Improving fiber-optic laser beam delivery by incorporating GRADIUM optics

OPTICAL ACTIVITIES IN INDUSTRY

Stephen D. Fantone

Optical Activities in Industry is re-ported by Stephen D. Fantone, OptikosCorporation, 286 Cardinal MedeirosAvenue, Cambridge, Massachusetts02141. Stephen welcomes letters,news, and comments for this column,which should be sent to him at theabove address. [email protected]

Improving fiber-optic laser beamdelivery by incorporating GRADIUM optics

Boyd V. Hunter and Keng H. Leong

The performance of a fiber-optic laser beam delivery system strongly depends on the fiber and the opticsused to image the fiber face on the workpiece. We have compared off-the-shelf homogenous ~BK7! andGRADIUM ~axial-gradient! singlets to determine what improvement the GRADIUM offers in practice tothe typical laser user. The realized benefit for this application, although significant, is much smallerthan would be realized by a conventional imaging application. The figure of merit for laser-basedmaterials processing is the 86% energy-enclosure radius, which is not directly supported by commercialray-tracing software. Therefore empirical rules of thumb are presented to understand when GRADIUM~or any other well-corrected optics! will yield meaningful improvements to the beam delivery system.© 1997 Optical Society of America

Key words: Axial-gradient lenses, GRADIUM, Nd:YAG, BK7, optical fibers, beam diagnostics.

1. Introduction

Current high-power industrial Nd:YAG lasers have anumber of limitations compared with industrial CO2lasers, particularly lower average power and poorerbeam quality. However, the ability to use opticalfibers to transmit the laser beam to the workstation

When this research was performed the authors were with theLaser Applications Laboratory, Technology Development Division,Argonne National Laboratory, 9700 South Cass Avenue, Building207, Argonne, Illinois 60439. B. Hunter is now with LightPathTechnologies, Inc., 6820 Academy Parkway E, NE, Albuquerque,New Mexico 87109.Received 21March 1996; revised manuscript received 19 August

1996.0003-6935y97y132763-07$10.00y0© 1997 Optical Society of America

offers significant practical advantages that can makea fiber-optic-delivered Nd:YAG the preferred plat-form. Many metal-processing applications have ir-radiance thresholds of 105 to 106 W cm22 ~Ref. 1!.For these irradiances to be achieved given the limi-tations of the Nd:YAG laser with fiber-optic beamdelivery, small fibers or small magnifications are re-quired for the output optics. Fast conventional ~ho-mogeneous! optics produce a substantial aberration~primarily spherical! and larger focused spot sizes.With limited laser power available, the aberrationsreduce the achievable irradiances and the laser’s pro-cessing flexibility is compromised.Improving the performance of the fiber-optic-

delivered laser beam is best effected by the properselection and use of the optical fiber ~length, refrac-tive index profile, and installation geometry! and the

1 May 1997 y Vol. 36, No. 13 y APPLIED OPTICS 2763

optics used to image the fiber face onto the workpiece.The issues associated with fiber selection are dis-cussed elsewhere2,3; in this paper we concentrate onimprovements to the imaging optics. The best per-formance from the imaging optics is realized whenthey are well corrected. Well-corrected systemshave typically required doublets or triplets, aspher-ics, or diffractive elements. Because the fiber issmall compared with the other dimensions of the sys-tem and is usually on the optical axis, the primaryaberration is spherical.It has long been recognized that gradient-index

materials were promising candidates for many appli-cations because the refractive-index gradient made itpossible to produce well-corrected optical elementswithout requiring aspheric surfaces.4 The earliestgradient-index materials had radial refractive-indexgradients. Selfoc lenses and endoscope lenses aresome current applications of a radial gradient-indexmaterial.Axial-gradient ~GRADIUM! glasses have recently

become commercially available. GRADIUM offers alarge refractive-index difference ~currently up to 0.3!.Lenses made from this material can reduce aberra-tions, especially at small f-numbers, while retainingthe ease of manufacture associated with sphericalsurfaces. The combination of axial refractive indexand spherical surfaces produces an effect comparablewith a single-term aspheric surface on a conventionalglass.5,6 Consequently, the performance of the fiber-optic beam delivery system and its processing abilitycan be improved by using GRADIUM optics. Thepurpose of this study was to determine the practicalbenefits a laser user could expect. This informationprovides the laser user with a basis for determiningwhen GRADIUM ~or any other well-corrected optics!will yield a meaningful improvement over homoge-neous singlets.

2. Equipment and Procedure

The laser used in these tests was an Electrox1.6-kW Nd:YAG with fiber-optic beam delivery.This laser operates in the pulsed mode and is capa-ble of delivering 0.1- to 10-ms pulses with up to 16kW of peak power. For these tests, the laser waspulsed at 25 Hz and delivered 6 ms, 24.8-J pulses~620-W average power, 4-kW peak power!. Thebeam was transmitted through a 10-m length of1-mm-diameter core step-index silica–silica fiber tothe workstation. At the workstation, the beam ex-iting the fiber was imaged by means of a simplecollimating-focusing lens assembly. These lenseswere mounted in quick-change holders in an opticshead supplied by Laser Mechanisms ~Southfield,Michigan!. The clear aperture of the lenses in thequick-change holders was 35.5 mm. The physicallayout of the optics head and beam profiling equip-ment is given in Fig. 1. The two distances to thecollimating lens reflect the difference resulting froma 50.8-mm spacer, which allows different focallength collimating lenses to be used.

2764 APPLIED OPTICS y Vol. 36, No. 13 y 1 May 1997

The focused laser beam was profiled by a laserbeam analyzer ~Prometec Laserscope!. As depictedin Fig. 1, this instrument spins a hollow needle witha pinhole aperture through the beam, sampling thebeam at various points. From this information andknowledge of the total beam power, the beam profileis displayed and various statistics, such as irradianceand energy enclosure radii, are calculated. ThePrometec samples a square window by using a 41 381 pixel grid. For this experiment, the samplingwindows were 13 1mm2, 23 2mm2, and 43 4mm2.The pinhole diameters used were 10 mm, 20 mm, and50 mm. The resolution of the Prometec is limited bythe larger of the pinhole diameter and the samplingpixel size; for the uncertainty for a specific samplingwindow to be determined, the greater of the pinholediameter or the average of the pixel length and widthwas chosen. For this experiment, the Prometec’smeasurement uncertainty is 637 mm for magnifica-tion ~umu! $ 1.5, 618 mm for 1.5 .umu . 0.6, and 610mm for umu # 0.6. Under some conditions, the beamprofiles were taken after different warm-up times,which resulted in greater spot-size variability fromthe laser than the measurement uncertainty of thePrometec. It is also important to realize that thepyroelectric detector used by the Prometec has athreshold; a few percent of the total beam energy willbe below this threshold. Thus any energy in thefocused spot below the detection threshold will not bedetected and the Prometec’s calculations will be sys-tematically biased downward.The location of focus was determined to be the

point at which the radius that encloses 86% of theenergy was minimized. The 86% energy-enclosureradius was chosen because it is an effective measureof the useful beam radius and because it is used forbeam quality ~M2! measurements.7

Fig. 1. Diagram of the equipment used to profile the focusedbeams from the optics head with fixed positions for the lenses;BFL, back focal length.

The planoconvex BK7 lenses ~stock items from CVILaser, Albuquerque, New Mexico! had a diameter of38.1 mm and were antireflection ~AR! coated for 1064nm and normal incidence. The effective focallengths ~EFL’s! of these lenses were 64.5, 76.2, and127.1 mm. The GRADIUM lenses were customizedby LightPath Technologies ~Albuquerque, New Mex-ico! by using an existing GRADIUMmaterial ~G4SF!and were AR coated by CVI Laser. The refractive-index profile versus axial position for the G4SF ma-terial is given in Fig. 2. LightPath was asked tomatch the EFL’s of the CVI lenses, in order to makethe comparison as simple and direct as possible.The design data for the lenses we received indicatethat the EFL’s of the lenses were 64.9, 77.1, and 132.2mm.The collimating lenses were the BK7 127-mm,

GRADIUM 132-mm, and BK7–GRADIUM 77-mmlenses. Different combinations of BK7, GRADIUM,and BK7–GRADIUM lenses were tested to provide arange of data with different magnifications ~umu! anddifferent amounts of aberration. At an r86 focus, theratio of rblury~umurfiber! ranged from 8.4% to 160% forthe rms blur and 11% to 700% for the geometricalblur. Both the rms and geometrical rblur valueswere calculated at the r86 focus by using ZEMAX 5.0~Focus Software, Inc., Tucson, Arizona!with a Gauss-ian apodization chosen such that the Gaussian 1ye2point and the r86 radius of the beam incident upon thecollimating lens were the same. The conventionthat is used when a lens combination is referenced isas follows: collimating lens-focusing lens.The lens protector is a 1.5-mm-thick AR-coated sil-

ica window. It protects the lens from splatter orcontamination by any of the particles that result fromthe metal-working processes for which this laser wasdesigned. Although a flat window in a convergingbeam is known to introduce spherical aberration, thestrongly paraxial apodization that is due to the fiberin our beam delivery system makes this effect negli-gible, adding less than 610 mm of rms blur.

Fig. 2. Axial refractive-index profiles for G4SF. The crossesmark the refractive indices of the front and back surfaces of the132-mm lens.

3. Imaging an Extended Source

The extended source image dimensions ~assumingthat aberrations from imaging the fiber peripherydominate! are given by

rimage 5 umursource 1 rblur , (1)

where rimage is the geometrical ~100% enclosure! ra-dius of the image,m is the magnification, rsource is theradius of the extended source, and rblur is the geomet-rical blur radius of points imaged from the edge of theextended source. The impact of highly corrected op-tics will be more significant for small imaged spots,obtained by using smaller magnifications or smallersources. In the limit of umursource3 0, the extendedsource becomes a point source and the improvementsin rms and geometrical spot sizes calculated by theray-trace software will be realized in practice.The smallest possible spot is produced when rblur3

0. There are two ways that this small blur can beachieved. The first is to use optics thatminimize theblur over the clear aperture. The second way is torecognize that minimal blur is meaningful only at theedge of the image. Significantly more aberrationcan be tolerated toward the center of the image; spe-cifically, as long as the blur from any point within theimage does not extend beyond the edge of the unab-errated image, it will not increase the overall size ofthe image. Restated mathematically, for a step-index fiber, the maximum allowable aberration tol-erance for imaging each point on the extended sourceas a function of radial coordinate in the image planeis given by

rblur~r! 5max~umursource2r, rmin! for r# umursource ,

(2)

where r is the radial coordinate in the image planeand rmin is some minimum amount of aberrationdeemed acceptable. This aberration tolerance willresult in a redistribution of energy, yielding an irra-diance profile with a symmetric dip around r5 0. Ina practical sense, at the edge of the image, the aber-ration ~rblur! only has to be small compared with theimage radius; this practical consideration and diffrac-tion effects mean that rmin will be nonzero.If we use the same rationale used for depth of focus

and allow up to a 5% increase in spot size, then rmin5 0.05 umursource. Our maximum allowable geomet-rical spot-size target for the ray-tracing software isrmin.

4. Using the Extended Source for MaterialsProcessing

Controlling the geometrical size of the image is ap-propriate for some applications. However, materi-als processing tasks impose irradiance thresholds.The usual figure of merit is the radius of the circlethat encloses 86% of the total energy ~r86!. Toachieve the highest possible irradiance, r86 is mini-mized. For the designer using commercial ray-


tracing software to design optics for use with a beamdelivery system, this figure of merit is generally notdirectly supported. In general, the measured loca-tion of focus as determined by r86 is not coincidentwith the calculated paraxial, rms, or geometrical foci.The location of the r86 minimum is driven by thebeam apodization, aberrations, and variations in ac-tual image size with varying amounts of defocus.From the data we collected, the r86 focus position iseither effectively at the paraxial focus ~well-correctedsystems! or often at 50–70% of the defocus requiredto reach the rms focus.A rule of thumb is needed to give the designer a

rational basis for setting the rms spot-size targets inthe design software. The rms spot-size calculationsare easy to generate and appear to provide the mostdirect indication of the performance of the system inthe absence of a r86 merit function. For our data, wehave plotted the relative increase in r86 versus therms relative aberration ~rms spot sizeymrfiber; seeFig. 3!. We see a lot of scatter in some of the databecause of the details of the configuration. For ex-ample, changing the distance from the fiber to thecollimating lens results in differences in the apodiza-tion created by the fiber. Below 80% relative aber-ration, the r86 increase is less than 5%. A linearregression through the data puts a 0% increase at25% relative aberration. Thus a conservative, em-pirical rule of thumb to allow no significant increasein r86 ~,5%! is that rrms blur # 0.25mrfiber.

5. Specific Example with m 5 0.5

Cross-sectional intensity profiles of the focused spotsfrom both the BK7 127–65 and GRADIUM 132–65lens combinations, which yielded the smallest mag-nifications in our study ~both have umu of 0.5! areshown in Fig. 4. The impact of the reduced aberra-tion is clear from the GRADIUM lenses, which pro-duced a sharper, more top-hat image of the fiber face,and the irradiance of the 86% energy enclosure ismuch higher. The measured spot size and irradi-ance as well as the calculated parameters for theselenses are summarized in Table 1. Table 1 also liststhe change in these parameters realized by replacing

Fig. 3. Comparison of the rms relative aberration ~at r86 focus!versus the increase in the r86 radius for the lens combinations usedin this study.


the BK7 singlets with GRADIUM singlets.Switching from BK7 to GRADIUM lenses reducedthe r86 of the imaged fiber face by 8.7%. The averageirradiance of the imaged fiber increased by 19%.Comparing these modest but significant improve-ments in the measured spot with the ray-trace calcu-lations ~91% reduction in calculated rms spot size!again highlights the effect of imaging an extendedsource.The importance of the sharper profile is illustrated

by considering howmuch energy is wasted because ofthe aberrations. Many processes, such as weldingand cutting aluminum, have specific threshold inten-sities. Figure 5 shows the percentage of the energy~using the data presented in Fig. 4! that falls belowthe threshold value ~plotted on the horizontal axis!.For thresholds well below the peak irradiance, theGRADIUM lenses waste half as much as the BK7lenses. These threshold values were chosen because

Fig. 4. Cross-sectional irradiance profiles of a focused spot fromBK7 127–65 and GRADIUM 132–65 lens combinations, showingthe sharper edge of the image generated with the GRADIUMlenses. Both profiles are at the same scale; the horizontal line inthe Y section shows the 86% radius irradiance.

Table 1. Summary of Calculated and Measured Parameters for the BK7 127–65 and GRADIUM 132–65 Lenses ~zmz 5 0.5!a

ParameterBK-7127–65 GRADIUM 132–65 Change

Measured data ~extended source!86% enclosure radius ~mm! 252 230 8.7% reduction100% enclosure radius ~mm! 517 391 24% reductionAverage irradiance ~W cm22! 1.76 3 106 2.09 3 106 19% increase

Calculated data at r86 focus ~point source!Working f-number 1.67 1.87Airy disk radius ~mm! 2.2 2.2rms radius ~mm! 360 32 91% reductiongeometrical radius ~mm! 1500 104 93% reduction

Calculated data at rms focus ~point source!rms radius ~mm! 260 7 97% reduction

aBoth measured values for the extended source and calculated values for a point source are presented for comparison. The changecolumn gives the percentage change ~relative to the BK7 values! realized when GRADIUM is used instead of the BK7 singlets.

they are representative of those required to weld var-ious aluminum alloys.A plot of the encircled energy as a function of radius

for these lenses is presented in Fig. 6. Both actualand computed data are presented. The computedencircled energy was calculated by using the effi-ciency calculation in ZEMAX’s image analysis feature,assuming Gaussian apodization of the entrance pu-pil. The rounding at the top ~90–100%! of the GRA-DIUM curve is due to the defocus ~from rms focus!;otherwise the GRADIUM curve would have been aparabola. The shape of the BK7 curve is driven bythe lens aberrations. The calculated encircled en-ergy curves are further to the right than the experi-mental data, which is consistent with systematicundersizing by the Prometec that is due to the detec-tor threshold. Because of less aberration, the GRA-DIUM encircled energy curve is closer to the datathan BK7. The detector threshold, beam apodiza-tion, and imaging requirements of this applicationcombine to make the difference between a GRADIUMprofile and a BK7 profile noticeable only when theenergy enclosure is greater than 80% ~i.e., near theedge of the fiber!. The calculated GRADIUM 100%enclosure point, however, is smaller than measured.This may indicate a difference between the Gaussian

Fig. 5. Plot of wasted energy as a function of the irradiancethreshold for the BK7 127–65 and GRADIUM 132–65 combina-tions presented in Fig. 4.

apodization used and the actual apodization createdby the fiber.Figure 7 shows the through-focus 86% and 100%

enclosure radii for a BK7 127–65 combination, whichis the most highly aberrated combination tested, andthe same radii for the GRADIUM 132–65 combina-tion, which has so little aberration that the differencebetween the positions of the paraxial, 86%, and 100%foci are not resolvable with our equipment. The ra-tio of the distances from paraxial focus to 100% and86% minima are consistent with the ratio of theoret-ical defocus required to reach the geometrical or rmsfoci ~3⁄4:1⁄2! and suggest that actual 86% and 100%focal positions may be modeled conveniently by usinga smaller entrance aperture for modeling thanpresent in the physical system. The different parax-ial focus positions for BK7 and GRADIUM ~despitenearly equal EFL’s! are because ~1! the positions ofthe rear principal planes are different and ~2! thefixed positioning of the collimating lenses resulted inslight collimation errors that added or subtractedpower from the focusing lenses.

6. Extending the Range of Magnification

Figure 8 shows the 86% radii of all of our data plottedagainst the magnification. The data were plottedagainst magnification instead of focal length becausedifferent collimating lenses were used. The unaber-rated line was calculated by using the magnificationand the radius of spot that would enclose 86% of thesurface area of the 1-mm core fiber. Fast GRA-DIUM lenses provide improved performance com-pared with BK7 lenses. Notice that many of theGRADIUM focusing lens data points and all of thedata at a magnification of 1.6 fall below the unaber-rated line. This is also consistent with the interpre-tation of downward biasing by the Prometec that isdue to the detector threshold. The data show thatfor a 5% improvement in 86% energy-enclosure spotsize over BK7 ~using the fiber!, umursource should be#300 mm.GRADIUM lenses generally yielded smaller 100%

enclosure spots, as shown in Fig. 9. We see this


when comparing the lens combinations with a BK7focusing element with the equivalent combinationusing a GRADIUM focusing element. All GRA-DIUM combinations are indicated by the hollowtriangles and, to the repeatability of the 100% radii~cf. Fig. 7!, do as well or better than any othercombination. All BK7 or BK7 focusing lens com-binations ~filled markers! generally perform worse,although at an umu of 0.6 and 0.8, using a BK7collimator and a GRADIUM focusing lens resultedin larger 100% radii than the all-BK7 combination.This poorer performance by the BK7–GRADIUMcombinations is the opposite of what was observedfor the 86% radii ~cf. Fig. 8!.The 100% radii for BK7–BK7 are less than the sum

of the aberration-free size and the geometrical spotsize ~ray trace!, as expected. The 100% radii forGRADIUM–GRADIUM are greater than the sum ofthe aberration-free size and the geometrical spot size~ray trace!. This larger than expected spot size isprobably due to the difference between the Gaussianapodization used for the calculations and the actualapodization from the fiber. Because the GRADIUMlenses have so little aberration, the apodization dif-

Fig. 6. Energy enclosure versus radius for the BK7 127–65 andGRADIUM 132–56 combinations shown in Fig. 4. Calculated re-sults for these lenses ~ZEMAX BK7 and ZEMAX GRADIUM!, whenGaussian pupil apodization is used, are given for comparison.

Fig. 7. 86% and 100% enclosure radii for the BK7 127–BK7 65and GRADIUM 132–65 lens combinations. The approximate po-sitions of the paraxial, rms, and geometrical foci are indicated.BFL, back focal length.


ference is noticeable; aberration dominates the BK7calculations.

7. Conclusions

The replacement of conventional optics with GRA-DIUM optics in a fiber-optic beam delivery systemresults in a measurable improvement in spot size andirradiance for fast lenses. For a large fiber ~1-mmcore! and paraxial magnification of 0.5, the 86% en-closure radius decreased by ;9% and the averageirradiance increased by ;19%, compared with theresults using BK7 lenses. Larger improvements areexpected for smaller core fibers or smaller magnifi-cations. The improvement was smaller than ex-pected from the single-point ray-trace data because ofthe size of the fiber image. In order to see at least a5% improvement in the r86 spot size over BK7 ~usingthe fiber!, the umursource should be #300 mm. Fromthe data collected in this study, a conservative rmsaberration design target can be set at rrms blur # 0.25mrfiber to keep the r86 spot size within 5% of theunaberrated size.The reduced aberration ~primarily spherical! from

the GRADIUM lenses is visible in beam profiles of thefocused spot and also manifest by the fact that thelocations of the 100% and 86% foci are, to the reso-lution of our equipment, the same. Another benefit of

Fig. 8. 86% radii for the BK7 and GRADIUM lens combinationsversus paraxial magnification. Using GRADIUM lenses resultsin improved performance when fast lenses are used.

Fig. 9. 100% spot sizes for all combinations of BK7 and GRA-DIUM lenses tested.

this reduced aberration is that focal shifts as the laserpower changes ~and the apodization changes! are ef-fectively eliminated.Because this application really only requires good

imaging of the fiber periphery, it was possible to de-velop an aberration tolerance budget for a step-indexfiber. This tolerance budget defines ~as a function ofcoordinate in the image plane! the acceptable aber-ration that will result in no significant increase inspot size. This function allowsmore aberration thanwould be tolerated in amore conventional applicationand may ease the lens-design constraints.The results of this study can be applied to general

optical systems used for fiber-optic beam delivery.The use of GRADIUM and BK7 optics provided aconvenient mechanism to vary the aberration in thesystem. The conclusions about the conditions underwhich GRADIUM offers a significant performanceimprovement can be extended to any other highlycorrected optical system.

This research was supported by the U.S. Depart-ment of Energy, Office of Energy Research, under theLaboratory Technology Research Program. The au-thors acknowledge the assistance and cooperation ofLightPath Technologies and Ken Moore of FocusSoftware, Inc. ~ZEMAX!.

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Glesias, and P. J. Laverty, “Selecting a high-power fiber-opticlaser beam delivery system,” in Laser Materials Processing:New Developments in Laser Sources and Applications, W. Du-ley, K. Shibata, and R. Poprawe, eds., Proc. ICALEO 81E, 173–182 ~1996!.

4. P. J. Sands, “Third-order aberrations of inhomogeneous lenses,”J. Opt. Soc. Am. 60, 1436–1443 ~1970!; “Inhomogeneous lensesII. Chromatic paraxial aberrations,” 61, 777–783 ~1971!; “Inho-mogeneous lenses III. Paraxial optics,” 61, 879–885 ~1971!;“Inhomogeneous lenses IV. Aberrations of lenses with axial in-dex distributions,” 61, 1086–1091 ~1971!; “Inhomogeneouslenses V. Chromatic paraxial aberrations of lenses with axial orcylindrical index distributions,” 61, 1495–1500 ~1971!; “Inhomo-geneous lenses VI. Derivatives of paraxial coefficients,” 63,1210–1216 ~1973!.

5. P. K. Manhart, K. R. Castle, M. C. Ruda, and T. W. Stuhlinger,“Advantages of non-linear axial gradients in optical design,” inCurrent Developments in Optical Design and Optical Engineer-ing III, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 2000,379–388 ~1993!.

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Improving fiber-optic laser beam delivery by incorporating GRADIUM optics

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