Figure 3.3c: An Illustration of spot sizes for a real lens with triangular shaped
aberrations in the image corner at f/2,8.
470 nm 520 nm 660 nm 880 nm 470 nm 520 nm 660 nm 880 nm
Figure 3.3d: How the pixels of a sensor interpret the spot sizes in figure 3.3c.
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u Ex. 3: Variation in Spot Size and Pixel Output with
Wavelength in Real Lenses Including Aberrations
This is a more realistic example of a real lens design at f/2,8 as it
includes a more realistic explanation of the behavior at the center
and corner of the image circle. These figures include aberrations inherent
in even the highest quality lens design, and effects related
to manufacturing tolerances. Aberrations misplace information and
alter the shape of the spots produced, leading to spots that are not
rotationally symmetric; the effects of the aberrations combine to create
this shape (more about aberrations can be found in Section 3.5).
Note, aberrations are more pronounced at the corner of an image
than the center. A great difference is seen in the spots shown in Figures
3.1a and 3.1b versus that of Figures 3.3a and 3.3b. Figure 3.1 is a
theoretical demonstration, while Figure 3.3 uses a real lens. Notice
how aberrations influence the spot shapes in the image shown in
Figure 3.3c and 3.3d.
Figure 3.3a: An Illustration of spot sizes for a real lens with aberrations in
the center of the image at f/2.8.
Figure 3.3b: How the pixels of a sensor interpret the spot sizes in figure 3.3a.
Figure 3.3: Variation in spot sizes and pixel outputs with wavelength in real lenses that include aberrations.
u Ex. 4: Real-World Lens Performance.
Actual Images.
Figure 3.4 is an application image that shows the difference in performance
of two lenses with the same focal length (16 mm), f/# (f/2,8),
and FOV (100 mm, horizontal). These images show all the concepts
detailed in the sections on f/#, modulation transfer function (MTF),
and wavelength (Sections 2.1, 2.5, 2.6, respectively). The target is a
multi-element Star Target that allows the concurrent visualization of
a wide range of frequencies (resolutions) in common field points in
all directions. More details on this target and other targets for benchmarking
system performance can be found on pages 168-173.
The differences in performance are seen by examining closeup sections
of the FOV. Figure 3.4 shows the complete star target imaged
by the two lenses; the highlighted areas in the center, bottom middle,
and corner of the target are points of interest in the comparison between
the two different lenses. A Sony ICX625 monochrome sensor
with 3,45 μm pixels and a total resolution of 5 MP, and a white light
backlight illuminator are used in this example.
The comparisons shown in Figure 3.4 show Lens A’s superior performance.
The corner of the image shows a large difference in contrast;
it is noticeably more difficult to differentiate black and white in the
Lens B example. Additionally, the directionality of different aberrations
(mainly astigmatism) are prominent;
more detail can be seen associated with
lines propagating in the radial direction.
The close-up of the corner of the image in
Figure 3.4 (yellow boxes) presents an additional
concern where each black and white
line pair covers approximately 10 pixels total.
Compared to the resolvable portion at
the center of the image, the corner has reduced
spatial resolution (due to the blurred
circle covering multiple pixels) from
5 MP (2448 × 2050) near the center, to approximately
500 × 400 pixels in the corner,
which is below what a VGA sensor (640 ×
480 pixels) can reproduce. Even at reduced
sensor resolution, some lenses still struggle
due to design constraints and manufacturing
tolerances, seen by the different contrast
of each lens. The contrast level in the
yellow box for Lens A is 45% and 7% in the
Figure 3.4 Lens A (left) Lens B (right)
Lens A (left) Lens B (right)
Lens A (left) Lens B (right)
Lens A (left) Lens B (right)
Figure 3.4: A star target is imaged with two lenses (A and B) with the same focal length, f/#, yellow box for Lens B.
FOV, and sensor. The superiority of Lens A is apparent in all areas but is most pronounced
along the edge and in the corner of the image.
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