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F NASA TECHNICAL NOTE z c 8. 4 z ABSOLUTE RAYLEIGH SCATTERING CROSS SECTIONS OF GASES AND FREONS OF STRATOSPHERIC INTEREST IN THE VISIBLE AND ULTRAVIOLET REGIONS t' Shurdunund und A. D. Prusud Ruo Wallops Flight Center Wullops Islund, vu. 23337 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. MARCH 1977 II I https://ntrs.nasa.gov/search.jsp?R=19770012747 2020-03-28T06:03:43+00:00Z

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  • F

    N A S A TECHNICAL NOTE

    z c

    8.

    4 z

    ABSOLUTE RAYLEIGH SCATTERING

    CROSS SECTIONS OF GASES A N D

    FREONS OF STRATOSPHERIC INTEREST

    I N THE VISIBLE A N D ULTRAVIOLET REGIONS

    t'

    Shurdunund und A. D. Prusud Ruo

    Wallops Flight Center Wullops Islund, vu. 23337

    N A T I O N A L AERONAUTICS A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. M A R C H 1977

    III

    https://ntrs.nasa.gov/search.jsp?R=19770012747 2020-03-28T06:03:43+00:00Z

  • - -

    TECH LIBRARY KAFB, NM

    Illllll1111111111IIIII1111lllllIll111111111 0334370

    ~~

    1. Report No. 2. Government Accession No.

    NASA TN D-8442 4. Title and Subtitle

    ABSOLUTE RAYLEIGH SCATTERING CROSS SECTIONS OF GASES AN0 FREONS OF STRATOSPHERIC INTEREST I N THE VISIBLE AND ULTRAVIOLET REGIONS

    ~~

    7. Author(s) Shardanand (NASA Wallops F l i g h t Center ) A. D. Prasad Rao (Computer Sciences Corpo ra t i on )

    -.9. Performing Organization Name and Address

    NASA Wallops F l i g h t Center, Wallops I s land , VA 23337 Computer Sciences Corpora t ion , Wallops I s l a n d , VA 23337

    2. Sponsoring Agency Name and Address

    Nat iona l Aeronaut ics and Space A d m i n i s t r a t i o n Washington, OC 20546 . ~- - ...

    5. Supplementary Notes

    - . - -.- . - - 6. Abstract

    3. Recipient's Catalog NO.

    5. Report Date March 1977

    6. Performing Organization Code

    8. Performing Organization Report No.

    10. Work Unit No.

    11. Contract or Grant No.

    13. Type of Report and Period Covered

    TECHNICAL NOTE

    14. Sponsoring Agency Code

    The l a b o r a t o r y measurements o f abso lu te Ray le igh s c a t t e r i n g c ross sec t i ons as a f u n c t i o n o f wave

    l e n g t h a r e r e p o r t e d f o r gas molecules He, Ne, A r , Nz, H z , O z , COz, CHI, and f o r vapors o f most commonly used f r e o n s CClZFz, CBrF3, CFs. and CHClFZ. These c ross s e c t i o n s a r e determined f rom

    t h e measurements o f photon s c a t t e r i n g a t an ang le of 54'44' which y i e l d t h e abso lu te values independent o f t h e va lue o f normal d e p o l a r i z a t i o n r a t i o s . The p resen t r e s u l t s show t h a t i n t h e

    0

    s p e c t r a l range 6943-3638A, t h e values o f t h e Ray le igh s c a t t e r i n g c ross s e c t i o n can be e x t r a p o l a t e d f rom one wavelength t o t h e o t h e r us ing l / X 4 law w i t h o u t knowing t h e va lues o f t h e p o l a r i z a b i l i t i e s . However, such an e x t r a p o l a t i o n can n o t be done i n the r e g i o n o f s h o r t e r wavelengths.

    .. ~

    7. Key-Words (Suggested by Author(s)j 18. Distribution Statement

    Ray le igh S c a t t e r i n g U n c l a s s i f i e d - U n l i m i t e d S c a t t e r i n g Cross Sec t ions STAR Category 46Atmospher ic Gas Molecules Freons P o l l u t a n t s

    ~~. ~.

    19. Security Classif. (of this report) 20. Security Classif. (of this page) U n c l a s s i f i e d

    - . I U n c l a s s i f i e d . ~- $4.00 ' For sale by the National Technical Information Service. Springfield, Virginia 22161

  • ABSOLUTE RAYLEIGH SCATTERING CROSS SECTIONS OF GASES AND FREONS OF STRATOSPHERIC INTEREST IN THE VISIBLE AND ULTRAVIOLET REGIONS

    Shardanand

    NASA Wallops Fl ight Center

    and

    A . D . Prasad Rao Computer Sciences Corporation

    INTRODUCTION

    Absolute Rayleigh sca t t e r ing cross sect ions provide useful data f o r defining the magnitude of photon molecule in te rac t ions . Generally, these cross sect ions a re computed from the index of re f rac t ion a t a wavelength and then extrapolated t o other wavelengths using l/X4 law ( r e f s . 1 and 2 ) . I t would be appropriate t o remark t h a t the re f rac t ive

    0

    indices f o r gases tabulated in most handbooks a r e a t 5893A, Na D l i nes . In recent years , however, there a re a few publications on the indices of re f rac t ion a t other wavelengths ( see bibliography). T h e e a r l i e r measurements ( r e f s . 3 t h r u 15) on the Rayleigh sca t te r ing using conventional l i g h t sources were l imited in scope because of the experimental d i f f i c u l t i e s concerning the in t ens i ty of l i g h t source, bandwidth, col l imat ion, and above a l l the lack of instrumentation f o r detect ing the weak sca t te red s igna ls . In recent years , these d i f f i c u l t i e s have been overcome w i t h the a v a i l a b i l i t y of l a se r s and w i t h the improved technology in l i g h t detect ion. Several inves t iga tors ( r e f s . 16 t h r u 30) have used these recent techniques f o r measuring the photon sca t te r ing from atoms and molecules a t selected l a s e r wavelengths i n the v i s ib l e region. However, there a re only a few measure-

    P

    ments i n the vacuum u l t r av io l e t ( r e f s . 31 t h r u 35) .

    To the best of our knowledge, there i s no publication concerning the d i r e c t measurements of the absolute Rayleigh sca t te r ing cross sect ions f o r atmospheric gas molecules as a function of wavelength. For the present inves t iga t ion , we have employed an Ar-ion l a s e r

    0

    (Model CR-5) f o r the wavelengths 5145, 4880, 4579, and 3638A and a He-Ne l a s e r (Spectra0

    1 I Physics Model 132) f o r the wavelength 6328A. The polar izat ion of the radiat ion emitted from Ar-ion l a s e r i s found t o be 95% in the the d i rec t ion perpendicular t o the sca t t e r ing plane. T h e He-Ne l a s e r i s l i nea r ly polarized i n the same d i rec t ion . T h i s study i s t o

  • r e p o r t f o r t h e f i r s t t ime such measurements f o r He, Ne, A r , NP, H2, 02, Con, CHI, as a f u n c t i o n o f wavelength. I n add i t i on , recogn iz ing t h e g r e a t impor tance o f f reon vapors as

    p o l l u t a n t s f o r problems r e l a t e d t o s t r a t o s p h e r i c s tud ies , s i m i l a r measurements a re a l s o

    presented f o r commonly used f reons CC12F2, CBrF3, CF4, and CHC1F2. The measured cross

    sec t i ons are compared w i t h o t h e r measured and c a l c u l a t e d data.

    THEORETICAL BACKGROUND

    The i n t e n s i t y , Is( @ , q , $ ) , sca t te red by gas molecules o f number dens i ty , N, per u n i t

    s o l i d angle i n t h e d i r e c t i o n e , q , and $ ( f i g . 1) f rom a p a r t i a l l y p o l a r i z e d i n c i d e n t beam o f i n t e n s i t y , Io,whose K vec to r i s along t h e Y-axis i s g iven by t h e express ion ( r e f . 35)

    where V i s t h e s c a t t e r i n g volume; os i s t he t o t a l cross s e c t i o n f o r Rayle igh s c a t t e r i n g ;

    pn = 6y2/(45a8 + 7y2) i s t h e normal d e p o l a r i z a t i o n f a c t o r and i s zero when y rep resen t ing t h e a n i s o p t i c p roper t y o f t h e gas molecule i s zero. The q u a n t i t y a. represents t h e mean

    p o l a r i z a b i l i t y o f t h e molecule. The f a c t o r g = (Ex/Ez) 2 i s r e l a t e d t o the degree o f p o l a r i z a t i o n , P, o f t h e i n c i d e n t beam by the r e l a t i o n P = ( 1 - g ) / ( l + g ) . It should po in ted o u t t h a t when e = q = $ = 54"44', t he s c a t t e r e d Isi s equal t o the average s i t y o f t h e sca t te red r a d i a n t energy and i s independent o f pn and g. However, i f

    observed f o r cond i t i ons such t h a t e = $, then Isi s independent o f g on ly . U t i l i z i n g t h e d i r e c t i o n cos ine r e l a t i o n , namely, cos2 e + cos' T- + cos2 $ = 1

    equat ion (1 ) can be w r i t t e n as

    e

    i n t e n

    i sS

    t h e

    1

    where rl represents t h e d i r e c t i o n o f observa t ion o f t h e s c a t t e r e d r a d i a t i o n w i t h respec t t o

    t h e d i r e c t i o n o f i n c i d e n t beam. I n t h e present exper imenta l setup, an i n c i d e n t beam o f

    p a r t i a l l y p o l a r i z e d r a d i a n t energy t r a v e l s a long t h e Y-axis ( f i g . 1 ) w i t h e l e c t r i c vec tors Ex and EZ. Also, i n t h i s experiment $ = 90' and q = 54"44'. S u b s t i t u t i n g these values,

    t h e express ion ( 2 ) may be w r i t t e n as

    where V54 i s t h e s c a t t e r i n g volume when the s c a t t e r e d r a d i a t i o n i s observed a t rl = 54'44'. I n t h e v i s i b l e reg ion o f e lec t romagnet ic spectrum, t h e values o f pn f o r most gases a re

    2

    I

  • --

    very small [ref. 36; pn (N2) = 0.0214; pn (02) = 0.0565; pn (H2) = 0.01881. In such cases pn = 0 , and the expression ( 3 ) f o r the p a r t i a l l y polarized incident beam becomes

    I t should be pointed out t h a t i n vacuum u l t r av io l e t region pn may not be t rea ted as ins igni f icant .

    The following two cases of special i n t e r e s t often a r i s e and may eas i ly be derived from equation ( 3 ) .

    1 . - Case I . When the incident beam of radiant energy i s unpolarized. In this case Ex = EZ and, therefore , g = 1. T h u s , the expression f o r the in t ens i ty of rad ia t ion sca t te red from an unpolarized incident beam becomes ( r e f s . 30, 31, 36)

    Here, i t i s important t o note t h a t Is i s independent of p n . Therefore, the equation ( 5 ) can be used in the e n t i r e spectral region ranging from v i s ib l e t o the vacuum u l t r av io l e t without knowing the spec i f i c value of p n .

    2 . Case 11. When the incident beam of radiant energy i s plane polarized in the d i rec t ion perpendicular t o the sca t te r ing plane. In th i s case Ex = 0 and, therefore , g = 0. T h u s , the expression f o r the in t ens i ty of radiat ion scat tered from a l i nea r ly polarized incident beam becomes

    2 P n + 1 2 + P ,

    Unlike the Case I , i t should be emphasized t h a t in the case of polarized incident rad ia t ion , the sca t te red radiat ion Is i s not independent of pn . This means t h a t the spec i f i c values of pn need t o be known in the spectral region where the contribution of normal depolar izat ion t o the sca t te red radiat ion i s s ign i f i can t . However, in the v i s ib l e , when pn 0 , the equation ( 6 ) may be wri t ten as

    I t should be noted tha t - the equations ( 5 ) and ( 7 ) a re ident ica l except f o r the f ac to r 1 / 2 i n the r i g h t hand s ide of equation ( 7 ) .

    3

  • EXPERIMENTAL ARRANGEMENT

    A block-diagram of the experimental arrangement i s shown i n Figure 2. I t employs a l a s e r as a l i g h t source, a gas pressure vessel ca l led a s ca t t e r ing chamber f o r f i l l i n g the samples of gases, and the photon counting equipment f o r monitor ing the sca t t e red and incident l i g h t s igna ls . T h e s ca t t e r ing chamber has been fabr ica ted w i t h g rea t precision which almost eliminated the generally encountered sources of e r r o r i n s ca t t e r ing measurements. Brief ly , i t i s made of s t a i n l e s s s t ee l and can withstand pressures u p t o 100 atm. There a re seven ports in the chamber sealed w i t h sapphire windows. The locat ion of the ports i s as shown in the f igure . The l a se r beam i s expanded and collimated by using a su i t ab le beam expander-cum-collimator before enter ing the incident por t . The beam is fu r the r collimated and made i n t o a rectangular cross sect ion (19 mm x 5 m m ) by means of a rectangular s l i t (S ) attached t o the incident p o r t ( 1 ) . The ports numbering 2 th rough 6 a re provided w i t h col l imators each f i t t e d w i t h 3 rectangular aper ture s l i t s (19 mm x 5 m m ) i n s e r i e s and are such t h a t the f ront aperture s l i t in each col l imator i s qu i t e close t o the sca t t e r ing volume. There a re f ive l i g h t t raps (LT) each s i tua t ed opposite t o the ports ( 2 t h r o u g h 6 ) which hold the photomultiplier f o r measuring the l i g h t s igna ls sca t te red a t 27", 54"44', go", 125"16' , and 153". These angles a re measured w i t h respect t o the d i rec t ion of incident beam. The configuration of the l i g h t t raps i s shown i n the l e f t hand corner of the f igure and i s s imi la r t o t h a t used by Pritchard and E l l i o t t ( r e f . 38). The l i g h t t raps a re made of s t a i n l e s s s t ee l and inside surfaces hold the polished p la tes of C o r n i n g black glass which a c t as the r e f l ec t ing surfaces . Most of the l i g h t enter ing the t r ap i s absorbed a t the f i r s t glass plate. The specular r e f l ec t ion i s directed fu r the r in to the t r a p , where i t is absorbed d u r i n g addi t ional r e f l ec t ions . The l i g h t leaving the t r a p i s from non-specular re f lec t ion a t the f i r s t surface. The glass used in these t raps has a low non-specular ref lectance of a b o u t ( r e f . 38) . I n the center of the sca t te r ing Chamber, there i s a p rov i s ion f o r mount ing a ca l ibra t ion carr iage and a f ron t surface mirror which i s used in measuring the angle of l i g h t s ca t t e r ing and in a l igning the rectangular aper tures i n the l i g h t col l imators , ( C ) . The inside surface of the chamber, the l i g h t t r aps , and the collimators a re coated with flat-black-chrome-finish t h a t provides the dark background which i n conjunction w i t h the l i g h t traps minimize any spurious radiat ion reaching the detector . The performance of the inside system was such t h a t the chamber under vacuum and l a se r light-on provided a background signal which was a few percent of sca t te red signal under a l l pressure conditions in the chamber. There a re other por t s , n o t shown i n the f igure , which a re used f o r gas o u t l e t , pumping, sa fe ty valve, and pressure gauge.

    The l i g h t sources used i n the present measurements a re an Ar-ion l a se r (Coherent , 0

    Radiation Model CR-5) f o r wavelengths a t 5145, 4880, 4539, and 3638A and a He-Ne l a se r

    4

    1

  • 0

    (Spectra Phys ics Model 132) a t 6328A. The ou tpu t o f t h e l a s e r i n use i s moni tored con

    s t a n t l y f o r changes i n r a d i a t i o n f l u x by means o f a p h o t o m u l t i p l i e r (PM2; EM1 95589). The

    i n t e n s i t y o f the, l a s e r beam was reduced by i n s e r t i n g a s e r i e s o f f o u r n e u t r a l d e n s i t y

    f i l t e r s i n t h e pa th o f beam be fo re e n t e r i n g t h e p h o t o m u l t i p l i e r housing. The a t t e n u a t i o n

    f a c t o r s o f t h e n e u t r a l d e n s i t y f i l t e r s were premeasured. The use o f t he 45" m i r r o r was

    t o d i v e r t t h e l a s e r beam. The ou tpu t o f t he P h o t o m u l t i p l i e r tube (PM2) i n con junc t i on

    w i t h an a m p l i f i e r - d i s c r i m i n a t o r (AD2: SSR 1120) and data conver te r i s used as an ex te rna l

    c l o c k i n p u t o f t h e d i g i t a l synchronous computer (SSR 1110). Th is ou tpu t i s a l s o recorded

    , on a s t r i p c h a r t recorder (HP Model 71018) and thus prov ides t h e mon i to r i ng o f t h e changes i n t h e i n c i d e n t r a d i a t i o n . The photon count ing technique i s used f o r t h e measurements o f bo th t h e i n c i d e n t and sca t te red r a d i a t i o n . For t h e purpose o f measuring sca t te red r a d i a

    t i o n , another p h o t o m u l t i p l i e r tube, (PM1; EM1 9558Q), enc losed i n a housing (SSR 1151), an

    a m p l i f i e r - d i s c r i m i n a t o r (AD1; SSR 1120) , a d i g i t a l synchronous computer (SSR 1110), and a d i g i t a l reco rde r (HP Model 5055A) mod i f i ed t o match the SSR photon count ing system, a re

    used. The h i g h pressure i n t h e s c a t t e r i n g chamber and a defocuss ing magnetic assembly

    hav ing an opening o f 19 mm i n d iameter i n f r o n t o f t he p h o t o m u l t i p l i e r tube a re used t o

    enhance t h e s igna l - to -no ise r a t i o which i s an e s s e n t i a l requi rement f o r measuring t h e weak

    s c a t t e r e d l i g h t s igna ls . The use o f t he defocuss ing magnetic assembly alone improved t h e

    s igna l - to -no ise r a t i o by about a fac to r o f 10 i n t h e present setup. The p o s s i b l e changes

    i n t h e response o f t he p h o t o m u l t i p l i e r a re i n t e r m i t t e n t l y checked by means o f a neon re fe rence source (N) which was employed w i t h t h e sca t te red i n t e n s i t y mon i to r i ng tube

    (PM1). Here, i t should be po in ted o u t t h a t no change i n t h e response o f t he tube was

    observed du r ing t h e p e r i o d o f observat ions. Besides, a mechanical chopper (PAR Model 125)

    i s employed i n f r o n t o f t h i s p h o t o m u l t i p l i e r housing t o account f o r t he changes i n the

    dark counts o f t h e photomul t i p 1 i e r .

    OBSERVATIONS AND RESULTS

    The examinat ion o f general express ion (1 ) f o r t he s c a t t e r e d i n t e n s i t y shows t h a t t h e f

    arevalues o f Is/Iol i n e a r l y p r o p o r t i o n a l t o the number d e n s i t y o f t he sca t te rs . The p l o t

    vso f Is/Iopressure o f gas [ P = Po (N/No) (T/To)] i s thus a s t r a i g h t l i n e which w i l l y i e l d t h e average va lue o f Ray le igh s c a t t e r i n g cross sec t i on f rom i t s s lope. Here p i s a p ressure corresponding t o number d e n s i t y N and temperature T; No i s a Loschmidt number and Po and To a re s tandard pressure and temperature, r e s p e c t i v e l y . Therefore, f o r t h e de te r m ina t i on o f t h e abso lu te va lue o f Rayle igh s c a t t e r i n g cross s e c t i o n i t i s requ i red t o

    measure t h e values o f Is/Ioand t h e s c a t t e r i n g volume V .

    5

  • Measurement of In tens i ty Ratio I s / Io

    Let us assume t h a t Io is uniformly d i s t r ibu ted radiat ion f lux incident on the s c a t t e r s i n the sca t t e r ing volume V and Is is the rad ia t ion sca t te red i n t o a so l id angle defined by the sca t t e r ing volume and o ther geometrical parameters of the experiment. Since the response of the de tec tor i s proportional t o the radiat ion f a l l i n g on the photocathode, the expression

    = cs/co (8)

    i s s a t i s f i e d provided the same de tec tor i s used f o r Is and Io. Here, Cs and Co a re the count r a t e s corresponding t o Is and Io , respect ively. This means t h a t the problem of measuring the value of I s / Io i s t o measure the responses of the de tec tor corresponding t o Is and Io . For t h i s purpose, the photomultiplier tube PM1 with an applied voltage of 9OOV ( t h i s voltage was kept constant t h r o u g h o u t the experiment) was used a t the e x i t p o r t number 7 of the sca t t e r ing chamber. A s e t of four neutral densi ty f i l t e r s of known a t tenuation f ac to r s were inser ted in the beam of the l a se r l i g h t . These f i l t e r s reduced the in t ens i ty of radiat ion f a l l i n g on the photomultiplier by about 10- 8 . The multiple re f lect ions a r i s ing from these f i l t e r s were considered. Their contr ibut ion was calculated t o be 0.01% and thus n o t taken i n t o account. From the known values of transmission f ac to r of sapphire window ( t h e transmission fac tors of the sapphire windows were premeasured - see Appendix A ) and the at tenuat ion fac tors of the neutral density f i l t e r s , the value of Co was determined f o r a pa r t i cu la r wavelength. The e r r o r estimated i n the determination of C s / C o was about ? 9.3% (Appendix A ) . The same procedure was repeated f o r other wavelengths. A t t h i s s tage onward, the photomultiplier PM1 w i t h the necessary equipment (amplif ier-discr iminator A D 1 , synchronous computer, and d i g i t a l p r i n t e r ) was used f o r the measurement of sca t te red rad ia t ion . However, t o monitor the f luc tua t ions i n the l a se r o u t p u t and subsequently t o account f o r t h i s f luc tua t ion second photomultiplier PM2 with another amplif ier-discr iminator A D 2 and data converter was used. The necessary setup t o accomplish t h i s i s shown i n Figure 2. The o u t p u t from the data convertor was recorded on the s t r i p char t recorder fo monitoring and i n i t i a l s e t t i n g of Io t o the same value f o r each r u n of the observation Also, t h i s o u t p u t was fed as an input t o the external clock of the synchronous computer and thus the f luc tua t ions in incident i n t ens i ty were accounted f o r .

    Measurement of Scat ter ing Volume

    The measurement of sca t te r ing volume i s the most tedious j o b . Therefore, the experiment was planned and s e t up i n such a way t h a t the incident l i g h t beam has almost n o d i vergence i n the domain of the sca t te r ing volume. The attempt was a l so made t o minimize

    6

  • t h e s o l i d ang le subtended by t h e s c a t t e r i n g volume a t a p o i n t i n the cen te r o f photo

    cathode o f t h e tube. For t h i s purpose a s e r i e s o f rec tangu la r aper tu res were so arranged t h a t one o f t h e aper tu re was very c lose t o t h e s c a t t e r i n g volume i n every case o f sca t

    t e r i n g angle o f observat ion. I f the s o l i d ang le so subtended i s zero, t h e s c a t t e r i n g

    volume viewed a t an angle rl w i l l va ry w i t h l / s i n Q w i t h respec t t o the s c a t t e r i n g volume a t go", namely,

    s i n rl

    where, Vgo and Vrl

    are t h e s c a t t e r i n g volumes viewed by t h e p h o t o m u l t i p l i e r a t t h e sca t

    t e r i n g angles o f observa t ion 90" and TI, r e s p e c t i v e l y . For a s p e c i f i c angle, 54"44', o f observa t ion i t has been shown ( r e f . 30) t h a t

    v54"44' 1.225 Vgo.

    The d e t a i l e d d i scuss ion o f equat ions (9 ) and (10) i s g iven i n re fe rence (30). As po in ted o u t e a r l i e r t h a t i n our experiment t h e i n c i d e n t and sca t te red beams are almost co l l ima ted .

    I n such a geometry t h e s c a t t e r i n g volume de f ined by t h e perpend icu la r i n t e r s e c t i o n o f

    these beams ( s c a t t e r i n g observed a t 90") would be a rec tangu la r p a r a l l e l o p i p e d whose volume can be determined by measuring i t s t h ree s ides . I n o rde r t o measure t h e dimensions

    o f t h e rec tangu la r p a r a l l e l o p i p e d , a c i r c u l a r ape r tu re o f 50 micron s i z e was p laced i n

    f r o n t o f t h e p h o t o m u l t i p l i e r (PM1). This aper tu re can be moved along t h e X and Y axes by

    means o f a X Y micrometer t r a n s l a t i o n stage. The aper tu re i s scanned along t h e X-axis a t a

    f i x e d Y-pos i t ion . Th is i s recorded on a s t r i p c h a r t recorder as a t rapezo ida l f u n c t i o n

    w i t h some d i f f r a c t i o n p a t t e r n superimposed on the top p o r t i o n . The w i d t h o f t h e f u n c t i o n

    a t h a l f maximum p o i n t s i s taken as the w i d t h a t t h a t p a r t i c u l a r Y-pos i t ion . The aper tu re

    i s moved 1 mm along t h e Y-axis and the w i d t h i s measured again. Th is procedure i s r e

    peated f o r every 1 mm i n t e r v a l a long t h e Y-axis. The average o f a l l these values i s taken

    as the w id th o f t he p a r a l l e l o p i p e d along the X-axis. S i m i l a r measurements a re taken a long

    t h e Y-axis (keeping f i x e d p o s i t i o n a long X-axis) and the h e i g h t determined. The depth o f

    t h e rec tangu la r p a r a l l e l o p i p e d i s then determined by moving the aper tu re and t h e de tec to r

    assembly t o t h e re fe rence p o r t ( p o r t no. 7 ) o f t he s c a t t e r i n g chamber and repea t ing t h e

    procedure a long t h e Z-axis. The produc t o f these th ree measured q u a n t i t i e s i s taken t o be

    t h e s c a t t e r i n g volume whose value was found t o be Vg0 = 0.64 cm 3 . Having determined t h e value o f Vgo, t h e c i r c u l a r aper tu re i s then removed f rom t h e view o f t he de tec to r . I n

    .

    orde r t o determine t h e value o f V54, t he procedure adopted i s as fo l l ows .

    The s c a t t e r i n g chamber i s p ressur ized t o a pressure o f about 35 atm and the sca t te red

    r a d i a t i o n i s observed a t 90" and 54"44'. It i s found t h a t

    7

  • - -

    Is (54O44') = 1.22 Is(90")

    0

    I n t h e s p e c t r a l bandpass a t 4880A where t h e above i n t e n s i t i e s a re measured t h e c o n t r i b u t i o n o f normal d e p o l a r i z a t i o n f a c t o r may be assumed t o be n e g l i g i b l e ( r e f . 30). There

    fo re , t he s c a t t e r i n g i n t e n s i t i e s may be taken as p r o p o r t i o n a l t o t h e respec t i ve s c a t t e r i n g

    volumes , Is(54"44')

    - v54 = 1.22 I s (90") v90

    I t should be po in ted o u t t h a t i f t h e i n c i d e n t and s c a t t e r e d beams were p e r f e c t l y co l l ima ted , t h e r a t i o V5s/V90 would have been 1.225. However, t h e r e was a smal l s o l i d

    angle, R = 4.35 x S r , subtended by t h e s c a t t e r i n g volume a t t h e de tec to r . The e r r o r

    es t imated i n t h e de te rm ina t ion o f s c a t t e r i n g volume i s about ? 5%.

    S c a t t e r i n g Cross Sec t ion Measurement

    The sample gases supp l i ed by A i r Products and Chemicals, Inc . , w i t h percentage p u r i t y o f He - 99.995, Ne - 99.99, A r - 99.998, NP - 99.998, 02 - 99.99, HZ - 99.997, C O Z - 99.9, and CHI, - 99.7 were used i n t h e present measurements. A l s o because o f the g rea t i n t e r e s t i n t h e s c a t t e r i n g p r o p e r t i e s o f f reons as p o l l u t a n t s which m igh t n o t o n l y cause t h e

    d e p l e t i o n o f s t r a t o s p h e r i c ozone b u t m igh t a l s o a f f e c t t h e atmospheric albedo, the Rayle igh

    s c a t t e r i n g cross sec t ions o f most commonly used f reons (12 - CClPF2 - 99%; 13B1 - C B r F 3 99%; 14 - CF4 - 99.7%; and 22 - C H C l F Z - 99%) supp l i ed by Matheson were measured. A l l these samples o f gases and f r e o n vapors were checked f o r t h e a t t e n u a t i o n o f r a d i a t i o n a t

    6328, 5145, 4880, 4579 and 3638i . It was found t h a t t h e r e was no measurable a t tenua t ion

    a t these wavelengths f o r these molecules w i t h the except ion o f CHI, which showed an a t tenu2a t i o n compat ib le t o t h e a t t e n u a t i o n cross s e c t i o n o f 2.5 x cm a t 3638i. However,

    i t may be po in ted o u t t h a t t h e a t t e n u a t i o n o f r a d i a t i o n by absorb ing species, i f present,

    cou ld be accounted f o r as t h e pa th lengths from the s c a t t e r i n g volume t o t h e de tec to rs were

    equ iva len t i n t h e present setup ( r e f . 33). Th is was accomplished i n t h e case o f CH4. The

    samples o f gases and vapors were a l lowed t o pass through a s e r i e s o f m i l l i p o r e f i l t e r s

    (VSWP 047 00) which f i l t e r e d t h e dus t p a r t i c l e s o f s i z e l a r g e r than 25 mu. The use o f these f i l t e r s min imized t h e s c a t t e r i n g due t o dus t p a r t i c l e s which a re be l i eved t o have

    h i g h s c a t t e r i n g cross s e c t i o n as compared t o t h e Rayle igh s c a t t e r i n g . The f i l t e r e d gas

    and vapor samples were then a l lowed t o e n t e r i n t o t h e s c a t t e r i n g chamber. The gas pres

    sures were measured by a Heiss pressure gauge which was c a l i b r a t e d i n abso lu te terms i n

    t h e range o f 0 - 100 atm. F i r s t , t he s c a t t e r e d s i g n a l s were measured as a f u n c t i o n o f s c a t t e r i n g angles, namely, 27", 54"44', go", 125"16', and 153" (measured w i t h respec t t o

    8

  • the d i rec t ion of incident beam) i n order t o check the asymmetry i n the sca t te r ing . For this purpose, the sca t t e r ing chamber was pressurized t o 34 atm by oxygen gas. I t was found t h a t there i s no not iceable asymmetry i n oxygen gas (.see Figure 3 ) . I t should be pointed out t h a t the d u s t pa r t i c l e s of size smaller than 25 mu would introduce + 2.2% disymmetry which i s small a s compared t o the e r r o r in the measurements (Appendix B). I t would be appropriate t o remark t h a t George e t a1 ( r e f s . 18 and 19.) noted a forward enhanced asymmetry i n the observations f o r argon and xenon, although an azimuth symmetry i s expected from the Rayleigh's theory ( r e f s . 39 and 40). A p lausible explanation of th i s asymmetry observed by George e t a1 was offered by Theimer (ref. 41) i n terms of f i n i t e s i z e e f f ec t s . However, the ca lcu la t ions of Feiock (ref. 41) do not support th is explanation. In spi te of the f a c t t h a t we did not no t ice the enhanced asymmetry i n forward d i rec t ion , i t was decided t o perform back sca t t e r ing measurements. T h i s would minimize the controversy o f the e f f e c t s of d u s t pa r t i c l e s i n the present measurements. In addi t ion , these measurements would be independent of normal depolarization f ac to r , p n , i f the measurements a re performed a t a sca t t e r ing angle 54O44'. T h e data presented below a r e f o r backscattering a t 54O44'.

    T h e measurements of sca t te red signal were made as a function of pressure f o r various 0

    gases He, Ar, N , , and 0, a t wavelengths 3638, 4579, 4880, 5145A emitted by Ar-ion l a se r 0

    and a t 6328A emitted by He-Ne l a se r . The plots of these measurements Is (54")/10 vs gas pressure a r e s t r a i g h t l i n e s a s predicted by the equation ( 1 ) and a re shown in Figures 4 t h r u 7. Additional, s imi la r measurements were performed f o r Ne, H , , C o n , C H 4 , and most

    0

    commonly used freons F-12, F-13B1, F-14, and F-22 a t 3638 and 5145A wavelengths. For reference, s imi la r measurements were repeated f o r 02 . These measurements a re shown in

    0

    Figures 8 and 9. Since the r e l a t ive measurements i n the wavelength range 3638-6328A were found t o be the same, the measurements of scat tered radiat ion a t o ther wavelengths (4579,

    0

    4880, and 6328A) were not made. In our determination of s ca t t e r ing cross sec t ion , the equation ( 4 ) f o r p a r t i a l l y polarized radiat ion and the equation ( 7 ) f o r l i nea r ly polarized radiat ion were employed. Obviously, the slopes of the s t r a i g h t l i n e p lo ts a r e the measures of the Rayleigh sca t t e r ing cross sect ions. F i r s t , the values of the slopes f o r He, Ar, N2 and O2 were determined (Figures 4 t h r u 7) and t h e n u t i l i z i n g the measured values of

    *

    and the sca t t e r ing volume V54 , the absolute values of the Rayleigh sca t t e r ing cross sect ions were determined and a r e shown i n Table I . The values of the r e l a t i v e cross sect ions

    0

    were determined a t 3638 and 5145A f o r Ne, H 2 , C O Z Y C H 4 , and freons and normalized w i t h respect t o the values of 02. Knowing the absolute values of the Rayleigh sca t t e r ing cross sect ion of O 2 a t these two wavelengths, the r e l a t i v e measurements of Ne, H 2 , C02, C H 4 , and freons were converted in to absolute units. The values t h u s obtained a re a l s o shown i n

    0

    Table I . The values f o r these molecules a t other wavele,ngths (4579, 4880, and 6328A)

    9

  • were determined us ing A-4 law. The est imated e r r o r i n t h e measured s c a t t e r i n g c ross

    s e c t i o n i s about f 11.0%. I n t h e t a b l e (column 7 ) a re a l s o shown t h e s c a t t e r i n g cross 0

    s e c t i o n va lues a t Lyman-a l i n e (1215.7A) measured by Shardanand and Mikawa ( r e f . 33) and

    Heddle ( r e f . 31). I n column 8 a r e g iven t h e r e c e n t values a t Lyman-a measured by Chopra

    and Heddle ( r e f . 35). I n columns 9 and 10 a re t h e s c a t t e r i n g c ross sec t i ons a t 6328 and 3 6 3 4 determined by Xm4 law e x t r a p o l a t i o n f rom t h e va lues g i ven . i n column 4 o f Table 11. I n t h e l a s t column of Table I a r e shown t h e t h e o r e t i c a l c a l c u l a t e d va lues of Layman-a (1215.7i) . The va lue f o r He i s due t o Chan and Dalgarno ( r e f . 43); Ne and A r a re ca lcul a t e d from Dalgarno and K ings ton ’s method ( r e f . 44) and f o r HP f rom t h e method o f Dalgarno

    and Wi l l iams ( r e f . 45). These Layman-a values o f He, Ne, A r and HZ a re c i t e d by Shardanand and Mikawa ( r e f . 33). It should be po in ted o u t t h a t t h e i n d i c e s o f r e f r a c t i o n are com

    p i l e d i n Table I1 f o r ready re fe rence (refs. 46 and 47). The r e f r a c t i v e i nd i ces o f O z , NP, A r , Ne, He, H z , C O P and CHI, a re due t o convent ional methods o f re f rac tomet ry whereas those o f f reons a r e determined f rom t h e values o f Rayle igh s c a t t e r i n g c ross sec t i ons us ing t h e

    r e l a t i o n

    3 2 ~ : ( ~ - 1 ) ~o = S 3No X

    Here, p i s t h e r e f r a c t i v e index a t STP, X i s t h e i n c i d e n t wavelength i n Angstrom, and No = 2.69 x 10’’ i s a Loschmidt number. I n column 4 (Table 11) are g i ven the values o f Ray le igh s c a t t e r i n g cross sec t i ons which are r e l a t e d t o t h e index o f r e f r a c t i o n by t h e

    above r e l a t i o n .

    D I S C U S S I O N

    As po in ted o u t i n t h e I n t r o d u c t i o n t h e Rayle igh s c a t t e r i n g cross sec t ions as a

    func t i on o f wavelength have been measured f o r t h e f i r s t t ime. However, t he re are a few 0

    recen t measurements a t i n d i v i d u a l wavelengths, ma in ly a t 6943 and 6328A. I n o rde r t o

    compare t h e r e s u l t s ob ta ined by var ious i n v e s t i g a t o r s , i t i s app rop r ia te t o reduce a l l t h e

    data i n t h e same form and t o one wavelength. Since o t h e r i n v e s t i g a t i o n s have expressed

    t h e i r r e s u l t s i n t h e form o f d i f f e r e n t i a l s c a t t e r i n g cross sec t ion , , de f ined by t h e re1a t i o n

    where

    10

    - .. ..... - ... . .. - .... . . . . . . .- ._._... _. . . . . .

    I

  • we a l so changed our values t o s a t i s f y the r e l a t ion (12) . Then u s i n g law, the present measured values a t 3638A and some other published data have been reduced t o 6943A and a re

    0

    shown i n Table 111. For comparison, the actual measured values a t 6943A a r e g iven i n columns 4, 5, and 6. In the l a s t column a r e g iven the theore t ica l values calculated from the index of re f rac t ion . I t can be seen t h a t there i s a good agreement between the values

    0

    f o r a l l the gases a t 6943A obtained by various inves t iga tors except by George e t a1 ( r e f . 19) whose values a r e about half of the others . T h i s agreement c l ea r ly gives a d e f i n i t e proof of the va l id i ty of the process of extrapolat ion of the value of Rayleigh sca t t e r ing cross sect ion from one wavelength t o the o ther u s i n g A-4 law without knowing the spec i f i c values of the mean po la r i zab i l i t y of the gas molecules in the spec t ra l range 3638 - 6943A. T h i s i s a l so shown graphical ly i n Figures 10 t h r u 13. T h e A V 4 law a l so suggests t h a t the r e l a t i v e cross sec t ions should be the same f o r a l l wavelengths. For the sake of convenience and ready reference such r e l a t i v e cross sect ions a re presented i n Table IV. I t can

    0

    be seen t h a t i n the spectral range 3638 - 6943A, the r e l a t i v e values f o r each gas a re the same and agree reasonably well with the value determined from the index of re f rac t ion a t

    0

    5893A. However, i t should be noted t h a t the r e l a t i v e cross sect ion values a t Lyman-a0

    (1215.7A) a r e s t r ik ing ly h ighe r . T h i s behavior i s a l so shown in Figures 10 t h r u 13. The 0

    value of s ca t t e r ing cross sect ion a t Lyman-a (1215.7A) f o r 02 i s not known and therefore , not shown i n Figure 13. The h i g h e r r e l a t i v e values a t Lyman-a suggest t h a t the simple process of extrapolat ion by A - 4 law may no longer be val id i n the shor t wavelength region. These higher r e l a t i v e values i n the vacuum u l t r av io l e t may well be due t o the wavelength dependent values o f the po la r i zab i l i t i e s which may be much higher i n the vacuum u l t r a v io l e t . Therefore, t o ca lcu la te the values of Rayleigh sca t t e r ing cross sec t ions , the spec i f i c values of the po la r i zab i l i t y as a function o f wavelength should be known.

    11

  • N

    TABLE 1. ABSOLUTE TOTAL CROSS SECTIONS FOR RAYLEIGH SCATTERING OF SELECTED GASES AND VAPORS

    ~~~

    Present Measured Values * 6328 5145 4880 4579 3638

    2.06 4.88 6.50 8.39 20.03

    2.24 5.61 7.26 10.38 23.82

    2.08 5.46 7.24 10.13 23.00

    0.103 0.25 0.33 0.42 1.01

    0.036 0.086 0.115 0.15 0.35

    0.493 1.17 1.56 2.01 4.80

    7.28 17.25 23.00 29.60 70.70

    5.26 12.44 16.59 21.40 51.10

    refs . r e f . 31&33 35

    1215.7

    7000 5370

    6400 5470

    150

    35

    2200 2280

    Extrapolatedfrom Table 2

    7328 3638

    2.20 20.19

    2.65 24.26

    2.38 21.78

    0.128 1.17

    0.039 0.36

    0.53 4.80

    6.22 57.00

    5.92 54.20

    ~

    Theoret ica l (see t e x t f o r refs.)

    1215.7

    6400

    140

    35

    2100

    Freon-12 C C l 2F2

    Freon-1 381 CBrF3

    Freon-14 CF4 Freon-22 CHCl F2

    *

    FREONS - IMPORTANT TO STRATOSPHERIC POLLUTION STUDY 41.23 97.56 130.18 167.80 401.00

    28.25 66.94 89.27 115.10 276.45

    5.62 13.30 17.74 22.83 54.62

    25.07 59.38 79.17 102.05 243.80

    Estimated error -< * 11.O%.

  • IHbLt Z . INUlCtb U t KttKHCIlUN HNU IUTAL

    Molecule

    O2

    N2 Ar

    Ne

    He

    H2

    c02

    CH4

    CC1 2F2

    ( f reon-12)

    CC1 2F2

    ( f reon- 112)

    CBrF3

    ( f reon- 13B1)

    F4

    ( f reon-14)

    C H C l F2

    ( f reon-22)

    a - ref. 46

    RAYLEIGH SCATTERING CROSS SECTIONS

    Index of R e f r a c t i o n Wa vel engt h (5s

    IJ

    1.000271

    1 .000296

    1 .000281

    1 ,0000671

    1.000036

    1 ,0001 32

    1 .000448

    1 .000444

    1.00133

    1 .001050

    1.001 1

    1.000475

    1 .0010036

    ci i , (lo-28 cm2) ref. 5893 27.90 a

    II 33.40 a I1 29.91 a I1 1.71 b I 1 0.49 a 11 6.62 a II 7.82 a I 1 74.73 a

    5145 996.10 P

    6328 31.40 C

    5145 682.8 P

    5145 135.72 P

    5145 605.70 P

    b - ref. 47 c - ref. 24 p - presen t

    13

  • ----- ---- -----

    ----- ----- ----- -----

    -----

    TABLE 3. COMPARISON OF u VALUES AT 6943i 0

    UNITS: cm2

    I Extrapolated From Measured Value A t

    0 0

    3638A 6328A Present Trapy e t a1

    r e f . 26

    1.80

    2.14 2.17

    2.07 1.87

    0.091 0.106

    0.032 0.03

    0

    Measured Value a t 6943A

    Rudder George Geindre e t a1 e t a1 e t a1

    r e f . 22 r e f . 19 r e f . 27

    0.9

    2.12 1.04 2.38

    1.88 0.843 2.13

    0.048 0.106

    EXTRAPOLATED FROM THEORETICAL VALUE

    DETERMINED FROM INDEX OF REFRACTION

    G I V E N I N TABLE 2

    1.73

    2.07

    1.85

    0.106

    0.03

    0.41

    4.84

    4.63

    Molecule

    O2

    l\l2

    A r

    Ne

    He

    H2

    , 0.296 0.033

    0.431 0.440 0.438

    6.35 5.09 2.76

  • --

    --

    Wavelength (i\)--za-

    02

    N2 Ar

    Ne

    He

    H2

    co2

    CH4

    Freon-1 2

    Freon-1 3B1

    Freon-1 4

    Freon-22

    TABLE 4. RELATIVE RAYLEIGH SCATTERING CROSS SECTION

    ~ ~~ ~ ~

    ref. 22 From Measured Values

    Present ref,31,33 6943 6328 5145 4880 4579 3638 1215.7

    57.0 56.8 56.6 56.7 56.7

    71.6 62.0 65.0 63.1 70.2 67.4

    63.5 57.5 63.3 62.9 68.6 65.1

    2.86 2.86 2.86 2.83 2.86

    1.o 1.o 1.o 1.o 1.o 1.o 14.8 13.64 13.5 13.6 13.6 13.6

    201.4 200.0 200.0 200.2 200.2

    154. 145.5 144.3 144.3 144.7 144.7

    140.0 1132.4 1132.1 135.0 1135.3

    781.8 776.2 776.4 778.3 782.8

    155.5 154.3 154.3 154.4 154.7

    693.6 688.6 688.6 690.3 690.3

    ref. Calculated from 35 Table 2

    1215.7 5893

    56.5

    67.6

    60.5

    3.5

    1.o 13.4

    158.1

    151.2

  • Z

    \

    \* = 90" /

    / /

    / / S C A T T E R I N G P L A N E

    / / O R P L A N E O F O B S E R V A T I O N

    /

    / / ( X - Y P L A N E ]

    Figure 1. Geometry o f l i g h t s ca t t e r ing : The radiat ion i s scat tered i n the d i r ec t ion 0 , TI, 9 . The incident radiat ion is along the Y-axis. The X - Y plane is the plane of observation and JI = 90" = o + TI.

    16

    I

  • 0

    S C A T T E R I N G CHAMBER

    L - LASER L I G H T SOURCE L T - L I G H T T R A P S

    C-B - COLLIMATOR-BEAM EXPANDER S - RECTANGULAR S L I T IV - S A P P H I R E IVINDOWS C - L I G H T COLLIPIATORS-EACH

    WITH 3 RECTANGULARAPERATURES

    tl - S C A T T E R I N G ANGLE, 27" n1 - SCATI'ERING ANGLE, 5 4 " 4 4 ' M

    N - NEON LAMF

    P - KNOB FOR MOVING NEON LAMP

    M - DEFOCUSSING MAGNETIC ASSEMBLY

    PM - P H O T O M U L T I P L I E R S (EMI95SSQ)

    ND - NEUTRAL D E N S I T Y F I L T E R S

    AD1

    AMPLIFIER-DIOCRIMINATOS

    MR - MIRROR CH - CHOPPER

    L/

    I JI

    N

    RECORDER

    HP- 7 101B

    An. SYNCHRONOUS '.-l COMPUTER

    SSR- 1 1 2 0 S S R - 1 1 1 0

    H P - 7 1 0 1 B

    Figure 2. The block diagram o f the present experimental setup.

  • 0

    = 5 1 4 5 A

    0 2 ATMOSPHERE

    1

    180 150 120 90 60 30 0

    ANGLE OF S C A T T E R I N G (v )

    F igu re 3. I n t e n s i t y response o f t he p h o t o m u l t i p l i e r as a f u n c t i o n o f ang le i n O2

    atmosphere. S o l i d curve represents t h e symmetry expected f rom molecu la r

    s c a t t e r i n g whereas t h e c i r c l e p o i n t s are. the measured data p o i n t s .

    18

    1

  • - - -

    30 I 1 I I / 1 I 1

    "81,/*,

    HELIUM 25

    /20 - t'

    a¶ / I /0 ' c /Y

    0'/ 0 Y 0

    0 /

    10 - / / 0

    0 0 0.

    / e/ /

    0 4 0 r

    0 .0

    5 - 1 / a /

    ''// /

    t 0

    /

    /'

    t /' IjJIih O -' *' 0 / 0 /--/ ,$+S4 -0- / - -

    / / /4 . - - - /-- 0

    0 4 I 1 I I I I

    / A N ,--e 0

  • 30 I 1 I I 1 I 1 I /

    .c&b/ O\a* /

    ARGON P25 I /

    / 20 t /

    I 0 - / 0 /

    .D I= x

    I U *

    0 5 10 15 20 25 30 35 PRESSURE. X lo6 'dyn/cu2

    F i g u r e 5. The r a t i o o f 54" 4.4' s c a t t e r i n g r a d i a t i o n t o i n c i d e n t r a d i a t i o n co r re spond ing t o d i f f e r e n t wavelengths f o r argon a s a f u n c t i o n o f gas p r e s s u r e . Data p o i n t m a r k e d 0 i s common t o a l l l i n e s .

  • 30

    25

    20

    15

    11

    5

    0

    I I '/ 1 I I /r 1 / /

    //

    5 10 15 20 25 30 35 40 PRESSURE, X lo6 dyn/cr2

    Figure 6. The r a t io of 54" 44' scat ter ing radiation t o incident radiation corresponding t o different wavelengths fo r nitrogen as a function of gas pressure. Data point marked0

    i s common t o a l l l ines .

  • N N 30 - 1 I I 1 I I I I

    / OXY6EN

    25 t

    0 5 10 15 20 25 30 35 40 PRESSURE, X 106 dyn/cm2

    Figure 7. The r a t io of 54" 44' scat ter ing radiation t o incident radiation corresponding t o d i f fe ren t wavelengths for oxygen as a function o f gas pressure. Data point marked0 i s common t o a l l l ines .

  • Ii

    48

    44

    40

    36

    32

    2 1

    24

    20

    16

    12

    8

    4

    01 0 3 6

    A 5 1 4 5 i

    c02 1 1 - 1 4 / /

    / P/ '7/2

    8 12 15 1 1 21 24 PRESSURE, x i o 6 dynlcm

    0

    Figure 8. P h o t o m u l t i p l i e r response from 54" 44' s c a t t e r i n g of 5145A r a d i a t i o n f o r Ne, H 2 , 02, C02, C H 4 , f reon-12, freon-13B1, f reon-22, and freon-14 a s a func t ion of pressure. Note t h a t O2 measurements a r e f o r r e l a t i v e comparison. Data p o i n t m a r k e d 0 is common t o a l l . l i n e s .

  • u, c.

    0

    4; I 41 I

    41

    31

    3;

    -. 21 V

    u,. = 24 0 V n--*- 21 c M= W c

    1E

    12

    0

    4

    0' 0 2 4 6 8 10

    PRESSURL, X 106 dyn/cm2

    0

    Figure g. Photomultiplier response from 54" 44' s ca t t e r ing 3638A radiat ion f o r Ne, H 2 , 02, C02, C H 4 , freon-12, freon-13B1, freon-22, and freon-14 a s a function of pressure. Note t h a t the O2 measurements a re f o r r e l a t i v e comparison. Data point marked0 i s common t o a l l l i nes .

    24

  • -

    10,001 I I

    1,001

    101

    N= u

    QD cy

    '= 1(= b

    1

    .1 .1 1 10 100 1,000

    17 -41 , ,~x i o~ CM

    Figure 10. Variation of the measured values o f Rayleigh sca t t e r ing cross sect ion w i t h l/A4 f o r helium and neon. Note t h a t the value of Ne corresponding t o 1215.7i does n o t f a l i on the s t r a i g h t l ine .

    25

  • 100,001

    10,001

    1,001

    -E lo[-" '5)

    K

    b

    10

    1

    .1 .1 1 10 100 1,000

    1 1 ~4 x IO" CM -4

    Figure 11. V a r i a t i o n o f the measured v a l u e s o f Rayleigh s c a t t e r i n g c r o s s s e c t i o n w i t h l / X 4 f o r a rgon and hydrogen. Note t h a t the va lues

    0

    c o r r e s p o n d i n g t o 1215.7A do n o t f a l l on the s t r a i g h t l i n e s .

    26

  • 100,000 I 1 I

    NITROGEN

    10,000

    1,001

    N

    Li-hl

    'c = 101 b"

    11

    1 I 1 I 1 1 10 100 1,001

    Figure 12. Variation of the measured values o f Rayleigh sca t t e r ing c ross sec t ion w i t h l/X4 f o r nitrogen. Note t h a t the value corresponding

    0

    t o 1215.7A does not f a l l on the s t r a i g h t l i ne .

    27

  • N m I I I I

    N z * N lo c

    x

    b-

    OXY6EN2*1 0-

    QD

    24 pr)CCI pr)

    20

    16

    12 - 0-UJ

    0

    0 4 QD

    4 -

    0 1 I I I I I 0 1 2 3 4 5 6

    VA', x d7CM - 4

    F igu re 13. V a r i a t i o n o f t he measured values o f Rayleigh s c a t t e r i n g cross

    sec t i on w i t h l/X4 f o r oxygen. Note t h a t t h e va lue corresponding0

    t o 1215.7A is n o t known and therefore, n o t shown.

  • REFERENCES

    1.

    2.

    3.

    4.

    5.

    6.

    7.

    8.

    9.

    Penndorf , R. : Tables o f the Ref rac t ive Index f o r Standard Air and the Rayleigh S c a t t e r i n g C o e f f i c i e n t f o r the Spec t r a l Region between 0.2 and 20.0 ~.rand Their Appl ica t ion t o Atmospheric Opt ics . J . Opt. SOC. Am., vo l . 47, 1957, pp. 176-182.

    S t e r g i s , C. G.: Rayleigh S c a t t e r i n g i n the Upper Atmosphere. J . Atmosph. Terrest. Phys., V O ~ . 28, 1966, pp. 273-284.

    Cabannes, J . : Sur l a Di f fus ion de l a lumiere pa r l ' a i r . Academie des Sc iences -Compt. Rend., vol. 160, 1915, pp. 62-63.

    S t r u t t , R. J . : S c a t t e r i n g of Light by Dust-free Air, w i t h A r t i f i c i a l Reproduction of the Blue Sky. Proc. Roy. SOC. (London), vol . 94, 1918, pp. 453-459.

    S t r u t t , R . J . : T h e L i g h t S c a t t e r e d by Gases: I t s P o l a r i z a t i o n and I n t e n s i t y . Proc. Roy. SOC. (London), vo l . A95, 1919, pp. 155-176.

    Wood, R. W.: L i g h t S c a t t e r i n g by Air and the Blue Colour of the Sky. Ph i l . Mag., V O ~ . 39, 1920, pp. 423-433.

    Cabannes, J . : Sur l a Di f fus ion de l a Lumiere Par l e s Molecules des Gaz Transparents . Annales de Physique ( P a r i s ) , vol . 15, 1921. p p . 5-149.

    Gans, R . : Asymmetrie von Gas molekeln. E i n Be i t r agzur Bestimmung d e r molekularen Form. Annalen d e r Physik, vo l . 65, 1921, pp 97-1 27.

    Rao, R . , : Determinat ion and Discussion of L gh t -Sca t t e r ing Data f o r 10 Gases and 63 Vapours o f Organic Compounds. Indian. J . Phy., V O ~ . 2 , 1927, pp. 61-96.

    10. Cabbannes, J.: T h e b ib l iography given i n La Dif fus ion Moleculaire de l a Lumiere. Les Presses Universi t a i res de France , P a r i s , 1929.

    11. Ananthakrishnan, R.: Redeterminat ion of the Depolar iza t ion of Light S c a t t e r i n g i n Gases and Vapours. Proc. Ind. Acad. Sc i . A , vol . 2 , 1935, pp. 153-160.

    12. de Vaucouleur, G.: Optique Moleculaire - sur l a d i f f u s i o n molecu la i r e de l a lumiere p a r les gaz e t l ' a b s o r p t i o n atmospheric . Academie des Sc iences - Compt. Rend., vo l . 228, 1949, pp. 1485-1486.

    29

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    17.

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    19.

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    21.

    22.

    23.

    24.

    Parthasarathy, S.: L i g h t S c a t t e r i n g i n Gases. Ind ian. J . Phys., v o l . 25, 1951, pp. 21-24.

    Powers, J . ; Keedy, D. A.; and Ste in , R . S . : D e p o l a r i z a t i o n o f Scat tered L i g h t by n - P a r a f f i n Vapors and t h e A d d i t i v i t y o f Bond P o l a r i z a b i l i t y Tensors. J . Chem. Phys. , V O ~ . 35, 1961, pp. 376-377.

    D i n t z i s , F. R.; and S t e i n R. S.: Observations on D e p o l a r i z a t i o n Rat ios o f

    Scat tered L i g h t by Some Low Molecular Weight Gases and n - P a r a f f i n Vapors. J . Chem. Phys., V O ~ . 40, 1964, pp. 1459-1460.

    Br idge, N. J . ; and Buckingham, A. D.: P o l a r i z a t i o n o f Laser L i g h t Scat tered by Gases. J . Chem. Phys., v o l . 40, 1964, pp. 2733-2734.

    0

    Watson, R. D.; and Clark , M. K.: Rayle igh S c a t t e r i n g o f 6943A Laser Radiat ion i n a N i t rogen Atmosphere. Phys. Rev. L e t t e r s , vo l . 14, 1965, pp. 1057-1058.

    George, T. V . ; Slama, L.; Yokoyama, M.; and Goldste in , L . : S c a t t e r i n g o f Ruby-Laser Beam by Gases. Phys. Rev. L e t t e r s , vo l . 11, 1964, pp. 403-406.

    George, T. V . ; Goldste in , L.; Slama, L.; and Yokoyama, M. : Molecular S c a t t e r i n g o f Ruby-Laser L i g h t . Phys. Rev., v o l . 137, 1965, pp. A369-A380.

    Bridge, N. J . ; and Buckingham, A . 0.: The P o l a r i z a t i o n o f Laser L i g h t Scat tered by Gases. Proc. Roy. SOC. A, vo l . 295, 1966, pp. 334-349.

    Weber, A.; Porto, S. P. S.; Cheesman, L. E.; and B a r r e t t , J . J . : High-Resolut ion Raman Spectroscopy o f Gases w i t h CW-Laser E x c i t a t i o n . J . Opt. SOC. Am., vo l . 57, 1967, pp. 19-28.

    Rudder, R. R.; and Bach, D. R. : Rayleigh S c a t t e r i n g o f Ruby-Laser L i g h t by Neutra l Gases. J . Opt. SOC. Am., v o l . 58, 1968, pp. 1260-1266.

    Penney, C. M.; Goldman, L. M.; and Lapp, II.: Raman S c a t t e r i n g Cross Sections,

    Nature Phys ica l Science, vo l . 235, 1972, pp. 110-111.

    Horvath, H.: The R e f r a c t i v e Index o f Freon-12. Appl. Opt., v o l . 6, 1967,

    pp. 1140-1141.

    30

  • 25. Bhardwaja, P. S.; Charlson, R. J . ; Waggoner; and Ahlquist, N. C.: Rayleigh Scatt e r ing Coefficients of Freon-12, Freon-22, and C02 Relative t o t h a t of Air. Appl. Opt., V O ~ . 12, 1973, pp. 135-136.

    26. Trapy, J . ; Lelievre, J. C.; and Picard, J.: Mesure des Sections Efficaces De Diffusion de l a Lumiere a L'aide d'un Laser He/Ne de Faible 'Puissance. Phys. LeH, V O ~ . 47A, 1974, pp. 85-86.

    27. Geindre, J . P.; Gauthier, J. C. ; and Delpech, J. F.: Rayleigh Light Scat ter ing w i t h a Low Power He-Ne Laser. Phys. LeH., vol. 44A, 1973, pp. 149-150.

    28. Kaye, N.; and Havlik, A. J.: Low Angle Laser Light Scattering-Absolute Calibration. Appl. Opt.,vol. 12, 1973, pp. 541-550.

    29. Skowronek, bl.; Vite l , Y . ; and Bayer, C.: Measurement o f Rayleigh Dif fe ren t ia l Cross Section by Means o f a Switched Ruby Laser. J . Phys. (French), vol. 34, 1973, pp. 229-234.

    30. Shardanand; and Gupta, S. K.: On the Measurement of Rayleigh Scat ter ing by Gases 0

    a t 6328A. NASA TN D-7442, 1973.

    31. Heddle, D. I.J. 0.: Photon Scat ter ing Processes. J . Quant , Spectrosc. Radiat. Transfer, vol. 2, 1962, pp. 349-357.

    32. G i l l , P . ; and Heddle, D. W. 0.: Determination of the Refractive Indices of Gases i n the Vacuum Ul t rav io le t . 11. T h e Rayleigh Scat ter ing Method. J. Opt. SOC. Am. , V O ~. 53, 1963, pp. 847-851.

    0

    33. Shardanand; and Mikawa, Y.: Photon Scat ter ing Cross Sections a t Lyman< (1215.7A) f o r He and Ne. J. Quant. Spectrosc. Radiat. Transfer, vol. 7, 1967, pp . 605-609.

    34. Cairns, R. 6.; Marmo. F. F.; and Samson, J . A. R.: Photon Scat ter ing by Argon i n the Vacuum Ul t rav io le t . J . Opt. SOC. Am., vol. 60, 1970, pp. 211-213.

    35. Chopra, P. D.; and Heddle, D. W . 0.: Polarization Free Measurements of Rayleigh Scat ter ing of Lyman-a. J . Phys. B: Atom. Molec. Phys., vol. 7, 1974, pp. 2421-2428.

    31

  • 36. Samson, J . A. R . : On the Measurement of Rayleigh Sca t te r ing . J . Quant. Spectrosc. Radiat. Transfer, vol. 9, 1969, pp. 875-879.

    37. Rowell, R. L.; Aval, G. M. ; and Barre t t , J. J.: Rayleigh-Raman Depolarization of Laser Light Scat tered by Gases. J. Chem. Phys., vol. 54, 1971, pp. 1960-1964.

    38. Pri tchard, B. S.; and E l l i o t t , W. G.: Two Instruments f o r Atmospheric Optics Measurements. J . Op t . SOC. Am., vol. 50, 1960, pp. 191-202.

    39. Rayleigh, Lord: On the Light from the Sky, its Polar izat ion and Colour. P h i l . Mag., vol. 41, 1971 , pp. 107-120 and 274-279.

    40. Rayleigh, Lord: On the Scat ter ing of Light by Small Pa r t i c l e s . Phil Mag., vo l . 41, 1871, pp. 447-454.

    41. Theimer, 0.: Scat te r ing Cross Section of Ideal Gases f o r Narrow Laser Beams. Phys. Rev. Letters, vol. 13, 1964, pp. 622-625.

    42. Feoick, F. D.: Finite-Size Effects i n Rayleigh Scat ter ing. Phys. Rev., vol. 169, 1968, pp. 165-171.

    43. Chan, Y. M.; and Dalgarno, A , : The Refractive Index of Helium. Proc. Phys. SOC. (London), vol. 85, 1965, pp. 227-230.

    44. Dalgarno, A . ; and Kingston, A. E.: The Refractive Indices and Yerdet Constants o f the Inert Gases. Proc. Roy. SOC. [London), vol. A259, 1960, pp. 424-429.

    45. Dalgarno, A.; and Williams, D. A.: Rayleigh Sca t te r ing by Molecular Hydrogen. Astrophys. J . , vol. 136, 1962, pp. 690-692.

    46. Gray, D. E.: American I n s t i t u t e of Physics-Handbook. Third Edition, McGraw-Hill Publication, 1972, pp. 6-110.

    47. Allen, C . W . : Astrophysical Quant i t ies . Third Edition, The Athlone Press, University o f London, 1973, pp. 92.

    48. Van de Hulst, H . E.: Light Scat ter ing by Small Pa r t i c l e s , John Wiley and Sons, Inc. (London), 1957.

    32

  • - -

    BIBLIOGRAPHY

    Smith, P. L . ; Huber, M. C. E.; and Parkinson, W. H.: R e f r a c t i v i t i e s o f H2, He, 02, C02, and K r f o r 168 5 A 288 nm. Phys. Rev. A, vo l . 13, 1976, pp. 1142-1434.

    Smith, P.L.; Parkinson, W. H.; and Huber, M. C. E.: The R e f r a c t i v e Index o f Krypton f o r 168< X < 288nm. Opt. Communications, vo l . 14, 1975, pp. 374-377.

    0

    Huber, M. C. E.; and Tondel lo, G.: R e f r a c t i v e Index of He i n t h e Region 920-1910A. J. .Opt. SOC. Am., vo l . 64, 1974, pp. 390-392.

    Bideau-Mehu, A.; Guern, Y.; Abjean, R.; and Johannin-Gi l es , A.: I n t e r f e r o m e t r i c Determinat ion o f t h e R e f r a c t i v e Index o f Carbon Diox ide i n t h e U l t r a v i o l e t Region. Opt. Communications, vo l . 9, 1973, pp. 432-434.

    Peck, E. R.; and Reeder, K.: D ispers ion o f A i r . J. Opt. SOC. Am., vo l . 62, 1972, pp. 958-962.

    Abjean, R.; Mehu, A,: and Johannin-Gi l les, A.: I n t e r f e r o m e t r i c Determinat ion o f Xenon and Krypton R e f r a c t i v e Ind i ces i n t h e U1t r a v i o l e t Region. Opt. Communications, vo l . 3, 1971 , pp. 45-47.

    Mans f ie1d , C. R.; and Peck, E. R.: D ispers ion o f Helium. iJ. Opt. SOC. Am., vo l . 59, 1969, pp. 99-204.

    Chashchi na G. I.;and Shreider, E. Ya.: Determinat ion o f Xenon and Krypton R e f r a c t i v e Ind i ces i n the Vacuum Region o f t h e Spectrum. Opt. Spectrosc., vo l . 27, 1969, pp. 79-80.

    Peck, E. R.; and Khanna, B. N.: D ispers ion o f Ni t rogen. J . Opt. SOC. Am., vo l . 56, 1966, pp. 1059-1 063.

    Peck, E. R.; and Fisher , D. J.: Dispers ion o f Argon. J. Opt. SOC. Am., vo l . 54, 1964, pp. 1362-1 364.

    Wi lk inson, P. G.: R e f r a c t i v e D ispe rs ion o f N i t rogen i n t h e Vacuum U l t r a v i o l e t . J . Opt. SOC. Am. , vol . 50, 1960, pp. 1002-1005.

    33

  • Abjean, R.; Mehu, A.; and Johannin-Gilles, A.: Mesure InterfGromGtrique des Indices '

    de Refraction de L'azote et de L'argon dans L'ultraviolet. C. R. Acad. Se. (Paris) B,

    V O ~ .271, 1970, pp. 411-444.

    Abjean, R. ; Mehu, A. ; and Johannin-Gilles, A. : Mesure Interf6rom6trique des Indices de

    Refraction de L'H6lium et du Neon dans L'ultraviolet. C. R. Acad. Sci (Paris)B, vol. 271,

    1970, pp. 835-838.

    Chashchina, G. I.; Gladushehak, V . I.; and Shreider, E. Ya.: Determination of the

    Refractive Index of Argon and the Oscillator Strength of its Resonance Lines. Opt.

    Spectrosc.,vo1. 24, 1968, pp. 542-543.

    34

  • APPENDIX I

    ERROR ESTIMATES I N THE MEASUREMENTS

    The parameters and t h e i r measured accuracy which may i n f l u e n c e t h e t o t a l accuracy o f

    t h e Rayle igh s c a t t e r i n g cross sec t i ons a re tabu la ted as f o l l o w s :

    Parameters

    c S

    cO N

    V

    M u l t i p l e r e f l e c t i o n s a r i s i n g f rom n e u t r a l d e n s i t y f i l t e r

    Transmission o f l i g h t through

    sapphi re windows

    Absorpt ion by molecules and/or

    impur i t i e s

    Background s i g n a l

    -~ .

    Standard D e v i a t i o n % E r r o r and Remarks

    + 9

    2 2.5

    2 1.0

    + 5

    The i n t e n s i t y a f t e r two successive r e f l e c t i o n s

    was c a l c u l a t e d t o be about 0.01% o f t h e i n c i

    dent i n t e n s i t y . Therefore, i t s c o n t r i b u t i o n

    i s n e g l i g i b l e .

    The t ransmiss ion o f l i g h t v a r i e d f rom one

    window t o t h e o t h e r by l e s s than 0.1% and

    was assumed t o be t h e same f o r a l l windows.

    The c o n t r i b u t i o n due t o these a re accounted

    f o r as t h e pa th leng ths f rom t h e S C E t e r i ng

    volume t o t h e windows a re t h e same n t h e

    experiment.

    The background s i g n a l was measured n vacuum

    cond i t i ons (pressure < l o m 4 mm-Hq r e f e r r e d as zero pressure i n t h e t e x t ) and then sub

    t r a c t e d f rom each observat ion. The back

    ground s i g n a l was measured be fo re and a f t e r

    each s e t o f measurements. The v a r i a t i o n was

    negl ig i b l e .

    35

  • Examination o f the t a b l e shows t h a t the e r r o r i n the values o f os will depend on the accuracy o f the values o f Cs, Co, N and V . From t h e equation (5) i t may be shown t h a t

    IS0S

    = 4 n - Io NV '

    Since Is / Io = Cs/Co, the above expression can be wri t ten a s

    0 =471- cS S Co NV

    Therefore, the e r r o r i n the values of f f s can be calculated from the expression

    Using the e r r o r values shown in the t ab le , the value of the r i g h t hand s ide i s found t o be 0.011325. This gives the e r r o r o f 5 11.0% i n the values o f os reported i n t h i s study.

    Note - os . s ca t t e r ing cross sect ion u standard deviation

    36

  • APPENDIX I 1

    ERROR ESTIMATE DUE TO THE PRESENCE OF PARTICULATE MATTER

    According t o Van de H u l s t ( r e f . 48) t h e r a t i o o f forward t o backward s c a t t e r i n g may

    be expressed as

    T h i s r e l a t i o n ho lds good f o r X < 1.0. For Rayle igh s c a t t e r i n g t h e r a t i o I s (o = 0)/ I s ( u = 180) i s u n i t y . I n t h e present exper iment t h e p a r t i c u l a t e ma t te r o f t h e s i z e g r e a t e r than 25 mu i s f i l t e r e d . Therefore, p a r t i c l e s o f s i z e sma l le r than 25 mp are s t i l l present . L e t us c a l c u l a t e asymmetry t h a t might be caused by t h e p a r t i c l e s o f

    0

    t h e s i z e 25 mp. T h i s has been c a l c u l a t e d f o r a wavelength 5145A. Assuming t h e index of r e f r a c t i o n o f these p a r t i c l e s as p = 1.55, t h e va lue o f X = T D / X would be 0.1526. Here D i s t h e d iameter o f t h e p a r t i c l e s which i s assumed t o be 25 w. Using these q u a n t i t i e s , we f i n d

    Is (n = 0 )

    Is (n = 180) = 1.022 .

    T h i s means t h a t a enhanced asymmetry i n t h e forward d i r e c t i o n would be 2.2%.

    NASA-Langley, 1977 37

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