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telecentric lens has the uniqueproperty of maintaining aconstant magnification over aspecific range of object dis-tances. This property lets in-spection systems make accu-

rate dimensional measurements of three-dimensional (3-D) parts and components ofdiffering heights. Telecentric lenses actuallytake advantage of an old concept that only re-cently has found successful application in op-tical metrology.

When you use a conven-tional lens to inspect 3-Dparts, an inherent distortionof the image results. Thechange in magnification withdistance in a conventionalimaging system is so funda-mental that people generallytake it for granted. After all,our eyes are a typical conven-tional imaging system. We ac-cept that an object placed far-ther away appears smallerthan the same object close athand. The image of the chess-board in Figure 1a illustratesthis effect, called perspective.

We know the squares in achessboard all have the samesize. Yet, in the image, thesquares farther away appearsmaller than those closer tothe observer. This perspective

gives the imagethe appearance ofdepth. But if youweren’t familiar with achessboard, you wouldn’tbe able to determine from theimage whether the smaller squaresare farther away or are, in fact, actuallysmaller. Likewise, conventional optical sys-tems cannot accurately measure dimensionson 3-D objects.

FIGURE 1 a) The side view of a chessboard through aconventional wide-angle lens shows the effect of per-spective. b) The same chessboard viewed through atelephoto lens shows less of a perspective effect. Tele-centric lenses produce similar results.

Ronald A. Petrozzo and Stuart W. Singer Schneider Optics Hauppauge, NY

The proper lens let

inspection systems

accurately

dimension 3-D

parts.

Telecentric lensessimplify non contact metrology

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(a)

(b)

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T h eimage in

Figure 1b wastaken using a telephoto

lens—a lens with a long focal length—placed much further away from thechessboard. The longer distance mini-mizes, but doesn’t eliminate, the per-spective differences between the frontand rear squares on the board. Theimage in Figure 1b approaches a tele-centric perspective, in which no differ-ence would appear in the sizes of thefront and the back squares in the image.

A true telecentric lens produces im-ages in which the foreground and back-ground images have the same magnifi-cation. If they have the same physicaldimensions, they will maintain thosedimensions in the image. By eliminatingthe perspective distortion, telecentriclenses let inspection and machine-vision systems make accurate metrol-ogy measurements.

Yet, you can’t use these lenses in allapplications. Lens manufacturers canmake telecentric lenses that producevirtually distortion-free images onlyover a defined depth, called the telecen-tric depth. It would prove difficult, if

not impossible, to design a lens witha telecentric depth that could cover theentire depth of a chessboard. Manufac-turers can produce lenses with telecen-tric depths of up to 1 in. (2.54 cm).(Telecentric lenses are available asstock items from various optical man-ufacturers.) If your vision system needsto measure a connector’s pin lengths,positions, and straightness, a telecen-tric lens may provide the necessary accuracy.

The side view of a lens in Figure 2shows a simplified representation of aconventional machine-vision lens. Allimaging lenses have an aperture stop, aphysical device that limits the amountof light energy that can pass through thelens, or a group of lenses. In a conven-tional lens, the opening or closing of theaperture stop changes the overallbrightness of the image across the entireimage, without affecting the size of theimage. In your eye, the iris forms theaperture stop.

In addition, all lenses contain pupils.Specifically, every lens has both an en-trance and exit pupil. The entrancepupil is the image of the aperture stopin object space, and the exit pupil is theimage of the aperture stop in imagespace. That is, the entrance pupil is theimage of the aperture-stop image asyou would see it viewed from the objectside of the lens. The exit pupil is the

aperture-stop image as you would seeit if viewed from the image side of thelens.

A lens diagram such as the one shownin Figure 2 typically includes three raysdrawn from any point on the objectthrough the lens to the image. The chief,or principal, ray passes obliquelythrough the center of the aperture stop.The two remaining rays, called marginalor paraxial rays, are drawn to coincideor come close to the edges of the aper-ture. They represent the outside limitsof the “bundle” of light rays that passthrough an optical system of one ormore lenses.

The diagram in Figure 2 shows thepaths of three light rays that start at areal object—in this case, the tip of anarrow. The three rays trace light pathsthrough the lens to finally produce acorresponding point on the image.When all the rays that pass through alens converge in a plane, they producean image.

In most conventional lenses theaperture stop is located within the lensassembly. The images of the aperturestop, that is, the entrance or exit pupils,are made up of converging light rays. Ina telecentric lens, the aperture stop islocated at the focal point of the lens.Due to this unique position of theaperture stop, the light rays that formthe images of the aperture stop travel

FIGURE 2 A conventional machine-vision lens passes lightthrough an aperture stop, through the glass lens itself, andprojects an image onto a camera detector (not shown).

parallel to the optical axisand are considered to be lo-cated at infinity.

If you were to lookthrough a telecentric lensfrom the object side, for ex-ample, you would see theentrance pupil of the lens.The same is true with a con-ventional lens. On first ob-servation the pupils maylook the same. For the tele-centric lens. your eye fo-cuses at infinity, and the en-trance pupil of the lensremains in focus with nofurther refocusing of youreye as you move the lenscloser or farther. On theother hand, with a conven-tional lens, your eye wouldneed to refocus on theimage of the entrance pupilas you move the lens closeror farther away. The factthat the entrance or exitpupil is located at infinitymeans that the principal rayis parallel to the optical axisof the lens. This character-istic is what defines a tele-centric lens.

Three types of telecentriclenses are appropriate formetrology vision systems. Inan object-sided telecentriclens (Figure 3), the lens andaperture are configured sothe principal ray from theobject to the lens runs paral-lel to the lens’ optical axis. Asmall change in the distancefrom the object to the ob-ject-sided telecentric lensdoes not change the magni-fication of the resultingimage. But these small dis-tance changes can occuronly within a small region ofdistances—the telecentricdepth. Only within this region does the re-sulting principal ray from the image runparallel to the optical axis. In a conven-tional lens, the principal ray is not parallelto the optical axis, so the lens will magnifypoints on an object based on their dis-tances from the lens.

The image from an image-sided telecen-tric lens (Figure 4) is insensitive to smallchanges in the position of the imageplane. In a camera, small differences in thedistance between the lens and an imagedetector do not affect the size of theimage. Thus, these small changes do not

affect the accuracy of mea-surements made on the re-sulting images.

A bilateral telecentriclens (Figure 5) combinesthe advantages of both ob-ject- and image-sided tele-centric lenses into oneform, thus providing thehighest degree of measure-ment accuracy for objectswith different heights. A bi-lateral telecentric lens ac-curately reproduces di-mensional relationshipswithin its telecentric depth,and it isn’t susceptible tosmall differences in the dis-tance between the lens andthe camera’s sensor. In gen-eral, these lenses provide ameans of accurately imag-ing 3-D objects when critical measurements are necessary.

Compare performance parametersUnfortunately, optical man-ufacturers don’t use a com-mon set of parameters tospecify their lenses. Defini-tions of key terms will helpyou understand the basicnomenclature and perfor-mance criteria you’ll en-counter when you select atelecentric lens. The eightmost important specifica-tions are described below,and Table 1 lists some typi-cal values for a telecentriclens that will ensure accu-rate dimensional imagequality.● Magnification is theratio of the size of the imageto the size of the object. Amagnification specificationof 1:2 means the lens re-

duces the object by a factor of 2 when itprojects the image onto a camera’s sensor.● Numerical aperture specifies the size ofthe “bundle” of light rays that passesthrough the lens. The larger the numericalaperture, the more light reaches the imagesensor.

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FIGURE 5 A bilateral telecentric lens includes elements of ob-ject-sided and image-sided telecentric lenses.

FIGURE 3 In an object-sided telecentric lens, the principle ray re-mains parallel to the optical axis for objects within the telecen-tric depth.

FIGURE 4 An image-sided telecentric lens maintains the dimen-sional information in an image within the telecentric depth.Thus, slight changes in an image sensor’s position do not affectdimensional accuracy.

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● Image size or sensor format specifies themaximum image size a lens can form.● Object size or field of view gives themaximum size object that the lens canimage. Due to the way a telecentric lensworks, the field of view cannot exceed thediameter of the lens’ front surface. So, ingeneral, telecentric lenses cannot view ob-jects more than an inch or two across.● Working distance specifies the distancefrom the object to the front of the lenshousing. A telecentric lens operates prop-erly at only one working distance.● Telecentric depth or telecentric range isthe total distance above and below an ob-ject that remains in focus and at constantmagnification. You can place objects youwish to measure anywhere within the tele-centric range. But whatever you want tomeasure must exist entirely within thisrange.

Don’t confuse telecentric depth with thedepth of field specified for a conventionallens; they’re independent lens characteris-tics. For a conventional lens, depth of fielddefines the range of distances in which youcan locate an object and still have the lensproduce a focused image.● Telecentricity describes the angular de-viation of the principal ray from a ray par-allel to the optical axis. A lower angularvalue means a lens will reproduce an imagemore accurately.● Distortion is an absolute deviation, inmicrometers (µm), from a theoreticalperfect point. It is a function of imageheight. A smaller value means a more ac-curate measurement.

Telecentric lenses do have some limita-tions. They produce a fairly small image,which generally means you must use them

with small CCD arrays such as those usedin 2/3-in. C-mount cameras. And a tele-centric lens can only view objects within afield equivalent to the front diameter of thelens assembly. Of course, your inspectionsystem can move objects into the field ofview as needed.

Although telecentric lenses won’t fitevery machine-vision need, they have im-portant roles to play when you need accu-rate measurements that don’t all take placein the same plane. T&MW

For more information

Kingslake, Rudolf, Optical System Design, AcademicPress, New York, NY, 1983.

Laikin, Milton, Lens Design, 2nd ed., Marcel Dekker,New York, NY, 1995.

Lenhardt, Karl, Optical Measurement Techniqueswith Telecentric Lenses, Schneider-Kreuznach, BadKreuznach, Germany, 2001.

Malacara, Daniel, Handbook of Lens Design, 1994,Marcel Dekker, New York, NY, 1994.

Smith, Warren J., Modern Optical Engineering, 3rded., McGraw-Hill, New York, NY, 2000.

Walker, Bruce H., Optical EngineeringFundamentals, SPIE Press, Bellingham, WA, 1998.

Ronald A. Petrozzo has more than 17 years of ex-perience as an optical engineer and an optical sys-tems designer. He holds both BS and an MS in Op-tics, from the University of Rochester (Rochester,NY), and he holds a MS in Computer Science fromPolytechnic University (Farmingdale, NY).

Stuart W. Singer is a senior optical engineer andlens designer with more than 22 years experience.He is the technical director for Schneider Optics; heholds a BS in Physics from Hofstra University(Hempstead, NY).

TABLE 1. Typical specifications for high-quality telecentric lenses

SPECIFICATION VALUE COMMENT

Numerical aperture > 0.14 a larger value = more light

Telecentric depth 1:1 magnification lens > 4.0 mm1:2 magnification lens > 8.0 mm1:4 magnification lens > 16.0 mm

Telecentricity < 0.04° if this value is defined in terms of microradians (µrad) note that 1° = 17.453 µrad

Distortion < 6 µm max

Note: These values are based upon a numerical aperture of 0.14. They will change if your lens has an adjustable iris and the lens is stepped down.