Radiant exposure level comparison between Gaussian and top hat beams in various scanning patterns

Radiant exposure level comparison between Gaussianand top hat beams in various scanning patterns

Paweena U-Thainual,† Yi Yang,† Hanh N. D. Le, and Do-Hyun Kim*Center for Devices and Radiological Health, U.S. Food and Drug Administration,

10903 New Hampshire Ave., Silver Spring, Maryland 20993, USA

*Corresponding author: do‑[email protected]

Received 19 September 2014; accepted 2 November 2014;posted 14 November 2014 (Doc. ID 223466); published 19 December 2014

The radiant exposure of optical irradiation beams with different scanning parameters has been theoreti-cally studied. We analyzed the difference in radiant exposure introduced by Gaussian and top hat beams.Various parameters such as scanning pattern, aperture position, beam size and scan spacing were alsointroduced in this study. We found that Gaussian beams introduce higher calculated radiant exposure tothe aperture than top hat beams for certain beam size to aperture size ratios. However, as the scan spac-ing decreases, the radiant exposure difference calculated from Gaussian and top hat beams diminishes.© 2014 Optical Society of AmericaOCIS codes: (140.3360) Laser safety and eye protection; (170.5755) Retina scanning.http://dx.doi.org/10.1364/AO.53.008585

1. Introduction

Optical scanning technology has been embeddedwith many forms of medical devices in both thera-peutic and diagnostic applications. For example,optical coherence tomography (OCT) has becomean essential technology in ophthalmology to detectand monitor retinal diseases [1]. Such implementa-tions of OCTare accompanied by other novel develop-ments such as high speed iris microangiographyimaging [2], OCT-guided picosecond laser ablation[3], extreme long range and speed OCT [4], and sweptsource OCT for anterior segment imaging [5]. Otheroptical eye imaging modalities embedded with opti-cal scanning technology, such as confocal laser scan-ning microscopy [6] and photoacoustic microscopy[7], have been presented. Optical scanning technol-ogy can also be found in therapeutic devices. For in-stance, one study used an 800 nm diode laser to scanan area of 20 mm × 20 mm for hair reduction, andthe efficacy and safety of such a method was reported[8]. Another study combined a focused continuous

wave (CW) CO2 laser beam with a scanning devicefor skin resurfacing [9].

Although these systems are different in principle,their main scanning mechanisms are very similar.Beam scanning is accomplished with a 3D stagesystem [6], an X-Y galvanometer-mounted mirrorsystem [4,10], piezoelectric transducers [11], or mi-croelectromechanical systems (MEMS) [12]. Mostconfocal systems use resonant scanners or spinningpolygons. A scanning pattern is then chosen to opti-mize the image acquisition speed or field of view(FOV) [13]. Sinusoidal, sawtooth, and triangularscanning patterns have all been implemented inscanning devices [14,15], and their attributes areclearly defined.

For scanning devices, beam overlapping has been atopic of frequent discussion. In one case, increasingthe overlapping between two scanning spots to im-prove therapeutic efficacy is theoretically attractive;however, excessive spot overlapping can lead to epi-dermal vesiculation [8]. Other issues, such as remov-ing overlapping effects on scanned images, have beendiscussed in [16], and a study has been carried out onthe quantifying overlap factor as a way to achieveacute varnish removal [3]. However, there has been

1559-128X/14/368585-08$15.00/0© 2014 Optical Society of America

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a lack of information on the difference in laser radi-ant exposure introduced by Gaussian and top hatbeams in overlapping regions. The difference in beamenergy distribution between Gaussian and top hat[17] is significant. A Gaussian beam has a high con-centration of energy at the center, and the energyextends beyond the nominal beam radius, whereasthe energy inside an ideal top hat beam is uniformlydistributed and well contained inside the radius [17].Other scanning factors, such as an increase in imag-ing resolution, lead to more beam overlapping [2,18],application based FOV, or scanning range [2,19] canfurther complicate the measurement of radiantexposure.

The scanning source has a time-varying direction,origin, or pattern of propagation with respect to astationary frame of reference. As for evaluatingthe optical radiation hazard level of such technology,most commonly used guide documents [20,21] sug-gest treating scanning light sources as pulsed lightsources to determine the optical energy deliveredthrough a measurement aperture, given that thescan lengths are greater than the diameter of themeasurement aperture. Treating a scanning lightas a pulsed light is especially logical when a mea-surement aperture is used for safety evaluation.Light appears when the scanning light enters themeasurement aperture and then disappears whenit leaves the aperture, which resembles on and offof a pulsed light [22]. When evaluating the safeoptical radiation limit of scanning devices, the worstcase scenario for maximum irradiation needs to beconsidered. Other considerations for evaluating thesafe exposure level include unique characteristicsof scanning light sources, scanning patterns andspeed, radiant exposure variation due to the changein dwell-time, and overlap [22].

Therefore, the purpose of this study is to calculatethe radiant exposure through an aperture for threedifferent scanning patterns. Various scan spacingsare also introduced, and both top hat and Gaussianbeams with different beam sizes are simulated to an-alyze their combined effects on the calculated radi-ant exposure through the aperture. Three mostcommonly used scanning patterns are chosen in thispaper: (1) sinusoidal (S), (2) sawtooth (ST), and (3) tri-angular (T). Practical medical optical devices havingscanning sources may have more complicated scan-ning mechanisms, thus may have scanning patternsthat are different from S, ST, or T. For example, a fastscanning device employs a resonant scanner in a fastaxis and a galvo scanner in a slow axis. Also, manyadvanced scanning devices adapt various mecha-nisms to reduce issues in non-uniform scan spacing,or to block turning points of sinusoidal scans so thatslow scanning speed (thus longer dwell-time) can beexcluded from the scan pattern. Our study does notinclude such advanced scanning mechanisms; how-ever, our study results using basic S, ST, and T scan-ning patterns will also provide valuable informationon evaluating such devices.

2. Scanning Laser Modeling

Experimental measurements of radiant exposuredue to varying dwell-time and beam spot overlapfrom scanning light showed that radiant exposureis not evenly distributed over the entire scanningarea due to different dwell-time and beam overlap[22]. The type of scanning pattern, scanning speedin x and y directions, and spot size of the light sourcealso affect themeasurement. Thus, there is no simplegolden rule in finding the maximum exposure from agiven scanning system. However, it can be predictedthat the highest radiant exposure should be mea-sured either at the center (A of Fig. 1) or towardthe turning point (B of Fig. 1).

In this study, the aperture is placed at three loca-tions: (A) the turning point, (B) the center of the scanpath, and (C) between two scan paths, as shown inFig. 1. In regions A and B of Fig. 1, radiant exposurewill always be measured since it is on the scan path.When the beam spot size is small and the scan spac-ing is relatively large, no radiant exposure appears inregion C. However, as we reduce the scan spacing,beam overlap starts to introduce radiant exposurein the aperture.

Different parameters are used to calculate theradiant exposure difference between top hat andGaussian beams. The parameters are defined inTable 1. Despite the difference in FOV, scan spacing,and patterns, the scan time for each frame is set to aconstant time interval, t. Therefore, closer scan spac-ing (more scan lines in one frame) leads to higherscanning speed. However, this can be varied ondifferent systems. For example, for the scanninglaser ophthalmoscope (SLO), the line rate is set bythe resonant scanner [23], which cannot be adjusted,and for OCT the line rate is set by the camera not thescanning system. So, for OCT you will get a variable

Fig. 1. Beam spot and three different aperture locations relativeto a sinusoidal scanning pattern. The solid dot denotes the beamspot, and the red arrow points to the direction of scanning. Theaperture is placed at three regions of interest denoted as dottedcircles to study the radiant exposure it receives (A) at the centerand on the scan path; (B) at the turning point; (C) at the center andbetween two scan paths.

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scanning speed depending on the region size andspatial density.

The fundamental difference in modeling a tophat and a Gaussian beam spot is that the power dis-tribution inside an ideal top hat spot is uniform[Fig. 2(a)]; therefore, energy inside the aperture isproportional to the intersection area between thebeam spot and aperture. As for a Gaussian beamwith a nominal radius, R, the beam energy extendsbeyond the radius. This is illustrated in Fig. 2(b),where the whole aperture is filled with optical en-ergy. When modeling a top hat beam, the irradianceof the light source is first calculated by dividing thepower by the spot size. The optical energy (E) is foundfrom

E � IR × IA × dt; (1)

where IR is the irradiance, IA is the intersection areaof the optical beam and aperture, and dt is the timeinterval for each step of the simulation. As the beamspot propagates in steps of dt, the optical energy iscalculated and added to the energy value from theprevious iteration. Finally, the radiant exposure isfound by dividing the total energy by the area ofthe aperture.

The method for calculating the optical radiation ofthe Gaussian beam follows the same principle as atop hat beam, although the implementation is differ-ent due to the nonlinear variation in energy acrossthe beam diameter and beyond, prompting the needfor a different algorithm in finding the optical energyinside an aperture.

For Gaussian pulses, the beam irradiance profiles[17] are modeled as

J�x; y� � Joe−2

��x − xWx

�2�

�y − yWy

�2�; (2)

where J�x; y� is the irradiance beam amplitude at�x; y�; Jo is the amplitude at the Gaussian center;x and y define the center location; and Wx and Wydefine the horizontal and vertical radius at 1∕e2 ofenergy.

According to [24], when normalized to the totalpower (Po), the beam irradiance profiles are ex-pressed as

JP � 2Po

πR2 e−2

��x − xR

�2�

�y − yR

�2�; (3)

whereWx andWy are set to the equal beam radius.R.Unlike in the top hat case where optical energy is lin-early proportional to the IA [Fig. 2(a)], here, thepower inside the aperture (Pap) of radius, r, issummed as

Pap �Z�x−X�2��y−Y�2<r2

JPdxdy; (4)

where the aperture is centered at (X;Y) and the op-tical energy (E) encircled inside the aperture for eachiteration of dt is

E � Pap × dt: (5)

Once the beam spot leaves the region of interest, Efrom each iteration is added to produce the total en-ergy, and radiant exposure is found by dividing thetotal energy by the area of the aperture. The entiresimulation was implemented using MATLAB soft-ware (Mathworks, Natick, Massachusetts). In thesimulation, to achieve high precision and simulationspeed, the region of integration is defined as a 2Dsquare with side length of 5R encircling the Gaussianbeam, as shown in Fig. 3. Within this integrationarea of side length, 2.5R, more than 99.9996% ofthe beam power of a Gaussian beam is enclosed. Ra-diant exposure integration of a Gaussian beamthrough an aperture can be calculated as follows.First, the integration square defined above is dividedinto small grids with sides of Δx × Δy; preferablyΔx � Δy. The size of Δx will determine the overallaccuracy and speed of the calculation. The accuracyand calculation time are proportional and inverselyproportional to Δx. We determined Δx for different

Table 1. Parameters for the Radiant Exposure Calculation

Parameters Description and Values

Beam type top hat, GaussianBeam diameter (μm) 15–120Aperture diameter (μm) 30Central scan spacing (SS), (μm) 20–120Scan length on X-axis (mm) 3Scanning pattern Sinusoidal (S),

Sawtooth (ST),Triangular (T)

Aperture position (Fig. 1) A—at the center and on thescan path, called “on-path”B—turning pointC—at the center and betweentwo scan paths, called “off-path”

Fig. 2. Beam energy distribution inside the aperture. (a) In thesimulation, beam energy is contained inside the beam radius, R,for top hat laser beams; (b) a Gaussian beam profile lacks a distinctboundary, therefore the beam energy extends beyond the beam ra-dius.

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laser spot sizes so that we can achieve >99.85% ac-curacy in our numerical integration when comparedto the analytical calculation of Eq. (4).

3. Simulation Results

Radiant exposure was first calculated at region A (onthe scan path) and C (between two scan paths), asindicated in Fig. 1. The scan length in the x directionwas set to 3 mm, and the diameter of the aperturewas 30 μm, which is the smallest aperture size sug-gested in a commonly used consensus standard forretinal optical hazard evaluation [20].

The calculated radiant exposure difference be-tween Gaussian and top hat beams was dependentupon different scan spacing, and the relative sizeof the beam to the aperture. In order to demonstratethis relationship, we first calculated the radiant ex-posure (RE) ratio between top hat and Gaussianbeams (RTH∕G) for different beam sizes,

RTH∕G � �REtop hat�∕�REGaussian�: (6)

The aperture size was fixed at a diameter of 30 μm,while the beam sizes ranged from 15 to 120 μm withan increment of 15 μm. For a 30 μm aperture, 120 μmis a reasonable upper limit for the beam size. Thescan spacing (SS) between the scan paths at thecenter was varied from 30 to 60 μm. For actual scan-ning devices, SS half the size of the beamwill provide50% overlap between the scanning beams at thecenter; thus we limited the SS to 60 μm, which is halfof the largest beam size (120 μm) used in this study.

The comparison between top hat and Gaussianbeams is implemented based on radiant exposurelevels in three scenarios, corresponding to threeregions where the aperture was placed (Fig. 1).

A. Region A

First, we calculated the radiant exposures forscanning irradiation when the aperture was placed

on-path. The RTH∕G results are shown in Table 2and plotted in Fig. 4. Only the result for S scanningwas shown in Fig. 4 because the results for ST and Tscanning were nearly identical. The solid curve inFig. 4 shows the results for 60 μm central SS, whichis twice the aperture size. The dotted curves are re-sults for a 30 μm spacing case, which equals the aper-ture size. As shown in Fig. 4, when the aperture wasplaced on the scan path with a 60 μm central SS,RTH∕G first decreased as the beam size increased un-til it was 102 μm, which is larger than the aperturesize. This is due to the fact that Gaussian beams con-centrate most energy at the center. Therefore, as thebeam size increases, the aperture calculates a higherconcentration of energy from Gaussian beams thantop hat beams. However, as the beam size continuedto increase beyond 102 μm, the beam overlapping in-troduced more energy in the aperture and RTH∕Gstarted to increase. The difference between the radi-ant exposure from Gaussian and top hat beams wasas high as 25%.RTH∕G for 30 μmSS fluctuates aroundone as the beam size increases, indicating that thedifference in exposure introduced by Gaussian andtop hat beams is very small.

Fig. 3. Region of integration defined at a radius, 2.5R.

Table 2. Results for Region A “On-Path” Scanning

RTH∕G “On-Path”

S ST T

Beam Size (μm) SS-30 SS-60 SS-30 SS-60 SS-30 SS-60

15 1.02 1.00 1.00 1.00 1.00 1.0030 1.00 1.01 0.98 1.01 0.99 1.0145 0.94 0.90 0.95 0.90 0.95 0.9060 0.99 0.85 0.99 0.85 0.99 0.8575 1.02 0.79 1.02 0.79 1.03 0.7990 1.00 0.76 1.00 0.76 1.01 0.76105 0.99 0.78 0.99 0.78 0.99 0.78120 0.99 0.89 1.00 0.89 0.99 0.89

Fig. 4. Radiant exposure ratio as a function of beam size. The xaxis scan range is 3 mm with 60 and 30 μm SS. The aperture isplaced at the center, on the scan path. Only results for sinusoidalscan patterns are shown.

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B. Region B

As the beam spot moves through the turning point ofthe scanning path, depending on the location of theaperture, the calculated radiant exposure can in-crease due to beam overlap. To study this in detail,the aperture was placed at the turning point, andwas laterally moved in the x direction (Fig. 5) whileradiant exposure values were calculated along thepath. When the beam size was smaller than the aper-ture size, there was little difference in radiant expo-sure from Gaussian and top hat beams, similar to theresults shown in Section 3.A.

For beams larger than the aperture, central SSvalues of 120, 60, and 30 μm were analyzed. Theoptical beam diameter was 60 μm. This change inthe size ratio focuses the radiant exposure calcula-tion at a smaller region relative to the Gaussianbeam spot. The scanning range in the x directionremains 3 mm. In Fig. 6, the plots are grouped bySS. Figures 6(a), 6(b), and 6(c) show the change inradiant exposure as a function of aperture positionfor central SS of 120, 60, and 30 μm, respectively.Each plot displays both Gaussian and top hat beamcurves for sinusoidal, saw tooth, and triangularpatterns.

In Fig. 6(a), for the sinusoidal pattern case, as theaperture moves in the x direction and away from theturning point, the radiant exposure first increasesand reaches maximum, and then decreases. Table 3shows the radiant exposure levels of the 120 μm SScase. Here, the radiant exposure for Gaussian beamswas 13 times higher at the maximum than calculatedat the center of the scan path (Region A of Fig. 1).This difference is mainly due to the slower scanspeed at the turning point and no beam overlap atthe center. For the sinusoidal pattern, Gaussianbeams introduced higher maximum radiant expo-sure than top hat beams; however, the Gaussianbeam curve intersected with the top hat beam curveat x � −1.42 mm and maintained a lower radiantexposure level as the aperture moved in the x direc-tion. Both the saw tooth and triangular patterndemonstrated a similar yet gradual trend. Thiscan be intuitively understood since Gaussian beamsconcentrate most of the energy at the center. There-fore, as the beams overlap less with the aperture, the

Gaussian beams contribute less radiant exposure tothe aperture than top hat beams. In Table 4, themaximum radiant exposure for Gaussian beams is

Fig. 5. Radiant exposure analysis at the turning point. The smalldotted line is the scan path at the turning point of a sinusoidalpattern, the larger solid circle is the beam spot, and the smalldashed circle is the aperture.

Fig. 6. Radiant exposure as a function of aperture position. The xaxis scanning range is 3mm, beam spot size is 60 μm, and aperturesize is 30 μm. The aperture is laterally moved from the turningpoint located at x � −1.5 mm toward the center. Plots show thechange in radiant exposure for (a) 120 μm, (b) 60 μm, and(c) 30 μm central scan spacing. Each plot consists of 6 curves: 3scan patterns, each with 2 beam profiles.

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19% higher than that of top hat beams for the sinus-oidal pattern, and 14% higher for the saw tooth andtriangular patterns. As the aperture moves towardthe center along the x axis, all radiant exposurevalues decreased.

Figures 6(b) and 6(c) show the radiant exposurevalues when the central SS is reduced from120 μm to 60 μm and 30 μm, respectively. As the scanspacing decreases, the maximum exposure starts todrop due to increased scanning speed. However, themaximum exposure ratio between Gaussian and tophat beams maintain close to 20% as indicated inTable 4. In Figs. 6(a)–6(c), the radiant exposure atx � 0 mm increases as scan spacing decreases.However, increased overlap in this region also dimin-ishes the exposure difference between Gaussian andtop hat beams.

C. Region C

The calculation results of the radiant exposures forscanning irradiation when the aperture was placedoff-path, as shown in region C of Fig. 1, are shownin Table 5. The solid curves of Fig. 7 show the resultsfor a 60 μm central SS, which is twice the aperturesize. The dotted curves indicate the case wherethe spacing and aperture are equal (30 μm). Only theresult for S scanning was shown in Fig. 7 becauseresults for ST and T scanning were nearly identical.

As shown in Fig. 7, when the scan spacing is re-duced to 30 μm, radiant exposure is introduced inthe aperture even for small beam spot values of15 μm. Here, the RTH∕G is greater than 1, meaningthat, for this case, top hat beams still contain moreenergy than Gaussian beams. However, as the beamspot size increases, the radiant exposure differencebetween Gaussian and top hat beams diminishes,and RTH∕G approaches 1. Although the differencebetween radiant exposure Gaussian and top hatbeams can be as large as 100% for an off-pathaperture, the overall radiant exposure across theaperture is much lower than for the on-path aper-ture. Thus, the photothermal effect for off-pathapertures can be neglected.

4. Discussion

Our calculations indicate that there is a difference inoptical radiant exposure between Gaussian and tophat beams. Several of the conclusions with respect tothe most significant parameters are as follows.

Beam size: Depending on the relative size betweenthe beam and aperture, the calculated radiant expo-sure introduced by Gaussian and top hat beams canvary. For a central SS of 60 μm (Fig. 4), the Gaussianbeam introduced 25% higher radiant exposure thanthe top hat beam when the beam size was 3.4 timeslarger than the aperture size. However, the exposurelevel introduced by Gaussian and top hat beams wasthe same when the beam was smaller than the aper-ture. The same was observed when the aperture wasplaced at the turning point. When the beam spot istwice as large as the aperture [Fig. 6(a)], a Gaussianbeam can introduce 19% higher maximum radiantexposure than a top hat beam when the central SSis 120 μm. This 19%–25% higher radiant exposurefrom Gaussian beams compared to top hat beamsis mainly due to higher central concentration ofGaussian beam irradiance. Although a 25%difference may not cause a significant change in

Table 3. Radiant Exposure Level, at 120 μm Central Scan Spacing

Beam Type Aperture Position S (A.U.) ST (A.U.) T (A.U.)

Gaussian Center 0.60 0.94 0.94Turning PT 6.72 0.51 0.94Maximum 7.85 0.94 1.87

Top hat Center 0.52 0.82 0.82Turning PT 5.19 0.44 0.82Maximum 6.59 0.82 1.64

Table 4. Radiant Exposure Level, at 120 μm Central Scan Spacing

BeamType

AperturePosition

120 μm(A.U.)

60 μm(A.U.)

30 μm(A.U.)

Gaussian Center 0.60 0.30 0.21Maximum 7.85 4.05 2.05

Table 5. Results for Region C “Off-Path” Scanning

RTH∕G “Off-Path”

S ST T

Beam Size (μm) SS-30 SS-60 SS-30 SS-60 SS-30 SS-60

15 1.03 0.00 1.05 0.00 1.05 0.0030 1.05 0.00 1.06 0.00 1.05 0.0045 1.07 1.14 1.06 1.14 1.06 1.1460 1.01 1.27 1.01 1.27 1.01 1.2875 0.98 1.32 0.99 1.32 0.98 1.3290 1.01 1.24 1.01 1.24 1.02 1.24105 1.01 1.20 1.01 1.20 1.01 1.21120 1.01 1.10 1.01 1.10 1.01 1.10

Fig. 7. Radiant exposure ratio as a function of beam size. The xaxis scan range is 3 mm with 60 and 30 μm SS. The aperture isplaced at the center, between two scan paths. Only results forsinusoidal scan patterns are shown.

8590 APPLIED OPTICS / Vol. 53, No. 36 / 20 December 2014

the thermal damage threshold within the approxi-mate 10× safety margin of current exposure limitsin consensus standards, it can still be large enoughto influence safe operation time or dose of a scanningmedical device.

Scan spacing: The difference in radiant exposurebetweenGaussian and top hat beams is more obviouswhen the scan spacing is large compared to the beamsize. As the SS reduces, or as the beam size increases,beam overlap becomes the main factor in calculatingthe exposure level inside the aperture. However,RTH∕G is less than 1 for spot sizes larger than theaperture size, indicating that Gaussian beams intro-duce more radiant exposure in the aperture than tophat beams. As for the 30 μm central SS case, the dif-ference in exposure level between the two beams re-mains very small and the RTH∕G value fluctuatesaround 1. The radiant exposure difference betweenGaussian and top hat beams can be found whenthe aperture is placed between the two scan paths.As shown in Fig. 7, the RTH∕G values increase from0 to 1.32 when the central spacing is 60 μm, but re-main close to 1 when the SS is reduced to 30 μm. Asimilar trend can also be found in Table 2. When theaperture is placed at the center of the path, Gaussianbeams introduce 13% higher radiant exposure thantop hat beams for the central spacing of 120 μm, or abeam size to SS ratio of 0.5. However, when this ratiois increased to 2, Gaussian beams only introduce 5%higher radiant exposure than top hat beams.

Scan pattern: Gaussian beams introduced higherradiant exposure in the aperture than top hat beamsfor all three scan patterns. However, sinusoidal pat-terns introduced substantially higher radiant expo-sure at the turning point and maximum overlapregion, mainly due to the increased dwell time inthese regions. Therefore, among the three scan pat-terns presented in this study, more considerationshould be taken when measuring the radiant expo-sure level introduced by the sinusoidal pattern,and understand that maximum exposure occurs atthe maximum overlap point.

5. Conclusion

We have shown that the difference in calculated ra-diant exposure for Gaussian and top hat beams is de-pendent upon the beam and aperture size ratio,beam size to central scan spacing ratio, and scanningpatterns. When the aperture is placed on the scanpath, higher radiant exposure is calculated fromGaussian beams than top hat beams. The radiant ex-posure difference between the two beams reachesmaximum when the beam size is 3.4 times largerthan the aperture. Radiant exposure from Gaussianbeam can be 25% higher than that from the top hatbeam. However, this difference is also affected by thebeam overlap, which is determined by the relativespacing between the beam size and scanning pathdistance. The sinusoidal pattern introduces the larg-est radiant exposure level at regions close to theturning points compared to the sawtooth and

triangular patterns. The radiant exposure leveldifference shown here, as high as 25% differencebetween Gaussian and top hat beams, may not besignificant enough to overcome the safety marginembedded in most commonly used exposure limitvalues published in many consensus standards; how-ever, it can still be large enough to require differentclassification of optical light sources. These resultswill provide a valuable reference for calculatingaccurate radiant exposure values of various scanningoptical devices.

This work was in part supported by the CriticalPath Initiative of the U.S. Food and Drug Adminis-tration. The mention of commercial products, theirsources, or their use in connection with materialreported herein is not to be construed as either anactual or implied endorsement of such products bythe Department of Health and Human Services.

†These authors contributed equally.

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