Redshifting galaxies from DESI to JWST CEERS: Correction of biases and uncertainties in quantifying morphology

Observations of high-redshift galaxies with unprecedented detail have now been rendered possible with JWST. However, accurately quantifying their morphology remains uncertain due to potential biases and uncertainties. To address this issue, we used a sample of 1816 nearby DESI galaxies, with a mass range of $10^{9.75-11.25}M_{\odot}$, to compute artificial images of galaxies of the same mass located at $0.75\leq z\leq 3$ and observed at rest-frame optical wavelength in CEERS. We analyzed the effects of cosmological redshift on the measurements of Petrosian radius ($R_p$), half-light radius ($R_{50}$), asymmetry ($A$), concentration ($C$), axis ratio ($q$), and S\'ersic index ($n$). Our results show that $R_p$ and $R_{50}$, calculated using non-parametric methods, are slightly overestimated due to PSF smoothing, while $R_{50}$, $q$, and $n$ obtained through model fitting does not exhibit significant biases. We improve the computation of $A$ by incorporating a more accurate noise effect removal procedure. Due to PSF asymmetry, there is a minor overestimation of $A$ for intrinsically symmetric galaxies. However, for intrinsically asymmetric galaxies, PSF smoothing dominates and results in an underestimation of $A$, an effect that becomes more significant with higher intrinsic $A$ or at lower resolutions. Moreover, PSF smoothing also leads to an underestimation of $C$, which is notably more pronounced in galaxies with higher intrinsic $C$ or at lower resolutions. We developed functions based on resolution level, defined as $R_p/$FWHM, for correcting these biases and the associated statistical uncertainties. Applying these corrections, we measured the bias-corrected morphology for the simulated CEERS images and we find that the derived quantities are in good agreement with their intrinsic values -- except for $A$, which is robust only for angularly large galaxies where $R_p/{\rm FWHM}\geq 5$.