We propose an analytical solution of the focal ring generated at the focus of a toric lens. The analytical field of the focal ring is used with a Fourier transform lens to generate a Bessel beam. A comparative analysis between the use of an illuminated annular aperture, an axicon, and a toric lens to generate a Bessel beam is performed, and the benefits and drawbacks of each are discussed. This highlights the advantages of using a toric lens with a Gaussian beam to produce a focal line of increasing intensity, which is advantageous for applications such as high depth-of-field microscopy.

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We present a study of the diffraction pattern according to Richards–Wolf for an aplanatic and stigmatic singlet based on an exact analytical equation. We are able to put emphasis on the maximum diameter and illumination pattern, which are the two parameters that influence the diffraction pattern and how to compute it. Designs of low- and high-NA aplanatic and stigmatic lenses are implemented to display these effects.

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