Determination of the paraxial focal length using Zernike polynomials over different apertures

Tobias Binkele; David Hilbig; Thomas Henning; Friedrich Fleischmann

doi:10.1117/12.2251442

20 February 2017 Determination of the paraxial focal length using Zernike polynomials over different apertures

Tobias Binkele, David Hilbig, Thomas Henning, Friedrich Fleischmann

Proceedings Volume 10110, Photonic Instrumentation Engineering IV; 1011008 (2017) https://doi.org/10.1117/12.2251442
Event: SPIE OPTO, 2017, San Francisco, California, United States

Abstract

The paraxial focal length is still the most important parameter in the design of a lens. As presented at the SPIE Optics + Photonics 2016, the measured focal length is a function of the aperture. The paraxial focal length can be found when the aperture approaches zero. In this work, we investigate the dependency of the Zernike polynomials on the aperture size with respect to 3D space. By this, conventional wavefront measurement systems that apply Zernike polynomial fitting (e.g. Shack-Hartmann-Sensor) can be used to determine the paraxial focal length, too. Since the Zernike polynomials are orthogonal over a unit circle, the aperture used in the measurement has to be normalized. By shrinking the aperture and keeping up with the normalization, the Zernike coefficients change. The relation between these changes and the paraxial focal length are investigated. The dependency of the focal length on the aperture size is derived analytically and evaluated by simulation and measurement of a strong focusing lens. The measurements are performed using experimental ray tracing and a Shack-Hartmann-Sensor. Using experimental ray tracing for the measurements, the aperture can be chosen easily. Regarding the measurements with the Shack-Hartmann- Sensor, the aperture size is fixed. Thus, the Zernike polynomials have to be adapted to use different aperture sizes by the proposed method. By doing this, the paraxial focal length can be determined from the measurements in both cases.

Citation Download Citation

Tobias Binkele, David Hilbig, Thomas Henning, and Friedrich Fleischmann "Determination of the paraxial focal length using Zernike polynomials over different apertures", Proc. SPIE 10110, Photonic Instrumentation Engineering IV, 1011008 (20 February 2017); https://doi.org/10.1117/12.2251442

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