Morphological quantitative measurements and visual-like classifications are susceptible to biases arising from the expansion of the Universe. One of these biases is the effect of cosmological surface brightness dimming (CSBD): the measured surface brightness of a galaxy decays with redshift as $(1+z)^ $. This effect might lead an observer to perceive an altered morphology compared to the real one. Our goal is to investigate the impact of CSBD on morphological classifications to determine the true evolution of morphological classes over redshift for field galaxies, and to interpret these results in the context of morphological transformations and star formation quenching. We employed artificial redshifting techniques on a sample of 268 galaxies in the five CANDELS fields, spanning redshifts from $z=0.2$ to $z=3.0$. We compared the visual classifications and morphological coefficients ($G$, $M_ $, and $A_s$) obtained from the original and simulated images. Subsequently, we developed two correction methods to mitigate the effects of CSBD. Our findings reveal that CSBD, low resolution, and signal-to-noise significantly bias the visual morphological classifications beyond $z>1$. Specifically, we observed an overestimation of the fractions of spheroids and irregular galaxies by up to $50<!PCT!>$, while the fractions of early- and late-type disks were underestimated by $10<!PCT!>$ and $50<!PCT!>$, respectively. However, we found that morphological coefficients are not significantly affected by CSBD at $z<2.25$. We validated the consistency of our correction methods by applying them to the observed morphological fractions in the IllustrisTNG-50 sample and comparing them to previous studies. We propose two potential sources of confusion regarding the visual classifications due to CSBD. Firstly, galaxies may be misclassified as spheroids, as the dimming effect primarily renders the bulge component visible. Secondly, galaxies may be misidentified as irregulars due to their more diffuse and asymmetric appearance at high redshifts. By analyzing the morphological fractions of star-forming and quiescent subsamples as a function of redshift and stellar mass, we propose a scenario where late-type disks transform into quiescent spheroids through mergers or to early-type disks through secular evolution or active galactic nucleus feedback.
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