A Direct DESI--SDSS Two-Fibre Test of Aperture Bias in Optical Emission-Line Diagnostics

Fixed angular apertures sample different physical regions of nearby galaxies and can therefore bias optical emission-line diagnostics. We use 20,545 high-confidence emission-line galaxies observed by both the Dark Energy Spectroscopic Instrument (DESI) and the Sloan Digital Sky Survey (SDSS) as a two-fibre experiment, in which the DESI 1.5 arcsec fibre is nested within the SDSS 3 arcsec fibre. To isolate aperture effects from line-measurement systematics, we refit every spectrum using the same eMILES stellar-continuum and emission-line model while preserving the wavelength-dependent line-spread function of each spectrum. This common refit yields 20,200 quality-controlled matched galaxies. Relative to SDSS, the smaller DESI aperture produces small but highly significant offsets: Δ (N2)=+0.0067 plus or minus0.0002, Δ (S2)=-0.0148 plus or minus0.0003, Δ (O3)=-0.0246 plus or minus0.0006, Δ O3N2 =-0.0327 plus or minus0.0007, and Δ (H α/ H β)=-0.0195 plus or minus0.0003, where Δ denotes DESI minus SDSS. These offsets persist in Baldwin--Phillips--Terlevich-selected star-forming galaxies and in a near-concentric subset. Their amplitudes vary across the redshift distribution and retain a measurable dependence on apparent fibre coverage after redshift is controlled, showing that redshift and relative aperture coverage jointly modulate the aperture terms. We conclude that, for high-S/N emission-line galaxies, DESI--SDSS comparisons carry measurable, diagnostic-dependent fibre-aperture terms even when continuum modelling, emission-line fitting, and spectral-resolution treatment are held fixed.