We describe the concept of a super compact diffractive imaging spectrometer, with optical components a few millimeters across in all dimensions, capable of detecting optical fluorescence spectra within the entire visible spectral range from 400\mathrm{nm} to 700\mathrm{nm} with resolution of the order of 2 nm. In addition, the proposed spectrometer is capable of working simultaneously with multiple, up to 35, independent input optical channels. A specially designed diffractive optical element integrated with a planar optical waveguide is the key component of the proposed device. In the preliminary experimental tests, a uniform waveguide grating with a microlens was used to mimic operation of the diffractive optical element. A microspectrometer with optical components measured below 1 cm in all dimensions covers the spectral range from 450\mathrm{nm} to 650\mathrm{nm} and shows a spectral resolution of 0.5\mathrm{nm} at wavelengths close to 514\mathrm{nm} and 633\mathrm{nm} .