JWST ETC Point Spread Functions
The JWST Exposure Time Calculator (ETC) uses point spread functions (PSFs) from a precomputed library of PSFs produced by WebbPSF. (For more details on WebbPSF's optical model, check out the WebbPSF documentation pages.)
The PSF library
Each instrument aperture is represented by a precomputed set of roughly 30 PSFs, generated at log-normal wavelength intervals that span the entire wavelength range of all filters and dispersers used with that aperture. With the exception of coronagraphic imaging, all PSFs are generated on-axis, centered on the detector, and are thus devoid of any optical aberrations that may impact real PSFs at locations far from the detector center. Given that the ETC models sources close to the center, the effect is likely to be minimal.
Coronagraphic observations have multiple sets of roughly 30 PSFs each, generated at log-normal wavelength intervals in multiple spatial locations, to account for the effects of coronagraphic spots.
The PSFs are generated to relatively small sizes—the largest are the MIRI 4QPM PSFs (used in MIRI Coronagraphic Imaging), which cover 8.9" on a side; the smallest are NIRISS Imaging PSFs that are only 1.64" on a side. Nevertheless, the PSFs cover more than 99.9% of the expected flux.
ETC version 1.5.1 uses WebbPSF version 0.8.0, WebbPSF Data version 0.8.0, and POPPY version 0.8.0 to construct the PSF library for all science instruments (MIRI, NIRCam, NIRISS, and NIRSpec). Compared to ETC 1.5, the PSFs have been flipped vertically to reflect the actual orientation of the installed optical elements, which mainly affects modes with non-axisymmetric PSFs like the MIRI 4QPMs, NIRCam weak lenses, and NIRISS AMI and SOSS.
How the library is used
For a given observation, the entire set of PSFs for a given aperture are loaded into the ETC.
The scene generation process creates a cube with both spatial and wavelength dimensions for each source in the scene. It then takes those cubes and convolves each wavelength plane with the appropriate PSF; this PSF is produced by interpolating the set of PSFs at the specific wavelength of the cube slice. Thus, the apparent PSF in the output 2D images is the sum of multiple wavelength-dependent PSFs, scaled by the filter throughput curve.
The model cubes for each scene are then added together to form a combined scene cube, which is then "observed" onto a detector, and results extracted by use of the strategy.
The reason that the PSF convolution is done before the combination of all of the sources is to make it easier to use a positionally-dependent PSF, which is done for coronagraphy.
Position-dependent coronagraphic PSFs
The positionally-dependent PSFs are generated in a variety of patterns to suit the shape of the occulting elements. Though they are generated for different spatial positions, they are not interpolated spatially; instead, the ETC's code selects the closest PSF to the target location. This can result in step-function behavior with various sources.
The MIRI 4-quadrant phase masks (4QPM) used for coronagraphic imaging are assumed to have eight-fold symmetry: they can be reflected across each of the quadrant axes and across the primary axes of the detector (which is approximately correct). PSFs were generated in a triangular shape, covering the 0%, 33%, 66%, and 99% unobscured positions. The positions take into account the roughly 5° clockwise rotation of the MIRI masks.
The MIRI LYOT2300 mask is assumed to have radial symmetry. PSFs were generated along the Y-axis, at points that are 0%, 25%, 50%, 75%, and 99% unobscured.
The NIRCam MASKSWB and MASKLWB masks are assumed to have vertical symmetry. They are tapered wedges (where MASKSWB tapers toward negative X, and MASKLWB tapers toward positive X), such that each filter has an optimal position along the wedge where a point source is just barely fully obscured. Sets of five PSFs were generated at the optimal position, positions 1" and 2" on either side of the optimal position, and positions above the bar that are 33%, 66%, and 99% unobscured.
The NIRCam MASK210R, MASK335R, and MASK430R masks are assumed to have radial symmetry. PSFs were generated along the Y-axis, at points that are 0%, 25%, 50%, 75%, and 99% unobscured.