We have developed two types of algorithms, i.e., forward and backward, to retrieve the extinction coefficient at a wavelength of Λ = 532 nm for two types of aerosols, i.e., water-soluble and sea-salt or water-soluble and dust, at each layer from the dual wavelength polarized lidar measurements. Distinct from the algorithms developed to date, our algorithms can determine aerosol types and retrieve the vertical profiles of the lidar ratio and number concentration. We applied the algorithms to the data measured with the dual-wavelength polarized lidar of NIES installed on the vessel MIRAI over the tropical Pacific Ocean. The highlighted results are as follows: (1) Major components are water soluble and sea-salt and only a few dust particles were found in the whole observation period. Most of water-soluble and sea-salt particles exist below 1 km. (2) The overall pattern of the vertical and temporal distribution for sulfate, sea-salt and dust particles simulated by the SPRINTARS roughly in good agreement with those retrieved from the lidar measurements, except for the temporal distribution of sulfate particles. (3) The optical thickness for total aerosols increases as the latitude becomes higher or the longitude becomes lower. The distribution of the optical thickness for total aerosols is mainly affected by the water-soluble particles. We are planning to conduct quantitative comparison between the lidar and SPRINTARS, e.g., direct comparing the values of the extinction coefficient for each aerosol type. We will also apply the algorithms to the lidar data measured in the other MIRAI cruises, e.g., in the region between the Japan island and the island of New Guinea over the tropical Pacific Ocean in 2004. Further, we will apply the algorithms to the CALIPSO lidar data measured over the sea.