Intensity mapping is becoming a useful tool to study the large-scale structure of the universe through spatial variations in the integrated emission from galaxies and the intergalactic medium. We study intensity mapping of the Hα 6563 Å, [O III] 5007 Å, [O II] 3727 Å, and Hβ 4861 Å lines at 0.8 ⩽ z ⩽ 5.2. The mean intensities of these four emission lines are estimated using the observed luminosity functions (LFs), cosmological simulations, and the star formation rate density (SFRD) derived from observations at z ≾ 5. We calculate the intensity power spectra and consider the foreground contamination of other lines at lower redshifts. We use the proposed NASA small explorer SPHEREx (the Spectro-Photometer for the History of the universe, Epoch of Reionization, and Ices Explorer) as a case study for the detectability of the intensity power spectra of the four emission lines. We also investigate the cross-correlation with the 21 cm line probed by the Canadian Hydrogen Intensity Mapping Experiment (CHIME), Tianlai experiment and the Square Kilometer Array (SKA) at 0.8 ⩽ z ⩽ 2.4. We find both the auto and cross power spectra can be well measured for the Hα, [O III] and [O II] lines at z ≾ 3, while it is more challenging for the Hβ line. Finally, we estimate the constraint on the SFRD from intensity mapping, and find we can reach an accuracy higher than 7% at z ≾ 4, which is better than with the usual method of measurements using the LFs of galaxies
