Astigmatism
figure
1. Astigmatism - the green parts of the object are focused on the green
plane while the red part of the object is focused on the red plane
Image Object Where does astigmatism come from? The difference between these focal
lengths becomes greater with a greater difference in angle, which happens as
the object moves further off axis. This
difference is also affected by the power of the lens. Between the primary image and the
secondary image, there is a location where the spread of meridional and the
spread of sagittal rays is exactly the same.
The image at this location is an even spread out circle of the original
point object. This location is called
the circle of least confusion (figure 6). The circle of least confusion
increases in diameter as the astigmatism increases (which occurs as the object
moves further off axis). This means
that the image will continue to lose definition as the object moves off axis. If a round
object with a radial grating is imaged through a spherical lens, the circle
around the grating will be in focus at a different location than the grating. This occurs
because when you image a point off axis, the point forms an ellipse on the
lens, with the major axis radial to the lens and the minor axis
tangential. The radial projection is
therefore in the meridional plane and the tangential projection is in the
sagittal plane. The difference in focal
lengths between the meridional (tangential) and sagittal planes causes the
difference in locations where the circle focuses and where the grating focuses. What does astigmatism look like? Meyer-Arendt, Jurgen, Introduction to
Classical & Modern Optics, 4th edition, New Jersey: Prentice Hall,
1995. Pedrotti, Frank & Leno Pedrotti, Introduction
to Optics, 2nd edition, New Jersey: Prentice Hall, 1993.
Astigmatism is the aberration
that occurs when rays from an off-axis object that strike in different planes
are imaged at different distances. The
parts of an object that are radially outward from the optical axis are focused
in a different location than the parts of the objectthat are tangental to the
axis (figure 1).
As an object point is moved off
axis, it's incident rays start to strike the lenses asymmetrically (figure 2).
The incident rays strike in two planes
on the axis: the meridional plane and the sagittal plane (figures 3 and
4). The meridional plane is the plane
that contains both the optical axis and the chief ray. The sagittal plane is perpendicular to the
meridional plane, and contains the chief ray.
As
the object is moved off the axis, the sagittal plane tilts because the chief
ray's slope is altered (figure 5). The
slope of the ray can cause the incident rays to strike at different angles on
the sagittal and meridional planes.
This angle at which the rays strike affects the focal length, creating
two distinct focal lengths, one for the sagittal plane and one for the
meridional plane.
The
rays in the meridional plane focus first.
However, because the rays in the sagittal plane are not yet focused, the
image is a line in the sagittal plane called the primary image (figure 6). Moving beyond this line, the meridional rays
spread out again and the sagittal rays converge creating the image of a line in
the meridional plane called the secondary image (figure 6).