Modulation Transfer Function (MTF) and MTF Curves
This is Section 3.2 of the Imaging Resource Guide
MTF curves show resolution and contrast information simultaneously allowing a lens to be evaluated based on the requirements for a specific 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 Lens Performance Curves.
Figure 1 is an example of an MTF curve for a 12mm lens used on the SonyIXC625 sensor, which has a sensor format of 2/3" and 3.45μm pixels. 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 170mm 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.
Figure 1: MTF Curve for a 12mm Lens used on the SonyIXC625 Sensor
This curve provides a variety of information. The first thing to note is that the diffraction 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 field 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 associated with detail reproduction that is not in the center of the FOV. Due to aberrational effects, a lens will produce spots that are not completely round and will therefore have different 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 different contrast levels in different 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.
Comparing Lens Designs and Configurations
Example 1: Comparison of two different lens designs with the same focal length (fl), 12mm, at f/2.8
Figure 2 examines two different lenses of the same focal length that have the same FOV, sensor, and f/#. These lenses will produce systems that are the same size but differ in performance. In analysis, the horizontal light blue line at 30% contrast on Figure 2a demonstrates that at least 30% contrast is achievable essentially everywhere within the FOV, which will allow for the entire capability of the sensor to be well-utilized. For Figure 2b, nearly all of the field is below 30% contrast. This means that better image quality will only be achievable over a small portion the sensor. Also to note, the orange box on both curves represents the intercept frequency of the lower performance lens in Figure 2b with 70% contrast. When that same box is placed on Figure 2a, tremendous performance difference can be seen even at lower frequencies between the two lenses.
The difference between these lenses is the cost associated with overcoming both design constraints and fabrication variations; Figure 2a is associated with a much more complex design and tighter manufacturing tolerances. Figure 2a will excel in both lower resolution and demanding resolution applications where relatively short working distances for larger field of view are required. Figure 2b will work best where more pixels are needed to enhance the fidelity of image processing algorithms and where lower cost is required. Both lenses have situations where they are the correct choice, depending on the application.
Figure 2: MTF Curves for Two Lens Designs a (top) and b (bottom) with the same Focal Length, f/#, and System Parameters
Example 2: Two different high resolution lens designs with different focal lengths: 12mm and 16mm at f/2.8
Figure 3 examines two different high resolution lenses with focal lengths of 12mm and 16mm that have the same FOV, sensor, and f/#. By looking at the lens’s contrast at the Nyquist limit of Figure 3b (light blue line), a distinct performance increase can be seen when compared to Figure 3a. While the absolute difference is only about 10 - 12% contrast, the relative difference is closer to 33% considering the change from approximately 30% contrast to 42%. Another orange box has been placed on this graph, this time where Figure 3a hits 70% contrast. Note that the difference at this level is not as extreme as in the previous example. The tradeoff between these lenses is that the working distance for the lens in Figure 3b has an increase of about 33% but with a decent increase in performance. This follows the general guidelines outlined in 11 Best Practices for Better Imaging.
Figure 3: Two Different High Resolution Lens Designs a (top) and b (bottom) with Different Focal Lengths at the same f/# and System parameters
Example 3: Comparison of MTF for different f/#s of the same 35mm lens design
Figure 4 features the MTF for a 35mm lens design using white light at f/4 (a) and f/2 (b). The yellow line shows the diffraction-limited contrast at the Nyquist limit for Figure 4a on both graphs while the blue line denotes the lowest actual performance at the Nyquist limit of the same lens at f/4 in Figure 4a. While the theoretical limit of Figure 4b is far higher, the performance is much lower. This is an example of how a higher f/# can reduce the aberrational effects, greatly increasing performance of a lens, even though the theoretical performance limit is greatly reduced. The primary tradeoff besides resoultion is less light throughput at the higher f/#.
Figure 4: MTF Curves for a 35mm Lens at the same WD and different f/#s: f/4 a (top) and f/2 b (bottom)
Example 4: The Effect of Changing Working Distance on MTF
For Figure 5, working distances of 200mm (a) and 450mm (b) are examined for the same 35mm lens design at f/2. A large performance difference can be seen, which is directly related to the ability to balance aberrational content in lens design over a range of working distances. Changing working distance, even with refocusing, will lead to variations or reductions in performance as the lens moves away from its designed range. These effects are most profound at lower f/#s. More details on these effects can be found in Aberrational balancing of MTF in lens design and How Aberrations Affect Machine Vision Lenses.