The extragalactic background light (EBL) fluctuations in the optical/near-IR encode the cumulative emission of unresolved galaxies, integrated galaxy light (IGL), diffuse intra-halo light (IHL), and high-z sources from the epoch of reionisation (EoR), but they are difficult to disentangle with auto-spectra alone. Our aim was to decompose the EBL into its principal constituents using multi-band intensity mapping combined with cosmic shear and galaxy clustering. We developed a joint halo-model framework in which IHL follows a mass- and redshift-dependent luminosity scaling, IGL is set by an evolving Schechter luminosity function, and EoR emission is modelled with Pop II/III stellar emissivities and a binned star formation efficiency. Cosmic shear is modelled using the tidal alignment and tidal torquing model for intrinsic alignment. Using mock surveys in a flat Lambda cold dark matter (ΛCDM) cosmology with ten spectral bands spanning 0. 75--5. 0, in the north ecliptic pole deep fields over about 100, , , with uncertainties reduced by 5--30%, and the resulting star formation rate density constraints extend to z with source detections down to AB, =, 20. 5 for masking, and six redshift bins to z=2. 5, we fit auto- and cross-power spectra using a Markov chain Monte Carlo method. The combined SPHERExtimesEuclid analysis recovers all fiducial parameters within 1, σ and reduces 1, σ uncertainties on IHL parameters by 10--30% relative to SPHEREx EBL-only, while EoR star formation efficiency parameters improve by 20--30%. The predicted cross-correlations show a stronger coupling of IHL than IGL to the shear field within adopted model framework, enhancing component separation; conversely, the high-z EoR contribution shows negligible correlation with cosmic shear and galaxy clustering, aiding its isolation in the EBL. Relative to the SPHEREx EBL-only case, the inferred IHL fraction as a function of halo mass is significantly tightened over 10¹1–10^ 14 with uncertainty reductions of 15--30%. SPHERExtimesEuclid provides a robust systematics-aware route to component-resolved EBL measurements and improved constraints on galaxy formation.
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