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materials [37]. The energy efficiency determines the quality of focusing and should not be less than 85–95%. The high DOE efficiency dictates the choice of the method of calculation. A ray-tracing method provides greater efficiency, but at some expense to the accuracy of formation of the focusing spot.

3. For computing DOEs aimed at generating the binary images of multiorder diffraction gratings or matrix illuminators employed in optical neuron networks, one uses methods for solving linear sets of algebraic equations [41], stochastic methods [59], and other methods of nonlinear optimization [40,43]. The requirement that the profile of such DOEs be binary determines the choice of a particular method. Another requirement is that the binary phase diffraction grating should form a number of orders more than 64×64, characterized by equal amplitudes with an 80% efficiency and with a spread of energies between orders of not more than 10%.

Recent years have seen a growth of interest in the synthesis of diffraction gratings with ultrashort period, which means a period less than or equal to the wavelength of the light used. The calculation of the microrelief of such surfaces is based on the exact solution of Maxwell equations [60,61]. The formulation of an inverse problem in this situation appears to be quite a challenging task because of the absence of an explicit analytical relation between the shape of the grooves of the diffraction grating and the intensity of light scattered. Note, however, that gratings with ultrashort period have found use as polarizing splitters of laser light [61] and for turning the light polarization vector [62].

4. DOEs forming axial images possess, as a rule, the radial structure of microrelief zones, which means that levels of equal phase are found on the concentric rings. The calculation of such DOEs requires the use of iterative methods involving algorithms of the fast Hankel transform [28]. In the course of calculation of radial DOEs able to form annular intensity distributions, an undesirable intensity peak is found in the ring centre. To avoid this, phase rotor masks are employed [63,64].

Note also that in a number of cases the problem of calculating radial DOEs can be reduced to that of computing one-dimensional (1D) DOEs [48]. Such elements have found use for the enhancement of focal depth of microlenses in laser-based reading in to/out of a disk [65], for pointing the laser beam at large distances [66], in bifocal microscopes [67], etc.

5. Phase formers of wavefronts are employed as correctors of aberration for conventional lenses [51], as compensators for checking aspherical mirrors [52] or as formers of reference wavefronts in the Twyman-Green interferometer [53]. The task of calculating such DOEs via iterative methods may be thought of as an inverse problem to that of computing kinoforms, because it requires the calculation of the DOE using the pregiven phase distribution in a certain plane, rather than the pregiven intensity distribution.

The quality of correctors is evaluated not so much via their energy efficiency as via the accuracy of formation of the pregiven wavefront.