Strategies for Accurate Effective Point Spread Function (ePSF) Modelling on Undersampled Images

TL;DR

This work tackles pixel-phase systematics in photometry and astrometry arising from undersampled imaging by refining the empirical ePSF modelling workflow. By systematically varying oversampling, interpolation, gridpoint estimation, smoothing, star sampling, and dithering, the authors identify practical rules, such as using at least ~4 gridpoints per FWHM for near-Gaussian ePSFs and adopting a 2D polynomial surface fit for gridpoint values, with RBF cubic interpolation delivering robust results in undersampled regimes. They also emphasize degeneracy breaking by constraining both flux and centroid across dithered frames and show that uniform sub-pixel dithering outperforms random patterns. Applying these refinements to Global Jet Watch data demonstrates reduced pixel-phase biases relative to standard pipelines, highlighting the practical impact for precise photometry and astrometry in real, undersampled instruments.

Abstract

Accurate modelling of the effective point spread function (ePSF) is essential for high-precision photometry and astrometry, particularly in undersampled imaging regimes. In this work, we build on a well-established ePSF modelling framework and its commonly used open-source Python implementation and demonstrate that several simple but effective modifications to existing ePSF modelling routines can significantly improve model accuracy. We use synthetic ePSFs to generate simulated datasets of stellar images, allowing us to evaluate the accuracy of ePSF models and determine the scale of the pixel-phase errors in resulting flux and position measurements. We systematically investigate how specific modelling choices affect ePSF accuracy, and evaluate the influence of oversampling, interpolation, gridpoint estimation, smoothing, star-sample distribution, and dithering on photometric precision. We apply our refined ePSF modelling routine to images from the Global Jet Watch observatories, demonstrating its improved ability to recover an accurate ePSF for real astronomical images. Our findings highlight the importance of tailoring the modelling approach to the specific characteristics of the instrument and detector, as well as to the nature of the available imaging data used to construct the ePSF model. These results provide practical guidance for optimising ePSF construction, thereby improving the reliability of photometric and astrometric measurements.

Figures (27)

• Figure 1: Synthetic ePSFs constructed by integrating a PSF model over 'flush and flat' intra-pixel sensitivity profile. A: Circular Gaussian PSF with $\sigma = 0.5$ pixels. B: Rotated elliptical Gaussian PSF with $\sigma_x = 0.8$ pixels and $\sigma_y = 0.4$ pixels rotated by $45^\circ$. C: Skewed Gaussian with $\sigma_x = \sigma_y = 0.8$ and skew parameter $\eta = 5$. Dashed lines show pixel boundaries.
• Figure 2: Left: Sub-pixel positions of 1000 random centroid coordinate samplings used to generate star images. Right: Examples of $5 \times 5$ pixel star images generated using synthetic ePSF A in Fig \ref{['fig:input_epsfs']}, with the numbers indicating their input sub-pixel centroid positions.
• Figure 3: ePSF modelling and fitting accuracy of synthetic ePSF A, comparing different oversampling parameters. Rows top to bottom are: oversampling $=1, 2, 3$, and 4). Left: True ePSF (blue) and interpolated ePSF model (orange) at $y=0$; residuals ($\Delta \Psi_E =$ interpolated - true ePSF) are shown as green dashed line with a magnified view in the lower panel. Red points mark the tabulated ePSF values used in the interpolation. Middle: Pixel-phase bias in fitted fluxes of 1000 simulated stars. $\Delta x$ is the $x$-displacement of the centroid of the star from the centre of a pixel. Since $f_\mathrm{input} = 1$, the flux residual $\Delta f = f_\mathrm{fit} - f_\mathrm{input}$ represents the fractional flux error. Right: Pixel-phase bias of the fitted $x$ centroid positions, with residuals $x_{\text{fit}} - x_{\text{input}}$ in pixel units.
• Figure 4: Pixel-phase error amplitude in flux measurements as a function of oversampling for the three synthetic ePSFs in Figure \ref{['fig:input_epsfs']}. The amplitude is derived from the peak-to-peak variation in the median flux residuals across sub-pixel phase.
• Figure 5: Comparison of different interpolation methods for ePSF fitting photometry with the synthetic ePSF models A (left), B (middle) and C (right) shown in Figure \ref{['fig:input_epsfs']}, across a range of oversampling values. Each circular point represents the pixel-phase error amplitude in the flux measurements of 1000 simulated sources, for the given oversampling, interpolator and input model.