A diffractive plenoptic camera is a novel approach to the traditional plenoptic camera which replaces the main optic with a Fresnel zone plate making the camera sensitive to wavelength instead of range. Algorithms are necessary, however, to reconstruct the image produced by these plenoptic cameras. This paper provides the first quantification of the effectiveness of four different types of post-processing algorithms on a simulated Fresnel zone light field spectral imaging system. The four post-processing algorithms used were standard digital refocusing, 3D deconvolution through a Richardson-Lucy algorithm, a novel Gaussian smoothing algorithm, and a custom-made super resolution algorithm. For the digital refocusing algorithm, the image quality decreased as the wavelength difference from design increased. In comparison, in the Richardson Lucy deconvolution algorithm, the image returned to the same quality as at the design wavelength if enough iterations were used and generally provided results on par with the best near the design wavelength of the Fresnel zone plate and by far the best results far from design at the cost of extensive computation time. The super resolution method, in general, performed better than the standard digital refocusing while the Gaussian smoothing algorithm performed on par with digital refocusing. As a consequence, if time is not a factor, deconvolution should be used in general, while the super resolution method provides faster results if time is an issue. Still, each algorithm outperformed the others in specific cases which allows the best results to be obtained by choosing the algorithm that meets operational requirements and limitations.