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Updated: Jul 18, 2026
12:34
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
Published on: June 24, 2016
Zernike annular polynomials and atmospheric turbulence
Guang-Ming Dai1, Virendra N Mahajan
1AMO Laser Vision Correction Group, Santa Clara, CA 90245, USA. george.dai@amo-inc.com
Summary
This study analyzes imaging through atmospheric turbulence using annular pupils and Zernike polynomials. It provides analytical methods to calculate aberration coefficients, enabling better image quality assessment and correction for telescopes and optical systems.
Area of Science:
- Optics and optical engineering
- Astronomy and astrophysics
Background:
- Atmospheric turbulence significantly degrades image quality in optical systems.
- Annular pupils offer potential advantages in certain imaging scenarios but require specific analytical tools.
- Zernike polynomials are fundamental for describing optical aberrations.
Purpose of the Study:
- To develop analytical methods for characterizing aberrations in systems with annular pupils.
- To enable accurate calculation of image quality metrics like the Strehl ratio.
- To assess the effectiveness of aberration correction techniques.
Main Methods:
- Utilized Zernike annular polynomials and their Fourier transforms.
- Derived analytical expressions for aberration coefficient variance and covariance.
- Defined Zernike annular shape functions for analysis.
- Calculated Strehl ratio, phase structure function, and mutual coherence function.
Main Results:
- Provided analytical tools for understanding aberrations in annular pupil systems.
- Enabled quantitative assessment of image quality degradation and correction effectiveness.
- Demonstrated that circular pupils are a special case of annular pupils.
- Considered effects of long- and short-exposure imaging.
Conclusions:
- The developed analytical framework accurately characterizes imaging through atmospheric turbulence for annular pupils.
- The methods facilitate the design and optimization of adaptive optics systems.
- Offers a unified approach applicable to both annular and circular pupils.
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