TIPS/JIM Meeting
The JWST Point Spread Function:
Calculation Methods and Expected
Properties
Russell B. Makidon
Stefano Casertano, Colin Cox, & Roeland P. van der Marel
Telescopes Group & JWST OTE / WFS&C Team
Space Telescope Science Institute
June 21, 2007
Importance of PSF Quality and Stability
• The ability to obtain groundbreaking discoveries relies heavily on the
quality and understanding of the telescope’s point spread function (PSF).
– The Point Spread Function (PSF) describes the response of an
imaging system to a point source or point object.
• Critical elements:
– that the PSF is of the highest possible quality
– that the PSF is as stable as possible
– that the PSF can be accurately modeled and understood during the
data analysis stage.
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Changes in the HST PSF
• HST has a stiff, monolithic, temperature-controlled primary mirror.
• Changes in the HST PSF arise almost exclusively due to variations in the
distance of the secondary mirror from the primary mirror.
– Changes occur at the level of microns on orbital and secular
timescales
– Orbital “breathing” due to thermal variations associated with daynight transitions; Multi-year changes due to OTA desorption (150
microns since launch)
– See M. Lallo et al. (2005), Instrument Science Report TEL 2005-03
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Changes in the HST PSF: SM Motion During an Orbit
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Changes in the HST PSF: SM Position v. Time
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Challenges for JWST PSF Stability
• The situation will be quite different for JWST.
• The 6.5 m primary mirror consists of 18 semi-rigid segments.
– Each segment has 7 controllable degrees of freedom (tip, tilt,
clocking, piston, two translations, and radius of curvature)
– The secondary mirror has an additional 6 degrees of freedom (no
radius of curvature correction).
• JWST is passively cooled, but will never be fully in thermal equilibrium.
• Thermal variations combined with of 132 degrees of freedom will yield a
much higher-dimensional parameter space of JWST PSFs than for HST.
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Requirements on JWST WFE and WFS&C
• A good, stable PSF is critically important for many types of science
envisioned with JWST.
• Requirements on image quality exist at a high level
– Govern diffraction limit of JWST, change in encircled energy, and wavefront
error (WFE) over the FOV (OBS-1607, OBS-88, OBS-90, OBS-1599)
• Wavefront sensing and control (WFS&C) will enable correction of
misalignments in the primary mirror segments and secondary mirror.
– will ensure that the PSF never exceed the requirement of 131 nm RMS WFE
over the Optical Telescope Element (OTE) field of view (FOV).
• Many different PSFs are consistent with the JWST WFE budget.
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSFs Determined by Aperture Shape and WFE
• To lowest order the PSF of an imaging system is determined by two
things: the aperture shape and the wavefront errors.
• Often, the shape of the aperture is well known and relatively simple
– circular or annular apertures
– more complex apertures increasingly common (JWST and Keck)
• Errors in the wavefront arise from a variety of sources
– imperfections in the system’s optics (static or semi-static)
– atmospheric variations (as in the case for ground-based observations)
– can be extremely difficult to determine.
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of Aperture Shape
•
For an ideal system, the PSF can be calculated based on shape of the aperture
(Fourier Transform)
•
Circular Aperture yields Airy Function
– PSF shown with logarithmic grayscale stretch from 1.0e-7 to 1.0e-2; total = 1.0
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of Aperture Shape
•
Hexagonal Aperture, 6.5 m point-to-point
– Six-fold symmetry in PSF
– Flux in circular symmetric rings diffracted into “spikes” at 60 intervals
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of Aperture Shape
•
JWST “Tricontagon” outline
– 6.5 m flat-to-flat
– No segment gaps, though “missing” segment at center
– Rough six-fold symmetry maintained, but more complicated profile
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of Aperture Shape
•
JWST “Tricontagon” with segment gaps
– Adds more structure to previous PSF, though general morphology same
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of Aperture Shape
•
Full JWST entrance aperture with SM support obstructions
– Addition of bright diffraction bar across horizontal and along 60 and 120
lines
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Key PSF Parameters with Aperture Shape
Percentage Flux
Shape
FWHM
Ellipticity Parameters
Radius
within
within
within
outside 1
of 1st
first
50 mas
150 mas
arcsec
min
min
e1
e2
Total
Circle
0.064”
0.079”
84.4
79.1
91.7
0.8
0.0000
0.0000
0.0000
Hexagon
0.070”
0.086”
83.9
74.6
91.0
0.9
0.0060
0.0000
0.0060
Tricontagon
0.067”
0.080”
74.2
68.1
88.9
1.2
-0.0043
0.0000
0.0043
Tricontagon
0.069”
0.083”
72.4
65.3
87.0
1.8
-0.0025
0.0000
0.0025
0.067”
0.080”
70.8
64.9
85.6
2.8
-0.0145
0.0000
0.0145
w/gaps
JWST Pupil
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Optical Modeling Tools Used on JWST Project
• Many different tools available to model JWST optical systems
– Ray tracing codes: ZEMAX, CODE V, OSLO, MACOS, ASAP
– Wavefront manipulation: PROPER, JWPSF, MACOS
– Integrated modeling: ITM (Ball proprietary)
• JWPSF (James Webb Point Spread Function) developed in-house (Cox
and Hodge 2006)
• Extensive experience with ZEMAX exists at STScI; familiarity with
PROPER
• STScI purchasing single CODE V license
– All JWST optical models delivered to project as CODE V macros
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Calculation of PSFs using JWPSF
• Calculated PSFs using Fourier Transform method, as implemented in
JWPSF software
– pervious PSFs: apertures without wavefront errors
– subsequent PSFs: use JWST aperture and optical error budget
realizations provided by Ball Aerospace (Optical Error Budget
“Revision T”)
• Optical Path Difference (OPD) describes the difference between a perfect
wavefront and an aberrated wavefront
– all points on the wavefront no longer in phase
– result is a degraded PSF
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of OPD
•
At left: perfect JWST aperture
•
At right: one realization of
JWST Rev T optical error
budget
– OTE + ISIM + NIRCam
with reserves
•
OPD at left:
•
OPD at right: 110 nm RMS
•
PSFs at  = 2.0 µm
June 21, 2007
0 nm RMS
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of OPD
•
Two realizations of JWST
Rev T optical error budget
•
OPD at left: 110.3 nm RMS
•
OPD at right: 109.6 nm RMS
•
Measurable triangularity in
PSF core at left; relatively
circular core in PSF at right.
•
PSFs at  = 2.0 µm
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
NIRCam PSFs at 2.0µm
Sharpness
Ellipticity
Flux inside 0.15”
mean
min, max
e1
(total = 1.0)
e2
F070W
0.155
0.026
0.107, 0.194
0.72
0.01
0.046
0.154
-0.031
0.147
F200W
0.076
0.002
0.073, 0.082
0.80
0.01
0.014
0.024
-0.010
0.030
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of OPD and Wavelength
•
Two realizations of JWST
Rev T optical error budget
•
OPD at left: 110.3 nm RMS
•
OPD at right: 109.6 nm RMS
•
PSFs at top: F070W
•
PSFs at bottom: F200W
•
PSFs shown on same angular
scale; same logarithmic
grayscale
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF Variation with Wavelength
•
Quantified radial PSF
profile and encircled
energy for broadband
NIRCam filters
•
Cases shown for single
input OPD
•
PSFs approach ideal for
long wavelengths; still very
good at short wavelengths
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF Variation with Wavelength
•
Encircled energy within
0.15 arcsec shows peak at
 = 2.0 µm (diffraction
limit)
•
PSFs core width continues
to improve toward short
wavelengths (despite
absence of requirements)
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Now and the Near Future
• Currently able to do relatively simple optical analyses using a
combination of JWPSF and ZEMAX
• PROPER available, though STScI experience is limited
– has been used to support NIRCam coronagraph studies
– segmented primary; generation of OPDs
• Obtaining CODE V as a means to vet current models.
– All JWST optical models delivered to the Project as CODE V macros
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
ZEMAX Model: Monolithic JWST and NIRCAM
•
Monolithic primary with full NIRCam optical train
•
Useful to adjust positions of optical elements, and
determine OPDs due to defocus, misalignment, etc.
– Add changes to Ball OPDs
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Using ZEMAX Predictions with JWPSF
•
Left: PSF in F187N for single Rev T OPD error realization.
•
Right: PSF in F187N for same Rev T OPD error realization
– added 0.2 waves of defocus to Ball-supplied OPD map using the predictions
ZEMAX model with monolithic JWST primary mirror
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
PSF as a Function of OPD and Wavelength
•
Left: PSF in F187N for
single Rev T OPD error
realization.
– Top from JWPSF
– Bottom from PROPER
•
Right: PSF in F187N for
same Rev T OPD error
realization
– Top: ZEMAX model with
monolithic JWST primary
mirror; 0.2 waves defocus
– Bottom: PROPER with
0.15 waves of defocus
•
Zernike normalization issue?
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Conclusions
• Presented and explored various methods to calculate the PSF
http://www.stsci.edu/jwst/externaldocs/technicalreports
• Presented PSF properties of astronomical interest given current
understanding of telescope design
• Understanding JWST PSF will be a challenge
– First step toward providing an understanding of the PSF useful for
JWST observers
• Start of development of tools of use to S&OC developed to address
tradeoffs between PSF quality and operations scenarios
• JWST compares favorably with HST at wavelengths as short as 0.70
microns; far exceeds capabilities of NICMOS at NIR wavelengths.
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Comparison: HST/ACS with JWST NIRCam
Images courtesy M. Stiavelli
•
ACS image of HUDF in V, I, and Z-bands (left) and simulated JWST NIRCam
image in F070W, F090W, and F115W (right)
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting
Comparison: HST/ACS with JWST NIRCam
Images courtesy M. Stiavelli
•
ACS image of HUDF in V, I, and Z-bands (left) and simulated JWST NIRCam
image in F070W, F090W, and F115W (right)
June 21, 2007
Russell B. Makidon
TIPS/JIM Meeting