Lyman-alpha emitter (LAE) surveys have successfully used the excess in a narrow-band filter compared to a nearby broad-band image to find candidates. However, the odd spectral energy distribution (SED) of LAEs combined with the instrumental profile have important effects on the properties of the candidate samples extracted from these surveys. We investigate the effect of the bandpass width and the transmission profile of the narrow-band filters used for extracting LAE candidates at redshifts z ~ 6.5 through Monte Carlo simulations, and we present pilot observations to test the performance of tunable filters to find LAEs and other emission-line candidates. We compare the samples obtained using a narrow ideal-rectangular-filter, the Subaru NB921 narrow-band filter, and sweeping across a wavelength range using the ultra-narrow-band tunable filters of the instrument OSIRIS, installed at the 10.4m Gran Telescopio Canarias. We use this instrument for extracting LAE candidates from a small set of real observations. Broad-band data from the Subaru, HST and Spitzer databases were used for fiting SEDs to calculate photometric redshifts and to identify interlopers. Narrow-band surveys are very efficient to find LAEs in large sky areas, but the samples obtained are not evenly distributed in redshift along the filter bandpass, and the number of LAEs with equivalent widths < 60 angstroms can be underestimated. These biased results do not appear in samples obtained using ultra-narrow-band tunable filters. However, the field size of tunable filters is restricted because of the variation of the effective wavelength across the image. Thus narrow-band and ultra-narrow-band surveys are complementary strategies to investigate high-redshift LAEs.
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