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Scanning Lenses (F-theta)Product Information

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Figure 1: Scanning Lenses

Standard features include:

- Air-spaced 3 or 4-element designs

- Transmission of > 90%

- F-Theta condition accuracy of better than 0.1%

A scanning (F-theta) lens supplies an imagein accordance with the so-called F-thetacondition (y’ = f x θ) and, therefore, has aspecially corrected distortion.

F-theta lenses are used in engraving andlabeling systems, phototypesetting, imagetransfer and material processing, to read orwrite texts or image components with a laserbeam. For instance, a laser beam bundle isdirected by means of a movable mirror andfocused by an F-theta lens. The object whichis to be read or the material surface which isto be processed, is scanned in accordancewith the scanning angle θθθθθ derived from thedeflection (in a line or area).

Focusing in a plane despite swiveling ofFocusing in a plane despite swiveling ofFocusing in a plane despite swiveling ofFocusing in a plane despite swiveling ofFocusing in a plane despite swiveling ofthe mirrorthe mirrorthe mirrorthe mirrorthe mirrorThe focusing of the beam and a variable beamdeflection are necessary for the scanning.Focusing is achieved by means of a lens, andbeam deflection is facilitated most simply bya movable mirror.If the deflecting unit can be positioned in thebeam path behind the lens (Figure 2), the lensonly has to satisfy minimum demands with

respect to the image angle: It may have a smalldiameter and must form a sharp image onlyin the paraxial zone. The positioning of thedeflecting unit behind the lens, however, leadsto a curved scanning path which lies in acircular arc around the turning axis of thedeflecting unit.

This positioning is not suitable for the scanningof flat surfaces.

If the deflecting unit is positioned in the beampath in front of the lens (Figure 3), this resultsin a straight scanning path in a plane (imageplane) perpendicular to the optical axis. In thiscase, strict demands are placed on the imageangle of the lens, and moreover, otherrequirements must be met by the lens: It hasto provide a large diameter, its entrance pupilmust lie outside the lens at the point ofdeflection, it must be corrected for a fairly large

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image angle and must have a good flattening ofthe image field as well as a very special correctionof distortion.

F-theta lenses need a special distortionF-theta lenses need a special distortionF-theta lenses need a special distortionF-theta lenses need a special distortionF-theta lenses need a special distortionNormally, a lens is expected to be distortion-free inorder that the image obtained is geometricallysimilar to the object. Freedom from distortion isobtained when the image height y’ is proportionalto the object height. With reference to the objectangle θ, y’ = f x tan θ applies. However, such a lensis not suitable for scanning. According to Figure 3a linear relationship is required between thescanning angle theta and the image height y’.

To obtain this relationship, the lens has to have anegative (= a barrel-shaped) distortion defined bythe formula y’ = f x θ. F-theta lenses satisfy this so-called F-theta condition.

Identical angles have to be translated intoIdentical angles have to be translated intoIdentical angles have to be translated intoIdentical angles have to be translated intoIdentical angles have to be translated intoidentical scanning pathsidentical scanning pathsidentical scanning pathsidentical scanning pathsidentical scanning pathsProportionality between the scanning angle θ andthe image height y’ ensures proportionality betweenthe angular velocity of the deflecting system (e.g.of the mirror or polygon wheel) and the scanningspeed in the image plane. This property is of specialimportance in those cases where the duration ofexposure of the material surface to the beam is afactor (such as the exposure time of light sensitivefilm in phototype setting).

A deviation of the image formation geometry fromthe ideal position is called distortion in the case ofordinary lenses such as photographic lenses.F-theta lenses, however, must exhibit a well defineddistortion in accordance with the F-theta condition.

Cascade Laser Corporation can provide F-thetalenses that satisfy the F-theta requirements withan accuracy of better than 0.1%. (See footnote onTable 1, page 6)

A deviation from the F-theta condition manifestsitself as...

...a deviation in position of a point on thescanning path from its ideal value,

...a scale change along the scanning path,and

...non-uniform scanning speed despiteconstant angular velocity of the deflectingsystem.

Which of these effects is the most serious, dependson the particular application. For customized F-thetalenses, it is possible to adapt the optimization tothe application.

The entrance pupil lies outside the lensThe entrance pupil lies outside the lensThe entrance pupil lies outside the lensThe entrance pupil lies outside the lensThe entrance pupil lies outside the lensWhereas the entrance pupil of ordinary lenses liesinside the particular lens, in the case of F-thetalenses it has to lie relatively far outside in the regionof the location of the deflecting unit (e.g. at thegalvo-mirror or at the active mirror surface of thepolygon wheel). This is apparent in Figure 3 andFigure 5. Sufficient distance is necessary for themovement of the deflecting unit and for the entry ofthe beam bundle, especially when using a polygonwheel as the deflecting unit. A small distance,however, reduces the size and the cost of theF-theta lens. This should be taken into considerationin the design of the apparatus into which theF-theta lens is placed.

Figure 3: If the deflection of the laser beam occurs in thebeam path in front of the lens, the scanning path lies in aplane perpendicular to the optical axis of the lens. If the imageheight y’ is to be proportional to the scanning angle theta,then y’ = f x θ instead of y’ = f x tanθ.

Figure 2: If a laser beam focused by an ordinary lens isdeflected in the beam path behind the lens, the scanning pathproduced takes the form of a circular arc.

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Utilization of the whole entrance beam diameterUtilization of the whole entrance beam diameterUtilization of the whole entrance beam diameterUtilization of the whole entrance beam diameterUtilization of the whole entrance beam diameter,,,,,where possiblewhere possiblewhere possiblewhere possiblewhere possibleBecause of the optically advantageous propertiesof lasers (monochromaticity and coherence), it ispossible to achieve diffraction-limited quality of thepoint image by using high-class F-theta lenses. Inorder to exploit this property in practice, the wholeentrance pupil must be filled out by the entrancebeam bundle evenly or in a gaussian form,depending on the application.To satisfy this condition, the deflection unit(s) mustbe of sufficient size and, where necessary, e.g. inthe use of a gas laser, a beam expander must beused to achieve the required expansion of the laserbeam bundle.Therefore, the table with the most importanttechnical data of the standard-type F-theta lensesgives details of the recommended diameter of theentrance beam bundle and the position of thedeflecting elements.

This data sheet also shows the image pointdiameters where the intensity is reduced to 1/e2

Figure 4: A lens satisfying the formula y’ = f x tanθ yeilds adistortion-free image. In contrast, an F-theta lens must havean exactly defined negative (barrel-shaped) distortion, so thatthe image height y’ is proportional to the scanning angle θ.Only then a uniform rotation of the deflecting unit istransformed into a uniform scanning movement.

Figure 5, above: If only one line is scanned, then only one deflecting unit is necessary, e.g. a polygon wheel.In this case the lens may also have a rectilinear form, which requires less space.Below: An example for the use of an F-theta lens with beam deflection through two galvo-mirrors. Thisdeflection system permits a rapid access to any image point in the scanning plane.

(y 13.5%) for both uniform and gaussian pupilillumination. The corresponding values of all theselenses also match the physical limits determinedby diffraction.

If the entrance beam bundle fills out the pupil onlypartially or irregularly, then the point image diameter

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is increased. At the same time the depth of focus isalso increased, which is desirable in the scanningof non-flat surfaces (e.g. electric components onprinted circuit boards).

A design with two deflecting mirrors requires anentrance pupil diameter that is markedly larger thanthe diameter of the entrance beam bundle. This ratiois approximately 1.4 to 1.8 in the case of ourstandard-type F-theta lenses.

If only one deflecting unit is used with such a lens,then the diameter or the entrance beam bundle maybe correspondingly larger, whereby the resultingimage point diameter is considerably reduced.

A special case: telecentric F-theta lensesA special case: telecentric F-theta lensesA special case: telecentric F-theta lensesA special case: telecentric F-theta lensesA special case: telecentric F-theta lensesIf a non-flat surface is scanned, and the beam hitsthe surface at an angle, there will be a deviation inthe position compared to the projection of therespective point in the scanning plane. The extentof the deviation will be in proportion to the distancefrom the ideal scanning plane. This will result in adiscrepancy of scale. This error is avoidable throughuse of a “telecentric” F-theta lens, which isdistinguished from normal F-theta lenses in that theaxis of the focused beam is perpendicular to thescanning path (Figure 6).

Telecentric F-theta lenses require very large lensdiameters for long scanning paths (lens diametery 2y’ + entrance beam diameter).

A large scanning angle has a number of advantagesA large scanning angle has a number of advantagesA large scanning angle has a number of advantagesA large scanning angle has a number of advantagesA large scanning angle has a number of advantagesThe required scanning length can be achieved witha lens having a long focal length and a smallscanning angle, or with a lens having a shorter focallength and a larger scanning angle. There are,however, a number of advantages of using a shortfocal length and a large scanning angle. There are,however, a number of advantages of using a shortfocal length and a large scanning angle which istypical for Cascade Laser Corporations’ F-thetalenses.

• The short focal length associated with alarge scanning angle allows a shortconstruction of the total system and thusrequires less space in the machine.

• With a shorter focal length and the samerelative aperture, the lens and deflectingunit(s) are smaller, thereby reducing costs.

• Irregularities in the deflection movement,e.g. due to tolerances in the facet angles ofthe mirror polygon, have a less evidenteffect because of the short focal length.

Cascade Laser Corporation is able to customize

F-theta lenses for very different applications, so thatcomprehensive know-how is available to solve alarge range of problems.

Customized solutions permit optimizationCustomized solutions permit optimizationCustomized solutions permit optimizationCustomized solutions permit optimizationCustomized solutions permit optimizationFor example, extremely large scanning angles,achromatic F-theta lenses and telecentric F-thetalenses are possible. Cascade Laser Corporation isable to provide chromatic F-theta lenses forsystems in which lasers of different wavelengthsare used. The scanning angle was expanded insome other customized F-theta lenses toapproximately +/- 70°.

An important feature is the availability of customizedF-theta lenses in rectilinear form for scanning in aline (Figure 5, top). Because of their form, they takeup less space. Their measurements may be furtherreduced, as the movement of the deflecting unitand the entry of the beam bundle (perhaps evenoutside the scanning angle plane!) afford moreroom. The entrance pupil can therefore be locatedcloser to the lens. Due to a special assemblytechnology, Cascade Laser Corporation canmanufacture rectilinear F-theta lenses withextremely high precision.

Furthermore, a customized construction permits theoptimization of the performance to meet theparticular requirements, e.g. a certain spot size andenergy distribution, and takes into consideration thefitting conditions while minimizing the costs at thesame time. This holds true especially for totalsystems, e.g. including light pens and beamexpanders.

Serial production of standard-type F-theta RonarsSerial production of standard-type F-theta RonarsSerial production of standard-type F-theta RonarsSerial production of standard-type F-theta RonarsSerial production of standard-type F-theta RonarsThe table below contains the most important datafor the serially produced standard-type F-thetalenses used primarily in material processing andlabeling. They are suitable for scanning in a line

Figure 6: A telecentric F-theta lens differs from a normalF-theta lens in that the axis of the focused laser beam bundleis perpendicular to the scanning plane throughout.

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with one deflecting unit (in which case an entrancebeam diameter of 1.4 to 1.8 times larger is possible,and the image point diameter becomescorrespondingly smaller due to lower diffraction) andfor surface scanning with two deflecting units (in whichcase the diagonal determines the maximum scanlength).

Interchangeable protecting glasses for F-thetaInterchangeable protecting glasses for F-thetaInterchangeable protecting glasses for F-thetaInterchangeable protecting glasses for F-thetaInterchangeable protecting glasses for F-thetalenseslenseslenseslenseslensesIn material processing some material (metal,plastics, etc.) is burned away or vaporized by thelaser beam. To prevent this from settlingon the exit lens element, an interchangeable protectingglass is provided in most F-theta lenses (See chart).

Point images represent the very high image qualityPoint images represent the very high image qualityPoint images represent the very high image qualityPoint images represent the very high image qualityPoint images represent the very high image qualityThe following point images are proof of the highimage quality of our F-theta lenses throughoutthe entire scanning range. From the image center(0°) through to the corner (25°), the point imagesare almost identical.

Figure 7: Important dimensions of the F-theta Ronar (a1/a2= distance to mirror 1/2, d = entrance beam diameter, D =lens diameter, s’ = back focal length, θ = scanning angle, y’ =image height).

Figure 8: Point image cross sections for six scanning angles from 0° to 25° in the case of gaussian pupilillumination limited to 1/e2 (Cascade Laser’s F-theta Ronar 254 mm and laser wavelength 1064 nm).

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Cascade Laser Corp.Cascade Laser Corp.Cascade Laser Corp.Cascade Laser Corp.Cascade Laser Corp.101 N. Elliott Rd.Newberg, OR 97132Phone: 503-554-1926Toll Free: 800-443-5561Fax: 503-554-8285E-mail: info@cascadelaser.comWeb: www.cascadelaser.com

Scanning (F-theta) LensesJune 2001

TTTTTable 1 footnotes:able 1 footnotes:able 1 footnotes:able 1 footnotes:able 1 footnotes:*) Back focal length for protective glass.**) These lenses have an additional anti-reflective coating for the visual spectrum.***) The image point diameter in the case of uniform and gaussian pupil illumination is based on a decrease of intensity onto 1/e2.****) AR coating for 1064 nm + visa1: distance between first deflection unit and vertex of first lens element surfacea2: distance between second deflection unit and vertex of first lens element surfaceF-theta condition is met by all listed models with an accuracy of better than 0.1%

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