# Photometric Biases in Modern Surveys

## TL;DR

This paper demonstrates that maximum-likelihood photometric estimators systematically overestimate flux, especially for resolved sources and in multi-band fitting, with implications for survey data analysis and bias correction methods.

## Contribution

It reveals the extent and behavior of ML flux biases in modern surveys and provides correction prescriptions for these biases.

## Key findings

- ML estimators overestimate flux, especially for resolved sources.
- Bias increases with lower signal-to-noise ratio and more model parameters.
- Simulations and real survey data confirm the presence of these biases.

## Abstract

Many surveys use maximum-likelihood (ML) methods to fit models when extracting photometry from images. We show these ML estimators systematically overestimate the flux as a function of the signal-to-noise ratio and the number of model parameters involved in the fit. This bias is substantially worse for resolved sources: while a 1% bias is expected for a 10$\sigma$ point source, a 10$\sigma$ resolved galaxy with a simplified Gaussian profile suffers a 2.5% bias. This bias also behaves differently depending how multiple bands are used in the fit: simultaneously fitting all bands leads the flux bias to become roughly evenly distributed between them, while fixing the position in "non-detection" bands (i.e. forced photometry) gives flux estimates in those bands that are biased low, compounding a bias in derived colors. We show that these effects are present in idealized simulations, outputs from the Hyper Suprime-Cam fake object pipeline (SynPipe), and observations from Sloan Digital Sky Survey Stripe 82. Prescriptions to correct for the ML bias in flux, and its uncertainty, are provided.