Section 3: Understanding Lens
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Section 3.1: Diffraction Limit:
Every lens has an absolute upper performance limit dictated by the
laws of physics. This limitation is controlled by the working f/# of
the lens and the wavelength(s) of light that pass through the lens.
Known as the Di raction Limit, this limitation is given in line pairs/
mm and determines the theoretical maximum resolving power of the
lens. Even a perfect lens that is not limited by design will be di raction
limited. This limit is the point where two Airy patterns (Section 2.5) are
no longer distinguishable from each other. To calculate the di raction
limit, a simple formula that relates it to the f/# of the lens and the
wavelength of light can be used. Learn more about f/# in Section 2.4.
Diffraction Limit (lp/mm) = 1000 μm/mm
f/# x wavelength (in μm)
After the di raction limit is reached, the lens becomes incapable of
resolving greater frequencies. The di raction limit detailed in Table 3.1
shows contrast at 0% for given frequencies. These numbers may appear
rather high, but are strictly theoretical – a number of other practical
factors must also be considered. First, as a general rule, imaging
sensors cannot reproduce information at or near 0% contrast. Due to
inherent noise, contrast generally needs to be above 10% to be reliably
detected on standard imaging sensors. To avoid imaging complications,
it is recommended to target 20% contrast or higher at the application’s
critical lp/mm resolution. Additionally, lens aberrations and variations
associated with manufacturing tolerances also reduce performance.
Modulation Transfer Function (MTF) curves are used to determine
whether a lens will e ectively utilize a sensors capabilities and ful ll the
desired application’s requirements.
f/# 0% Contrast Limit (lp/mm) @ 0,520 μm
Table 3.1: The di raction limit calculated at di erent f/#s for
0,520 μm light (green light).
Section 3.2: Modulation Transfer
Function (MTF) and MTF Curves:
MTF curves show resolution and contrast information simultaneously allowing
a lens to be evaluated based on the requirements for a speci c application
and can be used to compare the performance of multiple lenses.
Used correctly, MTF curves can help determine if an application is actually
feasible. For information on how to read an MTF curve, see Section 2.6.
Figure 3.1 is an example of an MTF curve for a 12 mm lens used on
the Sony ICX625 sensor, which has a sensor format of ” and 3,45 μm
pixels. Sensor format is described in the camera section on Pages 148-
151. The curve shows lens contrast over a frequency range from 0 lp/
mm to 150 lp/mm (the sensor’s limiting resolution is 145 lp/mm). Additionally,
this lens has its f/# set at 2,8 and is set at a PMAG of 0,05X,
which yields a FOV of approximately 170 mm for 20X the horizontal dimensions
of the sensor. This FOV/PMAG will be used for all examples
in this section. White light is used for the simulated light source.
This curve provides a variety of information. The rst thing to note is
that the di raction limit is represented by the black line. The black line
indicates that the maximum theoretically possible contrast that can be
achieved is almost 70% at the 150 lp/mm frequency, and that no lens
design, no matter how good, can perform higher than this. Additionally,
there are three colored lines: blue, green, and red. These lines correspond
to how this lens performs across the sensor in the center (blue),
the 0,7 position at 70% of the full eld on the sensor (green), and the
corner of the sensor (red), respectively. It is clearly shown that at lower
and higher frequencies contrast reproduction is not the same across the
entire sensor and, thus, not the same over the FOV.
Additionally, it can be seen that there are two green and two red lines.
These lines represent the tangential and sagittal contrast components
MTF: f/2.8, 150mm WD, 12mm FL
Spatial Frequency in Cycles per mm
Figure 3.1: MTF curve for a 12 mm lens used on the Sony ICX625
associated with detail reproduction that is not in the center of the
FOV. Due to aberrational e ects (Section 6, pages 36-38), a lens will
produce spots that are not completely round and will therefore have
di erent sizes in the horizontal and vertical orientation. This size
variation leads to spots blending together more quickly in one direction
than the other, and produces di erent contrast levels in di erent
axes at the same frequency. It is very important to consider the
implications of the lower of these two values when evaluating a lens
for a given application. It is generally advantageous to maximize the
contrast level across the entire sensor to gain the highest levels of
performance in a system.