Filter Calibration Studies
Stuart Mufson, Nick Mostek
Indiana University
In our simple calibration scheme, we transfer calibration to primary
calibrators by observing them with the SNAP spectrometer and then
observing these stars photometrically. The
photometric errors require a consideration of filter uncertainties,
both
due to manufacturing and with respect to angle of incidence. We
have tried to make an initial attempt to address the issue of how well
the (filters+detectors) need to be calibrated in order for SNAP to
reach its science goals. This issue is clearly of great
importance to the hardware groups. We understand that detailed
answers will require simulations more detailed than we have been able
to generate until now. But there is some value in this exercise
to see if there are obvious showstoppers that can be identified now.
For those who want to know our prelimiary conclusions without having to
wade through the muck below, we have found that transfer of calibration
from the fundamental spectrophotometric standards to secondary field
standards, at least according to the simple plan we have discussed
several times before, can likely be fitted into the allotted SNAP
systematic error budget for calibration, assuming:
-- filter transmission calibration of 2-3%
-- calibration of angle of incidence to 0.25 degrees
Our R&D studies over the past year or so have shown that these are
not overly demanding requirements on the calibration.
Computations
We studied the transfer of calibration for 3 types of stars: (a) K0III
giants, (b) F8V dwarfs, and (c) hot white dwarfs. Some
non-negligible fraction of these stellar types are known to be
non-variable. It might be argued that we won't find stars of
these spectral types in the SNAP fields. Nevetheless, these
calculations do show that we need to find some similar range of color
variation in order to achieve the calibration precision required.
We investigated these three stellar types at visual magnitudes of V =
16, 19, and 22. The stars at V = 16 and 19 were meant to
represent the range of brightness useful for primary calibrators.
The faint V = 22 mag stars were reprentative of secondary field
calibrators, and they were only investigated to gain some insight into
how filter errors propagate to faiter field calibrators. The flux
templates for the K0III stars and the F8V stars were taken from
Pickles. The white dwarf flux file we used was the non-LTE model
of G191 B2B given to us by Ralph Bohlin. These flux distribuions
are shown below. The units are [W/m**2/m].
We used
17 filter files generated by Chuck Bower at angles of incidence from
15.0-20.0 degrees. The restricted range for the angle of
incidence is due to the fact that we investigated only the outer
annulus of the SNAP focal plane. We confined our investigation to
the outer annulus because that is where the wavelength shifts induced
by variations in the angle of incidence are greatest. These
filter files take into account Chuck's improved understanding of
manufacturing variations based on his experience with the Barr witness
samples.
An example of one of
these filter files is shown below
The photometric flux computations were made by integrating the stellar
flux through 4 randomly selected filter functions from the set at
angles of 15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19, and 19.5
degrees. The flux through each filter was perturbed according to
the Signal-to-Noise computed by a modification of the simple detector
model described in the fundamental calibration computations
fundamental
calibration computations ,
and assuming the star is observed for 36,000s in the optical and
72,000s in the near infrared. (As time permits over the next few
weeks, I will describe more completely the results of our computations
of the calibration transfer to the primary spectrophotometric
standards.) The flux was assumed to be the weighted sum, where
the weighting function for angles of incidence was taken from Alex
Kim's talk at the March collaboration meeting , or alternately
http://panisse.lbl.gov/~akim/incidence2.ps
This weighting function is shown below.
The computations of the calibration precision required were made by
separating the calibration procedure into two parts. We computed
the errors associated with manufacturing tolerances by systematically
perturbing the filter transmission by 1%, 3%, and 5%. Our R&D
has shown that this range spans what is easily achievable (5%),
reasonable with effort (2-3%), and very difficult to achieve
(1%). The relative errors were determined by computing the
variance in the quantity (measured flux-"true flux")/"true flux" in 25
simulated SNAP experiments. The calibration errors due to angle
of incidence were determined by systematically offsetting the filter
function in angle by 0.1, 0.25, and 0.5 degrees before computing the
filter flux. R&D at Indiana has shown that angle measurements
to a precision of 0.25 degrees do not required extraordinary
efforts. Again the quantity (measured flux-"true flux")/"true
flux" in 25 simulated SNAP experiments was computed as reprentative of
the relative error.
Only some results will be shown from this extensive grid of
computations. These results are for transmission calibration of
3% and angle calibration of 0.25 degrees. For the V = 19 stars,
the calibration transfer errors from the fundamental calibrators to the
primary calibrators are shown. For the V = 22 stars, only the
filter errors are relevant since the calibration transfer computations
to the secondaries is not yet complete.
K0III stars
For the K0III stars, filter errors down to V = 22 can be held to less
than 1% in the near infrared with 3% filter calibration and 0.25 degree
angle calibration. The errors in the visual and blue become
greater than several percent in the V = 22 star, mostly due to
transmission errors. Angle calibration does not add much at all
to the error, at least in these computations. It is interesting
to note that even in the near infrared, the systematic errors
associated with the fundamental calibrators dominate.
F8V stars
From the visual out to 1 micron, F8V stars keep the errors below 1%
with the nominal calibration requirements of 3% transmission
calibration and 0.25 angle calibration. With regard to the models
shown below, one comment must be made. The V = 22 star does not
show the calibration transfer from the primaries, so the relative
errors look to be smaller at some wavelengths than the primaries.
This is an artifact of the way the computations have been done until
now.
Again, we have found that errors in angle of incidence can be
calibrated out reasonably well.
White Dwarf stars
The computations with a hot white dwarf keep the filter errors below 1%
in the blue.
Conclusions
Our computations show that calibration of filter transmission to 3% and
angle of incidence to 0.25 degrees keeps calibration errors to 1% so
long as the calibrators span a range of color.
Of course, these computations are a work in progress. Comments,
suggestions, and criticisms will be incorporated into the work
downstream.