Analysis of Intensity Distribution in the Image Plane for Various Focus Errors in an Optical System Illuminated by Coherent Light Utilizing a Circular Aperture

Abstract

One common kind of aberration in optical systems that can seriously impair the quality of the images that are taken is focus errors. The objective of this study is to assess the impact of focus errors on the distribution of intensity in the image plane of the optical system, which is composed of a circular area nature. The Zernike coefficient W20 is used to compute quantitatively defined focus errors, and the results are verified both experimentally and through simulations that use the Fresnel diffraction integral. In excellent agreement with the theoretical prediction, the measurement results confirm that the fault-free optical system generates a central peak of higher intensity (Airy disk) surrounded by a Pearly ring structure of lower intensity (Airy rings). The phenomenon of Airy rings becomes more noticeable as the central peak tends to smear more and lose intensity from W20 = 0.25 to W20 = 1.25. The image quality consequently deteriorates over time. With an NRMS error of less than 0.1 for every position error condition, the experimental results exhibit a trend that is comparable to the modulated (simulated) intensity distributions. Low-quality imaging is caused by focus errors, which play a critical role in the design, optimization, and characterization of optical systems. This offers a variety of approaches to enhance computational imaging methods and create the best possible optical designs.

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