Electromagnetic scattering from a spherical polydispersionof coated spheres

George W. Kattawar and Dan A. Hood

The volume averaged cross sections for extinction, scattering, absorption, and radiation pressure along withthe elements of the phase matrix were computed for a spherical polydispersion of water coated carbon parti-cles. The wavelength used was 4910 A. Two cases were considered. For one we held the thickness of thewater coating constant over the polydispersion, while the parameter q = r/r, (the ratio of core radius to totalradius) was varied. For the subsequent case we held q constant over the polydispersion, while the thicknessof the coating varied. The results show that there are large differences in both the intensity and degree ofpolarization between dry and wet aerosols. Also interference phenomena can occur, which demonstrate thatthe assignment of an average refractive index to aerosols can be misleading and can lead to erroneous re-sults.

I. Introduction

If one is to calculate accurately the radiance andpolarization distribution in the earth's atmosphere, thenone must have a realistic model of the aerosols to com-pute the phase matrix from Mie theory. Virtually allcalculations that have been performed to date haveassigned an average refractive index to the aerosols,which neglects the fact that liquid is being adsorbed onthe surface. It is well established that relative humidityplays an important role on the size of atmosphericaerosols.'-3 There is also a large percentage of certaindry aerosols that are insoluble in water. For these sit-uations it is important to be able to calculate the phasematrix for a spherical polydispersion of coated particles.

The theory for electromagnetic scattering fromcoated spheres has been worked out by Aden andKerker. 4 A review of this subject can also be found inKerker.5 One of the first calculations to be performedthat was relevant for aerosols was for a monodispersionof water coated carbon particles.6 Unfortunately Fennand Oser6 used an incorrect refractive index for carbon.It is the purpose of this paper to consider the opticalproperties of a spherical polydispersion of water coatedcarbon particles at 4910 A with the correct refractiveindex and to show that interference phenomena canoccur that drastically change the character of the phasematrix.

11. Models Used and Computational Methods

The model we chose for the size distribution of theaerosols was

n(r) r6exp(-6r), (1)

where r is the outer radius of the particle. This distri-bution has a mode radius of 1 um. Although this dis-tribution function is not indicative of atmospheric hazes(see Deirmendjian 7 ), we chose it so coating thicknesseswould be of the order of the wavelength of the incidentradiation, namely 0.491 ,im. This was done to show howinterference effects can develop. The refractive indexof the water shell was taken to be 1.33-0.Oi, while thatof the carbon core was 1.95-0.66i. The radius of thecore is denoted by r and q = r/r, consistent with thenotation of Kerker.5 The minimum and maximumparticle radii used in the integration were 0.1 Am and4 Am, respectively. These values were fixed throughoutthe subsequent analysis. They were chosen so thedistribution function was four orders of magnitudebelow the mode radius of 1 gm. Two models wereconsidered. In the first model we held q constant overthe distribution. This model is consistent with thegrowth curve theory used by Winkler.3 It is clear thatholding q constant over the distribution implies that thethickness of the coating changes continuously. In thesecond model we held the thickness of the coatingconstant and varied q according to

q = 1 - tr,

The authors are with Texas A&M University, Physics Department,College Station, Texas 77843.

Received 31 January 1976.

(2)

where t is the thickness of the coating. When the radiusof the particle is less than or equal to the thickness, thenthe all shell values are calculated, i.e., the core disap-pears, and the sphere becomes homogeneous.

1996 APPLIED OPTICS / Vol. 15, No. 8 / August 1976

sa,3.2. . . . . .

a: 3.0 iext

E 2.8 lsca~~26 "flabs

S: 24 -\, ext ALLz 2.2 CORE VALUES0

> 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0~~~~~~~~q

6-J

0

Fig. 1. Volume averaged cross sections vs q for the constant q

model.

The coefficients used for the computation [seeKerker, 5 Eqs. (5.1.33) and (5.1.34)] involve sphericalBessel, Neumann, and Hankel functions with complexarguments in general. The spherical Neumann func-tions are stable for upward recursion, whereas thespherical Bessel functions are unstable when the orderexceeds the argument. We, therefore, used downwardrecursion to compute them. The spherical Hankelfunctions are easily obtained from the spherical Besseland Neumann functions. Although the computationappears to be straightforward, there are some pitfallsto be avoided. Perhaps the worst of these occurs whenthe core no longer has any effect on the series. Thereason for this is that the numerator and denominatorinvolve differences of terms, which are becoming small,and numerical significance is rapidly lost. When thishappens large errors occur in using the exact series. Toavoid this problem we begin computing the Mie series,assuming all shell, when the order of the exact series isequal to the size parameter of the core. We then testthe two series until they differ by no more than one partin 109; then the Mie series is used. This technique hasproven invaluable, and we have tested it under manyand varied circumstances. The entire calculation isperformed in double precision complex arithmetic.The majority of the calculations were performed on thenew AMDAHL 470V/6.

1ll. Discussion of Results

In Fig. 1 we show a plot of the volume averaged crosssections vs q for extinction, scattering, absorption, andradiation pressure denoted by /Text, /3sca, /3 abs, and /3 rads

respectively. It should first be noted that for values ofq < 0.1 the core has little or no effect on the opticalproperties. This result was also noted by Fenn andOser6 for a inonodispersion. The second most note-worthy feature is that there exists a region, 0.79 • q <0.975, where the absorption actually exceeds the ab-

sorption for an equivalent polydispersion of particlesthat have the properties of the core. This effect wasalso observed for monodispersions by Fenn and Oser6

for size parameters greater than 18. It is due to the factthat the thin water coating acts as a lens for the carboncore. Another interesting consequence of this phe-nomenon, which has never been reported, is that thepolydispersion for this range of q values will also ther-mally radiate more than an identical polydispersion ofall carbon particles. In this same region, however, I0sca

goes through a minimum.Figure 2 shows the corresponding quantities when the

thickness of the coating is held constant throughout thepolydispersion. For thickness t < 0.30 gim (corre-sponding to q > 0.70 at the mode radius of 1 ,gm) thesame phenomena are observed, i.e., /3abs > 0abs (all core);and Osca goes through a minimum. Beyond a thicknessof about 2 gim the core has virtually no effect. Themaximum radius considered in the integration over sizewas 4 gm.

In Fig. 3 we present the scattering function (P1 +P2)/8-r, where the notation is consistent with the fourelements of the phase matrix used by Deirmendjian.7

For the case of all shell, i.e., all water, we see the familiarcorona or diffraction peak at small scattering angles.Also there is a weak primary bow developing at 1500 andthe familiar glory at 180°. This should be contrastedwith the featureless behavior for the all core model,which has appreciable absorption. Although the glory

10-1 100THICKNESS (im)

Fig. 2. Volume averaged cross sections vs thickness t(,um) for theconstant thickness model.

August 1976 / Vol. 15, No. 8 / APPLIED OPTICS 1997

100

* ALL COREx t=0.05,umo t=0.10,um- t=0.14,um* t = 0.30 ,um* t = 0.80 pm- ALL SHELL

00

1 0-1-

0- 200 40° 600 800 1000 1200 100 1600 1800SCATTERING ANGLE

Fig. 3. Scattering function (P 1 + P2)/87r vs scattering angle for theconstant thickness model.

persists for coating thicknesses > 0.30,gm, it does notappear for thicknesses < 0.14,gm. It is also interestingto note that for t = 0.80 ,gm the glory peak is slightlyhigher than that for the all shell model. There is aninteresting phenomenon that occurs when t = 0.1 m.For scattering angles between 300 and 1080 the phasefunction lies below all others presented. This effect isborne out more strikingly in Fig. 4, which is a plot of thedegree of polarization vs scattering angle, i.e., (P1 -P2)/(P1 + P2). There is a strong negative polarizationat 650, which lies far below either the all core or all shellcases. This phenomenon is due to interference betweenthe rays reflected off the shell and those reflected off thecore. Also, a coating thickness of only 0.05,gm shifts themaximum polarization from 550 (all core) to 600 andreduces the maximum by 26%. This, of course, impliesthat it would be very easy to distinguish between wetand dry aerosols using polarimetry. In Fig. 5 the ele-ment P3 is presented. For thicknesses <0.14 ,m thesign of P is negative for scattering angles 1200.However for thicknesses >0.3, gm there is a region from1400 to 172° where the sign of P3 is positive. This ischaracteristic of water.

In Fig. 6 we show a plot of the scattering function forthe constant q case (compare with Fig. 3). If one com-

pares the q = 0.90 case (this corresponds to t = 0.1,gmat the mode radius) with the t = 0.10 gm case in Fig. 3,we observe that the striking minimum around 90° is nolonger pronounced. This adds further evidence to thefact that this is an interference phenomenon, sinceholding q constant varies the thickness over the poly-dispersion, which would tend to wash out certain in-terference effects.

This effect can be seen more clearly in Fig. 7, wherewe plot the degree of polarization for the constant qcases. If one compares this case with Fig. 4, the strongnegative polarization prevalent at t = 0.10 Am is absentin Fig. 7. Also, only for values of q < 0.5 do we see thestrong polarization at the primary bow. For q = 0.90the maximum in the degree of polarization is shiftedfrom 550 to 68° and reduced by 29% relative to the allcore case. This again demonstrates the relative easeone would have in distinguishing between wet and dryaerosols. In Fig. 8 we present the element P3 for theconstant q model. For values of q > 0.8 we obtain apositive region for P3 between 1400 and 1740 and anarrow negative region from 1760 to 1800 characteristicof the counter corona for water.

IV. Conclusion

We have presented an analysis of the effect of a watercoating on a spherical polydispersion of carbon particles,the conclusion being that one can get erroneous resultsby using a single refractive index for both insoluble anddeliquescent aerosols. Certain interference effects canoccur when the coating thickness is constant. However,these same features can be useful as a probe in studyingthese aerosols. It should be noted that a "typical" re-fractive index for atmospheric aerosols is 1.5 - (0.01 -0.05)i, which is larger than the shell but smaller than thecore. We have also found that under certain conditionsa spherical polydispersion of water coated particles canradiate more energy than an equivalent polydispersionof all core material.

600 800 1 ANG00ESCATTERING ANGLE

Fig. 4. Degree of polarization [(P1 - P 2)/(P1 + P 2)] in percent vsscattering angle for the constant thickness model.

1998 APPLIED OPTICS / Vol. 15, No. 8 / August 1976

I

t = 0.80 pm-~~~ a ~~~ALL SHELL

a.

1 Q-1:

10-2:

00 200 400 600 800 1000 1700 1400 1600. 1800SCATTERING ANGLE

Fig. 5. P/4r vs scattering angle for the constant thickness model.The regions where P3 are positive and negative are denoted by + and

-, respectively, on the graph.

tL0..

+-

SCATTERING ANGLE

Fig. 6. Same as Fig. 3, but for constant q model.

00xo21

+

0~

Q

600 800 1000 1200 1400 1600 1800SCATTERING ANGLE

Fig. 7. Same as Fig. 4, but for constant q model.

180°SCATTERING ANGLE

Fig. 8. Same as Fig. 5, but for constant q model.

This work was supported by Grant NGR 44-001-117from the National Aeronautics and Space Adminis-tration.

References1. D. Sinclair, R. J. Countess, and A. S. Hooper, Atmos. Environ. 8,

1111 (1974).2. P. Winkler, Proceedings of the 7th International Conference on

Condensation and Ice Nuclei (Prague and Vienna, 1969), Sup-plementary Volume, p. 168.

3. P. Winkler, J. Aerosol Sci. 4, 373 (1973).4. A. L. Aden, and M. Kerker, J. Appl. Phys. 22,1242 (1951).5. M. Kerker, The Scattering of Light and Other Electromagnetic

Radiation (Academic Press, New York, 1969).6. R. Fenn and H. Oser, Appl. Opt. 4,1504 (1965).7. D. Deirmendjian, Electromagnetic Scattering on Spherical Po-

lydispersions (Elsevier;New York, 1969).

August 1976 / Vol. 15, No. 8 / APPLIED OPTICS 1999

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18-23 October 1976 ANNUAL MEETING, Convention Cen-ter, Tucson, Arizona (Braniff Place Hotel) Information:J. W. Quinn at OSA or CIRCLE NO. 61 ON READER SER-VICE CARD

5-6 November 1976 OPTICAL FABRICATION AND TEST-ING ROAD SHOW, Auburn, Massachusetts Informa-tion: J. W. Quinn at OSA or CIRCLE NO. 63 ON READERSERVICE CARD

1-3 December 1976 OPTICAL PHENOMENA IN INFRAREDMATERIALS, OSA TOPICAL MEETING, Annapolis, Mary-land Information: J. W. Quinn at OSA or CIRCLE NO. 57ON READER SERVICE CARD

13-15 December 1976 ATMOSPHERIC AEROSOLS, THEIROPTICAL PROPERTIES AND EFFECTS, OSA TOPICALMEETING, Williamsburg, Virginia Information: J. W.Quinn at OSA or CIRCLE NO.58 ON READER SERVICE CARD

22-24 February 1977 OPTICAL FIBER TRANSMISSION 2,OSA TOPICAL MEETING, Williamsburg, Virginia Infor-mation: J. W. Quinn at OSA or CIRCLE NO.56 ON READERSERVICE CARD

9-14 October 1977 ANNUAL MEETING, Royal York, Toron-to, Canada Information: J. W. Quinn at OSA or CIR-CLE NO. 64 ON READER SERVICE CARD

21-27 October 1978 ANNUAL MEETING, Town and CountryHotel, San Diego, California Information: J. W. Quinnat OSA or CIRCLE NO. 53 ON READER SERVICE CARD

7-12 October 1979 ANNUAL MEETING, Holiday Inn/Flag-ship, Rochester, New York Information: J. W. Quinnat OSA or CIRCLE NO. 54 ON READER SERVICE CARD

2002 APPLIED OPTICS / Vol. 15, No. 8 / August 1976

AugustI? Australian Spectroscopy, 10th conf., University of

Western Australia, Nedlands A. Walsh, CSIRODiv. of Chemical Physics, P.O. Box 160, Clayton,Victoria 3168, Australia

26-Aug. 6 Photon Correlation Spectroscopy and Velocimetry,NATO Advanced Study Institute, Capri, Italy H. Z.Cummins, Phys. Dept., City College of N. Y., NewYork, N.Y. 10031

1-7 High Speed Photography, internat. congress, TorontoOntario Sci. Ctr., 770 Don Mills Rd., Don Mills, On-tario M3C 1 T3

2-3 Rocky Mountain Spectroscopy Conference, Denver J.R. Gaines, 1012 4th St., Golden, Colo. 80401

2-6 Coherent Optics, course, Ann Arbor Cont. Engineer-ing Ed., 300 Chrysler Center, U. of Michigan, AnnArbor, Mich. 48105

2-6 Glass, course, Plymouth A. M. Cruickshank, GordonRes. Confs., Pastore Lab., Univ. of Rhode Island,Kingston, R.I. 02881

2-6 Modern Optics, course, Cambridge R. S. Kennedy,Electrical Eng. Dept., MIT, Cambridge, Mass.02139

2-6 Infrared Spectroscopy: Applications, course, Bruns-wick D. W. Mayo, Chem. Dept., Bowdoin College,Brunswick, Me. 04011

2-13 Modern Industrial Spectroscopy, ann. mtg., Tempe J.Fuchs, Chem. Dept., Arizona State Univ., Tempe,Ariz. 85281

8-11 Photochemical Society of North America, ann. mtg.,Vancouver, B.C. F. A. Loewus, Dept. AgriculturalChem., Washington State Univ., Pullman, Wash.99163

8-13 Microbeam Analysis Society 11th Annual Conferenceand 34th Annual Meeting of the Electron Micro-scope Society, jt. mtg., Miami Beach P. Lublin,MAS Conf., Fountainebleu Hotel, Miami Beach,Fla.

9-11 Heat Transfer, conf., St. Louis ASME, 345 E. 47thSt., New York, N.Y. 10017

9-13 Molecular Electronic Spectroscopy, course, AndoverA. M. Cruickshank, Gordon Res. Confs., PastoreLab., Univ. of Rhode Island, Kingston, R.I. 02881

9-13 Optical Detection and Communication, course, Cam-bridge R. S. Kennedy, Electrical Eng. Dept., MIT,Cambridge, Mass. 02139

12-21 Photoelectronic Imaging Devices, course, San DiegoS. Nudelman, Arizona Medical Ctr., Univ. of Ariz.,Tucson, Ariz. 85724

16-20 Hot Stage Microscopy, course, Chicago Registrar,McCrone Research Instit., 2820 S. Michigan Ave.,Chicago, Ill. 60616

16-20 Transmission Electron Microscopy, course, ChicagoRegistrar, McCrone Research Instit., 2820 S. Michi-gan Ave., Chicago, Ill. 60616

16-20 International Astronomical Union, symp., CambridgeM. S. Longair, Cavendish Lab., Dept. Phys., Univ.of Cambridge, Madingley Rd., Cambridge CB3OHE, U.K.

16-20 Atomic and Molecular Interactions, course, WolfeboroA. M. Cruickshank, Gordon Res. Confs., PastoreLab., Univ. of Rhode Island, Kingston, R.I. 02881

19-28 Radiation in the Atmosphere, internat. symp., Gar-misch-Partenkirchen H.-J. Bolle, MeteorologischesInstitut, D-8000 Munchen 2, Thereseienstrasse 37,West Germany

21-24 Photographic Society of America, ann. mtg., ValleyForge PSA, 2005 Walnut St., Philadelphia, Pa.19103

23 Business Side of the Optical Industry, sem., San DiegoSPIE, PP.O. Box 1146, Palos Verdes Estates, Calif.90274

23-25 Scanning Electron Microscopy, course, Chicago Reg-istrar, McCrone Research Instit., 2820 S. MichiganAve., Chicago, Ill. 60616

23-26 Application of Holography and Optical Data Process-ing, ICO conf., Israel R. B. Weil, Israel Laser &Electrooptics Soc., co Technion, Haifa, Israel

23-27 Plasma Chemistry, course, Andover A. M. Cruick-shank, Gordon Res. Confs., Pastore Lab., Univ. ofRhode Island, Kingston, R.I. 02881

23-27 Infrared and Raman Spectroscopy, course, WolfeboroA. M. Cruickshank, Gordon Res. Confs., PastoreLab., Univ. of Rhode Island, Kingston, R.I. 02881

24-25 Optimum Utilization of Polarized Light, sem., SanDiego SPIE, P.O. Box 1146, Palos Verdes Estates,Calif. 90274

24-25 Advances in Image Transmission Techniques, sem.,San Diego SPIE, P.O. Box 1146, Palos Verdes Es-tates, Calif. 90274

24-25 Industrial Applications of High Power Laser Technolo-gy, sem., San Diego SPIE, P.O. Box 1146, PalosVerdes Estates, Calif. 90274

24-25 Optics in Solar Energy Utilization II, sem., San DiegoSPIE, P.O. Box 1146, Palos Verdes Estates, Calif.90274

24-25 Laser Scanning Components and Techniques, sem.,San Diego SPIE, P.O. Box 1146, Palos Verdes Es-tates, Calif. 90274

24-25 Optical Information Processing, sem., San DiegoSPIE, P.O. Box 1146, Palos Verdes Estates, Calif.90274

24-25 Unconventional Spectroscopy, sem., San Diego SPIE,P.O. Box 1146, Palos Verdes Estates, Calif. 90274

26-27 Applications of Optics in Medicine and Biology, sem.,San Diego SPIE, P.O. Box 1146, Palos Verdes Es-tates, Calif. 90274

26-27 Acousto-Optics, sem., San Diego SPIE, P.O. Box1146, Palos Verdes Estates, Calif. 90274

26-27 Methods for Atmospheric Radiometry, sem., San DiegoSPIE, P.O. Box 1146, Palos Verdes Estates, Calif.90274

August 1976 / Vol. 15, No. 8 / APPLIED OPTICS 2003

26-27 Practical Applications of Low Power Lasers, sem., SanDiego SPIE, P.O. Box 1146, Palos Verdes Estates,Calif. 90274

26-27 Advances in Precision Machining of Optics, sem., SanDiego SPIE, P.O. Box 1146, Palos Verdes Estates,Calif. 90274

26-27 High Speed Optical Techniques, sem., San DiegoSPIE, P.O. Box 1146, Palos Verdes Estates, Calif.90274

26-27 Modern Utilization of Infrared Technology II, sem.,San Diego SPIE, P.O. Box 1146, Palos Verdes Es-tates, Calif. 90274

29-Sept. 2 IES Annual Conf., Cleveland F. M. Coda, IES, 345 E.47th St., New York, N.Y. 10017

29-Sept. 2 Conf. of Commission on International Photobiology,Rome A. Castellani, C NEN-CSN della Casaccia,S. Maria de Galeria, 0060 Rome, Italy

30-Sept 2 Physics of the X-Ray Spectra, internat. symp.,Gaithersburg, Md. Sec. of the Conf., Rm A141Phys. Bldg. NBS, Washington, D.C. 20234

30-Sept. 3 Lattice Defects in Ionic Crystals, conf., Berlin F. W.Felix, Hahn-Meitner Inst. f. Kernforschung Berlin,D-1000 Berlin 39, Glienickerst 100, Postfach 39 0128, Federal Republic of Germany

30-Sept. 3 Solar Energy Utilization, symp., Geneva WMO, J.Peeters, 41 Ave. G Motta, CP5, 1211 Geneva 20,Switzerland

31-Sept. 2 Optical Computing Conference, Capri, Italy IEEE,P.O. Box 639, Silver Spring, Md. 20901

31-Sept. 3 Vacuum and Thin Film Technology, internat. symp.,Uppsala P. Andersson, Instit. of Technology, Box534, S-751 21 Uppsala, Sweden

September? Vibrational Spectroscopy, NATO Institute on Ad-

vanced Methods, Florence W. J. Orville-Thomas,Salford Univ., Chem. Dept., Salford, M5 4WT, En-gland

1-3 National Electronics Conference and National Com-munications Forum Joint Meeting, Chicago Na-tional Eng. Consortium, 1301 W. 22nd St., OakBrook, Ill. 60521

1-3 International Conference on Magnetooptics, Zurich P.Wachter, Bab. f. Festkorperphys, ETH Hongger-berg, CH-8049, Zurich, Switzerland

1-3 Advances in Magnetic Materials and Their Applica-tions, conf., London A. Cunningham-Swendell,Press Officer, EE, Savoy Place, London WC2ROBL, U.K.

2-3 Institute of Acoustics Autumn Conference, EdinburghP. G. Mylne, Sec. IOA, 47Belgrave Sq., London SWIX8QX, U.K.

2-8 Raman Spectroscopy, 5th internat. conf., Freiburg E.D. Schmid, Institut fur Physikalische Chemie, He-belstrasse 38, D- 78 Freibrrg I. BR., West Germany

5-10 Infrared High Resolution Spectroscopy, internat.symp., Liblice Czechoslovakian Academy of Sci.,Praha 1, Vlasska 9, Czech.

6-8 Astronomical Applications of Linear Response ImageReceptors, colloq., Meudon, France M. F. Walker,Lick Observatory, Univ. of Calif., Santa.Cruz, Calif.95060

6-10 Macroscopy in Art and Archaeological Conservation,course, London Registrar McCrone Res. Instit., 2McCrone Mews, Belsize,La., London NW3 5BG, U.K.

6-11 8th International Congress on Cybernetics, BelgiumSecretariat, Internat. Assoc. for Cybernetics, Palaisdes Expositions, Place Andre Rijckmans, B-5000Namur, Belgium

6-16 Solar Energy Conversion, course, Arizona G. Giaquin-ta, Internat. College of Applied Phys., Instituto diFisica, Corso Italia 57, Catania, Italy

7-9 Lasers and Applications, course, Arlington ContinuingEducation Courses, P.O. Box 3278, Falls Church, Va.22043

13-17 Spectral Line Shapes, internat. conf., London Mtgs.Office, Instit. of Phys., 47Belgrave Sq., London SW1X8QX, U.K.

13-17 MICRO-76, symp., London Administrator, Royal Mi-croscopical Soc., 37/38 St. Clements, Oxford OX41AJ, U.K

13-17 Royal Microscopical Soc., conf., London ClarendonHouse, Cornmarket St., Oxford OX1 3HA, U.K.

13-17 Microscopy in Art and Archaeological Conservation,course, London Registrar, McCrone Res. Instit., 2McCrone Mews, Belsize La., London NW3 5BG, U.K.

13-24 Synchrotron Light, course, Stanford, Calif. G. Gia-quinta, Internat. College of Applied Phys., Institu-to di Fisica, Corso Italia 57, Catania, Italy

14-16 Electrooptics/Laser Conference and Exposition, NewYork Technical Program Coordinator, 222 W.Adams St., Chicago, Ill. 60606

14-17 6th European Microwave Conference, Rome I. P. deSantis, Selenia, S.p.A., Via Tiburtina Km. 12.400,00131 Rome, Italy

15-16 Measuring Health and Safety Hazards in the WorkingAtmosphere, sem., London G. Dunn, Sira Instit.,South Hill, Chislehurst, Kent BR7 5EH, U.K.

15-17 Sensitometry: Modern Aspects and Future Trends,Binghamton, N.Y. R. H. Wood, Exec. Dir., SPSE,1330 Massachusetts Ave. N. W., Washington, D.C.20005

15-18 Magnetic Thin Films, internat. conf., Heslington M.Prutton, Phys. Dept., Univ. of York, Heslington,York Y01 5DD, U.K.

16-18 Applications of Optical Instrumentation in MedicineV, Washington SPIE, P.O. Box 1146, Palos VerdesEstates, Calif. 90274

17-18 OSA Optical Fabrication and Testing, workshop,Rochester J. W. Quinn, 2000 L St. N.W., Wash-ington, D.C. 20036

20 Practical Application of New Color Technologies,course, Newburgh, N.Y., and Tatamy, Pa. J. G. Da-vidson, Macbeth Division, P.O. Box 950, Newburgh,N. Y. 12550

20-23 Acoustics, internat. mtg., Heidelberg K. Tamm, Inst.f. Angewandte Physik, Univ., D-6900, Heidelberg,Albert-Ueberle-Str 3/5, Germany

2004 APPLIED OPTICS / Vol. 15, No. 8 / August 1976