Biased Moments of Undersampled Sources

TL;DR

This paper investigates how undersampling and finite pixel size introduce systematic biases in the measurement of spatial intensity moments used to analyze pixelized sources like stars and galaxies, affecting their inferred properties.

Contribution

It demonstrates the bias in geometric moments caused by undersampling and illustrates its impact on survey data analysis, providing insights into systematic errors in astronomical measurements.

Findings

Bias in first and second moments for Gaussian sources near pixel scale

Undersampling causes orientation angle patterns in sky surveys

Systematic errors affect centroid, size, and orientation measurements

Abstract

Spatial intensity moments computed on images can be used as a probe of the centroid, size, and orientation of pixelized sources such as stars and galaxies. However, all measurements made on images suffer from errors due to undersampling and finite pixel size, causing systematic biases in the computation of moments and other statistics. We show examples of bias in the first and second geometric moments computed on images of Gaussian sources with widths near the pixel scale, $0.1<\sigma<5$ pixels. We then illustrate how undersampling could lead to the orientation angle patterns seen in various modern surveys of the sky.