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This chapter is concerned with the methods of calculating the multi-order diffractive optical elements (DOE). The term multi-order indicates that the DOE carries out several transformations of the input beam in different diffractive orders. The currently available technologies of production of the DOE are based on the piecewise-constant or piecewise-linear approximation of the DOE phase. Technological errors can be described mathematically in the form of the non-linear transformation Φ[φ] of the initial phase function of the DOE φ. For example, in photolithography technology, the function Φ[φ] corresponds to the non-linear operation of quantisation of the phase. The non-linearity in the phase function ...

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