Point-spread Function
modeling for the James Webb
Space Telescope
Colin Cox and Philip Hodge
Space Telescope Science Institute
20 July 2006
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Objectives
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Provide a model of the JWST PSF for general use in
subsequent image simulation.
Should be generally available and useable on
computers most users will have without expensive
license fees.
Be expandable to incorporate telescope and
instrument data as it becomes available.
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Design decisions
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Program written in Python.
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Input and output in FITS format tables and images.
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Generally available and free.
A language which is gaining increasing acceptance for its flexibility
and ability to incorporate software written in other languages.
Includes a GUI (Tkinter) which makes it fairly easy to provide an
intuitive interface.
Has been in use in astronomy for many years.
Allows use of data produced by other programs.
Allows use of output in other programs.
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… Design Decisions
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Graphics use Matplotlib.
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Freely available as Python library.
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Easy to use and provides interactive plots with ability to export
resulting images.
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Based on Matlab.
Use of Matplotlib is not required for this software. Calculations can be
performed and FITS files produced without viewing intermediate
results.
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In the Fraunhofer region, the complex image produced by a converging spherical
wave of wavelength  is

 Ae
ikr
dS
integrated over the wavefront S, where A is the complex amplitude at any point on
the wavefront, k = 2 and r is the distance from a point on the wavefront to the
image position.
Variations in r are expressed as optical path differences d(x,y) and the overall
distance adds only a constant phase.
The extent and amplitude is described by the pupil image and the integration
becomes

 (u,v) 
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 e

2 i(uxvy )

P(x, y)dxdy
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The integral
 (u,v) 
 e

2 i(uxvy )

P(x, y)dxdy
Is recognizable as a two-dimensional Fourier transform involving the
phase and amplitude of the pupil function. The pupil function P is
obtained
from the aperture and optical path difference files as

P(x,y)=A(x,y)e2id(x,y)/
The image intensity at the focus is then the power |ψ|2 The phases are
obtained from the optical path differences divided by the wavelength.
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Model amplitude and phase of pupil function for JWST.
For the amplitude figure on the left, zero is black, while for the optical
path differences zero is mid-grey
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Source of OPD files
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Produced by Ball Aerospace
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Error budget incorporated to match Level 2
requirements (Revision R)
Total RMS error (OTE + ISIM + NIRCam)
~140nm
Some remaining inconsistencies
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Geometrical Modeling program OSLO
Scalar diffraction generated by program IPAM
Secondary mirror supports modeled at twice the
proper size
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Image Scales
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The angular size of the output elements is
/D radians where D is the pupil diameter as
represented by the size of the OPD array.
For JWST D is about 6.5m which leads to a
size of 0.032 arcsec at one micron.
We can increase the sampling factor by
embedding the pupil array in larger arrays,
surrounding the nominal array with zeros.
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Pupil arrays and
Oversampling
4X
2X
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Wavelength Weighting
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Two ways to select wavelength coverage
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Enter minimum and maximum wavelengths plus
number of steps. A single step gives the
monochromatic case.
Use a source spectrum and a filter function
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Spectrum may be supplied directly as a file or chosen by
the software based on stellar type.
The stellar type drives the selection from a library of
Kurucz model spectra supplied with the software.
Filter throughput function may be a user supplied file or
picked from a set of filter names
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Program Menus
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Calculation details
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Program integrates the product of source
strength and throughput across bandwidth
subdivided into a chosen number of sections.
PSF calculated at the center of each subband and combined according to integrated
weights.
Element size is wavelength dependent so
each monochromatic PSF is resampled onto
a common size in arcsec.
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Bandpass Weighting
Weights across F210M filter
Source Spectrum
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Calculated PSFs
Broad band
1 to 2 microns
Wavelength 2 microns
Wavelength 1 micron
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PSF Profiles
Unaberrated
Strehl=1.0
Aberrated
Strehl=0.8
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Encircled Energy
Plausible aberrations with Strehl ratio
of 0.8. 80% of energy falls within
0.17 arcsecond radius
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Unaberrated case obtained by setting
Optical path differences to zero
80% of energy within 0.12 arcseconds
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Detector Effects
Pixel sampling
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Detector Effects
Noise and charge diffusion
Assumed 0.01 counts per second per pixel dark noise and 10 electrons readout.
Pixel-to-pixel charge diffusion of 1%
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Detector Effects
Noise and charge diffusion
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http://www.stsci.edu/jwst/software/jwpsf
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