A multi-wavelength 3D fluorescence microscope, with transfer functions varying significantly with wavelength, is proposed. This microscope measures multiple wavelengths concurrently and scans through the object at a rate significantly below the Nyquist criterion, which gives a reduced image acquisition time. The sub-Nyquist sampling produces a set of images contaminated by aliasing. Due to the differing transfer functions, the aliasing effects are different in each image. This allows the aliasing operator to be inverted and a single unaliased image to be constructed. This is an application of the generalized sampling expansion first introduced by Papoulis. The instrument is demonstrated through simulation and shown to produce images of a similar quality to those that would be expected from a Nyquist-rate instrument.