Download Consequences of the WFC3 IR detector 24 degrees tilt

Instrument Science Report WFC3 2000-001
Consequences of the WFC3 IR
detector 24 degrees tilt
M. Stiavelli
May 31, 2000
ABSTRACT
I review the possible impact on WFC3 IR science of having a focal plane tilted by 24
degrees. The modeling assumptions and their relative uncertainties are presented and
their limitations fully discussed. The conclusion from this study is that some science programs requiring very high quality data will be negatively affected but that the overall feasibility of the WFC3 IR science is not affected. However, due to the present uncertainties
further modeling and laboratory measurements are recommended.
1. Introduction
The current optical design for the IR channel of WFC3 has a focal plane tilted by 24
degrees to the chief ray due to the off-axis correcting optics. A similar design is used in,
e.g., ACS but its effect is potentially amplified in WFC3 because of the bigger angle (it is
only 11 degrees in ACS) and thicker detector. An immediate consequence of the tilt is that
the field of view and the projection of each pixel on the sky are no longer square. The
resulting distortion is about 9 percent. Its effect on the WFC3/IR photometric accuracy
will be discussed in the separate ISR “The effect of WFC3/IR geometric distortion on
photometric accuracy.” The aim of this ISR is to explore the detector level effects of the
tilt. These effects are subtle and depend on the detailed properties of our detector. The goal
of a totally satisfactory modeling is hampered by lack of adequate information on the
detector physical properties, on the properties of the substrate material and on the detector
geometry. Thus, the results presented here should be considered as preliminary.
Instrument Science Report WFC3 2000-001
Section 2 is devoted to a description of our assumptions on the structure of the detector.
Section 3 describes the effects that have been identified and their possible science impact.
Section 4 sums up the results and presents my recommendations.
2. Modeling Assumptions
The major input ingredients are the refraction indices of the CdZnTe substrate and of the
HgCdTe detector material and their thicknesses. Even a rather extensive literature search
provided only partially satisfactory information on these parameters and this is the single
factor dominating the reliability of this modeling effort. The adopted values of the various
parameters are discussed individually below.
Refractive indices
The “Handbook of Infrared Optical Materials” by P. Klocek includes neither CdZnTe nor
HgCdTe in the listed materials. It lists however measurements for CdTe as a function of
wavelength. The value at 1 micron at a temperature of 300 K is 2.839. The Handbook also
provides an approximation formula of the Herzberger form for the CdTe refraction index
n as a function of wavelength with coefficients tabulated for different temperatures. The
values for T=150 K were obtained by interpolation from the T=80 K and T = 300 K data
and are given below:
2
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n = A + BL + CL + Dλ + Eλ
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with
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L ≡ ( λ – 0.028 )
–1
where λ is given in microns. The interpolated values of the coefficients are: A=2.668,
B=0.1189, C=0.03688, D=1.123 × 10-4, and E=-3.036 × 10-8.
The refractive indices of CdZnTe and HgCdTe are different from that of CdTe. Adopting
2.69 as the refractive index of pure CdTe, i.e. for the case with a Cd fraction X=1, and 3.41
for the case with X=0.29 (D. Hall 2000, private communication) we can interpolate to the
case X=0.60 (see below how X=0.60 is derived) relevant for our cutoff of 1.7 microns to
obtain n=3.10. The variation with wavelength of the refraction index is obtained by rescal-
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Instrument Science Report WFC3 2000-001
ing the relation valid for X=1. The resulting curve is shown in Figure 1. In most of the
analysis we will assume that the lattice matched CdZnTe and CdHgTe have the same
refraction index. This assumption while plausible has not been verified. This model should
be relatively reliable in the IR since it fits by construction the IR behavior of CdTe but
might break down at optical wavelength.
Figure 1: Adopted refraction index of HgCdTe as a function of wavelength for T=150 K.
Relation between mercury fraction and detector cutoff
In order to interpolate the refraction index to the value of our cutoff wavelength we need to
make use of the relation between detector cutoff and Cd fraction X (or -equivalently - Hg
fraction 1-X). In order to do this I have made use of the Hansen et al. (1982) fit to the
energy gap E (in eV) as a function of temperature and fraction X:
–4
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E ( X , T ) = – 0.302 + 1.93X + 5.35 ⋅ 10 T ( 1 – 2X ) – 0.810 ⋅ X + 0.832 ⋅ X
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This expression is somewhat less accurate than the ones by Chu et al. (1983) and Seiler et
al. (1990) but it is applicable for X up to at least 0.6 which is needed for our cutoff while
the Chu et al. formula is applicable only up to X=0.4 and the Seiler et al. only between
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Instrument Science Report WFC3 2000-001
X=0.2 and X=0.3. The error in the cutoff from Hansen et al. is of the order of 0.013
(Amirtharaj and Burnett 1997) , i.e., about 2 per cent at our cutoff.
By using T=150 K and a wavelength cutoff of 1.7 microns, corresponding to a band gap of
0.73 eV, Hansen’s expression can be inverted to yield X=0.60 which is the value used in
our analysis (see Figure 2.)
Figure 2: Relation between mercury fraction and detector cutoff. The solid line is for
T=150 K, the dotted line for T=77 K.
Detector Geometry
In the absence of precise information on the detector geometry for our modified Hawaii
arrays we have adopted the following numbers. The detector material has been assumed to
have a thickness of 13 micron (this value is in any case not critical for the model.) The
CdZnTe substrate has been assumed to have a thickness of either 130 micron or 1000
microns (Don Hall 2000, private communication).
Anti-reflection coating
In the absence of precise information on the anti-reflection coating of our detectors we
have considered the cases of an uncoated detector as well as that of well optimized single,
double and triple layer coatings.
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Other asumptions
The incoming beam is assumed to be F/11. The interface between the detector and the substrate is assumed to be smooth and planar but the possible consequences of a less regular
interface are also discussed.
3. Potential issues and their science impact
The main issues addressed in the study and the analysis results are the following:
•
change to the thickness of the AR coatings. In principle the coatings need to be optimized for the non-orthogonal illumination angle. To first order the effect is geometrical (ie the light path is longer.) I have explored the impact by designing simple single
and multiple layer coatings and found that the thickness of each layer needs to be
decreased by 3 to 9 per cent. Such values are comparable to the accuracy with which
coatings are deposited and we can probably ignore this effect.
Figure 3: Effect of a thick high refraction index substrate on the optical path
•
instrument focus. The substrate will have an effect on the focus of the instrument. In
the case of an ideal totally thinned substrate at one mm from the detector the edges of
the F/11 beam span an area of about 0.11 mm. Once the substrate is included the
instrument needs to be refocussed. The effect is negligible for a 130 micron substrate
but significant for a 1 mm substrate. In the latter case, compared to the case of the ideal
totally thinned substrate, the detector must be displaced in the forward direction by
roughly 0.75 mm (or -more practically - the focus must be changed.) In the absence of
this shift the effect on the PSF width would be of about 2 pixels. I have found also a
small degree of astigmatism (at the level of 0.2 pixels) due to the non symmetry of the
beam - detector configuration introduced by the 24 degree angle. Based on this modeling there are no chromatic effects on the focus (see Figure 3.)
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Instrument Science Report WFC3 2000-001
•
image distortion. There is no additional image distortion introduced by the detector
substrate in the sense that the shape of a point pattern is unaffected (any additional
distortion being less than 0.2 per cent) by the inclusion of a one mm substrate.
•
chromatic effects. The fact that the refraction index depends on wavelength shifts the
image center at different wavelengths and introduces a chromatic effect for the broad
band filters. For a 130 micron substrate the effect is negligible. For a 1 mm substrate
the effect is of the order of one tenth of a pixel for the broad band J and H filters. The
images in J and H are also shifted by a similar amount. The effect may be more significant at shorter wavelengths (close to our short wavelength cutoff) where, unfortunately, the model used is unreliable. Programs needed detailed PSF substraction (e.g.
QSO host galaxies, brown dwarf companion searches) may be affected.
Figure 4: Illustration of how a thick substrate can give rise to ghost images
•
ghost images. There is the possibility of forming ghost images or a STIS-like PSF halo
depending on the quality of the CdZnTe vs HgCdTe interface. The ghost image would
be about 2 pixels from the primary for a 130 micron substrate and 14 pixels from the
primary for the 1 mm substrate. It is hard to estimate the amount of energy in the secondary image from first principles since this number depends among others from the
refraction index mismatch between HgCdTe and CdZnTe and on the precise nature of
the AR coating. Assuming pessimistically that 15 per cent of the light is lost at the
HgCdTe-CdZnTe interface or at the HgCdTe front side and that 3 per cent of the light
is reflected back into the substrate at the location of the coating, one ends up with 0.5
per cent energy in the secondary image. This appears to be a problem only for bright
stars in the field of view. If the internal surfaces are not smooth and featureless the
same fraction of the flux may end up producing a (possibly asymmetric) PSF halo
instead of ghost images (see Figure 4.)
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Instrument Science Report WFC3 2000-001
Figure 5: Schematic illustration of the origin of scattered light from internal reflections in
the detector.
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scattered light. For an instrument with a detector perpendicular to the chief ray light
not detected is reflected back into the beam. In our case this light is reflected at an
angle of 48 degrees and has the potential of producing significant scattered light inside
the cold shroud due to multiple reflections. This may be up to 15 per cent of the
incoming light under unfavourable circumstances and with a cold shroud of reflectivity of unity. It is worthwhile to keep the reflectivity of the cold shroud to below 3 per
cent and possibly less in order to keep this effect below 0.5 percent (see Figure 5.)
•
edge effects. There is the possibility of having edge-effects on the detector depending
on how oversized the substrate is compared to the detector, whether it is masked etc.
A detailed evaluation of these effects would need a detailed knowledge of the geometry.
4. Discussion
Some of the issues considered in Section 3 are worth being revisited through more sophisticated optical modelling and with better knowledge of the instrument characteristics. In
order of importance I would recommend the following issues to considered in more detail:
1. Instrument focus
2. Scattered light
3. Ghost images
4. Optimization of anti-reflection coating.
Some uncertainty on the basic physical properties of the detector will likely remain. Thus
I recommend:
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1. to carry out laboratory measurements on IR detectors with the same technology as the flight ones and with a 24 degrees illumination.
2. to consider the possibility and cost of partially thinning the substrate to about
100 microns.
A laboratory measurement of the refractive index of the ZnCdTe substrate material
would also be useful.
Acknowledgements
I thank Don Hall, Jennifer Turner-Valle, and Bob Woodruff for providing me with (or
pointing me to) important information on the design and the detector, Massimo Robberto
and John MacKenty for useful discussions, and Casey Lisse, Pat Knezek for comments on
an earlier version of this manuscript..
References
P.M. Amirtharaj and J.H. Burnett, 1997 “Optical Properties of MCT” in Narrow Gap II-VI
Compounds for Optoelectronic and Electromagnetic Applications, Chapman & Hall, P.
Capper ed.
J. Chu et al., 1983 Appl. Phys. Lett. 43, 1064
G. L. Hansen et al., 1982 J. Appl. Phys. 53, 7099
P. Klocek, 1991, “Handbook of Infrared Optical Materials” Dekker editor (New York)
D.G. Seiler et al. 1990 J. Vac. Sci. Technol. A., 8, 1237.
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