Fringing Analysis and Simulation for the Vera C. Rubin Observatory's Legacy Survey of Space and Time

The presence of fringing in astronomical Charge-Coupled Device (CCD) images will have an impact on photometric quality and measurements. Yet its impact on the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) has not been fully studied. We present a detailed study on fringing for CCDs already implemented on the Rubin Observatory LSST Camera's focal plane. After making physical measurements and knowing the compositions, we developed a model for the e2v CCDs. We present a method to fit for the internal height variation of the epoxy layer within the sensors based on fringing measurements in a laboratory setting. This method is generic enough that it can be easily modified to work for other CCDs. Using the derived fringing model, we successfully reproduce comparable fringing amplitudes that match the observed levels in images taken by existing telescopes with different optical designs. This model is then used to forecast the expected level of fringing in a single LSST y-band sky background exposure with Rubin telescope optics in the presence of a realistic time-varying sky spectrum. The predicted fringing amplitude in LSST images ranges from 0.04% to 0.2% depending on the location of a CCD on the focal plane. We find that the predicted variation in surface brightness caused by fringing in LSST y-band sky background images is about 0.6 $\mu \mathrm{Jy}\ {\mathrm{arcsec}}^{-2}$ , which is 40 times larger than the current measurement error. We conclude that it is necessary to include fringing correction in the Rubin's LSST image processing pipeline.