Point-spread Function modeling for the James Webb Space Telescope

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1 Point-spread Function modeling for the James Webb Space Telescope Colin Cox and Philip Hodge Space Telescope Science Institute 9 November 2006 Leads Meeting 1

2 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. 9 November 2006 Leads Meeting 2

3 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. 9 November 2006 Leads Meeting 3

4 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. 9 November 2006 Leads Meeting 4

5 In the Fraunhofer region, the complex image produced by a converging spherical wave of wavelength λ is ψ = Ae ikr ds integrated over the wavefront S, where A is the complex amplitude at any point on the wavefront, k = 2π/λ 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 ψ(u,v) = e 2πi(ux +vy ) λ P(x, y)dxdy 9 November 2006 Leads Meeting 5

6 The integral 2πi(ux +vy ) λ ψ(u,v) = e 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)e 2πid(x,y)/λ 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. 9 November 2006 Leads Meeting 6

7 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 9 November 2006 Leads Meeting 7

8 Source of OPD files Produced by Ball Aerospace and files reprocessed by Marc Clampin at GSFC Revision R Based on IPAM optical modeling Errors introduced according to Level 2 error budget - 140nm for OTE + NIRCam 10 OPD files supplied using Monte Carlo generated variations within the error budget 9 November 2006 Leads Meeting 8

9 Image Scales The angular size of the output elements is λ/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 arcsec at one micron. We can increase the sampling factor by embedding the pupil array in larger arrays, surrounding the nominal array with zeros. 9 November 2006 Leads Meeting 9

10 Pupil arrays and Oversampling 2X 4X 9 November 2006 Leads Meeting 10

11 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 9 November 2006 Leads Meeting 11

12 Program Menus 9 November 2006 Leads Meeting 12

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15 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 subband and combined according to integrated weights. Element size is wavelength dependent so each monochromatic PSF is resampled onto a common size in arcsec. 9 November 2006 Leads Meeting 15

16 Calculated PSFs Broad band 1 to 2 microns Wavelength 1 micron Wavelength 2 microns 9 November 2006 Leads Meeting 16

17 PSF Profiles Unaberrated Strehl=1.0 Aberrated Strehl=0.8 9 November 2006 Leads Meeting 17

Encircled Energy Plausible aberrations with Strehl ratio of 0.8. 80% of energy falls within 0.

18 Encircled Energy Plausible aberrations with Strehl ratio of % of energy falls within 0.17 arcsecond radius Unaberrated case obtained by setting Optical path differences to zero 80% of energy within 0.12 arcseconds 9 November 2006 Leads Meeting 18

19 Four NIRCam PSFs at 1.8 microns 0.2 waves defocus In Focus 1 arcsec 0.5 waves defocus 9 November wave defocus Leads Meeting 19

20 9 November 2006 Leads Meeting 20

12.4 Alignment and Manufacturing Tolerances for Segmented Telescopes

330 Chapter 12 12.4 Alignment and Manufacturing Tolerances for Segmented Telescopes Similar to the JWST, the next-generation large-aperture space telescope for optical and UV astronomy has a segmented