In optics, the term tilt simply refers to a deviation in the direction a beam of light propagates. Tilt quantizes 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: $a\_1\backslash times\; \backslash rho\; \backslash cos(\backslash theta)$

Y-Tilt: $a\_2\backslash times\; \backslash rho\; \backslash sin(\backslash theta)$

where $\backslash rho$ is the normalized radius with $0\; \backslash le\; \backslash rho\; \backslash le\; 1$ and $\backslash theta$ is the azimuthal angle with $0\; \backslash le\; \backslash theta\; \backslash le\; 2\backslash pi$.

The $a\_1$ and $a\_2$ 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.

Tilt 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. This is often termed a "fast steering mirror", or FSM. A gimbaled optical pointing system cannot mechanically track an object or stabilize a projected laser beam to much better than several hundred microradians. Buffeting due to aerodynamic turbulence further degrades the pointing stability. However, light has no appreciable mass, and by reflecting from a computer-driven FSM, an image or laser beam can be stabilized to single microradians, or even a few hundred nanoradians. This almost totally eliminates image blurring due to motion, and far-field laser beam jitter. Limitations on the degree of line-of-sight stabilization arise from the limited dynamic range of the FSM tilt, and the upper frequency the mirror tilt angle can be changed. Most FSM's can be driven to several wavelengths of tilt, and at frequencies exceeding one kilohertz.

As the FSM mirror is optically flat, FSM's need not be located at pupil images. They are in fact located in the optical path prior to a deformable mirror (which must be located at a pupil image) to stabilize the position of the pupil image on the deformable mirror and minimize correction errors resulting from wavefront shearing.

References

• Malacara, D., Optical Shop Testing - Second Edition, John Wiley and Sons, 1992, ISBN 0-471-52232-5.

Optics