre-cryocooler) and Cycle 11 to study the change of this effect due to
the installation of cryo-cooler.
The Strategy of the Correction
In the PSF undersampling cases, if lights hit the center of a
pixel, the resulted PSF should be sharper than when lights hit
near the edge or corner of a pixel, because in the latter case,
the lights will spread out among a few pixels thus lead to a
broader PSF. One the other hand, if there exists intrapixel
sensitivity variations, the measured total flux will be different
in these two cases, even for the same star. Thus we expect a
correlation between the FWHM of the PSF and the measured
total flux. The aim of this study is to find such correlation and
use this correlation to correct the observed flux based on the
measured FWHM of a PSF. In practice, we use a parameter
called sharpness ratio rather than FWHM in the correction
procedure since the former is easier to assess. The sharpness
ration is defined as the peak flux of a pixel near the center of a
PSF vs the total flux within PSF. Either the sharpness ratio or
the FWHM is practically an indicator of the intrapixel position
that a PSF falls on a pixel.
Abstract
We present here the new measurements of the NICMOS (Camera 3)
intrapixel sensitivity after the installation of the cryo-cooler in Cycle 11. We
find a 27% decrease in the intrapixel sensitivity from Cycle 7 to Cycle 11 for
both J (F110W) and K (F160W) bands. The decrease in the intrapixel
sensitivity could not be attributed to the change of the PSF as the latter is
less than 5%. We also discuss a possible cause for the decrease of the
intrapixel sensitivity. In the end we present the formula to correct this
intrapixel sensitivity.
The Analysis
We define normalized total flux as Fn=Ftot /<Ftot>, where Ftot is the total flux of a star in
one dithered exposure and <Ftot> is the average of the total fluxes of that star over all
dithered exposures. We use median instead of average in practice. We define
sharpness ratio as S=Fpk/Ftot , Where Fpk is the peak flux of one pixel near the center
of a stellar image in one dithered exposure and Ftot is the total flux of that star in the
same exposure, as defined previously. As discussed earlier on, S indicates the
subpixel position of a stellar image while Fn reflects the relative total flux in one
dithered exposure. Ideally, if there is no intrapixel sensitivity variations, we don’t
expect Fn to change with S, however, if there is intrapixel sensitivity variations and if
the size of the PSF is comparable or smaller than that of a pixel, then we expect a
trend in the sense that higher sharpness ratios correspond to higher normalized
fluxes. The steeper the slope, the higher the intrapixel variations. Figure 1 shows an
example how the normalized flux changes with the sharpness ratio for different
dithered exposures of a single star.
Figure 2. The fits to both Cycle 2 and Cycle 11 data.
As discussed previously, the parameter a (slope) is a good indicator of the
intrapixel sensitivity. Table 1 and Figure 2 clearly show that this value
decreased from Cycle 7 to Cycle 11 for both F110W and F160W. The
decrease of a implies either a decrease of intrapixel variation or an increase
of the PSF. After a careful comparison of the PSF in both cycles, we rule out
the latter case and conclude that the decrease of the intrapixel sensitivity
variations from Cycle 7 to Cycle 11 is intrinsic (cf: Xu & Mobasher 2003). The
decrease of the intrapixel sensitivity is in line with the expectation that after
the installation of the cryo-cooler, the increase of the operation temperature
leads to a higher electron mobility so smoothes the differences of the
detector quantum efficiency (DQE) within a pixel. This effect is
mathematically similar to convolving with a function of larger FWHM.
The Correction of the Intrapixel Sensitivity
The Data and Reduction
This study was initiated by Storrs et al. (1999) using Hubble
Deep Field South (HDf-S) data, including data from proposal
8058,8073,8074,8087 and 8076 in Cycle 7. The data were taken
using NIC3 with filters F110W and F160W at different dither
positions. After the installation of cryo-cooler in Service
Mission 3, this study was continued in Cycle 11 (proposal
9638) through the observations of star cluster NGC 1850,
using NIC3 with the same 2 filters. The observations are
dithered at 25 steps so the stars in the field of view fall onto
different subpixel positions. The data are calibrated using
calnica 4.1.1 through the pipeline.
The total flux of a star and the peak pixel flux are measured
using Sextractor (Bertin & Arnouts 1996). The aperture radius
is set to 2.5 pixels, roughly twice of the assumed PSF FWHM
of 1.4 pixels. For a given star, if the measured FWHM is larger
than 2.8 pixels in certain dithered exposures, these exposures
are discarded to assure the data quality.
Figure 1: Normalized flux vs. sharpness ratio for a selected star. A linear fit to the data is over plotted.
Based on the parameters in Table 1, we can easily correct to the measured
total stellar flux in individual exposures to averaged flux, the latter is
considered the true flux of a star. The formula is simple:
Results and discussion
Fc = F x (aSm+b)/(aS+b)
We apply our method to both Cycle 7 and Cycle 11 data and find that the
intrapixel sensitivity decreased from Cycle 7 to Cycle 11, after the installation of
the cryo-cooler, as a result of the increase in the operation temperature. The
results are presented in Table 1 and Figure 2.
where Fc is the corrected flux and F is the measured flux, S is measured
sharpness ratio in that exposure, a, b, Sm are parameters in Table 1. This
correction is also applicable to any observation at their individual dithered
exposures. The users only need to measure the total flux and sharpness
ratio and plug them into this formula.
Table 1. Linear fit to the data.
Filter
Cycle 7
Cycle 11
Slope (a)
Intercept (b)
Median
dex
Sharpness (Sm)
F110W
0.689 ± 0.029
0.738 ± 0.011
0.374 ± 0.080
0.025
F160W
0.723 ± 0.030
0.727 ± 0.012
0.381 ± 0.086
0.038
F110W
0.497 ± 0.019
0.828 ± 0.007
0.346 ± 0.077
0.023
F160W
0.457 ± 0.015
0.839 ± 0.005
0.348 ± 0.079
0.019
References:
Bertin, E., and Arnouts, S., 1996, A&AS, 117, 393
Storrs, R., Hook, S., Stiavelli, M. et al., 1999, ISR NICMOS-99-005
Xu, C, Mobasher, B., 2003, ISR NICMOS-03-009