This study presents an algorithm to estimate the background optical properties for quantitative imaging, based on the initial pressure distribution obtained from photoacoustic tomography (PAT). The algorithm utilizes an alternative illumination mode of our original PAT system, which separately illuminates tissue from forward and backward directions toward an array transducer. The optical properties are determined by minimizing the difference between the following two ratios: one is the ratio of initial pressure distribution obtained from the illumination modes, the other is the ratio of the calculated light fluence distribution. We show that the algorithm estimates the background optical properties even if the initial pressure distribution is reconstructed under the limited-view conditions.