The Zwicky Transient Facility is a time-domain optical survey that has substantially increased our ability to observe and construct massive catalogs of astronomical objects by use of its 47 square degree camera that can observe in multiple filters. However the telescopes i-band filter suffers from significant atmospheric fringes that reduce photometric precision, especially for faint sources and in multi-epoch co-additions. Here we present a method for constructing models of these atmospheric fringes using Principal Component Analysis that can be used to identify and remove these image artifacts from science images. In addition, we present the Uniform Background Indicator as a quantitative measurement of correlated background noise and its relationship to reduced photometric error after removing fringes. We conclude by evaluating the effect of our method on measuring faint sources through the injection and recovery of artificial faint sources in both single-image epochs and co-additions. Our method for constructing atmospheric fringe models, and using those models for cleaning images, is available for public download in the open source python package fringez.
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