Simulation of laser induced retinal thermal injuries for non-uniform irradiance profiles and their evaluation according to the laser safety standard
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Simulation of laser induced retinalthermal injuries for non-uniformirradiance profiles and theirevaluation according to the lasersafety standard
Kotzur, Sebastian, Wahl, Siegfried, Frederiksen, Annette
Sebastian Kotzur, Siegfried Wahl, Annette Frederiksen, "Simulation of laserinduced retinal thermal injuries for non-uniform irradiance profiles and theirevaluation according to the laser safety standard," Proc. SPIE 11363, TissueOptics and Photonics, 1136314 (2 April 2020); doi: 10.1117/12.2555492Event: SPIE Photonics Europe, 2020, Online Only, France imulation of laser induced retinal thermal injuries fornon-uniform irradiance profiles and their evaluation accordingto the laser safety standard
Sebastian Kotzur a, b , Siegfried Wahl b, c , and Annette Frederiksen da Robert Bosch GmbH, Corporate Research, 71272 Renningen, Germany b Institute for Ophthalmic Research, Eberhard Karls University T¨ubingen, 72076 T¨ubingen,Germany c Carl ZEISS Vision International GmbH, 73430 Aalen, Germany d Robert Bosch GmbH, Chassis Systems Control, 71701 Schwieberdingen, Germany
ABSTRACT
Laser systems emitting radiation in the visible and near infrared region are potentially hazardous for the retinaof the human eye. This can result in irreparable injuries due to photomechanical, photothermal or photochemicallight-tissue interactions. This investigation focuses on the photothermal interaction for which a computer modelis used to simulate the thermal behavior of the retina and to predict the injury threshold values. The mostimportant factors are the wavelength of the radiation, the exposure time and the irradiance profile on theretina. For performing safety evaluations and classifications the laser safety standard IEC 60825-1:2014 hasto be considered. These evaluations are based on emission limits which depend on the same above mentionedfactors. According to the IEC 60825-1:2014, non-uniform retinal images are treated by an image analysis wherean averaged spot size is used. This averaged size is calculated by the extent of the irradiance profile along twoorthogonal directions. Unlike the laser safety standard, the computer model predicts the injury thresholds foran irradiance profile on the retina without averaging the spot size. In this investigation, a broad variety ofnon-uniform retinal images is investigated with regard to the injury thresholds predicted by the computer modeland to the classifications according to the laser safety standard.
Keywords: eye safety; laser safety; IEC 60825-1; retinal thermal injury; computer model; accessible emission;retinal image
1. INTRODUCTION
A laser represents a potential hazard for the human eye and the skin. Depending on the wavelength and pulseduration of the laser radiation different damage mechanism can lead to injuries. The ICNIRP guidelines provideexposure limits ensuring protection against all possible injuries. Another common document which providescorresponding emission limits is the laser safety standard IEC 60825-1:2014. This standards is a product safetystandard and is used for the classification of laser systems. Here, a laser system of Class 1 is considered as a safeproduct.This investigation focuses on the retinal thermal injury where a denaturation process can irreversibly damagethe retina leading to a permanent vision loss. The retinal thermal injury is induced by radiation in the visibleand near-infrared region and for pulse durations in the microsecond and second regime. The correspondingemission limits are derived from experimental threshold values. A lot of measurements were performed withnon-human primates (NHP) which represent a suitable model to derive emission limits as their retinas are moresensitive compared to the human retina.
The measured threshold values are often referred to as ED valuessince there is a probability of 50% to induce an injury. In the scope of this investigation the term threshold(THR) value will be used for the ED value. The emission limits are obtained by applying a safety factor, herereferred to as reduction factor (RF), to the threshold values.However, all threshold experiments which are used to derive the emission limits are based on investigationsof circular symmetric laser radiation with a Gaussian or tophat shape. For the eye safety analysis of arbitrary Tissue Optics and Photonics, edited by Valery V. Tuchin, Walter C. P. M. Blondel, Zeev Zalevsky, Proc. of SPIE Vol. 11363, 1136314 · © 2020 SPIE CCC code: 0277-786X/20/$21 · doi: 10.1117/12.2555492Proc. of SPIE Vol. 11363 1136314-1 on-uniform retinal irradiance distribution the laser safety standard and the ICNIRP guidelines instruct tomeasure the amount of the retinal radiant energy which is contained in a field stop and to compare it to thelimit. To be more precise, the field stop has to be varied in its size, position and orientation to obtain the mostrestrictive result. It is stated that the averaged field stop size and therefore the averaged retinal spot size isused for the calculation of the emission limit without giving a rationale. As there is currently no experimentaldata available, the question arises whether this procedure is justified or not.The main focus of this investigation is the consideration of non-uniform spots in the thermal damage regimewith regard to the threshold value and the emission limit according to the laser safety standard IEC 60825-1:2014. The threshold values are obtained by a computer model. The model is validated against retinal thermal injuryED data which are based on circular symmetric irradiance profiles. The computer model predicts the thresholdvalue and is valid for pulse durations longer than 100 µ s. The topic of non-uniform irradiance profiles concernsfor example line lasers which have a collimated and a divergent axis. These systems are generally allowed to havea higher output power than laser pointers as the radiation is imaged on a larger area on the retina. However,the retinal image can be basically described by a thin long line radiating the retina. A classification accordingto the laser safety standard IEC 60825-1 is based on the averaged spot size.
2. RETINAL THERMAL INJURY MECHANISM
The retinal thermal injury mechanism is dominant for exposure durations between the microsecond and secondregime. It is a denaturation of the proteins within the retina and can be described as a thermal burn. As aconsequence, necrosis of the cells occurs leading to a permanent vision loss in the concerned regions. If the retinais exposed to laser radiation, most of the radiant energy will be absorbed by the retinal pigment epithelium(RPE).
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The energy is converted into thermal energy. In the RPE, the temperature increase is the highest.The injury can be described analytically with the Arrhenius equation
10, 11
Ω ( t ) = A (cid:90) t exp (cid:18) − ERT ( t (cid:48) ) (cid:19) d t (cid:48) . (1)Here, R is the ideal gas constant. A is a frequency factor and E is the inactivation energy. Both of thesevalues can be measured experimentally. The temperature dependence of A is negligible small compared to theexponential function in the integrand and is assumed to be constant. The value Ω represents the percentageof denatured molecules with the relation c denatured ( t ) = 1 − exp ( − Ω ( t )) . (2)In general, a thermal injury occurs for Ω >
1. The computer model in this investigation is based on thedefinition of a damage threshold where Ω equals one. This corresponds to a degree of denaturation of 63% whichis commonly accepted to define the thermal injury. Equation (1) shows that the criterion for the denaturation process is not based on a temperature limit butrather on the temporal temperature profile. For this reason, the thermal damage is strongly coupled to the shapeof the retinal image and the exposure duration.
3. COMPUTER MODEL TO DESCRIBE LASER INDUCED RETINAL THERMALINJURIES
The computer model used in this investigation is a further development of the Seibersdorf Laboratories Model(SLM). The SLM was build by Jean who validated his model against 31 studies with 253 experimental ED values.
13, 14
The SLM is a two dimensional axial symmetric model for investigating circular symmetric irradiance profiles.The model predicts the ED threshold value in terms of the total intraocular energy of the retinal irradianceprofile. The principal procedure to build a retinal thermal injury model is to define a heat source within theretinal layer with the irradiance profile. Then, the heat transfer equation is numerically solved and the temporaltemperature behavior is used in the Arrehnius equation (1). Proc. of SPIE Vol. 11363 1136314-2 n the following, the main elements of the SLM are presented which are based on the validation against non-human primates. For obtaining the retinal image size, the LeGrand model for the relaxed human eye was used. Here, the eye model consists of four layers, namely the cornea, the aqueous, the lens and the vitreous body. Thesizes of these layers were scaled with a factor of 0 .
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As laser radiation cannot be focussed on an infinitely small spot, there is a minimum spot sizefor the retinal image. The measurements on non-human primates show that the threshold values converge to aconstant energy for laser sources smaller than 5 mrad.
This is set as the minimum spot size in the computermodel. The propagation of the laser radiation through the eye is accompanied by absorption at the layers of theeye model and by intraocular scattering.
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The amount of radiant energy that reaches the retina depends onthe wavelength and on the beam size. It is distinguished between the total transmission T Total which applies forrelatively large retinal images and the direct transmission T Direct26 which applies for small retinal images.It is suggested by Jean to use an equation that ensures a continuous transition from small to large retinalspot sizes. By describing the retinal spot size with the radius r Spot the effective transmission is given by T eff ( λ, r Spot ) = T Total (1 − g ( λ ) h ( r Spot )) (3)with g ( λ ) = 12 exp (cid:18) − λ
883 nm (cid:19) (4)and h ( r ) = exp (cid:18) − r µ m (cid:19) . (5)The amount of radiant energy that is absorbed by the retinal layers will be directly converted into thermalenergy and therefore the absorption behavior of the tissue defines a heat source q ( t, (cid:126)r ). The heat transferequation is given by ρC ∂T∂t = k ∆ T + q ( t, (cid:126)r ) . (6)The thermal properties of the tissue are listed in Table 1. They are assumed to be homogenous and similar to Table 1. Thermal properties of the retina to simulate the heat transfer by a laser source. thermal property valueconductivity k . Wm K specific heat C Jkg K density ρ kgm initial temperature T . Furthermore, the thermal properties are assumedto be independent of the temperature which results in a linear behavior with regard to the heat source or in caseof a laser irradiated retina, to the laser power.To determine the thermal injury threshold value, the Arrhenius equation (1) has to be solved. Here, thetemporal temperature behavior of the RPE layer is needed since the lesion is build within this layer.
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Inaddition, the model was validated with the definition that there is MVL which has a diameter of 50 µ m for thenon-human primate. Therefore, to determine the threshold value the temperature in the RPE layer at the edgeof the MVL circle has to be considered. This will result in a value for Ω ≥ To obtain the threshold values for human eyes, the following adjustments of the above described model haveto be made. The minimum visible lesion is set to 20 µ m even though such small lesions are not detected byophthalmoscopes. Furthermore, the minimum spot size is set to 25 µ m.
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At last, the focal length of therelaxed human eye is set to 16 .
68 mm which correspond to an air-equivalent focal length of the Le Grand eyemodel.
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Proc. of SPIE Vol. 11363 1136314-3 . THREE DIMENSIONAL COMPUTER MODEL TO DESCRIBE THERMALINJURIES OF NON-UNIFORM IRRADIANCE PROFILES
We improved the SLM and developed a three dimensional model to investigate non-uniform retinal images.In this investigation two different irradiance profiles are considered, the elliptical tophat and the rectangulartophat. Both of the irradiance profiles are illustrated in Fig. 1. As both profiles are axisymmetric the heat
Figure 1. Depiction of an elliptical (left) and rectangular (right) tophat retinal irradiance profile used to simulate thethermal injury threshold value. transfer equation (6) can be simplified by defining two symmetry planes where only two octants of the three-dimensional model have to be solved. In the following, the irradiance profiles are given in a coordinate systemwith an x - and y -axis. Both profiles are characterized by the two diameters d x and d y representing the extent ofthe image in the corresponding orthogonal axis.For applying the computer model which is validated against circular symmetric retinal images two issues haveto be discussed. The first issue is the determination of the transmission which gives the amount of radiant energythat propagates through the retina. In case of circular symmetric spots, this was given by equation (3) wherethe effect of intraocular scattering is taken into account. Regarding non-uniform retinal spots, it is currentlyunclear how the transmission is determined. Therefore, we propose a new transmission equation which is basedon equation (3). Here, equation (3) is integrated along the retinal spot shape and divided by the limits of theintegration.For an elliptical tophat irradiance profile with the widths d x and d y the averaged effective transmission iscalculated by T elleff ( λ, d x , d y ) = 2 π (cid:90) π T eff (cid:0) λ, r ell ( ϕ ) (cid:1) d ϕ. (7)with r ell ( ϕ ) = d x d y (cid:114)(cid:0) d x sin ( ϕ ) (cid:1) + (cid:16) d y cos ( ϕ ) (cid:17) . (8)For a rectangular tophat irradiance profile the averaged transmission is calculated by T recteff ( λ, d x , d y ) = 2 π (cid:32)(cid:90) ϕ C T eff (cid:18) λ, d x ϕ ) (cid:19) d ϕ + (cid:90) π ϕ C T eff (cid:18) λ, d y ϕ ) (cid:19) d ϕ (cid:33) (9)with ϕ C = arctan (cid:18) d y d x (cid:19) . (10)When it comes to small spot diameters which are in the region of the minimal spot size the transmission func-tion strongly impacts the threshold value. To illustrate this behavior two further definitions of the transmission Proc. of SPIE Vol. 11363 1136314-4 or non-uniform spots will be used in this investigation. In one definition the minimum of the spot diameters d x and d y will be used in equation (3). In the other the averaged spot size is inserted into equation (3).The other issue is the definition of the minimal visible lesion (MVL) which is set as a circle with a diameterof 20 µ m. However, in a non-uniform irradiance profile it is unclear how the shape of the MVL should look like.By using the definition of a circular symmetric MVL the temporal temperature behavior of the RPE layer in thedirection of the smaller spot diameter has to be investigated. Using the temperature curve along the larger spotdiameter leads to a higher temperature increase as there is less cooling and therefore leads to a lower thresholdvalue. This issue dominates for spot shapes where one diameter is in the region of the minimal spot size andthe other diameter is much larger. To illustrate the impact of the temperature curve, both the temperature in x - and y -direction of the MVL will be investigated.
5. REDUCTION FACTOR
The reduction factor (RF) is an essential value for laser and lamp safety issues. All available emission limitsfor coherent and incoherent radiation
1, 2, 33, 34 are derived from ED values which represent the 50 % probabilityof injury and are understood as threshold values (THR). In this study, the threshold value is given in termsof the total intraocular energy. By applying the laser safety standard to the investigated retinal images thecorresponding maximum permissible exposures (MPE) are calculated. The reduction factor is then defined asRF = THRMPE . (11)The calculation of the MPE is performed by varying the angle of acceptance with a field stop in the retinalimage. This procedure is in accordance with the laser safety standard and the ICNIRP guidelines. Thisimage analysis procedure is applied to the tophat profiles. Here, the diameters d x and d y are equal to theangular subtense of the apparent source α x and α y which is a term from the laser safety standard to describethe retinal spot size. In Fig. 1, the field stops are illustrated by the solid red line representing the shape of thetophat.The emission limits from the laser safety standard depend on the wavelength, the emission duration andthe angular subtense α of the apparent source. The angular subtense is limited to the minimum spot size of1 . α max ( t ) which depends on the emission duration and varies from 5 mradto 100 mrad. The average of both angular subtenses has to be calculated α = α lim x + α lim y For the retinal thermal injury thresholds,a high RF is not needed as this injury mechanism is well understood and a RF of two is sufficient.
6. RESULTS6.1 Overview of simulation parameters
In the following, the computer model was applied to both tophat shapes from Fig. 1 for a wavelength of 530 nmas the RF is here the lowest for single pulses.
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The simulation was performed on four parameter sets whichare listed in Table 2. The intervals, depicted with the squared brackets, show a parameter variation. The retinal
Proc. of SPIE Vol. 11363 1136314-5 able 2. Parameter sets used for the computer model to predict the retinal thermal threshold values. parameter set emission duration (s) spot size α x (mrad) spot size α y (mrad)1 [10 − ,
10] 1 . − . . , − . . , . . , d x and d y on the retina. Here, the size of the irradiance profile in x -direction is set to the minimum spot sizewhereas in y -direction it is varied or set to 150 mrad which produces a long thin irradiated area on the retina.With these parameter sets the averaged spot size from equation (12) may show the highest discrepancy betweenthe MPE and the THR. To illustrate the thermal behavior of the RPE layer, the isothermal curves for an elliptical tophat retinal irradianceare shown in Fig. 2 where the intraocular energy is set to the threshold value of about 375 µ J. Within the pulse0 50 100 150050100150200250 x ( µ m) y ( µ m ) t = 0 . x ( µ m) y ( µ m ) t = 1 . x ( µ m) y ( µ m ) t = 5 . Figure 2. Isothermal curve for an elliptical tophat retinal irradiance profile with the widths α x = 10 mrad and α y =25 mrad for a pulse duration of 1 ms. The isothermal curves show the temperature increase within the lesion depth of theRPE layer. duration of 1 ms the tissue is heated up inside the tophat profile and causes a strong temperature gradient atthe edge of the elliptical profile. As a finite element method is used, the isothermal curves show fluctuationsduring the heating process. At the time 5 . x -direction(THR x ) of the retinal irradiance profile whereas the blue curves show the results obtained by the temperaturebehavior along the y -direction (THR y ). Here, the corresponding threshold values were calculated by solving therelation Ω = 1 with equation (1). According to the definition of a retinal thermal injury the minimal visiblelesion is a circle with a diameter of 20 µ m. With this definition the THR x value is seen as the correct resultas this threshold value ensures to produce a damage within the MVL. Along the x -direction the temperatureincreases with a smaller slope at the edge of the MVL than along the y -direction as there is more cooling from Proc. of SPIE Vol. 11363 1136314-6 igure 3. Reduction factor (left), energy (center) and irradiance (right) for the elliptical tophat and for parameter set1 of Table 2 where the emission duration is varied. For the middle and right plot, the black solid line correspond theevaluation according to the laser safety standard. The red and blue curve show the threshold values according to thecomputer model for the consideration of the temperature behavior at the corresponding axis. The red and blue solid linesare based on the transmission function from equation (7). The corresponding dash-dotted line refers to a transmissioncalculation where the average spot size is inserted into equation (3) and the dashed line to a transmission where theminimum spot diameter is inserted into equation (3). the surrounding tissue. As a result, the THR x value is smaller than the THR y value. Both curves illustrate thedependence of the simulated threshold value from the definition of the MVL. In case of an MVL defined as anellipse, the THR y could be considered as correct.The solid red and blue curves show the results for our proposal according to equation (7) where non-uniformirradiance profiles are considered. The dashed curves are based on a transmission where the minimum spotdiameter is inserted into the transmission function which can be applied for symmetric spot shapes. The trans-mission values are lower than in our proposed equation which leads to higher threshold values and thereforehigher reduction factors. However, the differences are smaller than the comparison with the dashed-dotted curvewhere the averaged spot size is inserted into equation (3). Here, a higher radiant energy is assumed to propagateto the retina and therefore this consideration leads to more restrictive results.For an emission duration of 40 ms, the reduction factor shows a minimum. For the solid red curve thereduction factor is 1 .
833 with a threshold value of 5 .
965 mJ. In case of the solid blue curve, the reductionfactor is 1 .
642 with a threshold value of 5 .
344 mJ. The maximum permissible exposure according to the lasersafety standard IEC 60825-1:2014 is 3 .
254 mJ. Even for a less restrictive consideration where the minimum spotdiameter is used (dashed line) the minimum reduction factor for the red curve (THR x ) was 1 .
880 which is lowerthan the recommendation by the ICNIRP guidelines. The results for the parameter sets 2 to 4 of Table 2 are shown in Fig. 4. In these parameter sets thesize of the irradiance profile along the y -direction was varied for a constant emission duration. The impactof the transmission behavior is higher for an increasing retinal spot size. In case of the first parameter step α y = 1 . Here,the irradiance converges to a constant value which is caused by the maximum spot size limitation from the lasersafety standard and the creation of a local hot spot in the RPE layer where the cooling of the surrounding tissueis not sufficient to allow a higher irradiance level.
Proc. of SPIE Vol. 11363 1136314-7 igure 4. Reduction factor (left), power (center) and irradiance (right) for the elliptical tophat and for parameter setsfrom 2 to 4 of Table 2 where the retinal spot size is varied in y -direction. Further details are the same as in Fig. 3. By considering the transmission behavior from equation (7) the following minimum reduction factors listedin Table 3 can be found. The minimum values for the x - and y -direction do not always appear for the same size Table 3. Minimum reduction factors for the parameter set from 2 to 4 (Table 2, Fig. 4). parameter x -direction y -directionset RF () α y (mrad) THR x ( µ J) MPE ( µ J) RF () α y (mrad) THR y ( µ J) MPE ( µ J)2 1 .
926 110 1 . . .
647 110 1 . . .
835 100 7 . . .
662 90 6 . . .
335 150 467 . . .
198 150 439 . . α y which is the case for parameter set 3. The minimum reduction factor regarding the THR x value is about 1 . y about 1 .
6. If the different transmission functions are taken into account the minimumvalues are 1 .
892 (dashed line) and 1 .
459 (dash-dotted line) for the THR x value and 1 .
720 (dashed line) and 1 . y value regarding the same parameter set. Proc. of SPIE Vol. 11363 1136314-8 .3 Rectangular spots
In comparison with the elliptical tophat, the reduction factors are larger for the rectangular tophat profiles. Theminimum reduction factor also appears for an emission duration of 40 ms. For the solid red curve the reductionfactor is 2 .
332 with a threshold value of 7 .
588 mJ whereas for the solid blue curve the reduction factor is 2 . .
798 mJ. According to the laser safety standard, the maximum permissible exposureis 3 .
253 mJ. Furthermore, the irradiance which represents both the threshold and the maximum permissibleexposure is lower in case of the rectangular tophat than for the elliptical tophat. This is due to the thermalbehavior where the cooling is better for the elliptical shape. In case of the rectangular tophat there is less heatdissipation in the center point of the irradiance profile.For all parameter sets from 1 to 4 the maximum permissible exposure according to the laser safety standardIEC 60825-1:2014 is the same as it was for the elliptical distribution. This is due to the fact that different fieldstop shapes were used for the laser safety evaluation.By considering the transmission behavior from equation (7), the following minimum reduction factors listedin Table 4 can be found. The minimum reduction factor regarding the x -direction is about 2 . Table 4. Minimum reduction factors for the parameter set from 2 to 4 (Table 2). parameter x -direction y -directionset RF () α y (mrad) THR x ( µ J) MPE ( µ J) RF () α y (mrad) THR y ( µ J) MPE ( µ J)2 2 .
303 5 . .
468 47 .
961 1 .
970 5 . .
502 47 . .
317 30 3 . . .
098 30 2 . . .
880 120 460 . . .
714 120 433 . . y -direction about 1 .
9. By taking the different transmission functions into account, the minimum values are 2 . .
293 (dash-dotted line) for the THR x value and 1 .
993 (dashed line) and 1 .
962 (dash-dottedline) for the THR y value regarding the same parameter set.
7. SUMMARY AND CONCLUSION
A three dimensional computer model to simulate the retinal thermal injury damage mechanism by solving theheat equation and the Arrhenius equation with the temporal temperature behavior was used to predict thethreshold value of laser-induced retinal injuries for non-uniform irradiance profiles. The computer model wasderived from the work of Jean
13, 14 whose model is validated against experimental ED values of non-humanprimates. We investigated an elliptical and a rectangular tophat as retinal irradiance distribution and comparedthe simulated threshold values with the corresponding emission limits according to the laser safety standardIEC 60825-1:2014. Currently no measured threshold values exist for these profiles since experiments withnon-uniform profiles have not been performed in the past.We examined the applicability of the MVL definition to non-uniform retinal irradiance profiles whereas twodifferent threshold values were simulated. Both threshold values are obtained with Ω = 1 for the two orthogonaldirections along the retinal spot shape and show how the predicted threshold value changes.Here, four differentparameter sets were investigated. In one parameter set the emission duration was varied where in the othersets the retinal spot size was varied in one direction which shows the transition from the minimum spot sizeto an elongated spot. According to the laser safety standard the averaged spot size has to be considered. Thereduction factor which is calculated by the ratio between the threshold value and the maximum permissibleexposure according to the laser safety standard directly shows the validity of this calculation procedure. In thisstudy, the minimum reduction factor is 1 .
926 for the MVL definition of the smaller extend and 1 .
662 for theother direction, respectively. These minimum values are below the reduction factor of two which is defined bythe ICNIRP guidelines to be sufficient. According to the definition of a circular MVL, the minimum reductionfactor is 1 .
926 for the investigated non-uniform irradiance profiles. This is sufficient and proofs the applicabilityof the calculation procedure from the laser safety standard in these cases.In addition, different transmission behaviors were investigated. For small spot sizes intraocular scatteringdominates where the direct transmission has to be taken into account. In case of symmetric spot shapes, Jean
13, 14
Proc. of SPIE Vol. 11363 1136314-9 roposed an equation that ensures a transition from direct to total transmission. On this base, we propose amethod which can be applied to non-uniform irradiance profiles. To illustrate the influence of the transmissionon the threshold value, two different methods were additionally investigated. In one method the minimum spotdiameter was used and in the other method the averaged spot size was used in the formula for symmetric spots.In our results, the method with the minimum spot size is less restrictive and leads to reduction factors up to2 .
8. OUTLOOK
In a future study, this issue of the MVL can be avoided by setting the minimum spot diameter of the irradianceprofile to 5 mrad which is about four times larger than the MVL. In addition, using a larger minimum spotdiameter avoids several other issues that come with the minimum spot size in laser safety evaluations. The other issue is the transmission behavior for non-uniform retinal images. With a similar approach asdescribed above where the minimum spot diameter is set to 5 mrad this problem can be reduced but not solved.To get the transmission behavior for retinal images with widths of the minimum spot size the exact scatteringbehavior has to be taken into account. In this study a procedure was developed to calculate the transmission fora non-uniform retinal spot. However, this transmission factor is treated as a constant factor that is multiplied tothe irradiance profile on the retina. As a consequence, the reduction factor scales linearly with the transmissionfactor. In the region of the minimum spot size, this approach is currently only validated for radially symmetricretinal images.Also, in a future study an elliptical Gaussian distribution can be investigated with regard to the simulatedthreshold value and the maximum permissible exposure. In addition, as there is currently no explicit definition, an elliptical as well as a rectangular field stop can be used for the laser safety evaluation. Here, the differencesbetween both approaches can be discussed and compared to the simulated threshold values.At last, the same study can be expanded to the topic of pulsed irradiance profiles. The calculation procedureof the laser safety standard IEC 60825-1:2014 for pulsed retinal images shows a more complex evaluation wherethree criterions have to be applied. Here, the applicability of the laser safety evaluation method can be verifiedfor non-uniform irradiance profiles.
9. ACKNOWLEDGEMENTS
The authors would like to thank Mathieu Jean and Dr. Karl Schulmeister from the Seibersdorf Labor GmbH forinspiring discussions regarding the simulation of retinal thermal injury thresholds.
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