A polarization state detector (PSD) measures the state of polarization of the detected light. The state of polarization is fully described by the Stokes vector containing four Stokes parameters. A division-of-amplitude photopolarimeter (DOAP) measures the four Stokes parameters by simultaneously acquiring four intensities using photodetectors. A key component of the DOAP is the first beam splitter, which splits up the incoming beam into two beams. The effect of the beam splitter on the state of polarization of the reflected (r) and transmitted (t) beam is determined by six parameters: R, T, ψr, ψt, Δr, and Δt. R and T are the reflectance and transmittance, and (ψr, Δr) and (ψt, Δt) are the ellipsometric parameters of the beam splitter in reflection and transmission, respectively. To measure the Stokes vector with high accuracy, the six optical parameters must be chosen appropriately. In previous work, the optimal parameters of the beam splitter have been determined as R = T = 1/2, cos2 2ψr = 1/3, ψt = π/2 - ψr, and Δr-Δt modulo π=π/2 by calculating the maximum of the absolute value of determinant of the instrument matrix. Using additional quarter-wave plates eliminates the constraint on the retardance and hence simplifies the manufacturing process of the beam splitter, especially when broadband application is intended. ... mehrTo compensate a suboptimal value of Δr-Δt, the azimuthal angles of the principal axes of the retarders must be adjusted, for which we provide analytic formulas. Hence, a DOAP with retarders is also optimal in the sense that the same values for the determinant and condition number of the instrument matrix are obtained. When using two additional retarders, it is necessary to install both on the same light path in order to obtain an optimal DOAP. We will show that is also possible to get an optimal DOAP with only one additional quarter-wave plate instead of two, if one of the Wollaston prisms is rotated.