Instrument Science Report NICMOS-98-005
NICMOS Focus Field Variations (FFV)
and Focus Centering
A.Suchkov & G.Galas
March 16, 1998
ABSTRACT
NICMOS foci are known to vary across detector’s field of view. These variations must be
taken into account when determining ‘‘best’’ focus from a particular stellar image. Focus
field variations (FFV) may introduce substantial positional dependence in aperture corrections, thus they may also be important for high precision stellar photometry. In this
report, we present empirical results of a study of time dependence as well as PAM setting
dependence of FFV for the NICMOS cameras. Although the results are not easy to interprete because of substantial errors, they still suggest that some amount of both time and
PAM position dependence of FFV is consistent with the cameras 2 and 3 data. There is a
preliminary understanding of why FFV should depend on PAM setting and may change
with time. However a detailed interpretation of the actual FFV time and PAM dependence
is beyond the scope of this report and is left for future analysis. As a practical result, we
present the coefficients of the second order surface fit to the FFV data averaged over time
and PAM positions. They are recommended for use in the NICMOS focus monitoring program to reduce focus to the detector center (focus “centering”).
1. Introduction
Along with temporal focus instability, NICMOS focus was found to vary across detector’s field of view (Krist, 1997, Suchkov, Bergeron, & Galas 1997). For camera 2 and
camera 3, the magnitude of the effect is as large as ~1.5 mm in PAM (Pupil Alignment
Mechanism) space, comparable to the nominal tolerance of ± 1 mm . This is a fairly big
amount, which makes it necessary to take focus field variations into account as camera’s
focus is derived from PSF measurements at a particular place in the detector field of view.
FFV mean that there is essentially no single focus for a camera. One has to refer to a particular position on the detector, e.g., the detector center, when characterizing focus. Thus
the knowledge of the geometry of focus variations across the detector became an important component of the NICMOS focus monitoring program. Until now, focus from phase
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retrieval analysis was reduced to the detector center using the FFV parameters derived
from the data which were obtained on August 12, 1997. We have undertaken the present
study to obtain more robust centering parameters using the data from many observations
(visits of the focus monitoring program 7608). Also we wanted to see if those parameters
are changing with time and/or PAM position and quantify these changes. One may expect
to see some PAM dependence because at different PAM positions the detector’s field of
view is imaged on different parts of the curved focal surface. Also a time dependence cannot be ruled out because of the continuing mechanical processes within the cameras. So
the idea was that a subsequent analysis of any FFV dependence on time and PAM setting
might help to better understand the changing NICMOS optics and/or mechanics of the
detector motion in NICMOS cameras.
2. Data
To quantify FFV dependence on time and PAM position, we have used the data from
the first 8 visits of the NICMOS focus monitoring program 7608 (Suchkov, Bergeron, &
Galas 1998). The data cover the period of about 4 months, from June 9, 1997, through
September 24, 1997. The program was designed so that in each visit a stellar field of the
same target, the open cluster NGC 3603, is observed at 17 different PAM positions ranging from ~-8 mm to ~+8 mm in PAM space. This provides 17 image frames per camera
per visit. We have selected frames taken at three different PAM positions, which made 72
frames to study and about 1600 stars to do phase retrieval on. Three frames in a visit were
thought to be enough to check the magnitude and the sense of the FFV dependence on
PAM position while leaving the amount of efforts to do all the data reduction within reasonable limits. Two of the PAM settings were chosen to be adjacent and not too close to
cameras’ 1 and 2 best focus (which is basically in the middle of the PAM range in the case
of cameras 1 and 2, and beyond the PAM range in the case of camera 3). The third PAM
position was taken at the opposite side of the PAM range.
For camera 2 and camera 3, most of the frames have about ~25 stars which sample reasonably well the detector’s field of view and are suitable for focus measurements based on
phase retrieval (phase retrieval technique is described in Krist & Burrows 1995, its application to measurements of NICMOS foci is given in Burrows & Krist 1997 and Suchkov,
Bergeron, & Galas 1998). The stellar field in camera 1 frames is more sparse, and some of
the frames have too little stars to provide good sampling of the field of view, which makes
the results more noisy than for the other two cameras (because of that, camera 1 is discussed below much less then cameras 2 and 3).
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Figure 1: Time dependence of NICMOS focus (mm of PAM space) at the detector corner
(x = 0, y = 0) , as obtained from the first order surface fit to the focus values across the
detector field of view at three different PAM positions. R is the correlation coefficient, and
the thick straight line is the linear fit. A gap seen in the upper panels is due to visit 5 omitted in NIC 1 results.
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Figure 2: Time dependence of the FFV first order surface fit coefficients for NIC 1 at
three different PAM positions.
The results of phase retrieval were visually examined in the focus–XY-coordinate diagram to identify and remove outliers as well as to get an idea on the magnitude and
possible geometry of FFV. Only a few frames were found to have obvious one or two outliers which turned out to be either too faint stars or stars with overlapping PSFs. Those
stars were removed from subsequent analysis. In the case of camera 1, we dropped all
three frames from visits 1 and 5 as they had either insufficient number of stars or produced
too noisy focus results.
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Figure 3: Time dependence of the FFV first order surface fit coefficients for NIC 2 at
three different PAM positions
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Figure 4: Time dependence of the FFV first order surface fit coefficients for NIC 3 at
three different PAM positions
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Figure 5: Time dependence of the FFV second order surface fit coefficients for camera 1
at three different PAM positions (separated by thick horizontal bars)..
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Figure 6: Time dependence of the FFV second order surface fit coefficients for camera 2
at three different PAM positions (separated by thick horizontal bars).
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Figure 7: Time dependence of the FFV second order surface fit coefficients for camera 3
at three different PAM positions (separated by thick horizontal bars).
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3. Results
The actual results of phase retrieval for chosen visits and PAM positions are given in
Appendix (Figures 11 through 19) as the best focus at the position of a selected star (mm
in PAM space) plotted against x- and y-coordinates of the star (coordinates are given in
pixels). Overplotted is a second order polynomial fit to the observed focus values. One can
see that even a 1–D fit displays a sustained pattern across most of the frames, at least for
cameras 2 and 3. The pattern is obviously suggestive of a nonlinear focus trend across
detector’s field of view.
We have fitted the data points in Figures 11 to 19 with both a first order surface,
focus = a 0 + a x x + a y y ,
(1)
and a second order surface,
2
2
focus = a 0 + a x x + a y y + a xx x + a yy y + a xy xy.
(2)
The first order fit provides an easy way to see if there is any time and/or PAM position
dependence in detector’s tilt with respect to the focal plane. The fitting results are displayed in Figures 1 to 4 (see Table 1 for correspondence between visit number and the
date of observation). Figure 1 gives the focus at the detector corner (x = 0, y = 0) for
each camera at three different PAM positions. One may notice a slightly smaller camera 2
focus values at the negative side of PAM settings and an upward trend of camera 3 focus
persistent across PAM positions. With regard to FFV coefficients given in the next three
Figures, the most conspicuous feature is probably a substantial y-tilt in camera 2. The tilt
seems to be a bit larger at the negative PAM settings. One may also notice a trend in the xtilt, seemingly dependent on PAM position. Real or not, this trend does not present a big
problem for focus centering since the x-tilt is small. But, if real, it may be of interest for
interpreting camera’s detector–optics connections.
There is no doubt that the actual NICMOS focus field variations have a substantial second order component in x and y, and we want to take it into account in focus centering. To
derive centering coefficients, we have fitted the phase retrieval results with a second order
surface given by equation (2). Time dependence of the coefficients of equation (2) is
shown in Figures 5 through 7.
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Table 1. Date of observation for the visits of the focus monitoring calibration
program 7806 used in this study.
visit number
date of
observation
day since
January 1
1
9-Jun-97
160
2
30-Jun-97
181
3
14-Jul-97
195
4
28-Jul-97
209
5
12-Aug-97
225
6
25-Aug-97
237
7
8-Sep-97
251
8
24-Sep-97
267
Inspection of Figures 5 to 7 reveals that, of all the cameras, only NIC3 shows significant correlation of a x and a xy with the visit numbers at PAM = – 6 mm . However,
most of the correlation is due to the first two visits. If those are disregarded, one can state
that there is no or a very weak evidence that NICMOS FFV systematically changed over
the period under consideration. The first two visits are also the major contributors to the
large scatter in the fitting coefficients at PAM = 6 mm .
As for the PAM dependence, there are indications that, for camera 2, for which focus
variation occurs most significantly along y-axis, the y-tilt, i.e., a y , is a bit larger at
PAM = – 6 mm , just as in the case of the first order surface fit. A similar pattern can be
seen for camera 3 if the first two visits are ignored.
We leave a detailed interpretation of the results for future analysis. For the purposes of
focus centering, we prefer, for the time being, to average the fitting coefficients over all
visits and PAM positions. Table 2 presents the results of this averaging. In the case of camera 3, the first two visits were rejected for the reasons discussed above.
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Table 2. Coefficients of equation (2) obtained by averaging the results of individual fits for
18 frames for camera 1 and camera 3, and 24 frames for camera 2.
camera
a x × 10
3
a y × 10
3
a xx × 10
5
a yy × 10
5
a xy × 10
5
NIC1
-2.869 +/- 1.529
1.383 +/- 0.542
1.199 +/- 0.416
0.229 +/- 0.145
0.068 +/- 0.227
NIC2
-1.304 +/- 0.211
2.819 +/- 0.168
0.397 +/- 0.056
0.605 +/- 0.061
0.614 +/- 0.079
NIC3
-3.682 +/- 0.159
-6.578 +/- 0.120
1.580 +/- 0.066
1.710 +/- 0.039
-0.055 +/- 0.062
Figure 8 displays the surface describing camera’s FFV in terms of equation (2) with
coefficients from Table 2. It differs little from Figure 7 in Suchkov, Bergeron, & Galas
(1998) which displays the FFV fitting results obtained from a single visit (these results
were used in focus centering till the end of the focus monitoring program 7608 in February of 1998). Because of that, focus centering based on equation (2) and Table 2 should be
expected to produce the results not very much different from those in Suchkov et al
(1998). Comparison of Figure 9 and Figure 10 shows that this is indeed the case.
Despite the little difference between the FFV fit used before and the present “averaged” fit, we recommend to use for focus centering the results based on equation (2) with
coefficients from Table 2 as they are statistically more accurate and have well defined
uncertainties.
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Figure 8: NICMOS FFV as given by equation (2) with coefficients from Table 2 and focus
set arbitrarily to 0 at x=y=0.
4. References
Burrows, C.J. & Krist, J.E. 1997, Memorandum, March 19, 1997, ‘‘NICMOS Focus’’
Krist, J. 1997, in: 1997 HST Calibration Workshop, STScI.
Krist, J. E. & Burrows, C.J. 1995, Applied Optics, 34, 4951
Suchkov, A., Bergeron, L., & Galas, G. 1997, in: 1997 HST Calibration Workshop.
Suchkov, A., Bergeron, L., & Galas, G. 1998, ISR NICMOS-98-000
5. Appendix
The following Figures include the plots of NICMOS focus history (Figures 9 and 10)
and actual focus measurements used in this report to study FFV (Figures 11 through 19).
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Figure 9: NICMOS focus history from Suchkov et al (1998). Focus from phase retrieval is
centered with FFV coefficients from a single visit used through February 1, 1998.
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Figure 10: Same as in previous Figure but for focus centering based on equation (2) with
coefficients from Table 2.
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Figure 11: Focus in camera 1 measured at different x and y positions. Indicated are image
ID and PAM position. Focus is given in mm of PAM space.
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Figure 12: Same as in previous Figure but for a different PAM setting.
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Figure 13: Same as in previous Figure but for a different PAM setting.
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Figure 14: Focus in camera 2 measured at different x and y positions. Indicated are
image ID and PAM position. Focus is given in mm of PAM space.
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Figure 15: Same as in previous Figure but for a different PAM position.
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Figure 16: Same as in previous Figure but for a different PAM position.
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Figure 17: Focus in camera 3 measured at different x and y positions. Indicated are
image ID and PAM position. Focus is given in mm of PAM space.
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Figure 18: Same as in previous Figure but for a different PAM position.
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Figure 19: Same as in previous Figure but for a different PAM position.
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