The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication [Opt. Lett. 16, 523 (1991)]. Within the presented formulation good agreement is achieved between the geometrical-optics prediction and the numerically evaluated diffraction integral.

We show that the apodized annular-aperture logarithmic axicon preserves excellent uniformity of the on-axis intensity, energy flow, and lateral resolution. Numerical evaluation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions. Once again the geometrical law of energy conservation turns out to be a useful tool in designing axicons.

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