Focal stacks (FS) have attracted attention as an alternative representation of light field (LF). However, the problem of reconstructing LF from its FS is considered ill-posed. Although many regularization methods have been discussed, no method has been proposed to solve this problem perfectly. This paper showed that the LF can be perfectly reconstructed from the FS through a filter bank in theory for Lambertian scenes without occlusion if the camera aperture for acquiring the FS is a Cauchy function. The numerical simulation demonstrated that the filter bank allows perfect reconstruction of the LF.