Tunable spherical aberration in modified kinoform lenses

In this work, we propose a modified kinoform lens design capable of reproducing the effects of spherical aberration on the axial irradiance distribution under monochromatic illumination. The proposed lens introduces a novel phase distribution characterized by a sawtooth-like profile; however, unlike conventional kinoform lenses, its phase function exhibits a periodic dependence on the composite term αr⁴ − αr² + r², where r represents the radial coordinate in the lens plane and α is a tunable design parameter. By properly selecting the value of α, the generated phase profile can effectively emulate the influence of spherical aberration corresponding to a specific Zernike coefficient. Numerical simulations confirm that this approach accurately reproduces the irradiance patterns produced by refractive systems with controlled levels of spherical aberration. Furthermore, this design offers a flexible platform to intentionally introduce or correct aberrations in diffractive optical elements without increasing fabrication complexity. The proposed methodology can therefore be applied not only to compensate undesired spherical aberrations in imaging systems but also to engineer lenses with tailored focusing properties. In particular, the tunable phase function enables the generation of optical elements exhibiting an extended depth of focus, which could be advantageous in applications such as microscopy, optical trapping, and laser material processing.