1. The JWST Point Spread Function: Calculation Methods and Expected Properties TIPS/JIM Meeting 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

2. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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.

3. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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 day- night transitions; Multi-year changes due to OTA desorption (150 microns since launch) –See M. Lallo et al. (2005), Instrument Science Report TEL 2005-03

4. TIPS/JIM Meeting June 21, 2007Russell B. Makidon Changes in the HST PSF: SM Motion During an Orbit

5. TIPS/JIM Meeting June 21, 2007Russell B. Makidon Changes in the HST PSF: SM Position v. Time

6. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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.

7. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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.

8. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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.

9. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

10. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

11. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

12. TIPS/JIM Meeting June 21, 2007Russell B. Makidon PSF as a Function of Aperture Shape JWST “Tricontagon” with segment gaps –Adds more structure to previous PSF, though general morphology same

13. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

14. TIPS/JIM Meeting June 21, 2007Russell B. Makidon Key PSF Parameters with Aperture Shape Percentage FluxEllipticity Parameters ShapeFWHM Radius of 1 st min within first min within 50 mas within 150 mas outside 1 arcsec e1e2Total Circle0.064”0.079”84.479.191.70.80.0000 Hexagon0.070”0.086”83.974.691.00.90.00600.00000.0060 Tricontagon0.067”0.080”74.268.188.91.2-0.00430.00000.0043 Tricontagon w/gaps 0.069”0.083”72.465.387.01.8-0.00250.00000.0025 JWST Pupil0.067”0.080”70.864.985.62.8-0.01450.00000.0145

15. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

16. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

17. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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: 0 nm RMS OPD at right: 110 nm RMS PSFs at = 2.0 µm

18. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

19. TIPS/JIM Meeting June 21, 2007Russell B. Makidon NIRCam PSFs at 2.0µm Sharpness Flux inside 0.15” (total = 1.0) Ellipticity meanmin, maxe1e2 F070W0.155  0.0260.107, 0.1940.72  0.010.046  0.154-0.031  0.147 F200W 0.076  0.002 0.073, 0.082 0.80  0.010.014  0.024-0.010  0.030

20. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

21. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

22. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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)

23. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

24. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

25. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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

26. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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?

27. TIPS/JIM Meeting June 21, 2007Russell B. Makidon 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.

28. TIPS/JIM Meeting June 21, 2007Russell B. Makidon Comparison: HST/ACS with JWST NIRCam ACS image of HUDF in V, I, and Z-bands (left) and simulated JWST NIRCam image in F070W, F090W, and F115W (right) Images courtesy M. Stiavelli

29. TIPS/JIM Meeting June 21, 2007Russell B. Makidon Comparison: HST/ACS with JWST NIRCam ACS image of HUDF in V, I, and Z-bands (left) and simulated JWST NIRCam image in F070W, F090W, and F115W (right) Images courtesy M. Stiavelli

30. TIPS/JIM Meeting June 21, 2007Russell B. Makidon JWST Image Quality Requirements OBS-1607 (MR-110) Over the FOV of the NIRCam, the Observatory shall be diffraction limited at 2 μm defined as having a Strehl Ratio greater than or equal to 0.8. OBS-88 (MR-113) Without requiring ground commanded correction, there shall be less than 2.0% root- mean squared (RMS) variation about the mean encircled energy, defined to be at 0.08 arcsecond radius at a wavelength of 2 μm, over a 24-hour period. OBS-90 (MR-115) The encircled energy within a radius of 0.08 arcsecond at 2 μm shall not change by more than 2.5% in less than 14 days following a worst case slew from a thermal equilibrium condition at the coldest pointing environment to the hottest pointing environment. OBS-1599 (MR-228) The OTE unvignetted FOV shall have a WFE that is less than 131 nm RMS, within the dotted line boundary as shown in Figure 3-5 of the Mission Requirements Document (JWST-RQMT- 000634 rev N). MR-384 The JWST System shall perform image-based wavefront sensing and control to meet all image quality requirements.

31. TIPS/JIM Meeting June 21, 2007Russell B. Makidon PSF as a function of the Aperture Full JWST entrance aperture with SM support obstruction

32. TIPS/JIM Meeting June 21, 2007Russell B. Makidon HST Phase Errors Limiting High-Contrast Imaging Phase errors in the HST pupil (Krist 2005, Krist & Burrows 1995) The rms wave-front error that is due to zonal errors in the HST pupil 0.018 μ m, with minimum and maximum surface errors of -0.054 µm and +0.040 µm respectively. Uncorrected static errors in HST pupil are the main limitation for high-contrast imaging with HST Krist 2005