Imaging Lenses Explained
Understand what you can expect to achieve from your imaging lens.
While specifying a lens for an imaging system can seem like a complex task, we learned in our last article on imaging lenses (www.qualitymag.com/articles/91115-imaging-lens) that the key is breaking the selection down into manageable pieces. Last time we discussed resolution, working distance, depth of field and field of view, and this time we will be diving into distortion, relative illumination and telecentricity. These specifications help to give a more complete understanding of how a lens will perform and what you can expect to achieve.
If you’ve used a lens (whether on your camera phone or machine vision system), then you are probably familiar with distortion. Distortion is a geometric error in the imaging of an object or scene, resulting from variations in magnification across the field of view. Distortion can present itself in a number of different ways; barrel, pincushion and keystone are the most common forms that you might run into.
Barrel distortion is how negative distortion presents itself and it gets its name from its shape: the results are the corners of the image experiencing a lower magnification than at the center of the image. Pincushion distortion is how positive distortion presents itself and it also gets its name from its distinctive shape. It results in the corners of the image having a higher magnification than is experienced at the center of the image. Lastly, keystone distortion, also known as tombstone distortion, is caused when the imaging path and the object that is being imaged are not perpendicular to one another. This results in an image that is wider on one side to more narrow on the opposite side (think a projector misaligned to a screen). Now the interesting thing about distortion is that in many cases it can be corrected for with minimal loss of information, because unlike other aberrations, high amounts of distortion can be present while maintaining good resolution. With the use of a calibration target and image processing software, the distortion can effectively be removed from a system. While distortion can have a strong effect on the way the image looks, it does not stop an image from being useful. So you should not rule out a lens just because it has distortion.
Another specification of importance is relative illumination and it can affect the overall system resolution. Relative illumination can be thought of as the percent of image roll-off from the center of the image to the corner. The point of highest transmission is defined as 100% and generally this occurs at the center, hence the reason it is “relative” illumination. As image height increases the illumination is shown as a percentage of the high point. Relative illumination typically manifests itself as a darkening of the image as you approach the corner. This phenomenon is caused by a vignetting, or blocking, of different light rays travelling through the imaging lens. This could be soft vignetting or hard vignetting; soft vignetting is a gradual rolling off of the illumination, whereas hard vignetting is a severe quick drop off of the intensity to being fully black. But what does this mean for the images that are being captured? A lesser maximum intensity at a given point means that the maximum contrast that can be achieved at that point will be lowered. The net result is that a relative illumination drop-off can result in a lower overall resolving power of the system. However, this is not a hard and fast rule, as lens designers will often allow certain amounts of vignetting of rays if it brings up the overall image resolution. The moral of the story is that relative illumination is helpful in determining how a lens can be expected to perform, but you cannot fully anticipate the resolving power of the system with it.
Now a specification that is important, and mainly talked of with telecentric lenses, is telecentricity. Telecentricity is a measure of how close to collimated (parallel) that the chief ray (the ray that passes through the aperture stop of the system) of a lens is to the optical axis of a system. A 0.0° telecentricity would be considered “perfect” and would result in an identical magnification across the entire image, regardless of the location of the object. This manifests itself as an image that is the same regardless of the working distance or depth of the object (as long as it can be brought into focus), so it is a very powerful thing when trying to make highly accurate measurements or alignments.
There are three possible types of telecentricity: object space, image space and bi-lateral (double) telecentricity. Object-space telecentricity occurs when the systems stop is at the front focal plane of the lens and it results in an entrance pupil that is located out at infinity. Image-space telecentricity is the opposite of object-space, the system stop is at the rear focal plane and the exit pupil is at infinity. Lastly, double telecentricity is when both image and the object space telecentricity are occurring, meaning that both the entrance and exit pupils are at infinity.
Now what are the practical ramifications of telecentricity? Picture a set of railroad tracks going off into the distance and to your eye they appear to be converging, but you know that they are not. This perspective error is called parallax and lenses with a high degree of telecentricity nearly eliminate it. This results in always having the same (accurate) measurement of different features, regardless of where in the field of view they are located. A “standard” telecentric lens would be an object-sided telecentric lens and would produce an image with a high degree of measurement accuracy. Now the advantages of using a double sided telecentric over just an object-space telecentric are that the accuracy will be even higher in gaging applications, you will have a more even illumination profile and your relative illumination will be superior. Lastly, image space telecentricity is not a feature that is generally touted on its own, but a lens with a high degree of image space telecentricity will have a very even illumination profile. This is due to the fact that the light rays are entering the sensor at a perpendicular angle, meaning there they do not suffer from the large amounts angular falloff that would be caused if the rays were at large angles at the corner of the sensor. Telecentricity is an important concept to understand and knowing when it’s important will allow you to solve a greater number of applications.
Familiarizing yourself with the more advanced specifications of a lens system will make choosing the right lens upfront far easier and will help eliminate guess work. If any of these specifications that you need are not published, you should still be able to expect the lens manufacturers to provide them to help aid in your decision making process. Identifying the best lens for your application and eliminating under performers (and high cost “over” performers) will save you time, money and frustration.