Particle identification by laser-induced incandescence in a solid-state laser cavity

Michelle Stephens, Nelson Turner, and Jon Sandberg

The laser-induced incandescence of a particle of unknown size and composition can be detected simul- taneously with the light elastically scattered by the particle, providing information on both the size and composition of the particle. The technique relies on vaporization of the particle; detection of the incan- descence signal at the time of vaporization allows determination of the boiling point of the particle, which can in turn be related to the composition of the particle. The elastically scattered signal provides information about the size of the particle and confirmation that it was vaporized. The technique is demonstrated by directing particles through a Nd:YAG laser cavity with ϳ106 W͞cm2 of circulating intensity. Elements such as tungsten, silicon, and graphite, as well as common aerosols such as soot, can be detected and identified. © 2003 Optical Society of America OCIS codes: 010.1100, 010.1120, 010.1280, 120.0120, 290.5850.

1. Introduction years.6–14 Two-color optical pyrometry has been Real-time measurement of the size and composition used in conjunction with LII to measure the temper- of airborne particles is important for clean- ature of particles,15–17 and it has also been used in room evaluation, in-line vacuum monitoring, and conjunction with elastic-scattering measurements, environmental-pollutant detection. Information laser doppler vibrometry, and other LII techniques to about the size of airborne particles in the 0.1–1-␮m- simultaneously determine the size, velocity, and tem- diameter range is readily obtained with commercially perature of soot particles.18,19 However, this work available systems that relate the magnitude of the is, to our knowledge, the first to demonstrate a elastically scattered light to the particle size.1,2 method for using LII to provide information about the Data about the composition of airborne particles can composition of an unknown particle. Other be obtained through time-of-flight mass spectrome- authors20–22 have used LII to measure size distribu- try,3,4 molecular spectroscopy,5 and off-line through tions and concentrations of particles of different com- microscopical analysis; however, these techniques positions but have not used the incandescence are not well-suited to applications involving low con- information to determine particle composition. Un- centrations of particles. This work demonstrates like many time-of-flight mass spectrometry systems, the use of laser-induced incandescence ͑LII͒ simulta- our system requires no heavy vacuum equipment and neously with a measurement of elastically scattered is easily portable. light to concurrently determine the size and boiling In this demonstration a jet directs airborne parti- point of a single airborne particle. cles through a Nd:YAG laser cavity. The intersec- LII has been used for combustion diagnostics and tion between the jet stream and the intracavity beam to study the chemistry of soot formation for many forms an interaction region in which light is both elastically scattered and absorbed by the incident particle. The absorbed light heats the particle so that it begins to incandesce. The intensity of the When this work was done, the authors were with Research intracavity light is ϳ106 W͞cm2, which is enough to Electro-Optics, 5505 Airport Boulevard, Boulder, Colorado 80301. ͑ ͒ vaporize absorbing particles as they pass through the M. Stephens [email protected] is now with Ball Aerospace & beam. Several detectors image the interaction re- Technologies Corp., 1600 Commerce Street, Boulder, Colorado 80301. gion and detect the elastically scattered light as well Received 9 August 2002; revised manuscript received 7 March as the incandescent light. The spectral bandwidth 2003. over which the incandescent light is detected can be 0003-6935͞03͞193726-11$15.00͞0 changed by placing optical filters in front of the de- © 2003 Optical Society of America tectors. By analysis of the elastically scattered light

3726 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003 Fig. 1. Optical layout of the instrument. An interaction region is created by the intersection of a gas stream containing airborne particles ͑shown here with the gas jet perpendicular to the page͒ and the intracavity light of a high-finesse Nd:YAG laser. The particle is heated to incandescence as it is directed through the 1.064-␮m light, and both the elastically scattered light and the incandescent light are imaged by a variety of detectors.

͑at 1.064 ␮m͒ the size of the particle at the time of that has a high transmission at the wavelength of the vaporization can be determined. The abrupt termi- diode pump light ͑0.81 ␮m͒ and very high reflectance nation of elastically scattered light verifies that the ͑Ͼ99.99999%͒ at 1.064 ␮m. The other surface is particle has been vaporized. Analysis of the LII over coated with a very-low-loss antireflection coating. one or more spectral bandwidths provides the tem- The mirror is a high reflector with a leakage trans- perature of the particle during the vaporization pro- mission of 15 ppm; the leakage through the mirror cess. The precise relationship between the permits monitoring of the intracavity power. The temperature of the particle during vaporization and TEM00 beam diameter at the center of the cavity is the composition of the particle is quite complex, but, 500 ␮m. The pump is an SDL 2362 multimode diode to a good approximation, the particle’s temperature laser coupled to the cavity through an optical fiber. reaches the boiling point of its constituent material The circulating intensity at the center of the cavity is while it is undergoing vaporization. This method 1.3 ϫ 106 W at a pump power of 0.7 W. therefore permits a straightforward determination of The jet is a concentric-nozzle system. The air- the particle’s boiling point, which provides informa- borne particles exit through the center nozzle with a tion about the composition of the particle. Elements flow of 2.3 ϫ 10Ϫ6 to 4.7 ϫ 10Ϫ6 m3͞s. Gas exiting such as tungsten, graphite, and silicon are easily sep- through the outer nozzle forms a sheath that focuses arable. Airborne soot can also be detected and iden- the airborne particles. The sheath flow is typically tified. eight times greater than the nozzle flow. The jet can be translated perpendicular to and along the beam in 2. Apparatus order to align it directly over the center of the beam. Figure 1 illustrates the optical layout. A diode- Nonabsorbing polystyrene latex ͑PSL͒ spheres are pumped Nd:YAG laser cavity is built into an alumi- used to align the jet by measuring the localization of num block. A gas stream is focused through the the particles through comparison of the theoretical center of the laser cavity with a concentric-nozzle jet pulse-height distribution for localized particles with system.23 Test particles are introduced into the gas that measured with a multichannel analyzer. The stream by a Particle Measuring Systems PG-100 neb- waist of the particle stream is calculated from the ulizer. The elastically scattered light and the incan- pulse-height distribution of the PSL spheres and is descent light are imaged onto avalanche photodiodes typically half the laser beam’s waist. ͑APDs͒ by four compound-lens systems. Data is Each compound-lens assembly images light onto a taken with a digital oscilloscope and a desktop com- single-element APD to form a single detection chan- puter. nel. There are four detection channels—one scatter The 0.12-m-length Nd:YAG cavity consists of a 0.5- channel for detection of the 1.064-␮m elastically scat- cm-thick Nd:YAG crystal and a mirror with a 0.3-m tered light and three incandescence channels. One radius of curvature. Both surfaces of the crystal are lens assembly is designed to collect 1.064-␮m light superpolished flat. One side has a very-low-loss ͓Ͻ2 with minimal aberrations. This assembly images parts per million ͑ppm͔͒ multilayer dielectric coating the elastically scattered light onto a silicon APD

1 July 2003 ͞ Vol. 42, No. 19 ͞ APPLIED OPTICS 3727 ͑EG&G C30724͒ and forms the scatter channel. detection process, and then it will describe a more Two other lens assemblies are designed to correctly accurate, time-dependent model. image 0.300–0.800-␮m light. These assemblies also image light onto EG&G C30724 silicon APDs and form two separate visible incandescence chan- A. Simplified Model—Detection Limits nels. The fourth assembly collects 1.4–1.7-␮m light In the simplest model, the time dependence of the and images it onto a Judson J-16 germanium APD to laser intensity incident on the particle and the inter- form an infrared incandescence channel. nal heating of the particle are ignored. The system Filter glass can be inserted into the lens assemblies is assumed to be in a steady state in which the ab- without distorting the image. The elastic-scattering sorbed energy is balanced by the energy lost due to detection channel contains 2-mm-thick Schott RG850 heat conduction through the surrounding air. A filter glass, which blocks the 0.81-␮m pump light but simple expression relating the laser intensity to the passes the 1.064-␮m scattered light. The filter glass vaporization of a particle of a given radius ͑␣͒, boiling ␮ ͑ ͒ ͑ ͒ in the 0.300–0.800- m incandescence imaging as- point Tb , and absorption coefficient Kabs can be semblies can be varied, but for the work presented determined: here one channel contained 2-mm-thick Schott KG5 glass that transmits light from 0.310 to 0.770 ␮m, ␲ 2 Ϫ ͑ Ϫ ͒␲ 2 ϭ which includes most of the light imaged by the sys- Kabs a I hN Tb T0 a 0, (1) tem. The other channel contained 2-mm-thick Schott KG5 glass as well as a 2-mm-thick Schott where T is the ambient temperature of the unheated RG715 glass, which transmits incandescent light 0 air, I is the incident laser intensity, and h is the only from 0.7 to 0.8 ␮m. In the infrared imaging N Nusselt number and is approximately equal to k ͞ system a silicon lens acts as a filter so that no addi- air a,26 where k is the thermal conductivity of air. tional filter glass is necessary. air The first term represents the rate of the particle’s The APDs are attached to the lens assemblies and energy absorption from the laser. The second term can be translated in three dimensions to optimize represents the rate of the particle’s energy loss by alignment. Each compound imaging system is built heat conduction through the surrounding air. When as a separate assembly and screws directly into the more light is absorbed by the particle than is lost to aluminum block. The assembly seals against the conduction, the particle heats up until it begins to block with a Viton O-ring. The assemblies are easily vaporize. Although this approximation ignores in- interchangeable so that a variety of signals can be ternal heating of the particle and vaporization of the viewed simultaneously. particle, it is adequate for estimating the limiting A LeCroy LC334A digital oscilloscope is triggered factors for vaporizing particles in a given system. by the signal from the 1.064-␮m detection channel, When the time dependence of the system is added, a and signals as a function of time from all four of the higher intensity than predicted by Eq. ͑1͒ is needed to detectors are stored for a single particle. The data is vaporize a particle with a given radius and absorp- then transferred to a desktop computer, and the in- tion coefficient. For the system described in Section candescent signals are analyzed to determine the 2 the simplified model predicts vaporization intensi- temperature of the particle when it vaporized. The ties that are too low by a factor of four. scatter signal is analyzed to determine the size of the To determine the detection limits for a system us- particle and to confirm that it vaporized. Pulse ing a single detector for the incandescent light, some widths were typically 2–4 ␮s and were typically re- assumptions must be made about the instrument it- corded with a resolution of 0.01 ␮s. self. The magnitude of the incandescence signal de- 3. Theory pends on the particle’s radius, boiling point, and emissivity ͑ε͒ in the spectral region over which the This particle-identification technique uses the mag- incandescence signal is detected. It also depends on nitude and spectral dependence of the incandescence the responsivity ͑␩͒ of the detector, the fraction of signal to determine the vaporization temperature of incandescent light collected by the imaging system the incident particle. The composition of the parti- ͑d⍀͒, and the fraction of incandescent light emitted cle is then inferred from the vaporization tempera- over the spectral region of the detector ͑⌬͒. The ture. The size of the particle is inferred from the signal-to-noise ratio is approximately equal to 1 when magnitude of the elastically scattered light. The va- porization and light detection processes can be mod- eled to determine the capabilities of the instrument. d⍀⌬␩␴ T 44␲a2ε ϭ ͑N 2 ϩ I 2͒1͞2f, (2) The time dependence of the particle radius and tem- sb b N perature can be solved numerically with the energy and mass balance equations for the laser-particle sys- where N is the detector amplifier’s noise current, IN is tem.6,10,24,25 A simpler model can be used to esti- the photodetector’s noise current, and f is the detec- mate the incandescence-detection limits of the tor’s bandwidth ͑in this case, the detector’s band- instrument. Since the simpler model is useful for width was approximated as the inverse of the instrument design, this section will first describe a minimum pulse width of a vaporizing particle͒. ⌬ simplified steady-state model of the vaporization and represents the fraction of incandescent light that is

3728 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003 Fig. 3. Calculated temperature and radius for a graphite particle Fig. 2. Detection and vaporization limits of the system described with an initial radius of 0.25 ␮m. in Section 3 for a particle with absorption coefficient and emissivity both constant and wavelength equal to 1. The limits are shown for an incandescence-detection channel using KG5 filter glass. B. Time-Dependent Particle Heating and Vaporization Ϫ The values used in the simplified model were N ϭ 2 ϫ 10 12 Differential equations for the temperature and ra- A͞Hz1͞2, f ϭ 1 MHz, d⍀ϭ0.16, I ϭ 106 W͞cm2, k ϭ 2.6 ϫ 10Ϫ4 0 air dius of a particle can be derived from the time- WcmϪ1 sϪ1 KϪ1, ␩ϭ8W͞A, and I ϭ 10Ϫ12 A͞Hz1͞2 for the silicon N dependent energy balance equation10,11: APD. The values used for the thermodynamic properties for the ͑ ϭ ϫ 5 time-dependent model were the values for graphite Hv 7.8 10 ͞ ␳ ϭ ͞ 3 ϭ Ϫ1 Ϫ1 ϭ ͞ 2 2 Hv dM J mol, s 2.62 g cm , Cs 0.72 J g K , Wv 36 g mol, and K ͑a͒␲a I͑t͒ Ϫ h ͑T Ϫ T ͒␲a Ϫ ϭ ͞ ͒ ε ε abs N 0 Ws 12 g mol , with the exception of Kabs, , and Tb. Kabs and Wv dt were equal to 1, and T was varied from 1000 to 5000 K to deter- b 4 dT mine the detection limits. Ϫ ␴ 4␲a2͑T4 Ϫ T 4͒ ϭ ␲a3␳ C , (5) sb 0 3 s s dt emitted in the spectral bandwidth of the incandes- where the terms represent the absorption of power cence detector ͑ibw͒, from the laser, the rate of loss due to heat conduction away from the particle, the loss of energy due to vaporization of the particle, the energy loss due to blackbody radiation, and the rise in the internal tem- ͑␭͒ ␭ ͐ B d perature of the particle; the symbols are defined in ibw ⌬ ϭ , (3) Appendix A. Blackbody radiation is the smallest ϱ loss mechanism. It is typically 2 orders of magni- ͐ B͑␭͒d␭ tude smaller than the energy loss due to vaporization, 0 which is the dominant energy-loss mechanism. The loss due to heat conduction is generally an order of where magnitude smaller than the loss due to vaporization. The absorption coefficient and the Nusselt number do not remain constant as the particle vaporizes. 2ε␲hc2 1 Expressions that approximate their dependence on B͑␭͒ ϭ (4) ␭5 exp͑hc͞␭kT͒ Ϫ 1 the mass loss, particle temperature, and particle ra- dius were developed and are described in Appendix B. Those relationships and the relationship between the ϭ is the blackbody radiation at T Tb. In this simple radius of the particle and the mass loss, approximation it is assumed that the emissivity is constant over the spectral bandwidth of the detector. da dM 1 ϭ Ϫ , (6) Figure 2 shows the calculated detection and vapor- dt dt 4␲␳ a2 ization limits for the instrument, described in Section s 2, that uses the broadband visible incandescence de- can be used to derive two coupled differential equa- tection channel ͑KG5 filter glass͒. The detection tions that can be solved numerically to find the tem- limits for this instrument were not optimized for par- perature and radius of the particle as a function of ticles of any particular size or temperature. The de- time. Figure 3 shows the solutions of the coupled tection limits can be optimized for specific particles equations for a graphite particle with an initial ra- through the choice of the spectral bandwidth of the dius of 0.25 ␮m. incandescence detector, the design of the detection The magnitude and time dependence of the incan- electronics, the circulating power inside the cavity, descence and scatter signals can now be calculated. ͑ and modification of the jet and therefore the pulse The scatter signal, Sscat, can be calculated from Mie width of the signal͒. scattering. For a Rayleigh particle ͑a ϽϽ␭͞2␲͒ the

1 July 2003 ͞ Vol. 42, No. 19 ͞ APPLIED OPTICS 3729 Fig. 5. Calculated ratio of signals from the incandescent- Fig. 4. Calculated normalized scatter signals from an absorbing detection channels as a function of boiling point. It is assumed particle ͑graphite͒ that vaporizes before passing completely that the emissivity is wavelength independent. Two plots are through the laser light and a nonabsorbing particle ͑PSL͒ of the shown—one shows the ratio of signals from the two visible detec- same initial diameter ͑0.5 ␮m͒. Note the reduced pulse width for tion channels ͑KG5 and KG5*RG715 filter glasses͒, while the other the graphite particle, indicating that the particle vaporized before shows the ratio of the broadband visible channel ͑KG5 filter glass͒ traversing the beam. to the infrared channel. magnitude of the scatter signal is proportional to the pyrometry and take the ratio of the maximum value incident laser intensity and the sixth power of the of the incandescence signals from two detectors radius27: with different spectral bandwidths. This method uses the more reliable assumption that the emis- 8 2␲ 4 m2 Ϫ 1 2 sivity is constant with wavelength over the detec- S ͑t͒ ϭ ␩d⍀I͑t͒ ␲a6ͩ ͪ ͯ ͯ , (7) scat 3 ␭ m2 ϩ 2 tion bandwidth and also removes the dependence of the signal on the radius of the particle. The detec- where m is the complex index of refraction of the tion limits for a single channel with KG5 filter particle. The radius of the particle can be calculated glass, calculated with the time-dependent model, from the magnitude of the measured scattered light. are shown in Fig. 2. The calculated values for the If the particle’s composition, and therefore the index ratio of detection channel signals as a function of of refraction, is unknown, a value for m must be boiling points are shown in Fig. 5. assumed. The scatter signal for a nonabsorbing par- ticle is a Gaussian pulse. Vaporization can be con- C. Limits and Applicability of Model firmed by measurement of the pulse width of the The design of this detection method focuses on char- scatter signal. The strong dependence of the scatter acterization of the boiling point of airborne particles signal on the particle’s radius results in a measurably with a diameter in the range of 0.05–1 ␮m. The shorter pulse width when a particle vaporizes ͑Fig. 4͒. composition of the particle is inferred from the The signal, Sincand, from the incandescent power that boiling-point data. Therefore, by design, particles of reaches the detector is different composition but with similar boiling points will be indistinguishable. However, in many situa- ϱ tions, such as clean-room detection, where some in- ͑ ͒ ϭ ε ␲ ͑ ͒2 ⍀ ͓␭ ͑ ͔͒ ͑␭͒␩͑␭͒ ␭ Sincand t 4 a t d ͐ B , T t R d , formation about the type of airborne particles is 0 available, the discrimination between absorbing and (8) nonabsorbing particles and particles with high and low boiling points is useful and allows discrimination where R͑␭͒ is the transmission of the filter glass in between, for example, plastic and metallic particles. the incandescence-detection channel. The tempera- The model used assumes that the particles are ture of the particle when it vaporizes can be calcu- spherical, that they have a radius much less than the lated from the incandescence signal, and the wavelength, that their thermodynamic values, such particle’s radius can be derived from the scatter sig- as specific heat, are constant with temperature; that nal. The initial value of the scatter signal provides they do not melt before vaporizing, and that their an initial radius for the particle. Equation ͑8͒ can emissivity is constant with wavelength. Deviation then be used to calculate the temperature from from these assumptions typically leads to only a Sincand. To do so, one must assume the particle’s small increase in the uncertainty of the measure- emissivity. An alternative method for calculating ment. the temperature that does not rely on an assump- Aspherical particles can change the magnitude of tion of a value for the emissivity is to use two-color the incandescence signal since that signal depends on

3730 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003 Fig. 6. ͑a͒ Pulse-height distributions measured with a multichannel analyzer of 0.304-␮m PSL particles. ͑b͒ Calculated distribution for particles localized to half the laser beam’s waist size. the surface area of the particle. The magnitude of ing spectral regions for two-color pyrometry. Cop- the elastically scattered light from an aspherical par- per, for example, has an emissivity of 0.1 at 1.0 ␮m ticle does not follow from Eq. ͑7͒. The magnitude of and 0.56 at 0.5 ␮m.28 the scattered light will depend on the orientation of Finally, this model assumes that the particle heats the particle relative to the incident light. The scat- uniformly and instantaneously. This assumption is tering cross section for an oblate spheroid can vary valid since the relevant time scales for internal equil- from 0.5 to 2.5 times the cross section for a sphere ibration are short compared with the time scale for with a radius the same length as the spheroid’s semi- heating to vaporization. The time for heat to diffuse axis.27 Because of the a6 dependence of the elastic across the particle is cross section, a factor-of-two difference in the magni- ␳ C a2 tude of the elastically scattered signal will lead to ␶ ϭ s s only a 16% error in the value of the radius of the diff , (9) 4␬s particle calculated from Eq. ͑7͒. This level of accu- ␬ 25 racy for sizing particles is still of use in many appli- where s is the thermal conductivity of the particle. ␳ ϳ ͞ 3 ϳ Ϫ1 cations, such as clean-room contamination For a typical metal, s 10 gm cm , Cs 0.4 J g Ϫ1 ␬ ϳ Ϫ1 Ϫ1 ␶ ϳ ϫ Ϫ9 monitoring. K , and s 1Wcm K ,so diff 2.5 10 s The variation in the particle’s specific heat with for a 1.0-␮m-diameter particle. The time scale for temperature affects the time dependence of the par- vaporization with the apparatus described in Section ticle’s temperature but does not change the maxi- 2isϳ10Ϫ6 s. mum temperature the particle reaches. The dominant physical quantity for determining the max- 4. Experimental Results and Discussion imum particle temperature is the boiling point itself. PSL microspheres were used for the initial alignment Similarly, if the particle melts before vaporizing, the of the jet and to calibrate the elastic-scattering detec- thermodynamics properties will change,28 but the tion channel. By measuring the pulse-height distri- most important physical quantity is still the boiling bution of the elastically scattered light, it was point of the material. determined that the PSL spheres were localized with The emissivity can also change with tempera- a waist size close to half the laser beam’s waist size ture.28 This will affect the accuracy of the temper- ͓Fig. 6͑a͒–6͑b͔͒. The magnitude of the signal from a ature measurement by a small amount. For a 0.304-␮m-diameter sphere was used in conjunction particle with a relatively high emissivity ͑Ͼ0.75͒ the with Eq. ͑7͒ to calibrate the collection efficiency of the effect is of the order of 5–10%. For example, the lens assembly and the response of the photodetector. correction for radiation pyrometer readings for a This calibration was then used with Eq. ͑7͒ to deter- metal particle with an emissivity of 0.85 at 1800 K is mine the size of other particles from the scattered 90 K.28 If the emissivity is constant with wave- light signal. length and two-color pyrometry is being used, the effect is not important. The variation of the emis- A. Demonstration of Empirical Differentiation between sivity with wavelength, however, can still result in an Materials incorrect value of the particle’s temperature. In par- Vaporization temperatures were derived from two- ticular, the difference between the emissivity over an color pyrometry for a variety of metals. For these infrared bandwidth and the visible bandwidth may measurements two incandescence channels were be significant, and care should be taken when choos- used. One lens assembly had 2-mm-thick Schott

1 July 2003 ͞ Vol. 42, No. 19 ͞ APPLIED OPTICS 3731 Fig. 8. Demonstration of the ability of this instrument to distin- Fig. 7. Normalized signal from the elastically scattered light for guish between different metals. The left axis shows the ratios of graphite at two circulating intensities. Note that the particle the maximum values in the two incandescence detectors, and the vaporizes more quickly at the higher intensity, resulting in reduc- right axis shows the corresponding temperatures for particles with tion in the pulse width of the scattered signal. The signal from emissivities of 1 over the detection bandwidth. the particle vaporized at low circulating intensity shows both the poor signal-to-noise ratio caused by the reduction in circulating intensity and fluctuations in the signal that we attribute to non- spherical particles. circulating intensity, to calculate a more accurate value for the particle’s diameter, one could measure the rise time, tr, of the scatter signal and use Eq. ͑ ͒ ͑ ϭϪ ͒ KG5 filter glass that transmits wavelengths from A5 in Appendix A to calculate I t tr . How- 0.310 to 0.770 ␮m. The other assembly had 2-mm- ever, because of the a6 dependence of the scattered thick Schott KG5 filter glass and a 2-mm-thick Schott light, this correction for the data taken with this RG715 filter glass. This combination of glass trans- apparatus was typically less than 10% of the calcu- mits wavelengths from 0.7 to 0.8 ␮m. Sample par- lated radius. Another source of error in the parti- ticle suspensions were prepared by mixing cle sizing is due to the assumption that the commercially available finely powdered metals with particle’s diameter is much less than the wave- deionized water and were introduced into the jet’s gas length of light, a condition that was not always true stream with a Particle Measuring Systems PG-100 for some of the materials used. nebulizer. A digital oscilloscope captured a single The value of the scattering cross section depends on event by triggering on the signal from the detector for the complex index of refraction for the metal and is elastically scattered light. The maximum values different for different materials. If the composition from both incandescent channels and the scatter of the particle is unknown or the complex index of channel were transferred to a personal computer. refraction is unknown, no correction can be made to The pulse width of the scatter signal was also the scattering cross section. For these measure- measured and transferred to the personal com- ments the scattering cross section for PSL spheres puter. If the pulse width was less than the pulse was used, which led to an estimated 30% uncertainty width of a PSL particle, it was determined that the in the size of the particle. particle had vaporized ͑Fig. 7͒, and the ratio of the Figure 8 shows the results of two-color pyrometry ͑ ϭ ͒ 29 ͑ ϳ two incandescent values was compared with a for tungsten Tb 5828 K , graphite Tb 4200 ͒ 30 ͑ ϭ ͒ 29 ͑ ϭ ͒ 29 model to determine the temperature of the particle K , silicon Tb 3540 K , nickel Tb 3187 K , ͑ ϭ ͒ 29 at vaporization ͑Fig. 5͒. An alternative method for and aluminum Tb 2794 K . Nickel and silicon, determining whether the particle vaporized was which have similar boiling points, are not distin- also tested. In this method a split photodetector guishable from each other, while the other elements was used to detect the elastically scattered light. are easily distinguishable. Note that aluminum ap- The detector was aligned so that the signals on both pears to have a vaporization point lower than 2794 K. halves of the detector were equal when a nonab- This is probably due to its drop in emissivity over the sorbing PSL particle passed through the laser RG715 bandwidth.31 This may also explain the beam. When an absorbing particle vaporized, the slight difference between the expected and measured signals on the detectors were unbalanced and va- vaporization temperatures of silicon and nickel. porization was confirmed. The size of the particle was determined from the B. Measurements of Graphite; Detailed Comparison to maximum value of the elastically scattered signal Model by using Eq. ͑7͒ with I͑t͒ϭI͑0͒. Since the particle In the previous section the capability of this instru- typically vaporizes before reaching the center of the ment for discriminating between particles of un- beam and therefore before reaching the maximum known composition was demonstrated. In this

3732 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003 Fig. 9. Results of two-color pyrometry on graphite and compari- Fig. 11. Detection of soot using the LII method in a solid-state son with calculated values ͑shown as open circles͒. laser cavity. The open circles show the counts taken while sam- pling room air for 13 min. The closed circles show the counts taken with an oil lamp burning near the intake valve for 13 min. section measurements of graphite are compared with the predictions of the model. The absorption coeffi- cients and elastic-scattering cross sections are calcu- C. Detection of Atmospheric Aerosols lated from published values for the complex indices of One possible application for this measurement tech- refraction.32 We were unable to obtain graphite par- nique is air pollution monitoring. Common airborne ticles with a known size distribution, so the size of the pollutants include silicon, sulphur, oxides and nitrides particle is inferred from the complex index of refrac- of metals, and soot.21 We have already shown the tion and Eq. ͑7͒. capability of this instrument to differentiate between Figure 9 shows the results of two-color pyrometry various metals, including silicon and graphite. Soot on graphite and compares the model’s predictions detection, in particular, is ideal for this application with the data. The values for the KG5͞ because of soot’s high absorption coefficient ͑1.064 ͑ ͒ KG5*RG715 ratios compare well. Figure 10 shows ␮m͒. Filippov et al.21 have shown that LII can be how absolute values of the KG5 signal alone compare used to detect soot particles in air, however, that work with the model. Using a single incandescence chan- assumed that the majority of the emission was due to nel is an option if one either knows the emissivity of soot particles, whereas this technique ensures that the the particle to be detected or is willing to assume a emission is due to soot particles by measuring the va- value for the emissivity of a particle of unknown com- porization temperature of the aerosol. ϭ position. The values used in the model were Hv To demonstrate the capability of this instrument, ϫ 5 ͞ ␳ ϭ ͞ 3 ϭ Ϫ1 7.8 10 J mol, s 2.62 g cm , Cs 0.72 J g ambient air was introduced into the cavity through Ϫ1 ϭ ͞ ϭ ͞ ϭ K , Wv 36 g mol, Ws 12 g mol, Kabs 1, and the jet, then a burning oil lamp was placed under- ε ϭ 1. neath the intake. Figure 11 shows the result. The soot from the lamp is clearly detectable. Soot particles may form loose agglomerates.21 This leads to the questions of whether the particles break apart during vaporization and how that might affect this measurement technique. Following the arguments of Filippov et al.,21 the soot particles can be expected to disintegrate when the laser intensity is strong enough to induce electrostatic breakdown be- tween the agglomerated particles. Charge buildup due to thermionic emission of the hot particle over- comes the van der Waals attraction that holds the aggregates together. Using the model outlined by Filippov et al.,21 it is expected that any aggregates will disintegrate soon after entering the laser beam.

5. Discussion The fundamental limit of the incandescence- detection method will depend on the choices of the Fig. 10. Comparison of model predictions ͑shown as open circles͒ spectral-detection bandwidths for the incandescence to KG5 signal alone for graphite. channels, the electronic bandwidth of the detection

1 July 2003 ͞ Vol. 42, No. 19 ͞ APPLIED OPTICS 3733 channels, and the numerical aperture of the imaging the model used here, the absorption coefficient was system. The electronic bandwidth of the detection approximated with the empirical function channels is determined by the minimum pulse width of the incandescent signal. The speed with which 2 Ϫ a K Х Q tan 1 , (A1) the particle vaporizes depends weakly on the speed at abs abs ␲ adepth which the particle is moving through the beam ͑i.e., the flow rate of the jet͒ and strongly on the intensity where adepth represents an absorption depth for ␮ incident on the particle. The simple model de- 1.064- m light and Qabs is the absorption coefficient scribed in Section 3 can be useful for adjusting these for particles much larger than the absorption depth. parameters to optimize the instrument design for the The values for adepth and Qabs were assigned by solv- desired particle size and boiling point. ing the Mie equations at a few radii and using the The temperature resolution of the incandescence- values to fit the function in Eq. ͑6͒. detection method also depends on the choices of the In this model the Nusselt number used in the sim- spectral-detection bandwidths for the incandescence plified model is modified to include the effects of evap- channels as shown in Fig. 5. Additionally, it de- oration26: pends on the repeatability of the signal, which de- Ϫ dM dM 1 pends on the localization of the particles in the gas C C stream, the roundness of the particles, and the sur- 2K dt air dt air Х air ΂ ϩ ϩ ΃ h 1 . (A2) face emissivity of the particles, which may change N a 8␲ak 24␲ak with oxidation.28 air air This demonstration has shown that very simple The mass lost because of evaporation diffuses away assumptions can be made for the index of refraction from the particle at a rate26 and the emissivity for particles of unknown composi- ␲ Ϫ6 Ϫ Ϫ1 tion while still providing useful information. Even if dM 4 aPp DWv10 Pp Patm ϭ lnͩ1 Ϫ ͪ , (A3) the index of refraction is unknown, the particle size dt RT Pp ϩ Patm can be approximated from Eq. ͑7͒ by using the index 6 ϭ ͓ ͑ Ϫ ͒͞ ͔ of refraction of PSL. Because of the a dependence where Pp P* exp Hv T Tb RTTb is the partial of the magnitude of the elastically scattered signal, in pressure of the vapor from the particle10,26 and the determination of size the error arising from a lack ͞ 1072kTN 1 2 of knowledge of the index of refraction will be within D ϭ 2ͩ Aͪ kT106͑␲d 2P ͒Ϫ1 (A4) air atm 30–50%, even for particles with a very high index of ␲Wv refraction. The use of two incandescence-detection channels and two-color pyrometry can minimize the is the diffusion coefficient for vapor from the particle effect of an unknown emissivity, especially if the in air.33 emissivity is constant with wavelength. The choice Because of the Gaussian profile of the intracavity ͑ ͒ of the spectral filters for the two incandescence chan- laser light, the intensity I of the light incident on the nels is a trade-off between temperature resolution ͑a particle is also a function of time and can be written ͑ large separation between filter transmission bands assuming a straight-line trajectory through the cen- ͒ leads to greater resolution͒ and minimizing the ef- ter of the beam as fects of a wavelength-dependent emissivity ͑a large Ϫ P 10 3 t2 separation between filter transmission bands may I ϭ I͑t͒ ϭ IC expͩ ͪ . (A5) ␲ 2 2 decrease the accuracy of the temperature determina- w0 t0 tion if the emissivity is strongly dependent on wave- length͒. Appendix B: Nomenclature a, particle radius ͑cm͒. ͑ ͒͑ adepth, absorption depth cm obtained from a fitto 6. Conclusions the solution of the Mie equations͒. B͑␭͒d␭, blackbody radiation ͑WmϪ2 srϪ1͒. This work has demonstrated that rudimentary par- c, speed of light ͑m͞s͒. ticle sizing and identification can be performed in situ Ϫ Ϫ C , specific heat of air at 300 K ͑Jg 1 K 1͒. with a combination of LII and elastic-scattering de- air Ϫ Ϫ C , specific heat of the particle ͑Jg 1 K 1͒. tection. Despite many simplifying assumptions, a s D, diffusion coefficient in air for vapor from the number of materials that are relevant to clean-room incandescing particle ͑cm2͞s͒. and air pollution monitoring can be detected and dif- d , diameter of air molecule ͑cm͒. ferentiated, making this a viable technique for real- air dM͞dt, mass loss due to particle vaporization ͑g͞s͒. time aerosol measurements. d⍀, fraction of emitted light that is collected by the detection system. ⌬, fraction of blackbody radiation emitted in the Appendix A: Detailed Description of Kabs, hN, and I spectral band of the incandescence detector. The absorption coefficient can be calculated exactly ε, emissivity at incandescence wavelengths. from the Mie equations27 if the complex indices of f, photodetector amplifier bandwidth ͑Hz͒. refraction for the particle are known. To simplify h, Planck’s constant ͑Js͒.

3734 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003 ͑ Ϫ2 Ϫ1͒ laser vaporization of small soot particles in a flame,” Appl. Opt. hN, Nusselt number Wcm K . ͑ ͞ ͒ 23, 2209–2215 ͑1984͒. Hv, latent heat of vaporization J mol . I, 1.064-␮m intensity ͑W͞cm2͒. 7. S. Will, S. Schraml, K. Bader, and A. Leipertz, “Performance ͑ ͞ 1͞2͒ characteristics of soot primary particle size measurements by IN, photodetector noise current A Hz . ␬ ͑ Ϫ1 Ϫ1͒ time-resolved laser-induced incandescence,” Appl. Opt. 37, s, thermal conductivity of particle Wcm K . ͑ ͒ k, Boltzmann’s constant ͑J͞K͒. 5647–5658 1998 . ␮ 8. R. L. Vander Wal, “Laser-induced incandescence: detection Kabs, Mie absorption coefficient at 1.064 m. ͑ ͒ ͑ Ϫ1 issues,” Appl. Opt. 35, 6548–6559 1996 . kair, thermal conductivity of air at 300 K Wcm 9. R. L. Vander Wal and D. L. Dietrich, “Laser-induced incandes- Ϫ1 K ͒. cence applied to droplet combustion,” Appl. 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1 July 2003 ͞ Vol. 42, No. 19 ͞ APPLIED OPTICS 3735 30. F. P. Bundy, “Pressure-temperature phase diagram of elemen- 32. B. M. Vaglieco, F. Beretta, and A. D’Alessio, “In situ evalu- tal carbon,” Physica A 156, 169–178 ͑1989͒. ation of the soot refractive index in the UV-visible from the 31. R. A. Paquin, “Properties of metals,” in Handbook of Optics, measurement of the scattering and extinction coefficients in M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. rich flames,” Combust. Flame 79, 259–271 ͑1990͒. Wolfe, eds. ͑McGraw-Hill, New York, 1995͒, Vol. 2, pp. 35– 33. J. F. O’Hanlon, A User’s Guide to Vacuum Technology, 2nd ed. 49. ͑Wiley, New York, 1989͒.

3736 APPLIED OPTICS ͞ Vol. 42, No. 19 ͞ 1 July 2003