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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