This paper presents the formulation for the evaluation of external coupling in the alternating-phase feed single-layer slotted waveguide array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. A one-dimensional slot array is extracted from the array by assuming the periodicity in transversal direction and introducing the perfect electric conductors in the external region. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot pair which accelerate the iteration. Experiment at 25.3GHz demonstrates good uniformity of the aperture field distribution as well as the effects of the baffles. The directivity is 32.7dB which corresponds to the aperture efficiency 90.5% and the reflection is below -15.0dB over 1.3GHz.