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Point-spread Function modeling for the James Webb
Space Telescope
Colin Cox and Philip Hodge
Space Telescope Science Institute
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Objectives
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
Program written in Python. 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. Input and output in FITS format tables and images.
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
Graphics use Matplotlib. Freely available as Python library.
Based on Matlab. Easy to use and provides interactive plots with ability to export
resulting images. 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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€
ψ = Ae−ikr∫ dS
€
ψ(u,v) = e−
2πi(ux+vy )
λ
P(x,y)dxdy∫∫
In the Fraunhofer region, the complex image produced by a converging spherical wave of wavelength is
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
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€
ψ(u,v) = e−
2πi(ux+vy )
λ P(x,y)dxdy∫∫
The integral
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)e2id(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
Produced by Ball Aerospace Geometrical Modeling program OSLO Scalar diffraction generated by program IPAM
Error budget incorporated to match Level 2 requirements (Revision R)
Total RMS error (OTE + ISIM + NIRCam) ~140nm
Some remaining inconsistencies Secondary mirror supports modeled at twice the
proper size
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Image Scales
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
2X 4X
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Wavelength Weighting
Two ways to select wavelength coverage Enter minimum and maximum wavelengths plus
number of steps. A single step gives the monochromatic case.
Use a source spectrum and a filter function 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
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 sub-band 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
Source Spectrum Weights across F210M filter
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Calculated PSFs
Wavelength 1 micron Wavelength 2 microns
Broad band1 to 2 microns
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PSF Profiles
UnaberratedStrehl=1.0
AberratedStrehl=0.8
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Encircled Energy
Plausible aberrations with Strehl ratioof 0.8. 80% of energy falls within0.17 arcsecond radius
Unaberrated case obtained by settingOptical path differences to zero80% of energy within 0.12 arcseconds
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Detector EffectsPixel sampling
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Detector EffectsNoise 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 EffectsNoise and charge diffusion
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http://www.stsci.edu/jwst/software/jwpsf