Modulation transfer function (MTF), Spatial distortion and Spectral transmission
Lens resolving power: Modulation transfer function (MTF)
The modulation transfer function is the quantitative description of the image quality of a lens, considering all aberration. To define the MTF, the lens reproduces lines (grids) with different distances (spatial frequency in line pairs/mm). The loss of contrast due to the optical reproduction is shown in the MTF-graph for each spatial frequency. The more line pairs/mm that can be distinguished, the better the resolution of the lens.
The ideal lens would produce an image which perfectly matches the object, including all details and brightness variations. In practice this is never completely possible as lenses act as low pass filters. The amount of attenuation of any given frequency or detail is classified in terms of MTF and this gives an indication of the transfer efficiency of the lens. As a brief explanation, large structures, such as coarsely spaced lines, are generally transferred with relatively good contrast. Smaller structures, such as finely spaced lines, are transferred with low contrast.
For any lens there is a point at which the modulation is zero. This limit is often called the resolution limit and is usually quoted in line pairs per millimetre (lp/mm), or with some macro lenses in terms of the minimum line size in µm.
The MTF deteriorates as you move away from the centre axis of the lens towards the edges. This deterioration, often by a factor of 2 or 3, is an important consideration if the resolution is required across the entire image. MTF can also vary dependent on the direction of the lines at a point on the lens due to astigmatism, sometimes very significantly. This is often referred to as the T and S on some MTF charts relating to tangential (the MTF line pairs radiating from the centre of the lens) and sagittal (the MTF at 90 degrees to the T).
There are different ways to illustrate the contrast transformation in mathematical ways. However, two options are the most popular:
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The y-axis shows the contrast in percent. The x-axis indicates the location at the sensor (image height), while the zero value indicates the center of the sensor (e.g. Schneider datasheets).
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The y-axis shows the contrast in percent. The x-axis shows the spatial frequency in cycles per mm, while different graphs show the contrast at different distances from the center of the sensor. (e.g. SILL datasheets).
The following diagram illustrates how the MTF of a lens affects an image, as it is projected onto a sensor.
The optical resolving power of a lens is of great importance in imaging and machine vision applications. When selecting a lens, care has to be taken that the resolving power of the lens fits to the pixel size of the camera.
Pixel size varies from camera to camera, depending on the size and the resolution of the sensor (number of pixels). The smaller the pixels, the higher the resolution required from the lens.
It is important to consider the system as a whole when specifying resolution. Many modern megapixel cameras use small sensor sizes to reduce costs. However, these small sensors have very small pixels and thus need higher quality and therefore more expensive optics in order to resolve down to these smaller pixels. Sometimes it may be beneficial to select a more expensive camera with larger pixels that requires less demanding optics, which could reduce the overall system cost for some applications.
A conversion of sensor pixel size to lp/mm is possible with the following formula: Pixelsize [µm] = 1000 / (2*x), with x as the value of lp/mm
One final note when reviewing MTF curves from lens manufacturers. MTF is significantly affected by a number of factors such as the aperture setting. Comparing MTF graphs of lenses with different test settings could lead to the wrong conclusion. Please contact our experts when making selections, as we often have additional information to aid decisions.
Spatial distortion
In an ideal scenario, the image created by any lens would be an exact representation of the object in the field of view. Unfortunately all lenses suffer from distortion to different degrees. As the following diagram shows, the image produced is either stretched or compressed in a nonlinear way, making accurate measurements very difficult. Although there are software methods available to correct this, they cannot take the physical depth of the object into account and it is always preferable to choose a good quality low distortion lens rather than attempt to correct these errors in software.
As a general rule, a shorter focal length lens will have significantly more distortion than one with a longer focal length, as the light hits the sensor from a bigger angle. Using a more complex lens design, it is however possible to keep distortion low.
If distortion is likely to affect measurements in your application, it will be better to use a longer focal length lens and increase the working distance accordingly, although this will vary depending on the sensor size and any limited headroom may make this impossible. For this type of application a lens with reduced distortion and the same focal length might provide a solution.
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