Biomedical Engineering Reference
In-Depth Information
IMAGE FORMATION: EXTENDED SOURCES
An extended source, such as a cross, is formed by an infinite number of point
sources. In Figure 9-8, we show the images formed by major meridians of a
+
3.00
+
2.00
×
180 lens (the same lens as in Figure 9-7) when a cross is located
at infinity.
First, consider the horizontal line of the object. The points that constitute this
line emit light rays with vertical and horizontal divergence. Those rays with verti-
cal divergence are focused by the vertical meridian to form a horizontal line at
+
20.00 cm. The upper and lower edges of this line are sharply focused by the ver-
tical meridian. In comparison, the left and right edges are blurred. Horizontally
diverging rays emitted by the horizontal line, which are focused at
+
33.33 cm, form
these fuzzy edges.
The vertical line of the object is also made up of points that emit vertically
and horizontally diverging rays. Those rays with horizontal divergence are
focused by the horizontal meridian at
33.33 cm to form a vertical line with
sharply focused left and right edges. In comparison, the upper and lower bor-
ders of this line are blurred. The vertical line's vertically diverging rays, which
are focused by the vertical meridian at 20.00 cm, form these blurred upper and
lower edges.
Where is the circle of least confusion for this extended object? As is the case for
a point source, the circle is dioptrically centered between the focused images of the
two principal meridians (i.e., the point where the
defocus
of the vertical meridian is
equal to the
defocus
of the horizontal meridian). For the example in Figure 9-8, this
corresponds to a linear distance of 25.00 cm.
+
Vertical lens
meridian in focus
Horizontal lens
meridian in focus
Object
Lens
Circle of
least confusion
+5.00 S
+3.00 D
+20.00 cm
+25.00 cm
∞
+33.33 cm
Figure 9-8.
A spherocylindrical lens focuses an extended object in two planes. See
the text for further details.
