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Tech Papers

Eliminate Image Distortion

by Greg Hollows, Vision Integration Partners Coordinator - Edmund Optics

DistortionTelecentric lenses offer some of the lowest levels of distortion on the market today.

Many inspection applications require very precise measurements. While software algorithms, via sub pixel interpolation, can provide very fine measurements, they cannot provide accurate or repeatable results if there is any variation in the image created. The choice of optics for a given application can mean all the difference between the success and failure of a measurement system. Luckily, by leveraging certain optical principles, telecentric lenses are available that can overcome variations in object position, height differences on an object and other issues that can occur leading to incorrect image information being processed by the software.

Perspective errors, also called parallax, are part of everyday human experience. In fact, parallax is what allows the brain to interpret the 3-D world. Humans expect closer objects to appear relatively larger than those placed farther away. The ideal way to think of this is to imagine someone standing on a set of railroad tracks. Immediately in front of them the tracks appear to be several feet apart because they are. As the individuals looks toward the horizon these same tracks appear to converge. People know that they actually do not come together at some point in the distance or the train would fly off the tracks, but this form of perception is critical. It is what allows people to drive a car and perceive whether another vehicle coming toward them is very close and requires immediate concern or if it is a great distance away not warranting much thought.

This phenomenon also is present in conventional imaging systems in which the perceived size of an object—its magnification—changes with its distance from the lens. Telecentric lenses optically correct for this occurrence so that objects remain the same perceived size independent of their distance, over a range defined by the lens. In the example of the railroad tracks, a telecentric lens would make the tracks appear to be the same distance apart regardless of whether they are right in front of the lens or at the horizon.

For many applications, telecentricity is required because it provides nearly constant magnification over a range of working distances, virtually eliminating perspective angle error. This means that object movement does not affect image magnification.
In a system with object space telecentricity, movement of the object toward or away from the lens will not result in the image getting bigger or smaller. In addition, an object that has depth or extent along the optical axis will not appear to be tilted. For example, a cylindrical object whose cylindrical axis is parallel to the optical axis will appear to be circular in the image plane of a telecentric lens. In a non-telecentric lens this same object will look like the Leaning Tower of Pisa—the top of the object will appear to be elliptical, not circular, and the sidewalls will be visible.

In systems with image space telecentricity, image plane movements to focus or intentionally defocus the system will not change the image size. An additional advantage of image space telecentricity is that it can provide extremely uniform image plane illumination.

These factors result in images that are highly representative of the object because the lenses optically compensate for variations in the distance to the object and position within the field of view. This allows the software to perform its function with a high degree of accuracy and repeatability, leading to a highly reliable system.

Tech Tips

  • Telecentric lenses can overcome variations in object position, height differences on an object and other issues that can lead to incorrect image information being processed by the software. 

  • For many applications, telecentricity is required be-cause it provides nearly constant magnification over a range of working distances, virtually eliminating perspective angle error.

  • The improvement in measurement accuracy resulting from the use of a telecentric lens can often mean the difference between success and failure.
Centroiding algorithms

Non-telecentric and telecentric imaging results

A number of qualities inherent in telecentric lenses may be considered disadvantages. First, the optical elements in the region of telecentricity—image side or object side—tend to grow in size. In the case of a doubly telecentric design, one telecentric in both object and image space, both the front and rearmost lens groups need to be bigger than the object and image respectively to provide an accurate image. On the surface this may not sound like a significant issue, but it is.

For example, consider an object 4 inches square that needs to be inspected with a telecentric lens. This would mean that the front element of the lens system will need to be significantly larger than the diagonal of the part to provide a non-vignetted field of view. The diagonal of this object is almost 6 inches, so the one lens must be more than 6 inches in diameter. This would be a very large, very heavy lens that would require special attention to mounting. Lens size also would have to be considered before a machine to house it is built. Additionally the cost for making a lens that large, while holding the tight optical tolerances needed to meet other image quality requirements, will drive up the price of the lens. A telecentric lens with a 2-inch field of view could cost between $900 and $2,000 depending on the feature sets needed. Double that size to a 4-inch field of view and the price will easily exceed $4,000. Double it again to 8 inches, and the cost will be well over five figures.

As with many other subjects, there is a common misconception concerning depth of field and telecentricity. The misconception about telecentric lenses is that they have a larger depth of field than ordinary lenses.

In reality, telecentricity does not imply large depth of field, which only depends on F-number and resolution. With telecentric lenses, objects still blur farther away from best focus, but they blur symmetrically, which can be an advantage. As long as the object’s features are within the telecentric working distance, the magnification will not change. In other words, features closer to the lens do not appear lar-ger than those farthest away.

Another area that should be considered when thinking of highly accurate measurements is the principle of distortion. Distortion again is inherent in the way humans see the world. Human eyes have about 2% distortion, but the brain compensates to allow people to go about their daily business without any real problems.

In the same way all lenses essentially have some element of distortion associated with them. If the distortion is too high it will need to be compensated for in the software to produce the required level of accuracy in the system. Understanding the varieties of distortion will help determine what compensation is required.

Distortion is a geometric optical error, or aberration, in which information about the object is misplaced in the image, but not actually lost. Distortion can come in a several different forms. There is monotonic distortion, which means that the distortion is consistently positive or negative from the center of the image out the edges. Monotonic distortion is of two forms: barrel (negative) and pincushion (positive).

Distortion that is not monotonic will actually alternate back and forth between negative and positive distortion as one moves from the middle of the field to the edges. Distortion that is not monotonic can occur from efforts made during the design of the lens to reduce overall distortion or from factors specifically related to the design type. Whether the distortion is monotonic or not, software can be used to factor out the distortion so that accurate measurements can be made of the image.  

Using measurement software and a dot target of known size, the distortion can be measured at different distances from the center of the image. Note: Distortion is not linearly correlated to the distance from the center of the field; this is true for monotonic and non-monotonic designs. After this is done, distortion can either be processed out of the image or taken into account during measurement. It should be kept in mind that removing distortion from an image and redrawing it is one of the most processor-intensive operations to complete. For high speed or high resolution applications removing distortion may simply not be an option because time may run out while recalculating the image before the next image is presented for analysis. For this reason many lenses are designed with extremely low levels of distortion to simply eliminate this software step.

Again, telecentric lenses offer an advantage here. For the most part telecentric lenses can offer some of the lowest levels of distortion on the market today, which adds to their ability to provide reliable vision systems.

With the ever-increasing demands associated with today’s machine vision systems, choosing all the correct components is more critical than ever. Optics are a critical part of conditioning the image for analysis and should not be overlooked. Whenever critical measurements need to be taken, optics need to be considered to produce a system that will truly provide the required results.

Greg Hollows is the vision integration partners coordinator at Edmund Optics (Barrington, NJ).  For more information, call (800) 363-1992.

As seen in the September 2007 issue of www.visionsensorsmag.com.

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