Tilt (optics)

In optics, tilt is a deviation in the direction a beam of light propagates.

Overview

Tilt quantifies the average slope in both the X and Y directions of a wavefront or phase profile across the pupil of an optical system. In conjunction with piston (the first Zernike polynomial term), X and Y tilt can be modeled using the second and third Zernike polynomials:

X-Tilt:

a

1

ρ

cos

⁡

(

θ

)

{\displaystyle a_{1}\rho \cos(\theta )}

Y-Tilt:

a

2

ρ

sin

⁡

(

θ

)

{\displaystyle a_{2}\rho \sin(\theta )}

where

ρ

{\displaystyle \rho }

is the normalized radius with

0

≤

ρ

≤

1

{\displaystyle 0\leq \rho \leq 1}

and

θ

{\displaystyle \theta }

is the azimuthal angle with

0

≤

θ

≤

2

π

{\displaystyle 0\leq \theta \leq 2\pi }

.

The

a

1

{\displaystyle a_{1}}

and

a

2

{\displaystyle a_{2}}

coefficients are typically expressed as a fraction of a chosen wavelength of light.

Piston and tilt are not actually true optical aberrations, as they do not represent or model curvature in the wavefront. Defocus is the lowest order true optical aberration. If piston and tilt are subtracted from an otherwise perfect wavefront, a perfect, aberration-free image is formed.

Rapid optical tilts in both X and Y directions are termed jitter. Jitter can arise from three-dimensional mechanical vibration, and from rapidly varying 3D refraction in aerodynamic flowfields. Jitter may be compensated in an adaptive optics system by using a flat mirror mounted on a dynamic two-axis mount that allows small, rapid, computer-controlled changes in the mirror X and Y angles.