Formulations of the theory of automated photoelasticity are expressed simply by use of the Stokes parameters. In the automated photoelasticity, the measurement of the total relative phase retardation must often be performed over a wide wavelength range. The Stokes parameters (S0, S1, S2 and S3) need to be measured over a wide wavelength range. The Stokes parameters of monochromatic light can be measured by the adjustable azimuth settings of a retarder and analyzer (ARA) method. When undertaking the measurement of the Stokes parameters of light of an arbitrary wavelength over a wide wavelength range, the measurement of S3 by the conventional ARA method is dependent on the phase difference error ρ i of a quarter-wave plate mismatch as well as Stokes parameter S2. The measurement of S3 by a judicious choice of azimuth settings of a quarter-wave plate and a polarizer (JCAQP) as in the method proposed can be obtained by considering ρ I . The JCAQP method is clarified by employing the Poincaré sphere. It is shown that application of the JCAQP method yields the principal axis and the relative phase retardation of the birefringent plate free from the ρ i of the quarter-wave plate for incident elliptically polarized light of an arbitrary wavelength.