John Stack
Edmund Industrial Optics Div.
Edmund Scientific
Barrington, N. J.

System modulation transfer functions

Often, vision systems are built by simply picking a lens, a CCD imager, and some support electronics. Many neophytes assume that if they buy components with high-limiting resolution, they have the best solution. But that is not always the case. For many applications, high contrast at low spatial frequencies is more important. But purchasing more components or using those that are overspecified for the task can unnecessarily add to system cost.

To minimize these costs, consider the following optical system parameters, and how their application drives the specification of the system.

  • Field of view (FOV): The viewable area of the object under inspection. In other words, this is the portion of the object that fills the camera's sensor.
  • Working distance: The distance from the front of the lens to the object under inspection.
  • Resolution: The minimum feature size of the object under inspection.
  • Depth of field (DOF): The maximum object depth that can be maintained entirely in focus. The DOF is also the amount of object movement (in and out of focus) allowable while maintaining an acceptable focus.
  • Sensor size: The size of a camera sensor's active area, typically specified in the horizontal dimension. This parameter is important in determining the proper lens magnification required to obtain a desired field of view.

Because all of these items can't be discussed here in detail, consider only contrast, resolution, and their relation to a new metric called MTF or modulation transfer function. Resolution is a measure of the finest details observable by an imaging system. Imagine sampling a series of black and white squares or lines with separations that gradually become smaller with each pass. At some point, the imaging system cannot distinguish between any two adjacent lines. Resolution is thus often stated in terms of line pairs per mm (lp/mm).

This also introduces the concept of the spatial frequency of an imaging system. The more lp/mm the system can resolve, the higher the spatial frequency. Systems with high spatial frequency can produce crisper images because they can show object edges and finer features more clearly.

Contrast is a measure of the separation in light intensity between a white line and a black line and is defined as (Imax Imin)/(Imax + Imin). Object contrast is as important as object resolution because resolution is defined at a specific contrast.

The MTF describes this relationship between contrast and resolution. It is plotted by taking the contrast values produced by a series of different line pairs. The curve drawn from these points shows the modulation (contrast) at all resolutions (lp/mm). The limiting resolution of a system is often defined as the point where the MTF has fallen to 20% of the highest frequency value.

An imaging system's MTF is a composite of the MTFs of its component elements such as the lens, CCD imager, cables, monitor, and capture boards. The system's performance is typically limited by the poorest MTF element.

Before purchasing components, study and understand the measurement requirements of the application. For example, what is the resolution of the features to be measured? When imaging fine features, choose lenses and other elements with MTF curves that extend far to the right. On the other hand, applications requiring high contrast at low spatial frequencies, require components with MTF curves on the left.

For example, one of the most effective ways to increase image capture rates is to improve low-frequency contrast. In electronic terms this would be equivalent to raising signal-to-noise levels. Done properly the optical costs can be reduced by a factor of two or more. Understanding the trade-offs associated with the optical system will stave off putting components together by chance. By understanding and optimizing the entire system for the application, development time is cut drastically, time-to-market is reduced, and very possibly overall cost is reduced as well.