Image Processing Reference
Figure 3.13 Layout of a pyramid sensor showing the creation of four subpupils in the
thogonal axes. Furthermore, it can be shown that by vibrating the pyramid with
suitable frequency, the light collected by adding two images together, after an
appropriate integration time, is directly proportional to the gradient of the wave-
front in that direction, i.e.,
st T W
where I ab indicates the addition of image a and b in Fig. 3.13, I 0 is the total intensity
of the light in the two images, T is the transmission function, F is the ratio of the foci
of the telescope and achromat, and s is a spatial coordinate.
3.5.3 Shack-Hartmann sensor
Hartmann testing of optics, particularly large optics, is one of the standard tools
used when figuring an optic element. The Hartmann test involves placing in front
of the optic a mask that has a series of holes through it in a specific pattern. Light
generated by a point source located inside the radius of curvature, thus beyond the fo-
cal plane of the optic, passes through each hole and is reflected back. The reflected
light is recorded inside the focus or image plane. The deviation of the spot positions
from the ideal identifies the regions where the image deviates from the ideal.
The drawback to the Hartmann test is that, with large or long focal-length op-
tics, the test requires a lot of room. In 1971, Shack (Platt and Shack 1971) provided
a modification of the Hartmann test by introducing lenses into the openings. Even-
tually, this evolved into a regular array of lenses used to analyze the wavefront. A
schematic outline of a Shack-Hartmann system is shown in Fig. 3.14.