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Figure I.4 Linear characteristics of the DOE and the image

The quality of the DOE calculation and fabrication is evaluated via the range of deviation of the produced image from the desired one and via the fraction of light energy going onto the generation of the image. Quality of the DOE is determined by the parameters

• energy efficiency, the ratio of the light energy having come into a pregiven area to the entire light energy striking the DOE

• diffractive efficiency, the ratio of the light energy having come into the pregiven area to the light energy that has passed through the DOE or reflected from it

• image reconstruction error (root-mean-square deviation), the square root of the sum of squares of the difference of the produced and desired intensity, with averaging summation performed over the entire domain of definition of the image.

In the field of image processing, where high accuracy of the formation of wavefronts or intensity distributions is required, the principal characteristic of the DOE quality is the image reconstruction error. In the area related to the material treatment using high-power laser radiation, the emphasis will be on the high energy density in the area of pregiven image. For problems like this, one needs to use phase DOEs providing a fairly high energy efficiency (close to 100%). Therefore, for calculating different-purpose DOEs different methods are used: for optical data processing, methods for coding digital holograms have proved their suitability; whereas for purposes of laser treatment, iterative methods for calculating kinoforms or ray-tracing methods for computing focusators have found wide acceptance.

Technological stages of the DOE fabrication are shown in Fig. I.5.