Measurement of 1 -Am diam beams

Bruce Cannon, Timothy S. Gardner, and Donald K. Cohen

Measurements of beams of -1 ,um in diameter are presented. Three approaches, one using a Ronchi ruling,

the other two based on knife-edge scan techniques are compared experimentally. Effects of Ronchi rulingaccuracy and nonconstant scan velocity are discussed. Included are results of theoretical studies on the effect

of imperfect scanning edges and non-Gaussian beam profiles on measurement results.

1. Introduction

In a previous paper we presented a review of varioustechniques for measuring l-,gm diam Gaussian beams.'Here we present results of a more general investigationinto the measurement of l-,gm diam beams not limitedto a Gaussian profile. Comparison of various tech-niques was presented by Dickson2 for measuringGaussian beam diameters much greater than 1 im.He found poor correlation of the various techniqueswhen very non-Gaussian beams and hardware limita-tions existed. Some of the techniques described inRef. 1 are limited in their application to beams -1 ptmin diameter because of the size of the pinhole or slitrequired to scan the beam. Techniques that do workfor l-,am diameters rely on scanning a series of obstruc-tions across the beam, such as Ronchi ruling or a singleedge. Our objective is to present experimental resultscomparing these three techniques and the effects ofscanning-edge and beam quality on them.

Knife-Edge Scan Technique

The theory of beam-diameter measurement hasbeen well established in the literature. 3-"1 Consider abeam centered on a detector. As a knife-edge isscanned across the beam, the power detected as afunction of time P(t) is given by

P(t) =J J I(x,y)dydx, (1)

where v is the velocity of the scanning edge and xo is theinitial position of the scanning edge, as shown in Fig. 1.If we assume the field being scanned is separable, Eq.(1) reduces to

P(t) = A J F(x)dx, (2)

where A is the result of integrating over the coordinateperpendicular to the direction of scan and F(x) is the

The authors are with IBM General Products Division, Tucson,Arizona 85744.

Received 10 February 1986.0003-6935/86/172981-03$02.00/0.© 1986 Optical Society of America.

beam profile along the scan direction. In the treat-ment by Suzaki et al.,3 the beam under study is as-sumed to be Gaussian, which results in Eq. (2) becom-ing

P(t)/Po = 1/2 erfc(z) (3)

with

z = (2/w)(xo - t), (4)

where P0 is the total incident power, w is the beamradius at the /e2 irradiance point, and erfc is thecomplementary error function. By suitable manipu-lation, we find that the beam size in the scan directionis given by

w = 1.188vAt, (5)

where At is the time difference corresponding to the 80and 20% transmitted power level. This technique willbe termed the Suzaki approach throughout this paper.

III. Derivative Knife-Edge Scan Technique

The other knife-edge technique to be discussed re-lies on the properties of the derivative of Eq. (2), whichgives

dP(t)/dt = AF(xo - vt). (6)

By knowing the velocity of the scan, the derivativegives the actual beam profile in the direction of scan, ifthe beam irradiance function is separable.

IV. Ronchi-Ruling Technique

The Ronchi technique involves measurement of themodulation of the power either transmitted or reflect-ed by a ruling. Assuming that the beam is Gaussian,the following equation is solved by varying the beamradius to predict the measured modulation depth'2 :

Pmin/Pmax = l[erf(D) - erf(C)]/[erf(A) - erf(B) + 111 (7)

with

A = r/V\2w B = r8 + 2rb/V/2w C = rb/V\2w D = rb + 2r8 /V2w;

Pmin and Pmax are the minimum and maximum powertransmitted, respectively; rb and r8 are the widths ofthe bars and spaces, respectively; and erf is the stan-dard error function. Note that this technique will, in

1 September 1986 / Vol. 25, No. 17 / APPLIED OPTICS 2981

Knife edge

Sean'

K

xo.vt

Fig. 1. Knife-edge scan geometry.

general, give the effective Gaussian beam diameterindependent of the true irradiance function.

V. Experimental Results

A microscope objective was used to focus a colli-mated He-Ne laser beam onto the scanning apparatusconsisting of a linear actuator (General ScanningCCX650) having a glass substrate etched with a seriesof Ronchi patterns and effective knife-edge features(Fig. 2). Mounted directly behind the substrate was asuitable photodetector/preamplifier (United DetectorTechnologies, UDT 451), which detected the transmit-ted power. The signal was then routed to a Tektronics7854 digital oscilloscope, which was connected to amicrocomputer. Processing of the data was interacti-vely shared between the microcomputer and oscillo-scope.

Figure 3 is a graph of the measured diameter of theeffective Gaussian beam for a range of positionsthrough focus. All the measurements were in agree-ment to within 10%. The theoretical curve was deter-mined from well-known Gaussian-beam results giventhe parameters of the objective lens and input beamsize.

A primary source for errors in knife-edge measure-ments is the uncertainty of the velocity of the scan.Errors in velocity measurements correspond directlyto errors in the measured diameter. We scanned thepattern sinusoidally because the discontinuity of alinear scan at the position extremes leads to nonrepea-table errors. As described in Ref. 1, we determined thevelocity of the scan by noting the time needed to travela known feature on the etched substrate. An analysiswas performed for a sinusoidal scan, which indicatedthat if the width of the feature and the edge is within2% of the scan amplitude and located at the position ofmaximum velocity, the error contributed is <3%.From this analysis, together with the measured distri-bution for a given velocity, we determined that thevelocity error was -5-8%. Note that if care is taken, amore accurate and stable velocity can be achieved withthe apparatus described in Ref. 3. We used a linearactuator because it was available, but a rotating deviceof appropriate size and servo control can also be usedto minimize velocity errors.

The accuracy of the measurements with the Ronchiruling does not depend on the magnitude or functional

20pm 40 pm 10 pm 40,pm 20 pm

Fig. 2. Schematic of ruling used for measuring beam diameters andvelocity.

Fig. 3. Experimental results of beam-diameter measurements forvarious focal positions.

form of the velocity: it is the quality of the ruling andthe accuracy in measuring the ruling features thatdetermine the accuracy of the measurements. Withthe aid of an electron microscope, the Ronchi patternwas determined to consist of bars 0.8 0.1 m thickand spaces 1.1 0.1 ,gm wide, giving an -10% error inthe beam-diameter measurement.

Another limiting factor in the techniques describedis the mechanical stability of the scanning device. Be-cause beams -1 ysm in diameter have a depth of focusequivalent to a few beam diameters, any out-of-planemotion will lead to erroneous results.

Based on our experience with these techniques atthe micrometer level, we support the conclusions ofDickson2 which favor the Ronchi approach. We foundthroughout our work that the Ronchi technique wasthe easiest to perform and most repeatable. If mea-suring a range of beam diameters or beam profiles isdesired, the knife-edge techniques are preferable.But if the detection of a given beam size or the positionof best focus is desired, the Ronchi technique is betterbecause it is easier to use.

VI. Numerical Study of Knife-Edge Techniques

During the course of our work, the question of knife-edge quality and beam separability was addressed us-ing numerical modeling. The knife-edge was modeled

2982 APPLIED OPTICS / Vol. 25, No. 17 / 1 September 1986

- l l >

BY

*x

--- ' -11- -.. 'I�. = "I'll-32

-10 I _: O

Axlal poetry llxmA

-

I0-

RWD = hE/2w

-

Position along the knife edge

Fig. 4. Knife-edge transmission properties. The parameter RWDcorresponds to the ratio of the edge-transmission region to the beam

diameter scanned.

Fig. 5. Family of scans with various nonideal knife-edges. Each

curve is the result of a different value of RWD.

as having a transmission that varied linearly over theedge area (Fig. 4). Figure 5 shows a series of scans withknife-edges having various edge-width-to-beam-diam-eter ratios (RWD); Fig. 6 shows the error introducedinto the Suzaki and the derivative techniques as afunction of RWD.

In many applications, the formation of 1-,gm diambeams is done by illuminating a high-numerical-aper-ture lens with a Gaussian laser beam. As a result of thefinite aperture of the lens, the final beam irradiance inthe focal place is a convolution of the point spreadfunction of the lens (not separable) and of a Gaussiandistributions To examine the effects of beam sepa-rability, we used a numerical model of a pure Airypattern scanned by a perfect edge. With this model,the technique described in Ref. 3 predicted the beamradius at the full width half-maximum point to within3%, the derivative technique predicted the beam size towithin 1%.

VI. Conclusion

From the data given, it is evident that in the beam-diameter range of 1 ,um, the desired information dic-tates what technique to select for measurement. For aquick and simple indication of focus and limited beam-size measuring range, the Ronchi technique is prefera-ble, but for measuring the beam profile the knife-edgetechniques are better suited. Studies were presentedthat indicate that the knife-edge techniques are accu-rate to -5% as long as the knife-edge width is not morethan 20% of the beam diameter (e-2) being measured.Numerical studies demonstrated that the derivativetechnique is more accurate than the Suzaki technique

o 20

0.2 0. 4 0 . 0.8

RWD

Fig. 6. Percentage of error in the Suzaki and derivative techniquesfor various values of RWD.

for pure Airy patterns. However, each technique isaccurate to a few percent. Finally, note that both theRonchi and Suzaki techniques yield an effectiveGaussian beam radius for the field to be measured, butthe derivative technique produces the exact beam pro-file for separable fields.

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niques for Measuring Gaussian Beams One Micrometer in Dia-meter," GPD Tucson Tech. Rep. TR-82.0118 (11 Oct. 1983);Appl. Opt. 23, 637 (1984).

2. L. D. Dickson, "Ronchi Ruling Method for Measuring a Gauss-ian Beam Diameter," Opt. Eng. 18, 70 (1979).

3. Y. Suzaki and A. Tachibana, "Measurement of Micron-SizedRadius of Gaussian Laser Beam Using the Scanning Knife Ed-ge," Appl. Opt. 14, 2809 (1975).

4. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Cla-viere, E. A. Franke, and J. M. Franke, "Technique for FastMeasurement of Gaussian Laser Beam Parameters," Appl. Opt.10, 2775 (1971).

5. E. Stijns, "Measuring the Spot Size of a Gaussian Beam with anOscillating Wire," IEEE J. Quantum Electron. QE-16, 1298(1980).

6. J. E. Pearson, T. C. Mcgill, S. Kurtin, and A. Yariv, "TheFraction of Gaussian Laser Beam by a Semi-Infinite Plane," J.Opt. Soc. Am. 59, 1440 (1969).

7. M. B. Schneider and W. W. Webb, "Measurement of SubmicronLaser Beam Radii," Appl. Opt. 20, 1382 (1981).

8. C. Courtney and W. M. Steen, "Measurement of the Diameter ofa Laser Beam," Appl. Phys. 17, 303 (1978).

9. A. V. Khromov, "Measurement of Laser Beam Diameters Usinga Grating," Opt. Spectrosc., USSR 48, 186 (1980).

10. Y. C. Kiang and R. W. Lang, "Measuring Focused GaussianBeam Spot Sizes: A Practical Method," Appl. Opt. 22, 1296(1983).

11. J. M. Kosrofian and B. A. Garetz, "Measurement of a GaussianLaser Beam Diameter through the Direct Inversion of KnifeEdge Data," Appl. Opt. 22, 3406 (1983).

12. E. C. Broockman, L. D. Dickson, and R. S. Fortenberry, "Gener-alization of the Ronchi Ruling Method for Measuring GaussianBeam Diameter," Opt. Eng. 22, 643 (1983).

13. J. D. Gaskill, Linear Systems, Four Transforms, and Optics(Wiley, New York, 1978).

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