chapter 4, Ocular Wavefront Sensing and Reconstruction

Excerpt

Wavefront sensing and reconstruction are essential parts for wavefront-driven vision correction since they were first applied by Liang and coworkers[1] for ocular aberration measurement. Originated from astronomical applications, wavefront sensing is an indirect technique to measure the aberrations of an optical system, such as a telescope with an optical path through the atmospheric turbulence. Similarly, the technique is used to measure the ocular aberrations of the entire eye, consisting of the cornea, the crystalline lens, and the transparent media along the visual path. As will be discussed in the next section, when a wavefront has a local slope, the image formed on the focal plane has a shift. This image shift is linearly proportional to the average wavefront slope of a particular area. Furthermore, it is independent of the wavelength. For ocular aberration measurements, however, the image shift depends on the wavelength due to ocular chromatic aberrations, as most commercial aberrometers use an infrared light source for wavefront sensing to achieve patient comfort. Consequently, about half a diopter defocus adjustment is required.

Once the wavefront sensing is completed, a set of wavefront local slopes are measured. The entire ocular wavefront can be reconstructed from this set of local slopes by means of a least-squares fit. One such approach is the zonal reconstruction, where the wavefront is directly fitted from the neighboring local slopes using a least-squares criterion. The other approach is the modal reconstruction, where the wavefront is represented by a set of basis functions, and the wavefront is fitted by a matrix formulation that is also least-squares based.

4.1 Wavefront Slopes

Wavefront slope is the key to wavefront sensing. Figure 4.1 shows two simple examples of wavefront slopes and their related image shifts. Figure 4.1 (a) shows how a geometrical ray bends from its original direction of propagation by a prism, with an image shift linearly proportional to the angle of bending and the distance of the image plane, or Δx = dtanϕ. Similarly, in Fig. 4.1 (b), a wavefront is imaged through a lens on the image plane, and an image shift can be observed due to the local wavefront slope over the lens aperture. Again, the image shift is linearly proportional to the angle ϕ and the focal length f, or Δx = ftanϕ.