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tokens: the inhomogeneous Universe, in particular, by using the baryon acoustic oscillation (BAO) as a standard ruler (e.g. Cole et al. 2005 ; Eisenstein et al. 2005 ). The Baryonic Oscillation Spectroscopic Survey (BOSS) experiment demonstrated the ability of BAO measurements to provide a standard ruler to the per cent level at redshift 0.5 (Anderson et al. 2014 ). Though the BAO is known to be largely free of systematic errors (e.g. Vargas-Magaña et al. 2014 ; Ross, Percival Manera 2015 ), precise measurement requires surveys of a large number of sources over a large cosmic volume. The current and future dark energy surveys aim to efficiently sample tens of millions of faint galaxies/quasars at redshift 0.5 ≲ z ≲ 2.3 over the entire observable sky to measure BAO at the per cent level (e.g. eBOSS, 1 DESI, 2 PFS, 3 4MOST, 4 EUCLID . 5 ) The eBOSS survey (Dawson et al. 2016 ) in the SDSS-IV (Blanton et al., in preparation), started in Fall 2014 and is currently mapping the large-scale structure at redshift z > 0.6 with four different tracers: luminous red galaxies (LRGs; Prakash et al. 2015 ), emission line galaxies (ELGs; Comparat et al. 2015a ), QSOs, and Lyα absorption (Myers et al. 2015 ; Palanque-Delabrouille et al. 2016 ). It will provide the first density map covering the redshift range 0.6 z 2.5 over a large portion of the sky (7500 deg 2 of LRGs and QSOs, 1500 deg 2 of ELGs). To achieve these goals with a 2.5-metre telescope, eBOSS requires efficient methods to pre-select targets using both magnitude and colour cuts. For ELGs, there is an additional source of complication: their redshifts will be mainly determined by emission lines, and it is therefore important to characterize the sampling efficiency of ELGs with broad-band magnitude and colour selections (e.g. Comparat et al. 2015a ; Raichoor et al. 2016 ). Studies have shown that the future ELG surveys will sample the or the Hα emitters in an incomplete manner (Comparat et al. 2015b ; Tonegawa et al. 2015 ). A more precise quantification of this incompleteness is critical for a more detailed understanding of the selection effects and to enable more precise cosmological analysis. In the redshift range targeted by eBOSS (0.6 z 1.2 for ELGs), the strongest emission lines that can be observed in the optical are the oxygen , lines and the hydrogen Hβ (λ4861) Balmer line. All other lines are either outside of the optical window at these redshifts, or an order of magnitude weaker and therefore will not drive the completeness of the ELG survey. Of these three line luminosity functions (LFs), the LF is the most well-known. Its LF has been measured from redshift 0 to 4.7 (e.g. Ly et al. 2007 ; Zhu, Moustakas Blanton 2009 ; Gilbank et al. 2010 ; Bayliss et al. 2011 ; Sobral et al. 2012 ; Comparat et al. 2015b ; Khostovan et al. 2015 ), mostly due to interests in using as an empirical star formation rate (SFR) indicator (see Kennicutt 1998 ; Kewley, Geller Jansen 2004 ; Moustakas, Kennicutt Tremonti