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Understanding and calculating a lens's performance can be a difficult
task. There are many variables that will affect a lens's performance,
including the laws of physics, design criteria and philosophy, and manufacturing
tolerances and errors. In order to obtain optimal system performance,
both optical designers and the end users have access to several
metrics that can be used to measure a lens’s performance. These
curves are often provided to help specify the correct lens.
Modulation Transfer Function (MTF)
The Modulation Transfer Function (MTF) curve is an informationdense
metric that reflects how a lens reproduces contrast as spatial
frequency (resolution) varies. These curves offer a composite view
of how optical aberrations affect performance at a particular set of
fundamental parameters dictated by the application’s need. It is important
to understand that changing almost any setting on a vision
system, including the fundamental parameters, will change the performance
characteristics of the curve. How MTF is calculated and
the limits of MTF are detailed in Section 3.2; Fundamental parameters
are defined in Section 1.2.
Figure 2.6 shows a common type of MTF curve, which describes
the modulus of the optical transfer function (contrast) vs. frequency
(resolution). How frequency is determined is covered in Section 2.1.
This curve provides a broad overview of a lens's performance at a
specific working distance, f/#, sensor size, and wavelength range.
In regards to our presentation, there are multiple colored curves
(black, blue, green, and red) that are displayed. The solid black line at
the top is the diffraction limit of the lens, and represents the absolute
limit of the lens performance. No matter how advanced the lens performance
becomes, it will never rise above this line. The additional
to download comprehensive datasheets
for all TECHSPEC® imaging lenses which
feature these performance curves.
colored lines on the curve that are below the diffraction limit represent
the MTF performance of the lens. They correspond to different
field heights (positions across the sensor) that are to be used. In
this case, there are three different field heights represented: on-axis
(blue), which represents the center of the image circle; 70% of the
diameter of the image circle (green), which represents about half the
image area; and the full image circle (red), which is the corner of the
image sensor that is in use. Note that some curves will contain more
field points for analysis.
The other noteworthy feature within the curves is the difference
between solid and dashed lines, represented on the curve by the letters
T and S, which represent the tangential (T: yz) and sagittal, or
“radial” (S: xz) planes of focus, respectively. These fields are different
due to aberrations that are caused by asymmetry, such as astigmatism,
which is why there is not a separate curve for tangential and
sagittal on-axis. If element tilts or decenters existed, the asymmetry
would cause there to be different T and S curves on-axis, as well.
The MTF curve is a map of contrast vs. frequency. Interpretation
of an MTF curve is highly application dependant.
f/# and working distance parameters for this MTF curve
Spatial Frequency in Cycles Per mm
Figure 2.6: An MTF performance curve illustrates contrast vs. frequency.
Depth of Field (DOF)
The Depth of Field (DOF) plot displays how the MTF changes as details
of a specific size (resolution, given as a frequency) move closer to, or farther
away from, the lens without refocusing. In other words, how the contrast
changes above and below the specified working distance. Figure 2.7
shows the type of DOF curve provided in TECHSPEC® lens datasheets.
The depth of field plot shows the differences in MTF based on constant
field heights (the different colors of the individual curves) for a
fixed spacial frequency on the image side, with the diffraction limit
left out. As the MTF is sampled at different positions along the optical
axis, defocus is introduced into the system. In general, as defocus is
introduced, the contrast will decrease. The horizontal line toward the
bottom of the curve represents the depth of field at a specific contrast
level (in this case, 20%). The generally accepted minimum contrast for
a machine vision system to maintain accurate results is 20%.
MTF: f/2.8, 218mm WD, #63-777
Dashed Color Lines: Tangential plane MTF
Solid Color Lines: Sagittal plane MTF
pixel limited resolution by pixel size
15 - 20% contrast is typically the
minimum contrast for acceptable
field height (multiply by 2
for image circle diameter)
Lens Stock Number
Section 2.6: Lens Performance Curves