Instrument Science Report NICMOS-98 -004
NICMOS Focus Monitoring
A. Suchkov, L. Bergeron, & G. Galas
March 16, 1998
ABSTRACT
We describe techniques to measure NICMOS foci and present the results of the NICMOS
focus monitoring program as of February of 1998. Various effects which impact focus
measurements are examined. They include, in the first place, HST “breathing” and focus
spatial variations across NICMOS fields of view (focus field variations). Procedures to
correct for those effects are discussed.
1. Introduction
The NICMOS cameras were designed to share a common focus whose position can be
adjusted using the Pupil Alignment Mechanism, or PAM. PAM’s main part is an adjustable mirror which can be moved within +/- 10 mm about its zero position, thus allowing
fine tuning of the actual location of the focus. It was hoped that, whatever changes to the
HST optical path may happen, the focus can always be brought back to the position of the
detectors. Unfortunately, the unforeseen deformation of the NICMOS dewar has caused
large mechanical distortions within NICMOS, which resulted in loss of a common focus
for the three cameras. Worst of all, the camera 3 detector was pushed way out of the range
within which the PAM can adjust the focus position. Soon after the Servicing Mission, this
detector required a PAM position of about – 17 mm to be in focus, which was far beyond
the reach of the PAM (see Burrows 1997 for more extensive discussion).
The ongoing deformation processes in NICMOS keep changing the location of the
detectors with respect to the PAM zero position. This necessitates checking the NICMOS
camera foci on a regular basis so as to ensure timely adjustments of PAM nominal settings
if required. To this end a special focus monitoring program was designed to determine on
a biweekly basis the current focus position from observations of a stellar field of the open
cluster NGC 3603. The results of focus monitoring as of February 1, 1998 are presented in
Figure 1.
1
Figure 1: Nicmos focus history as of February 1, 1998 (focus at the detector center).
Focus is given in mm of PAM space. Focus at day 377 reflects the secondary mirror move
on January 12, 1998, which placed NIC3 in focus. At day 397, the secondary mirror was
reset to its nominal position. For days 351, 368, 377, and 397 the upper and lower points
represent focus values uncorrected and corrected for off-nominal FOM setting, respectively.
.
NIC1
NIC2
NIC3
Three different techniques based on: (a) phase retrieval, (b) encircled energy measurements, and (c) plate scale measurements, respectively, were used to obtain focus values
given in Figure 1. Phase retrieval and encircled energy provide direct measurement of the
focus position and absolute variations in focus position. Plate scale, which is defined as
the angle in the detector field of view subtended by one pixel, can serve as an indirect
diagnostic of focus variations whose interpretation depends on mechanisms causing plate
scale variation. The main reason for plate scale variation is believed to be the changing
distance between the detectors and the Field Divider Assembly. On the other hand, even a
2
large focus shift induced, for example, by a secondary mirror motion, such as the one that
placed NIC3 in focus on January 12, 1998, for NIC3 campaign, have essentially no effect
upon plate scale. So a tight coupling between phase retrieval and plate scale results seen in
Figure 1 till day ~200 or a bit later suggests that most of the early focus variation was
probably due to detector motion. Divergence between plate scale and phase retrieval/encircled energy measurements observed after that period is indicative of mechanisms other
than detector motion coming into play. It is worthwhile to remind at this point that focus
jump on day 351 is due to the new FOM setting which has moved focus up by ~1.5 mm
in PAM space.
2. Phase retrieval
Phase retrieval provides absolute value for the focus position. The method was developed by Krist & Burrows (1995) and expanded by Krist & Hook (1997b) to incorporate
the NICMOS cameras. The results presented in Figure 1 have been obtained on the basis
of the data from the focus monitoring proposal 7608 which was being executed bi-weekly
from June 9, 1997, through February 1, 1998. Earlier results from a SMOV proposal,
which was structured exactly as 7608, are also included. As described in Burrows & Krist
(1997), the program was designed so as to observe during each visit a stellar field of the
open cluster NGC 3603 at 17 different positions of the Pupil Alignment Mechanism
(PAM) which effectively changes the focus of the F/24 image that the NICMOS cameras
see (focus sweep). After routine calibration pipeline processing, all images were examined
and a star was selected to run phase retrieval on. The result of phase retrieval is the 17 values of Zernike coefficient Z 4 for each camera.
Burrows & Krist (1997) established the following relationship between Z 4 measured
at a given PAM position, PAM , and focus location in PAM space, F , based on the SMOV
focus monitoring data:
2
8 × 24
scale × breath
F = PAM + 3.887 × G i Z 4 × ----------------- + G i × 110 × ------------------------------------- ,
1000
1000
where PAM is PAM position in mm, breath is a correction for “breathing effect” provided by the thermal breathing model and scale is a scaling factor improving the estimate
based on that model (see below). The factor G i as derived from the SMOV data is as
follows:
G i = 1.171
(camera 1)
G i = 1.212
(camera 2)
G i = 1.083
(camera 3).
After focus is derived at each of the PAM positions (see Figure 2 for illustration), the
3
average focus value is calculated using 12 PAM positions in the case of camera 1 and
camera 2, and all 17 PAM positions in the case of camera 3. These averages are plotted in
Figure 1. The bars are focus standard deviations (the error of the mean is, of course,
–1 ⁄ 2
smaller by the factor of N
, where N is the number of PAM positions used to calculate
the average). As explained below, the errors in phase retrieval solutions are large for
images taken at PAM positions close to or at the best focus. Therefore, in the case of camera 1 and camera 2, 5 of 17 focus values obtained for PAM positions adjacent to best focus
are rejected. Since camera 3 is out of focus within the entire range of PAM positions, all
17 focus values are used in calculation of mean focus for this camera.
Optimization of phase retrieval results: rejecting measurements around best focus
Phase retrieval is known to produce better results if focus is measured far from the best
focus position. Therefore, for camera 1 and camera 2, we may expect better accuracy for
mean focus if the measurements around the best focus are rejected. However, as the number of focus values used to calculate the mean goes down, the error of the mean goes up as
–1 ⁄ 2
N
. An optimal procedure might be to remove a pair of data points next to the best
focus (and, of course, the point at the best focus too), check the new rms error of the mean
against the previous value, and continue this process until the minimum of the rms error is
reached. Figures 3 and 4 show the variation of the mean focus rms error for cameras 1 and
2, respectively, as dependent on the number of rejected focus measurements at PAM positions around best focus. Improvement of the focus accuracy as a result of rejection of PAM
positions in the neighborhood of best focus is beyond doubts. For practical purposes, it
was decided to uniformly apply rejection of measurements at 5 PAM positions closest to
best focus across all visits for both camera 1 and camera 2. This yields about the same
amount of improvement in the mean focus accuracy for the bulk of the visits, close to the
maximum possible value.
Focus accuracy and PAM usage
The above procedure is not applicable to camera 3 because the latter is out of focus
within the entire range of focus sweep. For this camera, as well as for cameras 1 and 2, the
dependence of the mean focus error on the number of PAM positions used to calculate the
mean is important for deciding how many of those we may need in focus sweep to obtain
reasonably good results. The issue is quite topical given the need to reduce mechanical
wear and tear of the PAM. As seen from Figure 5, the bulk of the gain in accuracy we
achieve typically from the first 5 to 10 PAM positions. Therefore we can quite safely
reduce PAM usage by a factor of 2 or more and still get good results for camera 3 focus.
As long as camera 3 is out of focus, it does not matter which PAM positions to drop from
the focus sweep. Based on this result, we recommended to reduce the number of PAM
positions to be used in the focus sweep for camera 3 by a factor of two.
4
Figure 2: Zernike coefficient Z 4 , focus, and thermal breathing correction as function of
PAM position. The results are from the data of August 12, 1997 (visit 5 of the program
7608). All the parameters are measured in mm of PAM space.
The dashed line in the second column
and the straight full line in the third column
of the panels indicate mean focus and mean
breathing correction, respectively
5
Figure 3: Error of the mean focus in camera 1 as a function of the number of rejected
focus measurements at PAM positions adjacent to best focus.
The recommendation has been implemented in the new focus monitoring proposal,
7901, which replaces the old proposal 7608 effective February 18, 1998. Inspection of
Figures 3 and 4 suggests that PAM usage for cameras 1 and 2 can also be reduced to about
5 positions without significant loss of focus accuracy. However in this case the PAM positions to be dropped must be the ones from the middle of the PAM range. The problem is
that those positions are necessary for focus estimates based on encircled energy. As long
as we want to maintain both phase retrieval and encircled energy measurements as independent sources of focus information, we will need to use both the middle and the
outskirts of the PAM range for these two cameras.
6
Figure 4: Error of the mean focus in camera 2 as a function of the number of rejected
focus measurements at PAM positions adjacent to best focus.
Breathing corrections
HST focus suffers from short term variations occurring on the HST orbital time scale.
They are caused by changing HST thermal conditions as the spacecraft moves from night
to day and back to night. The resulting effect is known as “breathing” (Hasan & Bely
1994; see also Suchkov and Casertano 1997 for the details of this effect and its impact on
photometry). In one orbital period, breathing may shift the focus position by as much as a
few tenths of a millimeter in PAM space (see below). Since a focus sweep for camera 1
and camera 3 takes approximately half an orbital period, this shift, if not taken into
account, would contribute to focus scatter and thus degrade the estimate of the mean.
7
Figure 5: Error of the mean focus in camera 3 as a function of focus measurements at
PAM positions used to calculate the mean. Diamonds: PAM counting goes in the sense of
increasing PAM values, dots: counting goes in the sense of decreasing PAM values.
Appropriately allowing for this effect, we can improve results of focus measurements.
The “thermal” model of the breathing effect relates the HST secondary mirror motion
to temperature variations as follows (Hasan & Bely 1994):
breath = 0.7 ( T – T average ) ,
where breath is the secondary mirror displacement (in microns) with respect to its
average position during the previous orbital period, T is the current light shield tempera-
8
ture (in Kelvin), and T average is the average temperature in the previous orbit. Breathing
correction, breath , as defined by the above equation, is typically no larger than a few
tenths of a millimeter (in PAM space), thus its application to focus results can improve
focus estimates by that amount. However, the thermal breathing model is known to be
insufficiently robust and may either underestimate or overestimate the actual moves of the
secondary by a substantial factor. Fortunately, the NICMOS focus monitoring program
provides the data which allows to improve the estimate of breathing. That new estimate
can then be applied to correct focus for the breathing effect.
In Figure 6 we display the correlation between the measured focus position in
camera 1 and “breathing”, i.e., the secondary mirror shift (expressed in mm of PAM
space) as derived from the thermal breathing model. The large value of the correlation
coefficient leaves no doubt that focus follows the telescope temperature variations. It is
also obvious that the thermal breathing model which converts temperature variations to
focus change is not ideal: if it were, the slope of correlation would have been 1, which is
not the case. Since the only plausible cause behind the regular component of focus variation during an orbital period is the secondary mirror shift, the actual amount of that shift is
given by the range of focus variation, hence the breathing correction, breath , must be
multiplied by the value of the regression slope, scale , to make it consistent with the
actual focus change during the focus sweep.
Focus field variations (FFV) and focus centering
Along with temporal variations, the NICMOS foci have been found to vary spatially
across detectors’ field of view. The effect is quite significant, especially in cameras 2
and 3, and observers doing high-precision photometry may need to be aware of it to better
assess accuracy of their photometry and be able to make appropriate corrections if necessary. For focus monitoring program, the effect is important because the focus results
depend on where on the detector the star selected for phase retrieval or encircled energy
measurement is located.
We have quantified focus positional dependence in all three cameras and used the
results in our focus monitoring program to reduce focus to the detector center. The geometry of focus field variations has been obtained from phase retrieval measurements of as
many as possible stellar images scattered across the detector and subsequent fitting of a
second order surface,
2
2
focus ( x, y ) = a 0 + a x x + a y y + a xx x + a yy y ,
to the derived focus values (a similar procedure has been implemented using focus
measurements based on encircled energy: see section 3). Figure 7 illustrates such a fit. It
9
Figure 6: Correlation between breathing and NIC1 focus residuals obtained from different PAM positions measured with respect to the mean focus. All panels except for one
present data from observations during one visibility period. The exposure sequence on
September 24 was interrupted by occultation, so the data points cover two visibility periods. The legend provides date of observation, correlation coefficient for the linear regression, and the slope of the regression line.
was obtained using data from exposures at three different PAM positions in visit 5
(August 12, 1997). The corresponding fit coefficients are given in Table 1. They have been
used to reduce focus from phase retrieval measurements to the center of the detector. The
“centered” focus is displayed in Figure 1.
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Table 1. Coefficients of the FFV fit used to center focus from phase retrieval
camera
a x × 10
3
a xx × 10
3
a y × 10
3
a yy × 10
NIC1
-2.212
0.010
-0.056
0.005
NIC2
-0.555
0.007
4.134
0.006
NIC3
-2.573
0.011
-8.169
0.019
3
As seen from Figure 7, camera 2 has the largest range of focus variation, of about 1.5 mm.
Comparable focus aberrations were found for camera 3. Less dramatic field variations are
present in camera 1. This is consistent with earlier results obtained by Krist (1997) from
different data sets as well as with the results obtained from encircled energy measurements.
3. Focus from encircled energy
The best focus in PAM space was also determined by measuring the encircled energy
of 30-50 stars spread across the image. The total number of counts inside a fixed radius
aperture (at the first airy minimum in NIC1 and NIC2) was measured at each of the points
in the focus sweep. A parabola was then fit through the ~8 points nearest best focus to find
the location of the peak energy in PAM space for each of the stars. A breathing correction
was applied amounting to 2 times the Bely thermal breathing model for each point in the
sweep. Breathing effects were readily visible as horizontal “breaks” in a smooth parabola,
which the correction tightened up.
The best PAM position for each star was then translated to what the best focus would
be at the detector center using the model shown in the equation below, and the average
value of all the measurements was taken to be the best focus at that epoch. The standard
deviation of the 30-50 measures at each epoch was measured as an error estimate and is
typically +/- 0.1 mm PAM. The encircled energy tehcnique was not applied to NIC3 since
the focus sweeps do not go through best focus in that camera, and any extrapolation
imparts a large uncertainty.
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Figure 7: Second order surface fit to focus variations across NICMOS detectors. Focus is
measured relative to a zero point, focus = 0 , arbitrarily placed at x = y = 0 .The range
of focus variation, ∆ ( focus ) = max ( focus ) – min ( focus ) , is indicated.
For the encircled energy (EE) data, a 2-D focus field dependence model for NIC1 and
NIC2 was derived, using all the EE data as of December 1, 1997 since launch (700-900
stars in each of the cameras). The EE focus results presented in Figure 1 use a single
model of field-dependence for all epochs (rather than fitting a curve to the Y vs. PAM
dependence at each separate epoch). There is essentially no difference in the results
between using this model and fitting a new model for each epoch, which shows that the
field dependent focus has not changed since launch (within the EE measurement errors of
~0.1 mm of PAM). For the fitting equation
focus =
∑i, j = 0 k j, i x y ,
q
i j
where q is the degree of the fit in one dimension, the following fit coefficients have
been obtained:
12
NIC1: k j, i =
– 0.239 0.0012 ,
0.00083 1.74e – 6
NIC2: k j, i =
0.438
0.0025
9.168e – 6
0.0018
– 2.417e – 5 4.950e – 8 .
– 4.826e – 6 6.070e – 8 – 6.182e – 11
The amplitude of the field dependence in NIC1 is of order of the size of the measurement error, but is measurable as a mostly Y “tilt”. It did not make sense to do a 2nd fit
given the S/N. The above fit for camera 2 is displayed in Figure 8. Figure 9 gives grey
scale representation of focus variation across the NIC2 field of view which has been
obtained from encircled energy measurements for 630 stellar images in the focus monitoring data.
Figure 8: Fitting fourth order surface for focus field variations in camera 2 as derived
from encircled energy focus measurements.
delta(focus)=1.68 mm
13
Figure 9: Grey scale presentation of focus variation across the NIC2 detector field of view
obtained from encircled energy measurements. Upper left is triangle interpolation between
all 630 encircled energy points in NIC2 through day 251, all normalized to 0 PAM at the
center and included in the fit. The upper right is a smooth surface fit to the interpolated
data. The lower 2 images are the same as above, but with the 630 measurement points
overplotted as crosses
4. Focus from plate scale
Each of the three cameras has a different focal length, giving each a different field-ofview and a different plate-scale. The separate focal lengths are measured from a common
pupil near the field-divider assembly (FDA) and cold-masks. Any changes in this distance
appear as changes in the measured plate scale, and the amplitude of the changes are
inversely proportional to the focal lengths of the separate channels. These changes also
affect the best focus position of each camera in PAM space.
The observed “dewar anomaly” which pushed the cold-well (where the detectors are
mounted) forward, effectively changed this distance and caused a measurable change in
the plate scales. As the cryogen is used up, the cold well has slowly (asymptotically)
relaxed back towards its initial position. By tracking the plate scale changes it is possible
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to measure this motion independently of focus changes ahead of the FDA (such as
“breathing” or other changes in the position of the HST secondary mirror).
At each focus monitoring epoch, the positions of a set of ~40 stars in the target cluster
are compared with the positions of those same stars at an earlier epoch. The stars are centroided for accurate positions, and then run through the GEOMAP task in IRAF, which
returns a magnification in X and Y. This magnification is the change in plate scale between
those two epochs. Eric Mentzell has provided numbers relating the change in plate scale to
a motion in millimeters relative to the FDA, and in turn, to an effective change in the camera focus in PAM mm. Since the plate scale measurements only show relative motion from
one epoch to another they must be tied to absolute focus values somehow. This was done
by measuring the average difference between the plate scale PAM values and the best
focus values as measured by phase-retrieval for the first ~300 days since launch. The zeropoint offset measured in this way was -14.555 mm PAM, which can be seen in Figure 1 as
the first plate scale measurement in NIC3. The same was done for NIC2 (0.187 mm PAM).
Since NIC3 has the shortest focal length, it is the most sensitive to changes in plate
scale. We do not have measures of the relative plate-scale changes in NIC1 because its
long focal length makes it rather insensitive.
5. Acknowledgment
We are grateful to John Krist for discussions of various issues related to NICMOS
focus and for his help in installation of phase retrieval software. A major contribution to
understanding NICMOS focus has been made by Chris Burrows, Eric Mentzell, and John
Krist as well as by members of the STScI NICMOS Instrument Group.
6. References
Burrows, C.J. 1997, in: 1997 HST Calibration Workshop, STScI.
Burrows, C.J. & Krist, J.E. 1997, Memorandum, March 19, 1997, ‘‘NICMOS Focus’’
Hasan, H. & Bely P. 1994, in: The Restoration of HST Images and Spectra II, eds. R.J.
Hanish & R.L. White (Baltimore: STScI), p.157
Krist, J. E. & Burrows, C.J. 1995, Applied Optics, 34, 4951
Krist, J.E. & Hook, R. 1997b, The Tiny Tim User’s Manual v4.4
Krist, J.E. & Hook, R. 1997, in: 1997 HST Calibration Workshop, STScI.
Suchkov, A.A. & Casertano, S. 1997, in: 1997 HST Calibration workshop, STScI.
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