An interferometric determination of the specific refractivities of the nitrogen and oxygen atoms

(1)

February, 1972.

OF THE SPECIFIC REFRACTIVITIES OF THE NITROGEN AND OJCYGEN ATOM3

by

Dale E. Wett1aufer

\

(2)

•

_{AN INTERFEROMETRIC DETERMINATION} OF THE SPECIFIC REFRACTIVITIES OF THE NITROGEN

AND

OXYGEN ATOMS

by

Da1e E. Wett1aufer

Submitted January, 1972.

(3)

ti

ACKNOWLEDGEMENT

I wish to thank Dr. G. N. Patterson, Director of the Institute for Aerospace Studies for the opportunity to work and study at UTIAS.

I also wish to thank Dr. I. I. Glass, supervisor of this research for his encouragement and generous help throughout the entire duration of the project.

Thanks are due to Dr. ~chael Bristow of UTIAS for his many fruit-~ul suggestions and opinions as weil as his kind technical advice at all stages of this project. The consultations with Professor R. W. Nicholls, Physics Department, York University which were quite helpful during the final analysis and interpretation of the data, are sincerely appreciated.

Special thanks are due

Mr.

Brian Whitten for his technical assistance during critical periods of my work, which saved me much time.

Mr.

James

Gottlieb was also helpful in this respect, and I should \ike to extend my thanks to him.

The assistance and carefu~ work of the staff technician,

Mr.

P. Crouse, was essential for the proper functioning of the experimental apparatus and is gratefully acknowledged.

(4)

SUMMARY

The specific refractivities (Gladstone-Dale constants) for the nitrogef and oxygen atoms were determined experimentally using dual-frequency laser

inter-ferometry. The following results were obtained for nitroge~:

KA = 0.331

~

2.5% cm3jg at

3471.5~,

KA

= .31

+ 10% cm3/g at 5300

R

*

~~

The data were obtained in the UTIAS

4

in. x 7 in. hypersonic shock-tube facility using a

9

in. dia. Mach-Zehnder interferometer over the following ranges of

shock Mach number, temperature, degree of dissociation, and initial pressure,

respectively.

For nitrogen:

13 < Ms < 21, 6150oK< T < 6910oK, 0.094<

a

< 0.448, 1.0 torr < Pl < 10 torr For oxygen:

11 < M < 15, 3564°K < T < 4100oK, 0.176 <

a

< 0.731, 0.5 < p < 10 torr,

s 1

at room temperature.

(5)

1. 2.

3.

4.

5.

. .,.} .. TABLE OF CONTENTS Notation INTRODUCTION THEORETICAL CONSIDERATIONS 2.1 General Discussion

2.2 Development of Relevant Equations

2.3 Theoretical Prediction of the Gladstone-Dale Constant EXPERIMENTAL APPARATUS & PROCEDURES

3.1 Initial Conditions

3.2 Molecular Gladstone-Dale Constant

3.3 Shock Parameters

3.4 Fringe Shift

3.5 Description of Experimental Procedure EXPERIMENTAL RESULTS AND DATA ANALYSIS

4.1 ~iscussion and Eva}uation of Data

4.2 Final Results 4.3 Discussion of Results 4.3.1' Nitrogen Resu1ts 4.3.2 Oxygen Resu1ts CONCLUSIONS PAGE 1 1 1

3

7

8

9

10 11 12 12 13 References 14

APPENDIX A: Determination of the Specific Refractivity for the Oxygen Atom

APPENDIX B: Measureme~t of the Fri~ge3Sfuift, S21' from an Interferogram

(6)

A A. 1 a '. b. 1 C d ~ E KA

~

KO 2

~2

K € KI L M s m. 1 n p

N.

₁

P

P l R SYMBOLS statistical average

constants in the Sellmeier Equation speed of sound at room temperature, N

2 O

2 :

~.327 mm/~sec

O.

349

mrnj~sec,

t . 1 d' t . t f f th . th f .

ver 1ca 1S ance on an 1n er erogram 0 e 1 r1nge

from a horizontal reference line speed of light in a vacuum

fringe spacing

electric field vector of the light wave

Gladstone-Dale copstant for the atomie species Gladstone-Dale constant for the molecular species

Gladstone-Dale constant for the oxygen molecule at room temperature

Gladstone-Dale constant for the nitrogen molecule at room temperature

dielectric constant

variable used by Anderson (2) to relate KA to ~

test section width

shock Mach number

molecular weight of the ith species

phase index of refraction partiele number density

dipole moment vector per unit volume of gas initial pressure in test section

specific gas COlli3tant

2.22630

x

103

cm

3

-torrjg-OK

=

_1.94899

x

103

cm

3

-torrjg- oK

fringe shift, fringe shift from state 1 to state 2

i.nitial temperature inthe test section

for for

N

₂

O

(7)

v

_p W W.A.

cx.

~

"

o

.

v

,v

o p w

phase velocity of a light wave statistical weight

weighted statistical average

polarizability of the ith species

degree of dissociation permeability of free space wavelength

wavelength at the natural frequency of a sub stance V

o : wavelength in vacuvm

frequency of light wave: natural frequency of a hypo

-thetical particle of a medium density

(8)

. - - - ---_ ..

_-1. INTRODUCTION

One of the cqntinuing projects at UTIAS concerns the determination of

the specific refractivities of vario~s gaseous species which are important in

areas of high-speed flight and atmospheric re-ent:tY".v. In dealing with these

problerns, the refractive indices of the releva~t gases are required before de-tailed laboratory investigations are possible. This information is also of

interest to the field of theoretical physics in that the polarizability, a quantity which is very difficult to compute, c~n be determined directly from empirical refractivity data. Alpher and

White~l)

:

pointed out that quantities

which are intimately related to the molecular polarizability are the long-range

intermolecular dispersion force constant, the Verdet constant of Faraday

opti-cal rotation, the diamagnetic susceptibility, the Rayleigh scattering

cross-section, and the dielectric constant. In fact the possibility exists of

de-termiiing the effective oscillator strengths from polarizability measurements.

A more accurate determination was made of the specific refractivity or the so -called "Gladstone-Dale" constant for the nitrogen (N) and oxygen (0)

than has previously bee~ possible. This was -' facili tated thro;ugh the use of

the

4

in. by

7

in. hypersonic shock-tube facility coupled with a dual-frequency

Mach-Zehnder laser interferometer. The possibility of experimentally determining

the specific refractivity of gaseous species, which only exist at elevated temp-eratures, by means of ShOCk-(tVbe interferometry was fitst suggested and utilized

by Alpher and White in

1959

2). Other authors~3 to la) determined the

refrac-tivities for other R~ecies, which are listed chronolog}c~lly in Table I. The papers of Anderson(Ö) and Anderson, Osborne and Glass

~9)

are especially rele-vant to this study since the experimental work was performed in essentially the same facility. It was thought expedient to begin the present research with

a test experimental determination of the Gladstone-Dale constant for the O-atom

in order to obtain some experience with the facility and obtain a point of

caLibration before comm~nc~ng the work on the N-atom. It should be noted that

the research of Bristow~lO) immediately prior to the present work, involved extensi ve modifications to the shock tube and interferometer faci li ty with a

view to increasing the accuracy of the physical measurements.

The theoretical part of the paper contains an elementary discus sion

of the entire problem along with a brief, technical treatment.

2. THEORETICAL CONSIDERATIONS 2.1 Ge~eral D~scussion

It has long been established that electromagnetic waves such as light do not passively transmit through a medium; they interact with the constituent atorns or molecules in a predictable fashion. The gener al effect can be viewed as a change in the phase \{elocity, V , of the wave within the medium leading

to the simple classical relation defïning the index of refraction, n

p'

v

_p

=

c/n

_p ( 1)

where c is the speed of light in vacuum. The explanation for this velocity change is that the individual molecules scatter the incident light and the resulting

scattered waves interfere with the primary wave, bringing about a change of phase

(9)

Ideally what one would like to achieve is to be able to describe the complete curve of index of refraction versus wavelength for a large range of the optical spectrum. A curve pres enting this data for a typical transparent

sub-stance is shown in Fig. la. It can be seen that n. varies with wavelength and

in addition the slope, dn. /dÀ, commonly called thePdispersion of the material,

also varies with À in sucK a way that one curve for one material is not simply derivable from another (e.g. a change of scale coordinates). The discontinui-ties such as those designated

K, L,

and

M

in the curve occur at major absorption

frequencies where almost all the light energy goes into exciting the electrons

at their natural frequencies rather than transmitting in the normal fashion.

In actual fact at such wavelengths, indicated as ~, À

2 and

À3'

the presence of

damping smooths out the discontinuities as indicated by the dotted lines in the

figure. Although it is possible to locate the various resonance freque~cies for a substance, in the present experiment the interest was only in the

be-haviour of n at optical frequencies not close to resonance frequencies where its

behavio~

yields dispersion curves much like those in Fig. lb. This figure

refers to the case of transparen~ solids and illustrates the lack of similarity

which so of ten occurs among similar substances, which is also typical of gases.

However, in the case of gases another dimension is required to completely

describe the dispersion because n also varies (linearly) with gas density,

P, or* ., p

(2)

The equation which precisely describes the above relation is the classical

Gladstone-Dale equation, which states that at any particular observing

wave-length, À~ the refractiyity, (np-l), is related to the density by means of

the specific refractivity, K, commonly

know~

as the Gladstone-Dale constant,(l)

n -1 = \ ' . K.p.

P L~ ~ ~

where the summation is over i species of t,he gaseous mixture. This esuation is developed further in the next section. One should consult Anderson(7) for a

full d.erivation and discussion, where i t is shown that K is independent of

temperature throughout our experimental range.

In principle the Gladstone-Dale constant could be determined from a

measurement of the velocity of light in the medium and the use of Eq. 1. However,

an indirect means of obtaining the constant is achieved by measuring phase changes in the wave with an interferometer, as direct velocity measurements are not

feasible at the present time. I~ ~articular, the

9

in-plate Mach-Zehnder

inter-ferometer used for this purpose(12) is shown schematically in Fig.2. It consists of an assembly of beam splitters and mirrors which are readily adjustable. They first split the coherent beam of light from the source (in our case a

dual-frequency laser) into two beams of identical phase and intensity, one of which

passes through the test section, the other going through the compensating chamber. Afterwards these two beams are recombined by a second beam splitter and focussed

on a photographic plate or viewing screen.

(10)

This investigation utilized the so-cal~ed fringe displacement method of operation of the interferometer, as follows. If the second splitter is rotated through a small angle with respect to the first splitter, the two coherent beams of light, which were initially in phase at the first splitter wi~, through a change in path lengths so introduced, interfere with each other at the screen. A parallel pattern of dark an~ light fringes is thereby produced by the destruc-tive a~d constructive interference of the two beams, as depicted in Fig. 3b. When the density of the gas in the test section is changed, while that in the compensating chamber is unaltered, all the light passing through the test section has its phase altered by scattering as previously described, which is equivalent to increasing the path length of the light through the test sectio~, thus

causing the fringes already established to move uniformly up or down_ the screen

according to the simple equation of basic interferometry\7)

À b. o s

L Kd

6p=

(4)

where

L is the test section width, K is the Gladstone-Dale constant, d is the fringe spacing distance, 6p is the change in density,

b.s is the distance moved byeach fringe from the initial state to the testJstate and,

À is the wavelength of the inpident beam in vacuUID.

This equation is dealt with in Sec. 2.1 and further developed for a mixture of gases.

The experiroental procedure itself is rather straight forward. One simply fills the test section with the gas under consideration, takes a pressure and temperature reading to obtain the dens~ty in both the test section and com-pensating chamber, records the fringe movement (or shift) on a photographic plate,

substitutes into Eq. 4_and obtains the qladstone-Dale constant.

In order to obtain sufficiently high temperatures

(~

10

4

OK) to

dis-sociate the gas in the test section, ~ s~ock tube (Fig.2) was utilized. In this shock tube~ described fUlly elsewhere\13) , a shock wave is propagated rapidly

through the quiescent test gas at the reference conditions, almost instantaneously generating the high temperature needed to dissociate the molecule into its con-stituent atoms. At the same time the shock speed is monitored electronically, enabling a determination of the exact temperature,density, and pressure behind the shock front tO(b~ made by substi~ution of the shock speed into the Rankine-Hugoniot equations 14).

2.2 Development of Relevant Equations

Alpher and White(l) point out that there are two methods for describing the phase index of refraction. The first of these may be regarded as basically an empirical approach, the result of many attempts to find an equation that could

(11)

The first approach noted above, should be mentioned because it was de-veloped both historicaltY and theoretically prior to the second approach. More-over it offers a useful model for understanding the causes of dispersion. First~

let us assume that we have a uniform medium through which propagates a wave of

light of one frequency,

v,

with a wavelength, À. As was classically done we

shall assume the medium composed of solid particles elastically suspended with natural frequencies V

o and Vl at corresponding wavelengths Ào and Àl' respec-tively. A plot of the dispersion curve for a hypothetical substance is illus-trated in Fig. lCD At very short wavelengths n is close to unity indicating that electromagnetic waves in this region have glmost no affect on the medium~

a result of the fact that the frequency of the electric vector ~is so much more rapid than the natural frequency of the particles in the medium. As À

increases the particles begin to oscillate more vigorously, always at the im-pressed frequency

v.

As the first fundamental frequency,

v

~ is approached

o

the oscillations continue to absorb more energy until at À just less than À .~

o the index of refraction takes on negatively large values~ owing ·to the fact

that-the elastic restoring forces of our simple mechanical model are 180 degrees out of phase with the impressed wave. The resultant high restoring forces

serve to propagate the wave at very high velocities (hence n is low) much as

if the medium had instantaneously become more rigid. It shoRld be noted that

the implication from this diagram that the velocity of the wave in the medium

in this region is higher than the velocity of light in vacuum is incorrect

since group velocity wi~l)still be less even though a particular phase velocity of the group is greater~7. As soon as the fundament al wavelength is just

exceeded~ the elastic restoring forces on the particle are almost completely in phase with the electric field vector, hence they act very weakly on the

wave and ~ becomes positively large. The equation to describe the behaviour exhibited Pin Fig. lc was developed by Sellmeier(15)~

À À2

i 2

n = 1 +

P

I.

_~

where the summation is over all i natural frequencies. In actuality the

be-haviour in the region of a natural frequency is not discontinuous but resembles the dashed curves of Fig. la at points K, Land M and Àl~ À₂and À3. This

less extreme and more realistic behaviour, of course~ is the result of energy

dissipation, or using

0lf.'

mechanical analogy again,~ damping is present. TlJ.e

equations that take dam ping into account were

ful~y

developed by

HelmhOltz~15)~

but are not given here, as the much si~pler Sellmeier equation, Eq. 5, is

completely sufficient to describe the dispersion curves at optical frequencies. ( It should be noted that the Helmholtz equation reduces to the Sellmeier

equa-tio~ at regions far from ~atural frequencies where damping is negligible). The second approach mentioned earlier, wherein our working equations are developed from basic theory, is worthy of a short develop~e~t here~ b~t for a complete derivation of Eq.3 see the report by Anderson ~7). This method views dispersion as a result of the microscopic electromagnetic behaviour of the

particles in the medium. In Sec. 2.1 it was stated that dispersion is actual~y

the result of scattering, and may be explained a.s follows: the molecules of the medium of transmissio~ are induced by the incident beam to emit their own

waves thro~gh a process of polarization, wherein each molecule acted on by the

(12)

It can be shown that the induced wa~e is 90 degrees lagging in phase behind the

incident beam. When all waves along the optical axis are superimposed the

re-sultant is found to have undergone a phase change, and since wave velocity is

defined as the velocity with which points of constant phase are propagated, we see a velocity change within the medium. Thep'î'eclse functional relation of the original wave and the resultant wave may be derived as follows. It is known that the dipole moment per unit volume of a neutral particle gas,

P

,

induced

by(a~ electric field is proportional to the electric field vector, ~ , according to

7)

,

(6)

N.

cx.

Ë

l l

where N. is the number density of the ith species and the proportio4ality constant,

l

ai' termed the molecular polarizability is directly related to the Gladstone-Dale

constant, K., from simple theoretical electromagnetic considerations. A solution

of the "telêgraph equation" (a special form of Maxwell's equations that retains

all cond~ction terms.for the case of severa~ ga~eous species) is p:e~ented by

Anderson~7). He derlves a very good approxlmatlon for the refractlvlty of a

mixture of i species having molecular weight, mi' as,

n -1 P i 1

cx.

l

2E

m. o l 2 W 1

P

2 ~ w

where E is the permeability of free space,w and w refer to the angular fre4uencies

of the

~lectron

plasma and the initial wave,PrespectivelY. Upon noting that the quantity w _p2/w2 _,is very small in the absence of ionization, and setting

K.

l 1 2E o

cx.

l m. l (8)

Equation 7 becomes Eq.

3,

already presented as the classical Gladstone-Dale e~ua

tion, where K. designates the Gladstone-Dale constant for the i th species. It

should be notêd that the Gladstone-Dale constant is a function of polarizability

and molecular weight only. Although ful~y explained in Ref. 7, the independence

of Ki on temperature for the case of non-polar molecules like 02 and N

2 results

from their lack of a permanent dipole fluid which consequently excludes the possibility of a preferential orientation contribution to the impressed electric field

Ë.

This is not true for polar molecules such as H

20 and N02, each of which has a built-in dipole that can align itself in a more orderly fashion with the external field at lower temperatures where random collisions would cease to

domi-nate, and consequently K. would become increasingly temperature dependent.

l

The relation from basic interferometric considerations which ~pon

(13)

where the subscripts 1 and 2 refer to the regions ahead and behind the shock

respective~y, and S21 is the fringe shift from state 1 to state 2, nondimensionalized by the fringe spacing, do Upon substitution of the generat Gladstone-Dale relation given by Eqo

7,

S21.

=

~L

K1:-

'

[ (Pi) - (Pi)]

o

t

2 1 1 [ 2 2 ]

- 2

(w) -(w

o

)

21.> P2 Pi (10) which si~plifies due to the absence of free electrons in the gas to,

=

~

\ ' K. [ (P.) -(p.) ]

AO

~

1 1 2

1 ~

1

(11) 1

In the present experiment we have to contend with only three species, so the above equation fakes the following form,

( 12)

where a

2 is the percentage of the gas dissociated, and the subscripts M, A and

N

2 (or 02) refer· to the molecular, atomic, and room-temperature species, res-pectively.

Equation 12 contains all that is needed to determine KA from experimental data. It may be used in a number of different ways, depending on whether one is willing to assume. as theory would predict, that the value for ~ is identical to the molecular va+ue at room temperature, ~ or K

O • This assumption was

2 2

borne out by the experimental work of(9) Therefore, we have made this assump-tion and proceeded by equating the above variables at the outset. (For further discussion of this problem see Sec. 4.1). This assumptio~ simplifies Eq. 12 in that only two species are required, hence,

(1.3 )

where

r

21 is the ratio o~ gas densi t,ies,

pip

1. Af ter a substi tution for P 1 using the equation of state for an ideal gas, Eq.13 becomes:

(14)

where Pi and Tl are the initial pressure and temperature in the test section, res-pectively, and R is the molecular gas constant for the gas under consideration. Of the quantitites whic~ appear in Eq.14, R, ~, Land

"0

are known constants, P

l , Tl and S21 are measured directly;

r

21 and a2 are catculated from the shock Mach number and the initial conditio~s (P

(14)

2.3 Theoretical Prediction of the Gladstone-Dale Consta~t

It was previously pointed out that there does not appear to be any direct similarity. (i.e, one curve is not obtainable from another by any simple

coordi~ate transformation) among the various dispersion curves, even for related substances, and unfortunately, information on the oscillator strengths for a molecule are very difficult to obt,ain. 'C ons equently, if one seeks to arrive at a theoretical prediction of the Gladstone-Dale constant, he is relegated t9 the molecular polarizability approach as outlined in the previous section. In~l) one can find a discussion of the theoretical polarizabilities for the 0 and N atoms as calculated by several investigators using a number of theoretical

approaches. All these methods however, give a rather wide variation of results, and more importantly they strictly hold only at the long wavelength limit.

Apparently the best theoretical calculation that one can perform to date, short of knowing the exact wave functions of the molecule, involves the combination of the Hartree-Fock wave functions with the polarization potential adjusted to

fit the atomic oxygen ion (0-) binding energy as performed by Klein and Breuckner(ll) who then extrapolated to a value for atomic nitrogen. Their theoretical results are listed in rable 11 along with the present experimental results and related references(1,9J.

3.

EXPERIMENTAL APPARATUS AND PROCEDURES

The experimental apparatus co~sisted essentially of a 9 in. dia. plate Mach-Zehnder interferometer(12) in conjU9ctton with a 4 in. x 7 in. hypersonic

shock tvbeq built and described by Boyer~13) with modifications as reported by

Bristow~lO). The tube was combustion driven using a stoichiometric mixture of hydrogen and oxygen gases diluted with 77-1/2% helium. Ignition was accomplished by an electric-discharge-heated tungsten wire. The diaphragms were of type 302

stainless steel with a "2B" finish and ranged in bursting pressure from 1500 psi

to 6,000 psi.

3.1 Initial Conditions:

Pl~l-The initial pressure in the driven section, P

l ) was measured approxi-mately by a Wallace and Tiernan mechanical gauge in the 10 mmHg. range, with the final measurement take~ by an oil manometer of the U-tube type, accurate to

~ 0.008 mmH~This corresponds to a maximvrn possiblè'error of 2-1/2% in the P l measurement. (It is of interest to subsequent discussions that Anderson(7,8,9) had only the mechanical gauge for his final P

l measurement).

Another new addition to the facility immediately prior to the present

investigation was a vacuum diffusion pump andRoote~blower vacuum pump for ~he purpose of obtaining better evacuation of the driven section of the tube. It

is noteworthy that a leak-outgassing rate of about 10-5 mmHg./min. and a value

of 10- 5 mmHg. for the achievable vacuum could be obtained af ter a one-day pump-down periode The latter value could be improved by an order of magnitude by extending the pumpdown period to two days.

(15)

nearest 0.10~., corresponding to an~error of approximately 0.03% of the absolute initial temperature.

3.2 Molecular Gladstone-Dale Constant: ~

The values used for

~

at

694~

and

3471.5~

were 0.2376 cm

3 jg

and

0.2~60

cm

3 jg,

resp~ctively,

as

o~tained

from the empirical dispersion formula of Peck and Khana ~16). These values are accurate to approximately 0.03%, which is ~wall enough in comparison to the errors in the other variables so as to be regarded as a constant.

The values used for KO at

6943~

and

3471.5~

were 0.1907 cm

3 jg

and 0.1988 cm3jg,respectivelY, as interpolated from the dispersion data of (17). The values for th

_x

other wavelengths listed in Table 11 were likewise determined

(except at 10,600Ä, which was determined by the present author by experiment) and again these values were regarded as constants throughout the experiment.

3.3 Shock Parameters: Ms~l' and

a

₂__

The electronic setup shown schematically in Fig.4 was used to determine the shock speed by means of two matched pressure transducers, one mounted on each side of the test section spanning a length of two feet. It was felt that a maximum possible error of 1% was to be expected in the shock velocity. This appears to be pessimistic. Attenuation of the shock wave itself was monitored by a series of equally-spaced pressure transdvcers as it progressed down the tube. It was found that the attenuation was negligible, averaging less than 0.5% of the original shock Mach-number per foot. The densi ty ratio across the shock, f

21, and the percentage of dissociation,

a

2, were obtained by substitution

of the initial conditions P

l, T and M into the appropriate Rankine-Hugoniot 1 s relations for a dissociating gas at equilibrium. ~h~s was facilitated through the use of the computer program of Law and Bristow(14) with the computational work done on the UTIAS IBM 1130 computer. The values obtained are listed in Table 111. The aforementioned computer program takes into account second order correction factors for the molecular partition function, and solves for T

2 and P

2 behind the shock to within 0.1%, which constitutes a considerable improve-ment over the tables of Bernstein(18), the best previously available data. 3.4 Fringe Shift

(16)

3.5 Description of Experimental Procedure

The test gas (see Table IV for an analysis of the gases) was admitted

to the test section and compensating chamber, and while it was allowed to

equili-brate to the tube temperature, the combustion driver gases were admitted, and the

initial conditions Pl,and Tl were recorded. Immediately thereafter the

"no-flow" interferograms were taken of the test section at room temperature. This

procedure took about 7 minutes, af ter which the firing immediatel~ commenced o

In order to avoid double exposure due to multiple pu+sing of the laser,

the laser flash lamp was fired approximately 950 ~secs before the shock reached

the test section o The exposure time was approximately 20-30 nanoseconds,

sufficient to give goed quality pictures with two-wavelength interferometry,

yielding two interferograms per run. For a complete description of this aspect

of the procedure see(lO), Sec o

3.20

The resulting interferograms were obtained

with Kodak Royal-X Pan film (ASA 1250) and analyzed for resu~tant fringe shift

as described in Appendix B.* The final values of 8

21 were then substituted

into Eqo 14 to obtain KA.

A few typical interferograms in nitrogen using wavelengths generated

from the ruby laser appear in Figs05 and

6,

and for oxygen in Fig07. Figure

8

shows a run in oxygen using wavelengths generated from the neodymium lasero

40 EXPERIMENTAL RESULTS AIW DATA ANALYSIS

4.1 Discussion and Evaluation of the Data

In Sec o202 the modified Gladstone-Dale equation, Eqo14 was developed

for use in interferometry and was shown to involve two unknowns KA and~. The

constant ~ could be eliminated by assuming that ~ was independent of

tempera-ture. This assumption is theoretically justifiable for the following reasons o

8ince the process which causes the velocity change of the wave in the medium is the production by the fluctuating electric field vector

1

of oscillating

mole-cular dipoles in all the molecules, we must examine this phenomenon in light

of its possible temperature dependenceo If the orderly arrangement of these

dipoles is disrupted by the increased frequency of collisions at elevated

temp-eratures, then the scattering process will be affected also, and the resultant

wave arising from the previously mentioned vector sum of all the superimposed

waves will change accordinglyo Fortunately, in actuality, it turns out that

the fluctuation of the impressed electric field is many orders of magnitude

greater than the collisional orientation changes of the particles themselves

(1015 cycles/seco compared to 1010 orientation Changes/sec., respectively).

Hence, the polarization process, which is the essence of refractivity phenomena,

should be independent of temperature changeso

If one chooses to test the validity of the above reasoning, there

are two avenues open; either to solve Eq.14 simultaneously for two separate

runs (thereby incurring excessi ve error s in KA and ~ from S21 inaccuracies)

or the ingenious tiK' -method" utilized by Anderson(7). This method in essence

combines the two variables KA and ~'

*

The interferograms at lO,600l were recorded on Kodak type I-Z spectroscopic

(17)

into one new yariable, K', thus,

This convenie~tly simplifies Eq. 12 t~,

K' =

which eliminates KA and KM from the experimental determination. If one then plots

K' versus

a

2 for each run and extends a line through them, it is clear that where

a

2

=

0, K'

=

KM

and where a2

=

1. (Le., complete dissociation), K'

=

KA.

Hence

one solves for both KA and

KM

by interpolation as demonstrated in Fig. 9a, where

various experimental results are plotted versus a20 Although it would seem that the "K'·-method" is obviously the best procedure for obtaining KA' there are

dis-advantages. The drawbacks of the "K'- method" are not intuitively obvious but

nevertheless turn out to be substantial. First, it must be noted that even though

the errors in each determinatio~ of K' are small (as illustrated in Fig. 9b),

interpolation itself will lead to considerable magnification of such errors,

directly in proportion to the interpolation distance. In other words a small error in KI where

a

2 is close to zero will introduce a large error in the

inter-polated value of KA and a small error in the value of ~ (the reverse also holds

true). A graphic ~llustratio~ of this phenomenon is given in Fig. 11. I~ presents the results of an error analysis performed for each run in nitrogen

at À

=

3471.5

.R,

where the final error in KA' designated as 6K

A is plotted versus a20 One can see that the errors incurred by the utilization of the "K'

-method" are consistently appreciably larger than would result in the assumption

of equivalence between

KM

and ~. It will be noted that Fig. 11 indicates that

2

determinations at lower values of

a

2 are relatively inaccurate, which implies

that if accuracy is the sole criter~on, then the majority of experimenta1

de-terminations should be c-arried out in the range 0.3

<

a

2 for

N

2 and 0.5

<

a

for O

2• This occurrence of a maximum in 6KA at the lower extreme of the

a

2 scale is easily explained. Throughout the experiment, errors in,

a

2, Pl and 821 a.re

constant; at very low values of

a

2, the error in this variable becomes relatively

large in comparison to

a

2, leading to excessive errors in KA.

In addition to the above considerations for rejecting the "K' - method"

is the fact that no significant difference was found betwee~

KK

at the t~st

~onditions and the room temperature value, KO ' in the works of Anderson~7,~),

( ~. 9) 2

and Anderson, Osborne, and Glass -: • There is no reason for nitrogen to be-have differently.

402 Final Results

A computer program was writtep to solve Eq. 14 for KA' and the values

were weighted according to the calculated probable error of each specific value

(18)

MA

= ( [

ClfJ 2

t::f:l

+[

Clf J2 t§32 + o •• ') 1/2 (16)

di

dS

21 21

and the 6 quantities are standard deviations (or the maximum estimated error where standard deviation was not obtainable). Each va~ue)of KA was averaged af ter having been weighted according to the following formula\19

Weighted Average, WoAo

=

*

based on one experiment

The pertinent KA results for both O

2 and N2 are listed in Table II and plotted against wavelength in Figs. 10a and lOb where experimental molecular dispersion curves for ~ (see Seco 4.1) are also presented. The case of oxygen is interesting enough to warrant a separate discussion in Appendix A, but the salient features will be discussed here in those aspects which it shares with nitrogen.

In Sec. 2.3 it was mentioned that the rather complicated dependence of polarizability upon oscillator strengths makes the behaviour of KA as a function of À impossible to predict to anywhere near the accuracy we desire here. It

would involve having detailed information on the electronic structure, excitation states, and oscillator strengths which are simply not available at presento

In fact we must agree with Alpher and White that, "one cannot make the tacit assumption that the specific refractivity of a~ ~tom is simply related to that of a diatomic molecule composed of such atoms,,~l).

(19)

nitro-the corresponding waVelength(l). (For further details see Ref. 20). 4.3.1 Nitrogen Results

The only poiNts of comparison for the nitrogen atom are those of(l)and the good ~greement with these results is clear from Fig. lOb. Taking error bars i~to acco~t (and it will be noted that those of the present work are considerably smaller)(t~e two points obtained at 3471.5R and 6943~ fall within the probable error of 1). This is quite remarkable considering the rather large wavelength

span involved. In good agreeme~t with the prediction of molecular orbital theory we also found that KJKA ~ 0.75 as in(l). Although i t was intended that a large number of corresponding determinations would be made at the two wavelengths of the neodymium rod, lQ,600~ and 5,300~, time did not permit sueh work to be undertaken. The pictorial results of a single run into ~itrogen at these wave-lengths are shown in Fig. 6 and the results are plotted in Fig. lQb and listed in Tab1e IIA. (The considerable errors resulting from the use of only one run are reflected in the Table and Figure). Here it should be noted that the fringe

shift for a given set of initial conditions is considerably less than one would obtain in oxygen at the same conditions; consequently a larger number of runs in nitrogen is necessary to obtain the same accuracy as one obtains in oxygen. This is a result of the fact that nitrogen is more difficult to dissociate than oxygen.

4.3.2 Oxyge~ Results

Four data points were obtained for oxygen,two with the ruby rod at 6943~ a~d 3471.5~, a~d two with the neodymium rod at the wavelengths of 10,600~

and 5,300~. A separate determination of the molecular specific ~efractivity

at room temperature was made at lo,6oeR because there was no value at this wave-length in the literature (this procedure is described in Appendix A). All

re-sults are presented in Fig. 10a along with the relevant data from the literature.

Ta~le 11 presents a summary of the same type.

The results of the prege~t experiment at both the ruby-rod wavelengths compare favourably with t,hose of~ 1), and are in fact contained in their rather large error bars. These two values also agree with the predictions of molecular orbital theory in that the ratio K]lKA ~ 1.04, being considerably larger than that obtained for nitrogen at these wavelengths, as one would expect. This too agrees with the results of(l). When the region of

5100~

is examined, however, one notices some rat her anomalous behaviour; three comparable determinations at three comparable wavelengths give three divergent findings. Refere~ce 7, at 5210~ found KA = 0.204 !~% cm3/ g lying above the molecular value of 0.1904 cr03/g (represented by the solid curve' in the figure). Reference 1, on the other hand,

if we discount his relatively, large error bar, found a value of K

=

.18 + 10% cm3/g at

5446~,

well below the molecular counterpart at that wave1ength. -The present determination at 53QOA fits directly between the other two, being

(20)

that the ratio ~KA be larger for oxygen than nitrogen. But the situation is rendered even more unclear by the fact that we have no readily available values of KA for nitrogen at the wavelengths in questio~ namely, 5210R,

5300R

and

5446

R,

to compare with. Furthermore the fact that the KA value at 5210R lies

above the ~orrespo~ding ~ value is not sufficient cause, in itself, for

dis-cardin~ it; in fact the present experiment yielded the same occurrence at

lo,6ooÄ (Fig. lOa). (It should be noted that yhe probable error in this latter

value is considerably_ higher owing to the very small fringe-shift obtainable

at these longer wavelengths, and the comparatively lower accuracy of our

experi-mental determination of ~ comparedto that available in the literature for the

other wavelxngths). The presence of a rat her large absorption band at approxi-mately 5000Ä (such as that sketched as the dotted line in the figure) would harmonize and explain all three di~ergent results. Unfortunately (see Appendix A) no such band has ever been observed in atomic oxygen and there is none pre-dicted in this region(29). But this possibility cannot be ruled out entirely. It seems more probable however that the explanation lies in the more conventional area of experimental error.

If we assume that there is no absorptio~ band in this area then we are left with tne alternative of explaining which result is wrongl and why.

This is attempted in Appendix A.

It should be noted in passing that the significantly smaller probable

error in the present work for a given number of experimental runs is easily accounted for by improvement in laser interferometry and accuracy in fringe evaluation over the older optical techniques, along with the more accurate solu-tion of the Rankipe-Hugoniot relations afforded by the computer solutions of

~aw and Bristow(14). 5. CONCLUSIONS

The resul ts of the experimentaL-determinations of the specific

refractivities of the oxygen and nitrogen atoms compare favourably with those of(l) with a significant improvement in accuracy over their pioneering work. In so doing, the shock tube, used in conjunction with laser interferometry has proven itself a very sensitive and most useful instrument for the study of properties of high-temperature gases. Indicative of the improved state of the art is the increased ease with which the measurements were obtained in the present facility compared to the difficulties encountered by Anderson(7) in

his earlier determination of the Gladstone-Dale constant of the oxygen atom at 5210R. The apparently anomalous behaviour of KA i~ this region wherein

he found the value of KA exceeded the molecular value,~, is not at present

fully explicable. A comparable but significantly different value of KA was

obtained in this report at 530oR, but this in itself is not theoretically

significant. Until an independent measurement is made to determine the possible

existence of an absorption band in this area, no definite conclusion can be drawn. It wo~ld be noted that with the advent of the tunable laser it should

(21)

1. 2. 3.

4.

5.

6.

7.

8.

9.

Alpher , R. A. White, D. R. Alpher, R. A. White, D. R. Alpher, R. A. White, D. R. White, D. R. Marlow, W. C. Bershader, D. Marlow, W. C. Bershader,

p.

Anderson, J .H.B. Anders on , J.H.B. Anderson, J.H.B. Osborne, P. J.K. Glass, I. 1. 10. Bristow, M.P.F. 11. Klein, Milton M. Brueckner, K.A. 12. Hall, J. G. 13. Boyer, A. G. 14. Law, C. K. Bristow, M.P.F. 15. Jenkins, F. A. White, H. E. REFERENCES

"Optical Refractivity of High-Temperature Gases:

I. Effects Resulting from Dissociation of Diatomic Gases". Phys. Flluids, VOl.2, No.2, p.153 (1959).

"Interferometric Measurement of Electron Concentratiou-in Plasmas", Phys. fluids. Vol. I, p.452 (1958). ..'

"Optical Refractivity of High-Temperature Gases, Ilo Effects Resulting from Ionization of Monatomic Gases", Phys. Fluids, VOl.2, p.162 (1959).

"Optical Refracti vi ty of High-Temperature Gases, 111. The Hydroxyl Radical". Phys. Fluids. VOl.4, p.40 (1961).

"A Shock Tube Study of the Electric Polarizability of Atomie Hydrogen", Stanford University, SUDAAR No. 149.

(1963).

"Shock-T-ube Measurement of the Polarizabi li ty for Atomie Hydrogen", Phys. Rev. Vol. 133, No.3A,

pp.

629-632 (1964).

"An

Experimental Determination of the Gladstone-Dale

Constant for Dissociating Oxygen", UTIAS Tech. Note. No. 105. (1967).

"Experimental Determination of the Gladstone-Dale'

Constants for Dissociating Oxygen", Phys. Fluids Svpplement I,

p.57 (1969).

"Gladstone-Dale Constants for the Oxygen Atom and Molecule", Phys. Fluids Research Notes, Vol. 10, p .1848 (1967).

"An' Experimental Determination of the Polarizabi l i ty for Singly Ionized Argon", UTIAS Report NO.158 (1971). "Interaction of Slow Electrons with Atomic Oxygen and Nitrogen", Phys. Rev. Vol. rIl, Nod4,p.lll5 (1968).

"Design and Performance of a 9" Plate Mach Zehnder Interferometer", UTIA Report No.f7 (1954).

"Design, Instrumentation and Performance of the UTIAS 4" x 7" Hypersonic Shock Tube", UTIAS Report No. 99,

(1965) •

"Tab les for Normal Shock-Wave Properties for Oxygen and Nitrogen in Dissociation Equilibrium", UTIAS Tech. Note No. 148 (1969).

(22)

16. Peck, E. R. Kharma, B. N • 17. Edelman, G.M. Bright, M.H. 18. Bernstein, L. 19. Tuttle, L. Satterly, J. 20. Herzberg, G. 21. HUber, M.e.E. 22. Hebert, G.R. Innanen, S. H. Nicholls, R.W. 23. Pope, T. P. Kirby, T. B. 24. Alpher, R.A. Grèy:b~r, H.D. 25. White, J?R. 26. Appleton,

J.P.

Steinberg, M. Liquornik,

D.J.

27. Cary, Boyd. 28. Byron, Stanley 29. Wiese, W. L. Smi th, M. W. G lennon, B .M.

"Dispersion of Ni trogen" , J. Opt. Soc. Amer. Vol. 56,

No.8, pp.1059-1062, (1966).

"Specific Refractivities of Gases for Various

Wave-lengths of Light", M.LT. Gas Turbine Lab. Rep. No.6.

(1941;3) •

"Tabulated Solutions of Equilibrium Gas Properties

Behind the Incident and Reflected Normal Shock Wave in

a Shock-Tube". 1. Nitrogen, 11, Oxygen, ARC CP No.626,

(1963) •

The Theory of Measurements, Longmans, N.Y. p.201., (1925).

Molecular Spectra and Molecular Structure I. Spectra

of Diatomic Molecules, D. Van Nostrand Co., Inc, Princeton,

N.J.

(1950).

"Iltterferometric Gas Diagnostics by the Hook Method",

in Progress in Gas Dynamic Research by Optical Methods,

Proc. of a Symp. held at Syracuse University, May 25,

1970, ed. D.S. Dosanjh, Plenum Press, New York.

Identification Atlas of Molecular Spectra No.4, the

Shumann-Runge System, York University, Dept. of Physics,

(1967).

"Modified Hypersensitization Procedure for Eastman

Kodak I-Z Spectroscopic Plates", opt. Soc. Amer. VoL 5,

No.7, PP.951-953 (1967).

"Calculation of Shock-Hugoniots and Related Quantities

for Nitrogen and Oxygen", GERL, Rept. No.58-RL-1915,

(1958).

"Shock Tube Studies of Nitrogen Vibrational Relaxation

and Methane Oxidation", A.R.L. Tech.Rept. ARL 70-0107,

(1970) •

"A Shock Tube Study of Nitrogen Dissociation Using

Vacuum Ultraviolet Light Absorption", ARPA. Order No. 31_{7,P_r_o_je_c_t No~400, AC-Electronics-Defense Research Labs, (1967).

"Shock-Tube Study of the Thermal Dissociation of

Nitrogen", Phys. Fluids VOl.8, No.l, pp.26-35 (1965).

"Shock-Tube Measurement of the Rate of Dissociation

of Nitrogen". J. Chem. Phys. VOl.44-, No~4 , pp.1378-88, (1966).

Atomic Transition Probabilities Vol. I H drogen

Throurh Neon, NSRDS-NBS ,At.omic and Molecular

(23)

APPENDIX A: DETERMINATION OF THE SPECIFIC REFRACTIVITY FOR THE OXYGEN ATOM

Prior to the present investigation a ~eries of similar experiments wer~

carried out in the same facility by

Anderson(~ ~nd

Anderson, Osborne, and Glass\ J,9) using oxygen as the test gas. Since the completion of that work considerable

modifications were made on the complete experimeqtal facility as described in

Sec. 3. Therefore, it was decided that as a check on any new work it would be best to duplicate the ear~ier oxygen data. Twelve runs were performed in total,

five at lo,6ooR and 5,300X, and seven at 6943R and 3471.5R. More than twice the

number of runs were ~ecessary in each case by Refs. 1 and 7 to obtain the same probable error. This is easily attributable to the modified interferometèr and

shock tube facility (see Sec. 3.4. '.). The pertinent KA results are plotted as a function of À in Figs. 9a and 19a. It should be noted that there need not

necessarily be any simple correspondence between the values of KA and ~ for a given substance. The dependence of refractivity upon the electronic configuration is complipated. Theoretical prediction of oscillator strengths at various

wave-lengths are of ten found to be as much as 50% (a~d seldom less than 20%) off from the experimental values. Nevertheless all gaseous dispersion curves to date have taken the form of smooth asymptotic curves. Let us proceed then, on the assump-tion that the anomaly is significant and must be accounted for. It was noted that two possible explanations may rationalize this anomaly, but neither is sufficient as it stands to completely remove all doubt.

If one chooses to accept the location of the data points and the size of

the error bars as correct as they stand, then one might postulate the existence of an absorption band in this area. A dotted line has been sketched in Fig. lOa

to illustrate the idea. Unfortunately, no such phenomenon has been observed in

the oxygen atom. It would appear that an independent experiment utilizing the Roshdestvenskii hook-method(21) of interferometry should be performed to test this hypothesis.

If one, on the other hand, seeks to explain the discrepancy as the

result of experimental errors, then we can propose at least three possible sources of consistent errors of this magnitude. The first brings the purity of the gas into question, the second involves inaccuracies in the measurement of shock

tube parameters, and the third centres around procedural errors in interferometry. If impurities were present in the test gas, the effects could be many-fold and diverse. The obvious case, where ordinary air is the impurity was

checked by performing two experimental runs into oxygen gas with a known

contami-nation of 10% air. These runs yielded a value of KA which was depressed by 18% from the expected value. An analysis of our usual Yest gas showed no excess impurities and furthermore, the results were checked by performing two of the experimental runs in ultra-pure (noted as 99.996% pure) research-grade gas,

These results further confirmed the assumption that impurities were not to blame, as no significant differences were noted. We ca~ot blame impurities for the

rather high value of KA which occurred at 5210R since the air impurities mentioned

above would have led to a value that-was lower than normal, not higher.

~he only feasible source of error in the shock-tube portion of the experimental apparatus would involve consistent negative reading errors in the measurement of P

(24)

of the rather non-linear calibration curves of some of these older instruments. The present facility like that of Alpher and White, is above reproach on this account since both used a Mcleod gauge and an oil manometer as more accurate measuring instruments (see Sec. 3.1. _).

In consideration of the interferometric procedures involved, the only significant differences that could arise would probably stem from the fact that---

,.---laser interferometry, used only in the present experimental work is inherently more foolproof than the spark source and exploding wire light sources employed earlier. In addition, earlier white-light sources had to contend with"roll-over" effects which made the measurement of fringe shifts rather involved and less clear. One specific problem in this area is noted in reference to the work of Refs.

8

and 9, in that no appare~t reference lines were used in their

interfero-grams. At that time it was tho~ght sufficient to use the central order fringe displacement of the white-light interferograms to determine the approximate fringe shift in order to identify each monochromatic fringe on both sides of the shock front. The exact fringe shift was measured as the change in locatioB of a fringe from its position in the "no_flow" picture to that in the "flow" position. However, as explained in Appendix B, a very significa~t error can be caused by movements in 4he entire fringe envelope between the times that the "no-flow'l and "flow" photographs are taken. These movements can be caused by thermal gradients, movements in optical equipment, or perhaps small vibrations in the interferometer at the exact time the picture is taken.

In light of these considerati~ns we must co~clude that possible

experimental errors in the works of(7-9) seem plausible: i.e., there are reasons to believe them to exist. Unfortunately, it was not possible for this author to perform a calibration of the facility used in this earlier work before the extensive modifications were completed by Bristow (Sec.3o _). In any case, it seems evident that the error bars listed as ~% of the KA value by(7-9) might be extended considerably beyond their earlier limits. Other than these considera-tions, the remote possibility exists of a relatively strong absorption band

(of the Shumann-Runge variety perhaps) in molecular oxygen in this region. In

fact there does seem to be some fairly strong tr~~sitions at 4905~, 5155~, a~d

5249~ which might concievably account for -this \.22). However, in view of the fact that the laser bandwidth is very narrow (less than 5o.~) and that these transitions are no stronger than many others at other wavelengths (which do not show up as a conspicuious hump on the dispersion curve) one should wait for independent experiments to confirm any such unusual phenomena.

Finally, it was noted in Sec. 4.3.2 that we found it necessary to

determine experimentally in the shock tube the molecular specific refractivity

(25)

APPENDIX B: MEASUREMENT OF FRINGE SHIFT, S21' FROM AN INTERFEROGRAM

What one obtains from each run is a set of four interferograms? two for

each wavelength, similar to those in Figs. 3, and 5 to 8. All those interferograms

obtained at 10,600~ were made possible through the use of a film sensitizatio~

technique of the Eastman Kodak I-Z plates used. This procedure, described in,23)

involves the ~se of NH

4

0H (ammonia) and ~acetic acid baths 15 minutes prior to

use. The designations "no-fl~" and "flow" refer to the interferograms taken

before the shock has reached the test section, and at the exact moment it reaches

the centre of the section? respectively. The shock front is located at the sharp

discontinuity at the left hand side of the shock zone, as indicated. Vib~a~ion~l

equilibrium is reached in the distance 8

V' (here 6.2 mm as calculated in ,2 ?25})

and dissociational equilibrium is reached in the distance Sd (28 mm as calculated

from (26,27))from the shock front. These phenomena will be discussed presently.

It can be seen that it is quite easy to trace any individual fringe through this zone? so that no special technique is needed (such as canting of the

interfero-meter.) to locate the fringe before and .,aft er the shock.

Fram theoretical considerations we have seen that the only variables

that might be significant in altering the fringe shift and which are not

con-sidered in the calculations are significant ionization (which would decrease

the fringe-shift) and incomplete vibrational relaxation. The former possibility

can be safely ruled out at these temperatures (see Ref.28). As to the

possibili-ty of in90mplete vibrational relaxation, the reaction rate cal~ulations such as

those of,24?25) for nitrogen (and similar studies for oxyge~) indicate vibrational

equilibrium is complete before sig~ificant dissociation takes place. (usually

complete vibrational equilibrium is obtained in less than 1 microsecond).

Sufficient work has been do~e in6the calculation of the extent of the

dissocia-tion relaxadissocia-tion zone itself,25,2 J to predict the length, Sd? quite accurately.

The actual measurement of the fringe shift consisted of obtaining a

statistical average of a large number (usually larger than 200) of the individual

fringe-shift measurements from each interferogram. One could simply make a

small number of very precise measurements, or even settle for just one

measure-ment (Bris~ow(lO)) reported accuracy of 8

21 measurement to within 0.05 fringes

with only one fringe-shift measurement being made per interferogram). It was

felt, however, that optical imperfections, leading to non-uniform fringe spacing,

along with the inevitable uncertai~ty in the location of the fringe centre, could

lead to consider~ble errors in any one particular measurement. The advantage of

taking the statistical mean of a large sampling is that the random errors just

mentioned would tend to cancel, yieldiug a more accurate result. In the absence

of systematic errors in measurement techniques, using the statistical method, one

could expect to approach the resolving power of his measuring device (in our

case a *Ruscom Digitizer). That is, ~f the measuring device is calibrated to

0.01 in. for example, then the standard deviation of the pop~lation mean will

approach 0.01 in. in the limit as the sample number approaches infinity. See Ref.19 for a more detailed discussion of this aspect.

The actual ~easurement procedure is rather straight-forward. It involves the use of both the "flow" and "no-flow" interferograms, horizontal and vertical reference lines (designated R. L. in Fig. 3a, b), and a digitizer

of the one-dimensional type. The reference lines in the figures were actually

(26)

wires strung on both sides of the test section at the beginning of the

experi-ment, which also se~ved to focus the camera on the centre of the test section. Although ip principle a microdensitometer is slightly more accurate tha~ a

simple distance measurement device like a digitzer, which depends on the

·ability of the eye to discriminate the centre of each fringe, the increased

complexity of analyzing densitometer traces and the greater expense was

con-sidered not worth the small increase in sensitivity. Indeed, most fringe-shift

measurernents had a statistical dispersion of

<

0.05 fringes, constituting a significant improvement over the 0.1 fringe accuracy which had been the best

available to date.

Af ter identifying one particular fringe on both "flow" and "no-flowfl interferograms, one simply measures:-cl;s the vertical dista:q.ce from a given

reference line to the appropriate fringe on each of the two related interfero-grams, and then divides ~y the fringe spacing at that region to obtain one value for S?l. In Fig. 3a for instance, which shows a typical "flow" inter-ferogram, tfie distance to fringe 1 from the lower reference line is designated

as "b

l". The same quantity in F;i.g. 3b is designated "b2". The fringe shift

then lS,

where "d" is the fringe spacing distal'lce as illustrated. This whole process

was repeated on approximately 40 fringes at each of three to five locations at varying posi~ions along the horizontal axis behind the shock location. Care was taken to align both interferograms in the same orientation during

measure-ment~ a~d any mag~ificatio~differences incurred during printing were taken

into account. What turned out to be a very important factor was the considera-tion of the movement which occurred in the complete fringe gro~p between the times that the "no-flow" apd the "flow" interferograms were taken, respectively. In Fig. 3a the vertical distance of fringe 1 from the reference line is shown

as "al", the same measurement in Fig. 3b is called "a

2". We are concerned

here with -rhe difference (a

l-a2) which results primarily from temperature

gradients (Bristow in(lO) observed that p temperature fluctuation of O.OloK

resulted in a fringe shift of Q.l fringes). Vibration~ of the entire inter-ferometer can also cause ~isible vibrations in the entire fringe group and

if they occurred during exposure time could result in erratic measured values of S?l. These factors were observed to proQuce consistent errors in fringe

shift which could easily approach 40% in the very low pressure, high-Mach number runs where the actual fringe shift is near to or less than unity. (It

is further noted in Appepdix A that this may be a co~tributing factor to possible errors in the work of

\7,8

and 9)~. Care should defi.ni tely be taken to watch

for this in all future investigatiorrs where slight time delays may allow sroall

movements in the location of the entire fringe group.

Worthy of further note is the fact that if one can safely assume that the errors in measuring 8

21 for each fringe are random, then the more fringes that one measures on each interferogram, the closer he will come to the

resolu-tion limit of the insyrument itself, which in our case was .-0.007511

• If we had

wished to spend more time on measuring 8

21 for each run, then in theory all the 6S~s (errors in S21 measurement) liste~ in Table 111 might have been 0.01 or

(27)

(28)

n 2.0 KL M , /' I

'~

I

I~~=~:=-==

=

: 11 1 ,

I

'À3 _ I I Xli "2/ Vf 1.01--~1 ~I ;:f~\:::"---l/~---;'~~::;::-~'-;I

--==:::.

=-:::---===:::==-'-I I ' I I ~Vislöle ~ar

I I 1"""-"':'" Neor ---...-... r l Radio waves

--- For ultraviolet Neor infrored

X-roys ultraviolet infrored.

OL-_~~~~~----~~~---L FIG. la Schematic diagram of a complete dispersion curve for

a sub stance transparent to visible spectrum (Ref. 15)

1.70I--+-+If-\---\--h:f:~~~~~~I--+----+----I

) .

-FIG. lb Dispersion curves for several different materials commonly used for lenses and prisms (Ref. 15)

t

ft

I

1).1 1 1 1 1 1 1 ) .

(29)

Camera System

FIG 2

First Mlrror

SCHEMATIC MACH - ZEHNDER INTERFEROMETER

System

_ Second Parabolic Mirrar

to M.Z.I.

Light Source (all distances in cm )

S.H.G.

Laser

~

--~Iens.

f=17.2cm

" ' . " " ' " Diffuser. single (coo.rse) double (f ine ) Diffuser •

Stop plate