What is the difference between multiple and zero-order retarders and when should I pick one over the other?

Multiple-order retarders (or waveplates) and zero-order retarders are interchangeable. Zero-order waveplates should be considered for more critical applications. The advantages of a zero-order waveplate include an increased bandwidth and a lower sensitivity to temperature changes. A ±2% change from the design wavelength will cause only a minor change in the retardation of a zero-order waveplate. With a multiple-order waveplate, a ±1% change from the designed wavelength will cause considerable problems with the retardation.