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Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry where knowledge of the illumination pattern beyond the native spatial resolution of the image may be required. Here, we introduce a method of PSF reconstruction where point sources are artificially sampled beyond the native resolution of an image and combined together via stacking to return a finely sampled estimate of the PSF. This estimate is then deconvolved from the pixel-gridding function to return a superresolution kernel that can be used for optimally weighted photometry. We benchmark against the <1% photometric error requirement of the upcoming SPHEREx mission to assess performance in a concrete example. We find that standard methods like Richardson–Lucy deconvolution are not sufficient to achieve this stringent requirement. We investigate a more advanced method with significant heritage in image analysis called iterative back-projection (IBP) and demonstrate it using idealized Gaussian cases and simulated SPHEREx images. In testing this method on real images recorded by the LORRI instrument on New Horizons, we are able to identify systematic pointing drift. Our IBP-derived PSF kernels allow photometric accuracy significantly better than the requirement in individual SPHEREx exposures. This PSF reconstruction method is broadly applicable to a variety of problems and combines computationally simple techniques in a way that is robust to complicating factors such as severe undersampling, spatially complex PSFs, noise, crowded fields, or limited source numbers. 

The size and structure of the dusty circumnuclear torus in active galactic nuclei (AGNs) can be investigated by analyzing the temporal response of the torus's infrared (IR) dust emission to variations in the AGN ultraviolet/optical luminosity. This method, reverberation mapping, is applicable over a wide redshift range, but the IR response is sensitive to several poorly constrained variables relating to the dust distribution and its illumination, complicating the interpretation of measured reverberation lags. We have used an enhanced version of our torus reverberation mapping code (TORMAC) to conduct a comprehensive exploration of the torus response functions at selected wavelengths, for the standard interstellar medium grain composition. The shapes of the response functions vary widely over the parameter range covered by our models, with the largest variations occurring at shorter wavelengths (≤4.5 μm). The reverberation lag, quantified as the response-weighted delay (RWD), is most affected by the radial depth of the torus, the steepness of the radial cloud distribution, the degree of anisotropy of the AGN radiation field, and the volume filling factor. Nevertheless, we find that the RWD provides a reasonably robust estimate, to within a factor of ~3, of the luminosity-weighted torus radius, confirming the basic assumption underlying reverberation mapping. However, overall, the models predict radii at 2.2 μm that are typically a factor of ~2 larger than those derived from K-band reverberation mapping. This is likely an indication that the innermost region of the torus is populated by clouds dominated by large graphite grains. 

Highly accurate closed-form expressions that describe the full trajectory of photons propagating in the equatorial plane of a Kerr black hole are obtained using asymptotic approximants. This work extends a prior study of the overall bending angle for photons (Barlow et al 2017 Class. Quantum Grav. 34 135017). The expressions obtained provide accurate trajectory predictions for arbitrary spin and impact parameters, and provide significant time advantages compared with numerical evaluation of the elliptic integrals that describe photon trajectories. To construct approximants, asymptotic expansions for photon deflection are required in various limits. To this end, complete expansions are derived for the azimuthal angle as a function of radial distance from the black hole in the far-distance and closest-approach (pericenter) limits, and new coefficients are reported for the bending angle in the weak-field limit (large impact parameter).