We present a time-efficient backprojection image reconstruction approach applied to frequency-domain (FD) optoacoustic tomography based on tissue illumination at multiple, discrete frequencies. The presented method estimates the Fourier transform of a spatial, circular profile of the underlying image using the amplitude and phase data. These data are collected over multiple frequencies using an acoustic transducer positioned at several locations around the sample. Fourier-transform values for absent frequencies are estimated using interpolation based on low-pass filtering in the image domain. Reconstruction results are presented for synthetic measurements using numerical phantoms, and the results are compared with FD model-based reconstructions.