Zernike

Zernike may refer to the Dutch physicist Frits Zernike (1888–1966), renowned for phase-contrast microscopy, and to Zernike polynomials, a family of orthogonal polynomials used in optical wavefront analysis that bear his name.

Frits Zernike was awarded the Nobel Prize in Physics in 1953 for the invention of phase-contrast microscopy, a technique that converts phase shifts in light passing through transparent specimens into intensity variations, enabling visualization without stains or dyes. The method greatly expanded the ability to study living cells and tissues.

Zernike polynomials are defined on the unit disk and form an orthogonal basis for representing wavefront errors. Each polynomial is denoted Z_n^m and comprises an angular part e^{imθ} and a radial part R_n^m(r). They satisfy the conditions n ≥ 0, |m| ≤ n, and n − |m| is even. Because of their orthogonality, they provide a compact, interpretable representation of optical aberrations.

Common low-order terms correspond to piston, tip and tilt, defocus, astigmatism, coma, and spherical aberration, making the basis convenient for describing aberrations in lenses, telescopes, and especially the human eye. Zernike polynomials have become standard in wavefront analysis, optical testing, and adaptive optics.

Applications include wavefront sensing and correction in astronomy and ophthalmology, quality control in optical fabrication, and computational optics where modal decompositions aid in diagnosing and compensating aberrations. The polynomials continue to be a foundational tool in both theoretical and applied optics.