[Paper Review] Telescope Optics and Weak Lensing: PSF Patterns due to Low Order Aberrations

Mike Jarvis, Paul L. Schechter+1 more|ArXiv.org|Oct 1, 2008

Adaptive optics and wavefront sensing4 references12 citations

TL;DR

This paper proposes a physical model of telescope optics to explain spatially varying PSF patterns in weak lensing surveys, using low-order aberrations (defocus, astigmatism, coma, tilt) to describe PSF size and anisotropy. The model explains over 90% of PSF variation in Blanco 4-meter telescope data, with gravity loading significantly correlated to astigmatism, and outperforms purely empirical PCA in PSF pattern fitting with a chi-squared of 7.5+7.0 vs. 8.5+7.0.

ABSTRACT

In weak lensing investigations, galaxy shapes are deconvolved for the effects of the point spread function (PSF) using stellar images. In this paper we use physical models of the telescope optics to understand the spatial variation of the PSF in the image plane. We introduce a set of parameters to model the key aberrations, which include defocus, focal plane tilt, primary and off-axis astigmatism. We also include the effects of guiding and seeing. We test our model with data from the Blanco 4 meter telescope in Cerro Tololo, Chile. We find that the physical model describes a substantial part of the PSF size and anisotropy over the field of view (over 90 percent of it, based on a chi-squared metric). We identify the primary contributors to the PSF patterns and study their covariances and principal components. We also identify correlations with the effect of gravity on the telescope. Finally, we discuss the improvements in PSF estimation that may be achieved by combining the physical model in this study with the purely empirical approach of Jarvis and Jain (2004).

Motivation & Objective

• To model the spatial variation of the point spread function (PSF) in weak lensing surveys using physical optics principles.
• To identify the dominant low-order aberrations—defocus, astigmatism, coma, and tilt—that cause PSF anisotropy across the focal plane.
• To test whether a physics-based model can explain PSF patterns better than purely empirical methods like PCA.
• To investigate correlations between PSF patterns and external factors such as gravity loading and telescope misalignment.
• To assess the potential for combining physical modeling with empirical techniques to improve PSF estimation in large-scale weak lensing surveys.

Proposed method

• The authors model PSF patterns using wavefront error expansions in the pupil plane, focusing on low-order Zernike modes: defocus, astigmatism, coma, and tilt.
• They derive the corresponding PSF patterns in the image plane via Fourier transformation of the wavefront, linking optical aberrations to observable PSF shapes.
• The model includes parameters for telescope misalignments (e.g., secondary mirror tilt, decentering) and primary mirror deformations, parameterized by 10 independent variables per exposure.
• They calibrate and validate the model using real data from the Blanco 4-meter telescope in Chile, analyzing hundreds of exposures.
• They compare the physical model’s performance to the empirical PCA method of Jarvis & Jain (2004) using a chi-squared metric on PSF size and shape.
• They analyze correlations between model parameters and external factors such as gravity direction and wind speed, identifying physical origins of PSF patterns.

Experimental results

Research questions

• RQ1 To what extent can low-order optical aberrations explain the observed spatial variation in PSF size and shape across the focal plane?
• RQ2 How do telescope misalignments and gravity-induced deformations contribute to PSF anisotropy in real observational data?
• RQ3 Can a physics-based model of telescope optics outperform purely empirical PCA in describing PSF patterns?
• RQ4 What is the role of gravity loading in inducing astigmatism-like PSF patterns, and how can it be modeled?
• RQ5 How might combining physical models with empirical techniques improve PSF estimation in weak lensing surveys?

Key findings

• The physical model explains over 90% of the PSF size and anisotropy variation across the field of view, as measured by a chi-squared metric.
• The model achieves a chi-squared value of 7.5+7.0 for PSF size and shape, slightly better than the empirical PCA method (8.5+7.0).
• Astigmatism parameters in the model show moderate correlation with the direction of gravity, indicating that gravity loading contributes significantly to PSF patterns.
• The model identifies defocus, astigmatism, and coma as the primary contributors to PSF variation, with off-axis astigmatism being a major component.
• Residual PSF patterns suggest contributions from atmospheric seeing and possibly unmodeled effects like telescope resonance or chip boundary artifacts.
• The study concludes that physical modeling can complement empirical methods, especially for non-stochastic, time-invariant PSF distortions, though complex dynamic effects (e.g., wind-induced resonance) remain challenging to model.