Telecentric Lenses: basic information and working principles
In recent years dimensional measurement applications using machine vision technologies have become very popular.
Improvements in cameras, software and illumination components have made it possible to reach accuracies sometimes even better than contact and laser-based methods.
Successful machine vision integrators are increasingly aware that quality optics produce superior system performances and Telecentric Lenses are required for any dimensional measurement imaging application.
Software engineers requiring precise measurement of mechanical parts need high contrast images with the lowest possible geometrical distortion.
Perspective effects, causing change of magnification when the object is not precisely positioned or is highly 3-dimensional, must also be minimized or eliminated.
Besides image processing problems, vision system designers must take in account that common, entocentric optics introduce several factors which limit measurement application accuracy and repeatability:
- magnification changes, due to object displacement
- image distortion
- perspective errors
- poor image resolution
- object edge position uncertainty, due to lighting geometry
Telecentric lenses reduce or even cancel most of these problems, and for this reason have become a "must" for all those developing high accuracy gauging applications.
Img 1: working principle of different types of lenses.
Now we'll try to explain how telecentric lenses work and why all of the above mentioned effects are reduced or eliminated.
A - Magnification Constancy
In measurement applications an orthonormal view of the object (i.e. where no image of the object sides is present) is frequently needed so that correct linear measurements may be performed.
Furthermore, many mechanical parts cannot be precisely positioned (i.e. because of vibrations) or a measurement must be performed at different depths or additionally the object thickness (and therefore the object surface position) may be variable; nevertheless software engineers need a perfect correlation between imaged and real dimensions.
 |
| Img 2: on the left an image of an internal spline on a cylindrical object taken with a telecentric lens (top) and the same object viewed by an ordinary lens (bottom). On the right an image of two identical machine screws 100 mm apart, taken with a telecentric lens (top) and an ordinary lens (bottom). |
Common lenses give a different magnification at different conjugates: as a consequence, the size of the image of the same object placed in different positions changes almost proportionally with object to lens distance, as everybody can easily experience with his eyes, taking pictures with a photographic camera or with any vision system equipped with an entocentric lens.
Img 3: standard lenses generate images of different sizes when an object changes its distance from the lens (in the drawing "s", the first optical conjugate, by definition). On the other hand, objects of different sizes can be viewed as if they had the same dimensions, if they subtend the same viewing angle.
With telecentric lenses the image size remains almost unchanged when the object distance changes, provided the object to be inspected stays within the given field depth/telecentric range.
This is due to the particular path of the rays within the optical system: the objective collects from the object to be imaged only cones of rays whose barycentric ray (or principal ray) is parallel to the opto-mechanical main axis (for this reason the front lens diameter is at least as large as the object field diagonal). This is made possible because the stop aperture is placed at the focus of the front optical group: this causes the entrance pupil to be seen, by the rays coming into the optics, as if it would be placed at the infinity. For this reason these lenses are called telecentric, because the pupil aperture (the center of an optical system), is virtually placed at infinity (tele-, which means far, from ancient Greek).
Img 4: in a telecentric system rays get into the optics only with an almost parallel-to-the-axis path.
Just to get the feeling of the difference between the two objective kinds, let suppose, for instance, a common lens of a focal length f = 12 mm, interfaced to a 1/3" detector, looking at an object of height H = 20 mm, at a distance s = 200 mm.
Assuming object is moved from its original position, of ds = 1mm, the change of its dimension appear to be about:
DH = (ds/s)·H = (1/200)·20 mm = 0,1 mm
In a telecentric lens the magnification change is determined by the telecentric slope: good telecentric lenses show an effective telecentric slope of about 0,1° (0,0017 rad); this means that the object dimension appear to change of only 0,0017 mm for each displacement ds of 1 mm. Thus, with telecentric lenses the magnification error is typically 1/10 to 1/100 in comparison with common lenses.
Img 5: the telecentric slope determines the magnification change.
As a consequence of the incoming ray path, the front lens of a telecentric lens must be at least as large as the object largest dimension; for this reason telecentric lenses are larger, heavier and therefore more expensive than common optics.
Img 6: a very big lens suitable for a field
of view of over 400 mm (diagonal).
B - Low Distortion
Distortion is one of the worst problems limiting measurement precision, because all lenses suffer at least of some distortion, and often even a single pixel of difference between the real image and the expected image is critical.
Distortion is simply defined as the percentage difference between the distance from the image center of real image point and the distance that would be measured in complete absence of distortion; it can be viewed as the deviation between "real world" dimensions and their representation projected by the lens onto the camera's detector. For instance, if the corner of the image of a square has a distance from the image center of 198 pixels, but a distance of 200 pixels would be expected in absence of distortion, the distortion, at that point, is
Dist = (198-200)/200 = -2/200 = 1%
Positive radial distortion is also called "pincushion" distortion, negative radial distortion is called "barrel" distortion: note that the distortion depends on the radial position and can also change of sign.
The distortion can be also viewed as a geometrical transformation from the 2D space of the real world to the virtual 2D space of the image created by the lens; as this transformation is not perfectly linear but is approaching 2nd or 3rd degree polynomials, the image becomes slightly stretched and deformed.
Img 7: Pincushion and barrel distortion. On the right the graph
of the distortion correction of a telecentric lens of Opto Engineering.
Common optics show distortion values ranging from some percent to some tens percent, making precise measurement really difficult; the correction of the distortion is made even more complicated by the absence of telecentricity. The presence of distortion is due to the fact that the human eye can easily compensate a distortion of 1, 2% and, as most of the optics used in machine vision has been developed for video-surveillance or photography applications, that is typically enough.
In some cases, like in fish eye lenses or webcam-style lenses, distortion is expressly introduced to help the lens to work on large angles and to guarantee an even illumination of the detector (distortion is helpful in reducing cosine to the fourth law effects).
Telecentric lenses normally show a very low distortion degree, in the range of 0,1%: this means that the maximum error due to distortion should be less than a pixel of an high-resolution camera (0,6 pixels on the semi-diagonal of a VGA).
Few people know that the distortion depends upon the distance of the object, not only upon the optics itself. For this reason it is very important that the nominal working distance be maintained and no focusing optical groups be present in the lens.
In any case, in most of applications, distortion has to be software calibrated: a precise pattern (whose geometrical inaccuracy should be less than 10% of the needed measurement accuracy) must be placed at the center of the field depth; then the distortion must be computed in several image points and the software algorithm must interpret the native image and transform it into a distortion-free image. To avoid non-axially symmetric distortion a lot of care has to be taken in order to provide a fine perpendicular alignment between the lens and the object to be inspected.
Img 8: on the left an image of a distortion pattern taken with a telecentric lens, where no radial or trapezoidal distortion is present. In the middle the image of a lens showing strong radial distortion. On the right an example of trapezoidal distortion.
Trapezoidal distortion (better known as "keystone" or "thin prism" effect) is also an important parameter to be minimized in a lens as it is asymmetric and very difficult to calibrate out in software
C - Perspective Errors limitation
When common optics are used to image 3D objects (non completely flat objects), as was said above, far objects will show smaller images than close objects. As a consequence, when an object like, for instance, a cylindrical cavity is imaged, the top and the bottom circular edges seem to be concentric even if the two circles are perfectly identical.
On the contrary, by means of a telecentric lens, the bottom edge disappears because the top standing circular edge covers it.
Img 9: Perspective error due to common optics (left image) and perspective error absence (right image) with a telecentric lens.
This effect is due to the specific path of the rays: in the case of common optics the geometric information "parallel" to the main optical axis shows a component on the detector plane direction, while in a telecentric lens this perpendicular component is not present at all.
You can think as if common lenses would build a correspondence between the 3-dimensional object space and the 2-dimensional detector (image) space: in the case of a telecentric lens the third dimension in object space is not displayed.
Img 10: Common optics (left) project longitudinal geometrical information onto the detector, while telecentric lenses are not.
D - Good image resolution
Image resolution is conveyed as CTF (contrast transfer function), a parameter describing the contrast ratio at a given spatial frequency on the camera detector plane, expressed in lp/mm (line pairs per millimeter).
Img 11: good and bad contrast achieved with optics of varying CTF looking at a standard USAF test pattern.
Frequently, inexperienced integrators choose cameras with huge amounts of small pixels paired with cheap, poor resolution lenses resulting in a blurry image. The resolution provided by telecentric lenses is typically compatible with even the smallest pixel size.
E - No edge position uncertainty
Very often back lighting the subject makes it difficult to determine the exact position of the object edge. This can happen because the signal of the bright pixels of the background tends to be overlapped to that of the dark pixels of the object edges, but if the object is highly 3D, another effect can strongly limit the measurement precision.
As shown in figure 12, rays coming from the peripheral zones of the object, being close to the object edges , can be reflected by the object itself (almost any material approach a mirror if the incidence angle is large) and can be interpreted as rays directly coming from the back of the object. This means that some marginal slices of the object can disappear making the measurement really imprecise and unstable.
 |
 |
| Img 12: border effects in a common imaging lens are strongly reduced by means of a telecentric lens. |
This effect can be efficiently limited if a telecentric lens is adopted, because, if the f-number is not too low (the aperture too "open"), the only rays which can be reflected by the object surface and come into the optics are those parallel or almost parallel to the optical main axis. As these rays are effected by very small deflections, the reflection on the object surface doesn't compromise too much the measurement accuracy.
To completely avoid this kind of problem collimated (often called "telecentric") illuminators can be interfaced to telecentric lenses taking care to match the lens aperture and FOV. With this option, all the light coming out from the illuminator is collected by the lens and delivered onto the detector, allowing extremely high signal-to-noise ratios and incredibly low exposure times. On the other hand, the only rays coming into the imaging lens are those that are expected to and no problems occur at the borders.
Img 13: Collimated or telecentric illumination projects into the
imaging telecentric lens only the rays expected to.
F - Benefits of Bi-Telecentric Lenses
1. Better Magnification Constancy
Common optics and normal telecentric lenses tend to have a worse behavior because the ray cones have different inclinations depending upon the field position and the optical system is not symmetric, as well. As a consequence of this, the spot generated by the intercept between the ray cone and the detector plane has a different shape and dimension at the image center and at the image borders (the point spread function changes and becomes non-symmetrical and the spot larger and elliptic).
In addition, when the object is displaced through the field depth, the spot generated by rays point moves back and forth over the image plane, causing a small change in magnification which is not suitable for the most accurate gauging applications.
For this reason non bi-telecentric lenses show a lower magnification constancy although their telecentricity, measured only in the object space, might be very good.
 |
 |
| Img 14: In a bi-telecentric lens (right) the ray cones intercept the image sensor in a way independent on the field position; in a non image space telecentric lens (left) this doesn't happen. |
2. Increased Field Depth
Field depth basically depends upon the optics F-number: the largest the f-number (that is the smaller the optics aperture) the larger the field depth, with a quasi-linear dependence. This happens because field depth is the maximum object position departure accepted from the best focus situation. Behind this limit the image resolution isn't any more accepted, because the rays coming from an object point don't intercept the detector surface within a sufficiently small "spot", more pixels are carrying by the same object information (blur) and the focusing becomes bad.
The effect of closing the lens diaphragm, which means raising the f-number, is lowering ray cones divergence; the rays spread is consequently lower, allowing a smaller spot size onto the detector. Over a certain F-number, the resolution becomes worse instead of increasing; this is due to diffraction effects which are limiting the minimum lens aperture size when a good contrast image is needed.
Image side telecentricity or bi-telecentricity is beneficial in maintaining a very good image contrast even when looking at very thick objects; the reason of this is the symmetry of the optical system which is helpful in maintaining the symmetry of the ray spots and, as a consequence, of the blur. This results in a field depth which is perceived a s being 20-30% larger in comparison with non bi- telecentric optics.
Img 15: Image of a thick object viewed through its field depth.
3. Even Detector Illumination
The even illumination of the detector, achieved by means of bi-telecentricity, is useful in several applications such as LCD, textile, and printing quality control.
When dichroic filters have to be integrated in the optical path for photometric or radiometric measurements, bi-telecentricity assures that the axis of the ray fan strikes the filter normal its surface preserving the optical band-pass over the entire camera detector surface.
Img 16: A double-sided telecentric lens is interfaced with a tunable LCD filter in order to perform high resolution colour measurements. The image-side telecentricity ensures that the optical bandpass is homogeneous over the entire filter surface and provides an even illumination of the detector when the object is evenly illuminated.
G - SOME APPLICATIONS OF TELECENTRIC LENSES
Tubes and shafts measurement and cylindric part gauging |
Engine and other precision mechanical parts dimensional measurement |
Holed metal sheets and objects gauging |
Screw, Nut and Threaded Object control and gauging |
Spring dimensional measurement and control |
O-ring and Plastic Parts dimensional control |
Glass Parts: tubes, vials, capslules, ... |
General purpose, off-line dimensional measurement benches and machine vision-based gauging devices |
|
H - SUMMARY: When Telecentric lenses must be used
- Whenever a thick object (thickness > 1/10 FOV diagonal) must be measured
- When different measurements must be carried on different object planes
- When the object to lens distance is not exactly known or when it cannot be previewed
- When holes must be inspected or measured
- When the profile of a piece must be extracted
- When the image brightness must be almost perfectly even
- When defects can be detected using a directional illumination and a dircetional "point of view"
Main Links related to telecentric lenses:
» Telecentric Lenses for Matrix Detectors up to 2/3"
» Telecentric Lenses for Large Detectors
» Telecentric Lenses for Line Detectors
» Telecentric Lenses Brochure (.pdf)
|
