Image Processing Reference
In-Depth Information
Wavefront Sensing
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where
k
is the wave number,
I
is the intensity,
z
is distance,
∇
is the partial deriva-
2
tive in 3 space, and
∇
is the Laplacian operator.
3.5 Local Slope Measurement
3.5.1 Babcock detector
In 1953, Horace Babcock began studing how to remove dynamic aberrations in-
duced by the atmosphere from astronomical images. As a means of measuring the
effect of these aberrations, he placed a square mesh in front of a detector and then
focused the light from the telescope on to the mesh. The image spot moved as the
atmosphere changed, also moving the spot on the mesh and reducing the intensity
reaching the detector. This provided a measure of the motion of the spot induced by
the atmosphere. The detector design and sample output is shown in Fig. 3.12.
3.5.2 Pyramid sensor
A pyramid sensor is a high-efficiency sensor for low-order aberrations. It is a glass
pyramid that is placed at the focal plane of the telescope. A schematic diagram of
this sensor can be seen in Fig. 3.13. The shallow pyramid in conjunction with an
achromatic lens of appropriate focal length forms four images of the entrance pupil
of the telescope. It is easy to demonstrate that the linear combination of these im-
ages produces the equivalent of Foucault knife-edge test measurement or the com-
plement of a knife-edge test (depending on which images are added together). This
is valid in the orthogonal direction, giving the gradient of the wavefront in two or-
Figure 3.12
Babcock detector for star motion consisting of a screen in front of a de-
tector. A schematic of the detector output is shown on the right, corresponding to
image motion.
