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In this paper, we derive the period–luminosity ( P–L ) relation for Large Magellanic Cloud (LMC) Cepheids based on mid‐infrared  AKARI  observations.  AKARI 's  Infrared Camera  sources were matched to the Optical Gravitational Lensing Experiment‐III (OGLE‐III) LMC Cepheid catalogue. Together with the available  I ‐band light curves from the OGLE‐III catalogue, potential false matches were removed from the sample. This procedure excluded most of the sources in the   S 7  and   S 11  bands; hence, only the  P–L  relation in the   N 3  band is derived in this paper. Random‐phase corrections were included in deriving the  P–L  relation for the single‐epoch  AKARI  data; even though the derived  P–L  relation is consistent with the  P–L  relation without random‐phase correction, however there is an ∼7 per cent improvement in the dispersion of the  P–L  relation. The final adopted   N 3 ‐band  P–L  relation is   N 3 =−3.246 log( P ) + 15.844 , with a dispersion of 0.149.

Cepheid period–luminosity relation from the AKARI observations