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Morphology and color patterns hold fundamental insights into the earlyformation history of high-z galaxies. However, 2D reconstruction of rest-frame(RF) color maps of such systems from imaging data is a non-trivial task. Thisis mainly because the spectral energy distribution (SED) of high-sSFR(starburst) galaxies near and far is spatially inhomogeneous and thus thecommon practice of applying a spatially constant "morphological" k-correctioncan lead to serious observational biases. In this study we use the nearby bluecompact galaxy Haro11 to illustrate how the spatial inhomogeneity of the SEDimpacts the morphology and color maps in the observer's frame (ObsF) visual andNIR, and potentially affects the physical characterization of distant starburstgalaxies with the JWST and Euclid. Based on MUSE spectroscopy and spectralmodeling, we first examine the elements shaping the spatially varying opticalSED of Haro11, namely intrinsic stellar age gradients, strong nebular emissionand its spatial decoupling from the ionizing stellar background, and differingextinction patterns in the stellar and nebular component both spatially and intheir amount. Our simulations show, inter alia, that an optically bright yetdusty star-forming (SF) region may evade detection whereas a gas-evacuated(thus, potentially Lyman continuum photon-leaking) region with weaker SFactivity can dominate the ObsF (RF UV) morphology of a high-z galaxy. We alsoshow that ObsF color maps are affected by strong emission lines moving in andout of filter passbands depending on z, and, if taken at face value, can leadto erroneous conclusions about the nature, evolutionary status and dust contentof a galaxy. A significant additional problem stems from the uncertainprominence of the 2175 {\AA} extinction bump that translates to appreciableinherent uncertainties in RF color maps of high-z galaxies. (abridged)

On the challenge of interpreting the morphology and color maps of high-z starburst galaxies with the JWST and Euclid