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Figure I.3 (a) Continuous and (b) quantized microrelief of the DOE

between zone structures depends on how the DOE phase function was calculated. If the solution to the problem has been found in an analytical form, the DOE microrelief will be regular, whereas the use of an iterative procedure with a stochastic initial estimate in solving the problem will result in irregularity of the DOE microrelief and the structure of zones.

The DOE microrelief can be either continuous (see Fig. I.3a) or multilevel (quantized, see Fig. I.3b).

The depth of DOE microrelief is a multiple of the wavelength for which it is calculated. For example, for the reflecting DOE, the maximum relief height h_max (see Fig. I.3a) is estimated using the relationship

(I.1)

where λ is the light wavelength and θ is the angle of light incidence on the DOE surface. For the transmitting DOEs, instead of Eq. (I.1) the following equality should hold.

(I.2)

where n is the refractive index of the DOE material.

The minimum modulation period of DOE microrelief (the minimum zone width) would be estimated in much the same way as the distance between the ring centres of neighbouring Fresnel zones [3], and is also specified by the angular size of the image formed by the DOE. Shown in Fig. I.4 is a phase DOE with radius R which, being illuminated by the light of wavelength λ, produces at the distance z a desired intensity distribution (image) characterized by the maximum linear size D in the transverse direction. Then, the minimum linear size d_min of modulation of the DOE microrelief can be found from

(I.3)

The parameter d_min of Eq. (I.3) specifies the resolution of the technological equipment used in the fabrication of the DOE.