Image Quality

Previous experience with other space telescopes, and in particular the Hubble Space Telescope (HST), has shown that the ability to obtain groundbreaking discoveries relies heavily on the quality and understanding of the telescope’s point spread function (PSF). The critical elements are: (a) that the PSF is of the highest possible quality; (b) that the PSF is as stable as possible; and (c) that the PSF can be accurately modeled and understood during the data analysis stage. HST has a stiff monolithic temperature- controlled primary mirror. Changes in the HST PSF therefore arise almost exclusively due to variations in the distance of the secondary mirror from the primary mirror changes occur at a level of microns both on an orbital timescale ("breathing") due to thermal variations associated with day-night transitions, and on a timescale of years due to desorption.

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) and the secondary mirror has an additional 6 degrees of freedom (its radius of curvature cannot be varied). The telescope is passively cooled, but due to the changing attitude of the telescope with time (as it observes targets at different positions on the sky) the telescope will never be fully in thermal equilibrium. Thermal variations combined with the existence of (at least) 132 degrees of freedom will result in a parameter space of JWST PSFs that is much higher-dimensional than for HST.

Impact of the Pupil Shape on the PSF

To lowest order the PSF of an imaging system is determined by two things: the pupil shape and the wavefront errors. Often, the shape of the pupil is well known and relatively simple, as in the case of a circular or annular aperture. However, more complex pupils are increasingly common for large systems (the JWST and Keck pupils are prime examples). Errors in the wavefront can arise from a variety of sources, including imperfections in the system�s optics (which tend to be static or semi-static) or atmospheric variations (as in the case for ground-based observations), and can be extremely difficult to determine. Here, we illustrate how the pupil shape affects the PSF, building from an open circular pupil of diameter ~6.5 m (left), a hexagonal pupil of diameter ~ 6.5 m (center), and a realistic representation of the JWST pupil (right).

In this figure, the PSF corresponding to each aperture is displayed on a logarithmic grayscale from 1.0e-7 to 1.0e-3 counts. The total number of counts in each of these simulated PSFs is 1.0.

PSF Dependence on wavefront errors

In order to quantify the impact of expected variations of the PSF over time, we consider a number of different realizations of the JWST PSF provided to us by the JWST Project. These PSFs differ in the specific distribution of the wavefront error across the pupil; all satisfy, in a statistical sense, Revision T of the wavefront error budget, both in total rms wavefront error and in its distribution as a function of wavenumber (cycles across the pupil). As long as the error budget is satisfied, comparing these PSFs provides an upper limit to the PSF differences that could be encountered in the normal course of observations; the reason is that some wavefront errors, primarily higher frequencies and those arising inside NIRCam, are likely to be highly correlated between different times, and therefore using completely independent realizations can overestimate the temporal variation in the properties of the PSF.

In the above figure, we compare two JWST Rev T OTE error budget Optical Path Difference (OPD) files (top) and their associated PSFs (bottom) for a wavelength of 2.0 microns. OPDs are displayed on a linear grayscale from -400 to 400 nm, while PSFs are displayed on a logarithmic grayscale from 1.0e-6 to 1.0e-3. The OPDs include wavefront error (WFE) contributions from the JWST Optical Telescope Element (OTE), the Integrated Science Instrument Module (ISIM), and the Near-Infrared Camera (NIRCam). The RMS WFE of both OPDs is ~110 nm. While the differences in total RMS WFE are small, the impact of these differences on the resultant PSFs is measurable.

Overall Image Quality

Despite the potential challenges apparent with a relatively complicated PSF like the one we expect for JWST, we do expect that the overall image quality of JWST will still be very good. In Figure 3, we show a comparison between simulated JWST + NIRCam images actual HST Advanced Camera for Surveys images of the Hubble Ultra-Deep Field. These images, kindly made available by Massimo Stiavelli, shows that JWST can achieve depth and resolution in the far visible and near-IR that will be better than achievable with HST for the wavelengths they have in common.

The figure above shows an ACS image of the HUDF field (top left) in V-, I-, and Z-band, compared with a simulated JWST/NIRCam image in F0707W, F090W, and F115W (top right). A 500 x 500 pixel detail of the galaxy group in the upper-right of the field is shown beneath each image. Even though JWST is not optimized for optical observations, its large primary mirror produces a PSF that is small enough to compare favorably with HST/ACS imaging.

Point Spread Modeling using JWPSF

There are numerous tools available to model the point spread function from an optical system. Many of the simulated PSFs shown here made use of the JWPSF software tool (Cox and Hodge 2006). JWPSF was initially written as a user-friendly means to model the PSF at representative locations in the JWST optical train (including the respective instrument focal planes) at a variety of wavelengths. JWPSF was written in the Python programming language, and makes use of freely available compilers and software for analysis and visualization.