Sinusoidally structured illumination is used in concert with a phantom-based lookup-table (LUT) to map wide-field optical properties in turbid media with reduced albedos as low as 0.44. A key advantage of the lookup-table approach is the ability to measure the absorption and reduced scattering coefficients over a much broader range of values than permitted by current diffusion theory methods. Through calibration with a single reflectance standard, the LUT can extract from with an average root-mean-square (rms) error of 7% and extract from with an average rms error of 6%. The LUT is based solely on measurements of two parameters, reflectance and modulation at an illumination period of . A single set of three phase-shifted images is sufficient to measure both and , which are then used to generate maps of absorption and scattering by referencing the LUT. We establish empirically that each pair maps uniquely to only one pair of and report that the phase function (i.e., size) of the scatterers can influence the accuracy of optical property extraction.