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[Hiroshi Honda](https://orcid.org/0000-0003-0011-9063), [Makoto Watanabe](https://orcid.org/0000-0002-5064-9583)

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[Measurement of Laser Absorptivity of Inconel Powders with Additive Manufacturing Machine](https://mdr.nims.go.jp/datasets/a7d0e6a7-7900-4877-812a-250963de740d)

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Measurement of Laser Absorptivity of Inconel Powders with Additive Manufacturing MachineMeasurement of Laser Absorptivity of Inconel Powders with AdditiveManufacturing MachineHiroshi Honda+ and Makoto WatanabeResearch Center for Structural Materials, National Institute for Materials Science, Tsukuba 305-0047, JapanThe nickel-based superalloy Inconel is considered suitable for near-net-shape manufacturing using additive techniques, primarily due to itsmachining difficulties. In laser metal-based powder-bed fusion additive manufacturing, the laser absorptivity of metal powder is one of theparameters that must be known in order to elucidate, optimize, and numerically simulate manufacturing. Therefore, we tried to measure the laserabsorptivities of Inconel 718 and Inconel 738LC powders using a commercially available additive manufacturing machine.[doi:10.2320/matertrans.MT-M2024124](Received August 27, 2024; Accepted October 17, 2024; Published December 25, 2024)Keywords: additive manufacturing, powder-bed fusion, laser absorptivity, Inconel 718 powder, Inconel 738LC powder, Ti-6Al-4V powder1. IntroductionThe nickel-based superalloy Inconel is used in theaerospace and plant industries because of its high strength,high corrosion resistance, and high oxidation resistance athigh temperature. However, it is known to be difficult to cut.Therefore, it is expected to be manufactured in near-net shapeby additive manufacturing.Laser powder-bed fusion is one of the additivemanufacturing methods for metals. In this technique, laserenergy absorption is a crucial initial step in the manufacturingprocess, with absorptivity being a key parameter forelucidating or optimizing processes. For numerical simu-lation of the manufacturing process, laser absorptivity isindispensable. Understanding the temperature-dependentnature of laser absorptivity is also essential for a detailedcomprehension of the phenomena occurring in the manu-facturing process.One method of measuring the light absorptivity of powdersis to utilize an integrating sphere. Brandau et al. [1] measuredthe absorptivity of various metal powders across a widerange of light wavelengths by using a spectrometer with anintegrating sphere.Calorimetric methods have also been used to measure thelaser absorptivity of materials. Haag et al. [2] measured theabsorptivity of aluminum, copper, iron, and titaniumaluminide powders for a CO2 laser in different atmospheresusing specialized equipment. Wieting et al. [3] measured thelaser absorptivity of stainless steel sheets in a vacuum furnacefor a CO2 laser. The temperature dependence of laserabsorptivity has also been investigated by varying thefurnace temperature. Rubenchik et al. [4, 5] assembled ameasurement system with a laser diode to assess thetemperature-dependent laser absorptivity without a furnacesetup. The laser absorptivities of both plates and powderforms for various materials were measured [4–6]. Trapp et al.[7] measured the overall laser absorptivity, encompassingall phenomena that occur during the manufacturing process.The total laser absorptivities during the manufacturingprocesses for various laser irradiation conditions, such aslaser power and scanning speed, were reported [7, 8].Among nickel-based superalloy Inconel powders, how-ever, there are few reports on laser absorptivity measurementsspecifically for Inconel 625 [6]. Further, material surfaceconditions change depending on the production method andthe storage conditions, and surface conditions are thought toinfluence laser absorptivity. Therefore, measuring the laserabsorptivity of powders used the powder-bed fusion additivemanufacturing is considered important. The laser and themanufacturing environment, which affect laser absorptivity,vary based on the additive manufacturing machine and themanufacturing process. Therefore, it is necessary to knowthe laser absorptivity in each manufacturing situation in orderto understand the additive manufacturing process and realizethe desired product.In a previous study [9], we proposed a simple method ofmeasuring laser absorptivity under the same circumstancespresent in the manufacturing process by using a commer-cially available additive manufacturing machine andpresented the experimental results for titanium alloy Ti-6Al-4V. Using this method, in the present study, we tried tomeasure the laser absorptivity for Inconel 718 and Inconel738LC powders in addition to titanium alloy Ti-6Al-4Vpowder. We also modified the laser irradiation conditionsto extend the measurement temperature range to highertemperatures than those used in the previous study.2. Experimental ProcedureLaser absorptivity was measured using the calorimetricmethod employed previously, similar to the technique ofRubenchik et al. [4, 5]. The laser absorptivity wasdetermined by analyzing energy conservation during thetemperature alteration of a specimen irradiated by the laser.To enable the use of a commercially available additivemanufacturing machine, the laser irradiation conditionswere chosen to ensure their feasibility for the machine’soperation. The experimental setup was the same as that inthe previous study, as shown in Fig. 1 [9]. The powder tomeasure laser absorptivity was spread out on a tray, and the+Corresponding author, E-mail: HONDA.Hiroshi@nims.go.jpMaterials Transactions, Vol. 66, No. 1 (2025) pp. 107 to 112©2024 The Japan Institute of Metals and Materialshttps://doi.org/10.2320/matertrans.MT-M2024124laser beam scanned the powder area repeatedly as shown inFig. 1.Laser absorptivity can be calculated by analyzing powerconservation during the heating process induced by laserirradiation for a specimen consisting of a tray and powder. Itcan be written as follows:AðT Þ ¼ ðm1c1ðT Þ þm2c2ðT ÞÞ�T þ LðT Þ�tEð1ÞHere, t is time, T is temperature, and A(T ) is laser absorptivityat temperature T. m1 and m2 are the masses of the powder andtray, respectively. c1(T ) and c2(T ) are the specific heats ofthe powder and tray at temperature T, respectively. L(T ) isthe thermal loss from the specimen to the surroundings attemperature T. E and ¦T are the irradiated energy and thetemperature rise during the time interval ¦t, respectively. Thethermal loss can be evaluated from the specific heats and thecooling rate dT/dt at temperature T as follows:LðT Þ ¼ �ðm1c1ðT Þ þm2c2ðT ÞÞdTdtð2ÞThe thermal loss was estimated based on the temperatureevolution during the cooling process following heating, withthe cooling conditions maintained to be identical to thoseduring heating in order to minimize the difference betweenthe thermal losses during the heating and cooling processes.The SLM Solutions SLM280 was used as a commerciallyavailable laser powder-bed fusion additive manufacturingmachine. The laser was a Gaussian beam with a 1070 nmwavelength. The specimen was set in the machine’sprocessing chamber. The chamber was filled with argongas, mirroring the environment of the machine’s manufactur-ing process.The powders were commercially available. The Inconel718 and Inconel 738LC powders used were Concept LaserCL 100NB and Höganäs Amperprint 0151, respectively. Tocompare the results with those of the previous study, laserabsorptivity measurements were conducted for the titaniumalloy Ti–6Al–4V powder as the laser irradiation conditionswere changed from those in the previous study. The titaniumalloy Ti–6Al–4V powder used was Concept Laser CL 41TIELI. The tray material was titanium alloy Ti–6Al–4V, as inthe previous study.The tray dimensions were 10mm © 10mm © 1mm, andits top surface had a machined recessed flat portion with a0.10mm depth. The flat recessed portion was filled flat withthe metal powder up to the level of the rim. A thermocouplewas attached to the center of the bottom surface of the tray tomeasure the temperature.The mass of the tray was 0.4083 g. The powder masseswere evaluated by measuring those on trays of the sameshape. The masses of the nickel-base superalloy powderswere in the ranges of 0.0273 « 0.0018 g and 0.0332 «0.0006 g for Inconel 718 and Inconel 738LC, respectively.The mass of the titanium alloy Ti-6Al-4V powder was inthe range of 0.0159 « 0.0005 g. The errors of the massesrepresent the standard errors.The laser beam was nearly perpendicular to the specimenand scanned the powder area in a meander hatch pattern asshown in Fig. 1. To prevent the metal powder from melting,the scan speed was set to high, which was estimated to beabout 16m/s. The spot size of the laser beam on thespecimen was also expanded, which was estimated to beabout 2.2mm. The laser power was 50W.The laser was turned on while scanning along each hatchline and off while moving between lines. To reduce the non-irradiation time of the laser and increase the average powerof laser irradiation on the specimen during the heatingprocess, the time interval between scans of the meander hatchpattern was shortened compared to the previous study. Thetime interval in this experiment was estimated to be about0.0339 s. The temperature around the laser irradiation pointrises locally, with the increase becoming remarkable whenthe hatch lines are dense, due to rapid and repetitive heating.To increase the mean moving speed of the laser beam movingperpendicular to the hatch line and reduce the localizedtemperature rise around the laser irradiation point on thespecimen, the number of hatch lines was also reducedcompared to the previous study; in this experiment, therewere 17 hatch lines in the powder area of the specimen. Thescanning process of the meander hatch pattern was replicated1000 times.For the temperature-dependent specific heat used in thecalculation of laser absorptivity, the fitting functions derivedfrom experimental data were used. The fitting line for thetitanium alloy Ti–6Al–4V [10] used in the calculation isdrawn alongside the experimental data [11] in Fig. 2. Theexperimental data for Inconel 718 [12] and Inconel 738 [13]are also shown with the fitting lines used in the calculations.3. Results and DiscussionFigure 3 illustrates the temperature history measured forthe titanium alloy Ti-6Al-4V powder. Because the temper-ature sampling interval was 0.1 s, which was longer thanthe interval between scans of the meander hatch pattern, thetemperature history’s heating curve shows continuousheating without showing temperature changes correspondingto the time interval between scans of the meander hatchLaser beamThermocoupleTrayPowderBeam scanningFig. 1 Schematic of the experimental setup [9].H. Honda and M. Watanabe108pattern. The values of ¦T and ¦t for the laser absorptioncalculation in eq. (2) were determined as depicted in Fig. 3,and the value of ¦t was set to 2 s.As seen from the magnified temperature histories in theinsets of Fig. 3, the cooling curve gradient changed notablyaround 35 s after the peak temperature was reached, whilethe heating curve gradient shifted around 2 s into the heatingprocess. As considered in the previous study, these gradientchanges are thought to be caused by the uniformization of thetemperature distribution in the specimen.To investigate the gradient changes, a simplified numericalsimulation was performed as in the previous study. FEMcalculations were conducted in the simulation usingcommercially available software, Wolfram Mathematica. A2D model was adopted by assuming uniformity in the hatchline direction due to the laser beam’s very high scan speed.Because the heat capacity of the powder is less than that ofthe tray, the calculation region was set as a rectangle 10mmwide and 1mm high, and consisted of a single material forsimplification. The initial temperature within the calculationregion was set at 40°C, with the boundary condition of theregion indicating no thermal loss. A heat source placed on thetop surface boundary of the region was moved from left toright corresponding to the movement of the laser beam inthe perpendicular direction to the hatch line during scanning.The intensity profile of the heat source was adjusted to matchthe Gaussian shape corresponding to the laser irradiationintensity profile. The settings for the intensity profileincluded a laser power of 50W and a spot diameter of2.2mm. The material of the calculation region for thesimulation was titanium alloy Ti–6Al–4V. The physicalproperty values of the material in the simulation were heldas constants at 40°C. The laser absorptivity was assumed tobe 0.6, which is the value measured for titanium alloy Ti–6Al–4V powder in the previous study.Figure 4 shows the temperature history at the center of thebottom surface for the numerical simulation with a singlemovement of the heat source. The start time of the heatsource movement was set to 0. The temperature rose as theheat distributed at the top surface propagated towards thecenter of the bottom surface, subsequently stabilizing to aconstant value to homogenize the temperature distributionacross the calculation region. The temperature became almostconstant about 3 s after heating.Considering the simulation result, the change in thecooling curve gradient around 35 s, seen in Fig. 3, is thoughtto be caused by the uniformization of the temperaturedistribution in the specimen. To eliminate this influence onthe estimation of thermal loss from the cooling rate, the initialpart of the cooling process from 3 s after the temperature wasmaximized was excluded from the estimation.The measured temperature history after 3 s in the coolingprocess was smoothed and differentiated to estimate thecooling rate dT/dt in eq. (2). Figure 5 shows the estimatedcooling rate plotted against temperature T for the coolingcurve shown in Fig. 3. A fitting function of the plots is alsoshown. The thermal loss L(T ) was calculated from the fittingfunction of the cooling rate and the temperature-dependentspecific heats of both the tray and the powder. This fittingfunction and the calculation of thermal loss were performedfor each powder experiment.0.00.20.40.60.81.0Specific heat, c/Jg-1K-1Temperature, T/ C Ti-6Al-4V       Fitting line Inconel 718       Fitting line Inconel 738       Fitting line0 100 200 300 400 500 600 700Fig. 2 Temperature dependencies of the specific heat of Ti-6Al-4V, Inconel718, and Inconel 738 along with their respective fitting lines.0100200300400500Temperature, T/CTime, t/sΔtΔT400450500550Temperature, T/CTime, t/s−4 −26 28 30 32 34 36 38 402 0 2 4 6 8 10050100150200250Temperature, T/CTime, t/s0 20 40 60 80 100Fig. 3 Temperature history measured for the titanium alloy Ti-6Al-4Vpowder.39404142Temperature, T/CTime, t/s2 50 1 3 4Fig. 4 Temperature variation at the center of the bottom surface in thenumerical simulation with a single movement of the heat source.Measurement of Laser Absorptivity of Inconel Powders with Additive Manufacturing Machine 109The temperature measured early in the heating processwas also thought to be influenced by the uniformization ofthe temperature distribution. A 2D numerical simulation wasperformed to estimate the influence on the measuredtemperature history in the heating process. The simulationconditions were the same as those described above exceptfor the repetition of the heat source movements at 0.0339 sintervals. The temperature history obtained from thesimulation is shown in Fig. 6. The time derivative of thetemperature is also shown in Fig. 6 to illustrate thetemperature gradient more clearly.Despite the lack of thermal loss, the temperature gradientundergoes a change for about 3 s, stabilizing to an almostconstant level after this period. In the numerical simulationwith a single movement of the heat source, it also takes about3 s for the temperature to become almost constant. Thechange in the temperature gradient in the numericalsimulation with multiple movements of the heat source isthought to be caused by the uniformization of the temperaturedistribution. The change in the heating curve gradient shownin Fig. 3 is similar to that in the temperature gradient in thesimulation and is attributed to the uniformization. Therefore,the initial segment of the heating process beginning 3 s afterheating initiation was omitted from the laser absorptivitycalculation to mitigate the impact of the temperaturedistribution homogenization process. Of course, the tem-peratures measured after 3 s are also influenced by theuniformization of temperature distribution. Nevertheless, thetemperatures recorded from approximately 3 s after the startof heating include the influence of the uniformization at thesame level. Consequently, it is plausible that the influence ofthe temperature difference ¦T on the calculation could bemitigated through cancellation.Figure 7 shows the measured laser absorptivity data for thetitanium alloy Ti–6Al–4V powder. The temperatures areintermediate values of upper and lower temperatures for ¦Tcalculation, and the range of error bars corresponds to theupper and lower temperatures. The temperatures employedfor calculating laser absorptivity represent intermediaryvalues between the upper and lower temperatures for ¦Tcalculation. The ranges of error bars of laser absorptivityare calculated from the upper and lower temperatures andthe errors of the powder mass. In the previous study, themeasurement temperature range of laser absorptivity wasbelow 150°C. By changing the laser irradiation conditions,specifically the time interval of the scanning process in themeander hatch pattern, the temperature range was broadened,spanning from about 150°C to about 400°C. No significanttemperature dependence of the laser absorptivity was seen inthis temperature range. The laser absorptivity of the titaniumalloy Ti–6Al–4V powder was about 0.6, which was almostthe same as that for the same powder in the previous study.The laser absorptivity of the tray without the powder wasalso measured. The laser absorptivity data for the machinedflat surface of the titanium alloy Ti–6Al–4V tray are shownin Fig. 7. The laser absorptivity is labeled Plate. The laserabsorptivity was about 0.37, which was almost the same asthat for the tray in the previous study.The laser absorptivity data measured for nickel-basedsuperalloy Inconel 718 and Inconel 738LC powders are−15−10−50  Experiment Fitting curveCooling rate, dT/dt/Cs-1Temperature, T/ C0 100 200 300 400 500Fig. 5 Temperature dependence of cooling rate in the cooling process inFig. 3 and its corresponding fitting curve.050100150200Temperature, T/CTime, t/s Temperature010203040 Time derivative of temperatureTime derivative of temperature, dT/dt/Cs-120 1 3 4 5Fig. 6 Temperature variation and its time derivative at the center of thebottom surface in the numerical simulation with repeated movements ofthe heat source.100 150 200 250 300 350 400 4500.00.20.40.60.81.0AbsorptivityTemperature, T/ CTi-6Al-4V Powder PlateFig. 7 Measured laser absorptivities of the Ti-6Al-4V powder and the Ti-6Al-4V tray.H. Honda and M. Watanabe110shown in Figs. 8 and 9, respectively. The laser absorptivityvalues were calculated in the same manner as for the titaniumalloy Ti–6Al–4V powder. The measurement temperatureranges were from about 150°C to about 400°C. No significantdifference was observed in the laser absorptivities of Inconel718 and Inconel 738LC powders, falling within the marginsof error. The laser absorptivities were almost the same asthose of the titanium alloy Ti–6Al–4V powder. The valueswere about 0.6, and no significant temperature dependencieswere seen.The values were slightly lower than the experimentalvalue, about 0.67, of nickel-based superalloy Inconel 625 forthe laser wavelength of 970 nm reported by Boley et al. [6],which was obtained by the calorimetric method [5]. In astudy by Sainte-Catherine et al. [14], the laser absorptivity ofthe polished flat surface of Inconel 718 at a wavelength of1.06 µm from an Nd-YAG laser was determined to be 0.30at 300°C, utilizing an integrating sphere in atmosphericconditions. The ratio of the measured laser absorptivity ofthe powder to that of the flat surface was close to the valueobtained from the ray-tracing simulation by Boley et al. [6].Because the thermocouple couldn’t be positioned at thelaser irradiation point, the temperatures measured by thethermocouple attached to the center of the bottom surfaceare thought to differ from the actual temperature at the laserirradiation position. To check the difference in the temper-atures, the temperature distribution was investigated by usingthe numerical simulation described above. The simulationconditions were the same as those for the simulation withmultiple movements of the heat source. Figure 10 showsthe temperature distributions on the top and bottom surfacesof the calculation region as well as the laser intensity profileon the 200th movement of the laser from left to right. Thetime was 6.76 s after the heat source started moving; thiswas later than the excluded time at the initial part of heatingprocess described above.The temperature distribution on the top surface exhibitssignificant convex nonuniformity across the entire specimen,showcasing a localized rise corresponding to the laserintensity profile. The local temperature rise was about 10degrees Celsius, a decrease from a few tens of degreesCelsius in the previous study achieved by enhancing themean moving speed of the laser beam perpendicular to thehatch line. However, the temperature on the top surfacevaries, ranging several tens of degrees Celsius due to thelarge convex nonuniformity. The nonuniformity seems tobe caused by the overall laser intensity distribution on thespecimen.To examine the cause of the large convex nonuniformity, anumerical simulation similar to that described above, exceptfor the laser irradiation conditions, was performed. In thesimulation, the laser intensity distribution on the top surfacecomprised the time-averaged distribution encompassing allthe intensity profiles of the hatch lines, with its positionremaining fixed. The top surface was heated continuouslyby the fixed distribution. Figure 11 shows the simulationresults of the temperature distributions on the top and bottomsurfaces at 6.76 s after the commencement of heating,aligning with the time of the 200th movement in thesimulation involving multiple movements of the heat source0.00.20.40.60.81.0AbsorptivityTemperature, T/ CInconel 718100 150 200 250 300 350 400 450Fig. 8 Measured laser absorptivities of the Inconel 718 powder.0.00.20.40.60.81.0AbsorptivityTemperature, T/ CInconel 738LC100 150 200 250 300 350 400 450Fig. 9 Measured laser absorptivities of the Inconel 738LC powder.−5 −4 −3 −2 −150200250300Temperature, T/CPosition, x/mm Top surface Bottom surface05 Laser intensityLaser intensity, I/arb. unit1 0 1 2 3 4 5Fig. 10 Temperature distributions on the top and bottom surfaces and thelaser intensity profile on the 200th movement of the laser from left to rightin the numerical simulation.Measurement of Laser Absorptivity of Inconel Powders with Additive Manufacturing Machine 111as shown in Fig. 10. The laser intensity distribution,comprised of all the intensity profiles of the hatch lines, isalso shown, appearing as a flat top with gradual slopes at theedges. The temperature distributions on the top and bottomsurfaces show large convex nonuniformities, and the shapesof the distributions are almost the same as those shown inFig. 10. Therefore, the large convex nonuniformity intemperature across the entire specimen is thought to stemfrom the laser intensity distribution generated by the meanderhatch pattern with a broader Gaussian intensity profile and asmaller laser irradiation area than the specimen size.The measured laser absorptivities in this experiment arepresumed to be values averaged over such temperaturevariation ranges. Reducing the nonuniformity of the temper-ature distribution caused by the laser intensity distribution onthe specimen is vital to achieve a more precise temperature-dependent laser absorptivity. In practical additive manufactur-ing operations, temperatures exceed the melting point.Therefore, it is necessary to extend the temperature rangefor laser absorptivity measurements to encompass highertemperatures.4. ConclusionWe tried to measure the laser absorptivity of metalpowders and their temperature dependence under identicalconditions in laser powder-bed fusion additive manufactur-ing, employing a commercially available additivemanufacturing machine.We measured the laser absorptivities of nickel-basedsuperalloy powders including Inconel 718 and Inconel738LC, as well as titanium alloy Ti-6Al-4V powders. Themeasurement temperature ranges were about 150°C to about400°C. The laser absorptivites of those powders were allabout 0.6 at a laser wavelength 1070 nm. Within this range,no significant temperature dependence was observed for thelaser absorptivity of these powders.AcknowledgmentsWe would like to thank Mr. Masaru Suzuki for technicalassistance with the experiments and Mr. Mitsugu Sato forpreparation of the experimental devices.REFERENCES[1] B. Brandau, A. Da Silva, C. Wilsnack, F. Brueckner and A.F.H.Kaplan: Absorbance study of powder conditions for laser additivemanufacturing, Mater. Des. 216 (2022) 110591.[2] M. Haag, H. Hügel, C.E. Albright and S. Ramasamy: CO2 laser lightabsorption characteristics of metal powders, J. Appl. Phys. 79 (1996)3835–3841.[3] T.J. Wieting and J.L. DeRosa: Effects of surface condition on theinfrared absorptivity of 304 stainless steel, J. Appl. Phys. 50 (1979)1071–1078.[4] A.M. Rubenchik, S.S.Q. Wu, V.K. Kanz, M.M. LeBlanc, W.H.Lowdermilk, M.D. Rotter and J.R. Stanley: Temperature-dependent780-nm laser absorption by engineering grade aluminum, titanium, andsteel alloy surfaces, Opt. 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Sinha: Thermal model based simulation of nanosecond pulsed laserirradiation of Ti6Al4V alloy, J. Laser Appl. 31 (2019) 032008.[11] K.C. Mills: Recommended Values of Thermophysical Properties forSelected Commercial Alloys, (Woodhead Publishing, 2002) pp. 211–217.[12] K.C. Mills: Recommended Values of Thermophysical Properties forSelected Commercial Alloys, (Woodhead Publishing, 2002) pp. 181–190.[13] Alloy IN-738 Technical Data, (The International Nickel Company,Inc.).[14] C. Sainte-Catherine, M. Jeandin, D. Kechemair, J.P. Ricaud and L.Sabatier: STUDY OF DYNAMIC ABSORPTIVITY AT 10.6 µm(CO2) AND 1.06µm (Nd-YAG) WAVELENGTHS AS A FUNCTIONOF TEMPERATURE, J. Phys. IV 01 (1991) C7-151–C7-157.−5 −4 −3 −2 −1 0 1 2 3 4 5150200250300Temperature, T/CPosition, x/mm Top surface Bottom surface05 Laser intensityLaser intensity, I/arb. unitFig. 11 Temperature distributions on the top and bottom surfaces and thelaser intensity profile at 6.76 s in the numerical simulation of continuousheating.H. Honda and M. Watanabe112https://doi.org/10.1016/j.matdes.2022.110591https://doi.org/10.1063/1.361811https://doi.org/10.1063/1.361811https://doi.org/10.1063/1.326083https://doi.org/10.1063/1.326083https://doi.org/10.1117/1.OE.53.12.122506https://doi.org/10.1364/AO.54.007230https://doi.org/10.1364/AO.55.006496https://doi.org/10.1364/AO.55.006496https://doi.org/10.1016/j.apmt.2017.08.006https://doi.org/10.1016/j.apmt.2017.08.006https://doi.org/10.1002/adem.201900185https://doi.org/10.2320/matertrans.MT-M2023156https://doi.org/10.2320/matertrans.MT-M2023156https://doi.org/10.2351/1.5091748https://doi.org/10.1051/jp4:1991741