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UV optical constants of water and ammonia ices

HIDE
 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Figures
 Abstract
 I. Introduction
 II. Theory for optical constant...
 III. Experimentation
 IV. UV optical constants
 V. Conclusions
 Appendices
 1. Details of experimental...
 2. Alignment procedures
 3. Error analysis
 Bibliography
 Bibliographical sketch
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Material Information

Title: UV optical constants of water and ammonia ices
Physical Description: vii, 81 leaves. : ill. ; 28 cm.
Language: English
Creator: Browell, Edward Vern, 1947- ( Dissertant )
Anderson, Roland C. ( Thesis advisor )
Keefer, Dennis R. ( Reviewer )
Clarkson, Mark H. ( Reviewer )
Green, Alex E. S. ( Reviewer )
Ballard, Stanley S. ( Reviewer )
Chen, W. H. ( Degree grantor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1974
Copyright Date: 1974

Subjects

Subjects / Keywords: Ice   ( lcsh )
Ice crystals   ( lcsh )
Crystal optics   ( lcsh )
Ultraviolet radiation   ( lcsh )
Aerospace Engineering thesis Ph. D
Dissertations, Academic -- Aerospace Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract: The real refractive indices for amorphous and hexagonal water ices were measured between 1610 A and 3200 A and those for amorphous ammonia ice were determined from 1925 A to 3200 A. Upper limits on the absorption coefficients for these ices were established from extinction coefficient measurements made in a region of absorption. Amorphous iced were deposited from the gaseous phase onto a gold-coated sapphire substrate which was cooled to 77 K. Hexagonal water ice was deposited at 155 K. The ice films were illuminated with monochromatic light at two angles of incidence. The interference fringe periods, that were observed as the film thickness grew at a constant rate, were used to determine the real refractive index of the film. The damping of the fringe amplitude with increasing film thickness was used to establish the extinction coefficient of the ice at that wavelength. At 3200 a the real refractive indices for amorphous and hexagonal water ices and amorphous ammonia ice are 1.270, 1.341, and 1.485, respectively. From 2200 A to 1610 A the water ice refractive indices rapidly increase to 1.468 for the amorphous phase and to 1.656 for the more dense hexagonal phase. The refractive index for amorphous ammonia ice shortward of 2400 A quickly approaches 1.827 at 1925 A. Upper limits for the absorption coefficients of water ices at 1475 A and of amorphous ammonia ice at 1760 A are 1.96x105 cm and 2.46x105 cm, respectively.
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 77-80.
General Note: Typescript.
General Note: Vita.

Record Information

Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000580944
oclc - 14100560
notis - ADA9049
System ID: UF00085804:00001

Permanent Link: http://ufdc.ufl.edu/UF00085804/00001

Material Information

Title: UV optical constants of water and ammonia ices
Physical Description: vii, 81 leaves. : ill. ; 28 cm.
Language: English
Creator: Browell, Edward Vern, 1947- ( Dissertant )
Anderson, Roland C. ( Thesis advisor )
Keefer, Dennis R. ( Reviewer )
Clarkson, Mark H. ( Reviewer )
Green, Alex E. S. ( Reviewer )
Ballard, Stanley S. ( Reviewer )
Chen, W. H. ( Degree grantor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1974
Copyright Date: 1974

Subjects

Subjects / Keywords: Ice   ( lcsh )
Ice crystals   ( lcsh )
Crystal optics   ( lcsh )
Ultraviolet radiation   ( lcsh )
Aerospace Engineering thesis Ph. D
Dissertations, Academic -- Aerospace Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract: The real refractive indices for amorphous and hexagonal water ices were measured between 1610 A and 3200 A and those for amorphous ammonia ice were determined from 1925 A to 3200 A. Upper limits on the absorption coefficients for these ices were established from extinction coefficient measurements made in a region of absorption. Amorphous iced were deposited from the gaseous phase onto a gold-coated sapphire substrate which was cooled to 77 K. Hexagonal water ice was deposited at 155 K. The ice films were illuminated with monochromatic light at two angles of incidence. The interference fringe periods, that were observed as the film thickness grew at a constant rate, were used to determine the real refractive index of the film. The damping of the fringe amplitude with increasing film thickness was used to establish the extinction coefficient of the ice at that wavelength. At 3200 a the real refractive indices for amorphous and hexagonal water ices and amorphous ammonia ice are 1.270, 1.341, and 1.485, respectively. From 2200 A to 1610 A the water ice refractive indices rapidly increase to 1.468 for the amorphous phase and to 1.656 for the more dense hexagonal phase. The refractive index for amorphous ammonia ice shortward of 2400 A quickly approaches 1.827 at 1925 A. Upper limits for the absorption coefficients of water ices at 1475 A and of amorphous ammonia ice at 1760 A are 1.96x105 cm and 2.46x105 cm, respectively.
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 77-80.
General Note: Typescript.
General Note: Vita.

Record Information

Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000580944
oclc - 14100560
notis - ADA9049
System ID: UF00085804:00001

Table of Contents
    Title Page
        Page i
    Dedication
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
    List of Figures
        Page v
    Abstract
        Page vi
        Page vii
    I. Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    II. Theory for optical constant determination
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
    III. Experimentation
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
    IV. UV optical constants
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
    V. Conclusions
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
    Appendices
        Page 59
    1. Details of experimental components
        Page 60
        Page 61
        Page 62
        Page 63
    2. Alignment procedures
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
    3. Error analysis
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
    Bibliography
        Page 77
        Page 78
        Page 79
        Page 80
    Bibliographical sketch
        Page 81
        Page 82
        Page 83
Full Text












UV OPTICAL CONSTANTS OF
WATER AND AMMONIA ICES












BY
EDWARD VERN BROWELL












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY




UNIVERSITY OF FLORIDA


1974

































Dedicated in memory of my father,

Martin M. Browell














ACKNOWLEDGMENTS

The author wishes to express his gratitude to Dr. Roland C.

Anderson for his enthusiastic encouragement and timely technical

assistance in the completion of this investigation.

The author would also like to thank Dr. D. R. Keefer, Dr. A. E.

S. Green, Dr. S. S. Ballard, and Dr. M. H. Clarkson for their time

and effort contributed as members of his supervisory committee.

A special indebtedness is owed to his wife, Judith, for her

effort in typing this manuscript while under a strenuous work

schedule.

The author also wishes to thank Mr. H. E. Stroud for his

energetic assistance in material and equipment acquisition for

initial construction and continued servicing of the experimental

apparatus.

This research was funded by the Department of Engineering Science,

Mechanics, and Aerospace Engineering at the University of Florida.














TABLE OF CONTENTS


Page

Acknowledgments iii

List of Figures v

Abstract vi

I. Introduction 1
A. Background Discussion 1
B. Design Criteria 2
C. Basic Results 5

II. Theory for Optical Constant Determination 7
A. Semitransparent Thin Films 7
B. Optical Constant Determination 16
1. Real Refractive Index 16
2. Absorption Coefficient 17

III. Experimentation 20
A. Experimental Components 20
1. Light Source 20
2. Monochromator 20
3. Experiment Chamber 23
4. Optical Components 24
5. Associated Instrumentation 25
6. Residual Gases and Source Gases 26
B. Experimental Procedures 28

IV. UV Optical Constants 36
A. Amorphous Water Ice 36
B. Hexagonal Water Ice 43
C. Amorphous Ammonia Ice 47

V. Conclusions 54

Appendices 59
Appendix 1. Details of Experimental Components 60
Appendix 2. Alignment Procedures 64
Appendix 3. Error Analysis 69

Bibliography 77

Biographical Sketch 81














LIST OF FIGURES


Figure Page

1. Light Reflected from a Semitransparent Film on an Absorbing
Substrate 8

2. Diagram of Experimental Apparatus 21

3. Photographs of Experimental Apparatus 22

4. Experimental Arrangement for Refractive Index and Extinction
Coefficient Determinations 29

5. Typical Photomultiplier Signals used in Refractive Index
and Extinction Coefficient Determinations 30

6. Refractive Index of Amorphous Water Ice 37

7. Molar Absorption Coefficients for Water Ices and Water Vapor 40

8. Absorption Coefficients for Amorphous Water Ice 42

9. Refractive Index of Hexagonal Water Ice 44

10. Refractive Index of Amorphous Ammonia Ice 48

11. Molar Absorption Coefficients for Ammonia Ices and Ammonia
Gas 51

12. Normalized Absorption Coefficient Curve for Amorphous Ammonia
Ice 53

13. UV Reflectances of Water Frosts 55

14. UV Reflectances of Ammonia Frosts 57

15. Hydrogen Light Source, Spectral Distribution of Intensity 61

16. Alignment Techniques 66
17. Water Ice Film Reflectivity at 1475 A 76
17. Water Ice Film Reflectivity at 1475 A 76









Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy


UV OPTICAL CONSTANTS OF
WATER AND AMMONIA ICES

By

Edward Vern Browell

June, 1974

Chairman: Dr. Roland C. Anderson
Major Department: Aerospace Engineering

The real refractive indices for amorphous and hexagonal water ices
0 0
were measured between 1610 A and 3200 A, and those for amorphous ammonia
0 0
ice were determined from 1925 A to 3200 A. Upper limits on the absorp-

tion coefficients for these ices were established from extinction coef-

ficient measurements made in a region of high absorption. Amorphous

ices were deposited from the gaseous phase onto a gold-coated sapphire

substrate which was cooled to 770K. Hexagonal water ice was deposited

at 155K. The ice films were illuminated with monochromatic light at

two angles of incidence. The interference fringe periods, that were

observed as the film thickness grew at a constant rate, were used to

determine the real refractive index of the film. The damping of the

fringe amplitude with increasing film thickness was used to establish

the extinction coefficient of the ice at that wavelength.
0
At 3200 A the real refractive indices for amorphous and hexagonal

water ices and amorphous ammonia ice are 1.270, 1.341, and 1.485,
0 0
respectively. From 2200 A to 1610 A the water ice refractive indices

rapidly increase to 1.468 for the amorphous phase and to 1.656 for the

more dense hexagonal phase. The refractive index for amorphous ammonia








0 0
ice shortward of 2400 A quickly approaches 1.827 at 1925 A.

Upper limits for the absorption coefficients of water ices at
o o 5 -1
1475 A and of amorphous ammonia ice at 1760 A are 1.96x10 cm
5 -1
and 2.46x10 cm respectively.














CHAPTER I
INTRODUCTION


Background Discussion

Increased interest in the optical properties of solid gases has

been motivated by the desire to interpret albedo measurements of planets,

and the ultraviolet region of the spectrum is being studied more exten-

sively as a result of the space program. In particular, the UV reflec-

tance properties of ammonia and water frosts were recently investigated
1 2
at this laboratory in an effort to explain the UV albedo of Jupiter.

Similarities were noticed between the Jovian and ammonia frost spectra;
0
however, due to uncertainties in the solar spectrum below 2200 A and

unknown physical properties of the frosts, the results were not con-

clusive. The determination of the UV optical constants for ammonia and

water ices reported in this thesis will permit modeling techniques to

be used in the study of the UV albedo of planets where these ices are

suspected to be found.

In addition to the ammonia ice clouds on Jupiter, it is speculated
3-5
that water or perhaps ammonia frost covers Saturn's rings and the
6
Galilean satellites. These conclusions were based on measurements in

the near infrared and the visible regions of the spectrum. Preliminary

analysis of the data gathered by a UV photometer aboard Pioneer 10 as it

passed by Jupiter indicates that there is definite hydrogen Lyman-a
7
emission coming from the innermost satellite lo. This suggests that

there may be present hydrogen-bearing ices of NH and H 0 as was
3 2






8
postulated by Johnson and McCord in 1970. It is anticipated that Uranus

and Neptune have substantial amounts of ammonia in their atmospheres,
9
and that due to low temperatures condensation of the ammonia is expected.

The importance of knowing the optical properties of planetary cloud

layers should not be underestimated. When remote sensing techniques are

employed, the vertical temperature distribution, atmospheric constituents,

and radiative heat balance for a planet cannot be completely determined

or understood with certainty until the optical characteristics of the

aerosols are taken into account.

Measurements of the absorption coefficients for ammonia and water
0 0
ices in the ultraviolet have been made between 1400 A and 2200 A by
10
Dressler and Schnepp. The complex dielectric constants for amorphous
o o 11
water ice between 400 A and 2000 A were determined by Daniels using

high-energy electrons. These references are in disagreement by a factor

of two when the absorption coefficients for amorphous water ice are com-

pared. Schnepp and Dressler measured the transmission of ice films with

a photographic technique, and indicated that errors as large as an order

of magnitude could exist in the absolute level of their absorption
12
coefficient curves.

This investigation determined the real refractive indices for
0 o
amorphous and hexagonal water ices from 1610 A to 3200 A and for
o o
amorphous ammonia ice from 1925 A to 3200 A. Upper limits for the

absorption coefficients of these ices were also established.


Design Criteria

The technique used to obtain the UV optical constants of ices had

to be readily adaptable for use inside a vacuum chamber, appropriate for
O 0
use with ultraviolet radiation between 1450 A and 3200 A, applicable to







semitransparent thin films, and independent of the optical constants of

the substrate onto which ice films were to be deposited. The last

criterion was necessary so that changing substrate properties due to

condensation of contaminant gases would not influence the optical

constant determination of the H 0 or NH ice films.
2 3
Upon reviewing the literature for techniques to determine the
12-23
optical constants of semitransparent films, a method used by
24
Tempelmeyer and Mills for transparent films was selected, after it

was theoretically shown that it could also be applied to semitransparent

films. The derivation is given in Chapter II. In this method, radiation

is incident on the semitransparent film at two different angles. One

is near normal incidence, and the other is at an oblique angle. The

film is grown slowly at a constant rate while the reflected light is

detected by two photomultiplier tubes located at the specular reflection

angles. The signal from each photomultiplier tube oscillates as the

radiation reflected from the film-vacuum interface constructively and

destructively interferes with the radiation reflected from the film-sub-

strate interface. The period of the oscillation depends upon the angle

of incidence of the radiation, the real refractive index of the film, the

wavelength of the radiation, and the rate at which the film thickness is

changing. If the wavelength is known and the periods can be determined

at two angles of incidence, the real refractive index and the deposition

rate of the film can be determined explicitly. This was found to be

true even if the amplitude of the oscillations decreased due to the film

being slightly absorbing or scattering. Damping of the interference

oscillations in a spectral region where the film was highly absorbing

was used to determine the extinction coefficient of the film.








Consideration had to be given to the physical properties of solid
25
water and ammonia. Dowell and Rinfret used x-ray diffraction techniques

to determine temperature ranges in which water vapor will deposit into

amorphous, cubic, and hexagonal water ices. Amorphous water ice is

formed by vapor deposition below 1130K. Cubic water ice results from

deposition between 1130K and 1530K, and hexagonal water ice is formed

at temperatures above 1530K. Only the optical constants of amorphous

and hexagonal water ices were determined in the present investigation.
26
Mauer established the temperature ranges in which ammonia formed

amorphous and cubic ice phases. Amorphous ammonia ice is formed by

deposition of NH gas below 1250K, and cubic ammonia is produced by de-
3
position of the gas above 1250K. It was pointed out that the x-ray

diffraction experiments were not completely conclusive because diffrac-

tion patterns appeared at 400K which were similar to those for cubic

ammonia ice. This observation was made for an ice film deposited at

LHe temperatures (3.1K) and allowed to slowly warm. Deposition at LN
2
temperatures (770K) is assumed, however, to cause the formation of

amorphous ammonia ice. Instrumentation complications at chamber pressures

above 1 pHg, which were caused by the high equilibrium vapor pressure

of NH above 1250K, prevented determination of the optical constants
3
for cubic ammonia ice. The equilibrium vapor pressures for amorphous
-25
water and ammonia ices at LN temperatures were estimated to be 10 torr
-12 2
and 10 torr, respectively, and the vapor pressure for hexagonal water
-7
at 1550K was estimated to be 2.0x10 torr. These vapor pressures were

extrapolated from emperical data using the general equation log =

-(a/T)+b, where a = 1630.2 and b = 9.9974 for NH and a = 2666 and
3
b = 10.551 for H 0.
2




5


Basic Results

Real refractive indices were determined for amorphous and
0 0
hexagonal water ices between 1610 A and 3200 A and for amorphous
0 o
ammonia ice from 1925 A to 3200 A. Extinction coefficients were

also established for these ices.

Gas was deposited at a constant pressure onto a cooled gold-
o 0
coated substrate at rates from 200 A/min to 1900 A/min. Perpendicu-

larly polarized, monochromatic radiation was incident on the film at

9.60 and 56.80. The period of the interference fringe at the near

normal incidence angle was 0.5 min to 4 min depending on the deposi-

tion rate, refractive index of the film and wavelength of radiation used.

Amorphous water and ammonia ices were formed by deposition of

their respective gases at 770K, while hexagonal water ice was de-

posited from water vapor at approximately 1550K. The vacuum chamber
-7
pressures were approximately 10 torr before deposition to between
-6 -5
10 torr and 10 torr during deposition.

The refractive index for amorphous H 0 was determined to be
o 2
1.270 at 3200 A. The refractive index slowly increases to 1.303 at
0
2100 A where it begins to increase rapidly to a value of 1.468 at
0
1610 A. Hexagonal H 0 ice exhibits a similar trend, but since the
2 23
density of the hexagonal ice is greater than the amorphous ice,
0
the refractive index is also larger. Thus, at 3200 A the refractive
0
index is 1.341. It slowly increases to 1.386 at 2100 A and then
o
rapidly approaches 1.656 at 1610 A.

An upper limit for the absorption coefficient for amorphous H 0
o 2
ice at 1490 A was determined by the extinction coefficient to be
5 -1
approximately 2.0x10 cm This is more than a factor of two below








the previously reported value of Ref. 10. A comparable result was

obtained for hexagonal H 0 ice.
2
The refractive index for amorphous NH ice shows a uniform
o 3 o
change from a value of 1.485 at 3200 A to 1.596 at 2400 A, and it
o
then rapidly increases to 1.827 at 1925 A. The upper limit for the
5 -1 o
absorption coefficient was established to be 2.5x10 cm at 1760 A.

This is almost a factor of four less than the value reported by Dressler
10
and Schnepp.

All the ice films which were produced exhibited some scattering

properties as was evidenced by the damping of the interference fringes

in spectral regions where the ices do not absorb. Amorphous H 0 ice
2
was found to scatter the least of the ices examined, while both the

hexagonal H 0 and amorphous NH ices were highly scattering. For
2 3
example, only ten interference fringe periods could be readily detected
0
at near normal incidence for the amorphous NH ice at 2400 A. At
3
least twice that many periods could be detected for amorphous H 0 ice
2
at the same wavelength.

The following chapters include a presentation of the theory used

for determine the optical constants of semitransparent thin films, the

components and procedures used in the experiments, and the UV optical

constants for amorphous and hexagonal H 0 ices and amorphous NH ice.
2 3
Details of the experimental components, alignment, and error analysis

are discussed in the appendices.











CHAPTER II
THEORY FOR OPTICAL CONSTANT DETERMINATION


Semitransparent Thin Films

Most of the available techniques for determining the index of

refraction using reflection measurements assume that the film is per-

fectly transparent. Since the films in this investigation cannot be

considered nonabsorbing throughout the whole spectral region of inter-

est, absorption effects must be included in establishing the real

refractive index. Approximations to the complete theory will be made,

when it is appropriate to do so, using criteria which are assumed valid

for expected values of film refractive index and for maximum absorption

coefficients. The resulting, simplified expressions are employed to

show theoretical justification for the procedures used in the determi-

nation of the optical constants.

The monochromatic specular reflectance for perpendicularly polarized

radiation illuminating an absorbing film on an absorbing substrate is

given by the expression17

-4v2n -2v n
p2 +p2 e + 2p p e cos(2u n+q -4 )
12 23 12 23 2 23 12
R = 2v (1)
1+p2 p2 e +2p p e cos(2u fn+2 +c )
12 23 12 23 2 23 12

where the subscripts 1, 2, 3, 12, and 23 refer to the gas over the film,

the film, the substrate, the gas-film interface, and the film-substrate

interface, respectively (see Fig. 1). The quantities p and p
12 23
represent interfacial reflection coefficients, and 1 and <2 are
12 23



























Vacuum


1

Ice Film

= n (l+iK )
2 2


Cryogenically Cooled
Gold-coated Substrate

S= n (+iK )
3 3 3



Figure 1. Light Reflected from a Semitransparent Film on an
Absorbing Substrate


7-
hh
n
2










the corresponding interfacial phase changes for the electromagnetic

radiation. The quantity n is a nondimensionalized film thickness and

is defined by n = 2rh/x where h is the film thickness, and A is the
o 0
vacuum wavelength of the radiation being used. The quantities p p ,
12 23
1 and 23 are defined below in terms of the angle of incidence, e ,
12 23 1
and the refractive indices of the gas, n the film, n = n (1+iK ), and
1 2 2 2
the substrate, n = n (1+iK ). The interfacial reflectances and phase
3 3 3
shifts are given by

(n cose -u )2 + v2
1 1 2 2
2= (2)
12 (n cose +u )2 + V2
1 1 2 2

(u -u )2 + (V -V )2
P2 2 3 2 3
23 (U +U )2 + (V +V )2
2 3 2 3

2v n cose
_1 2 1 1
S = tan (3)
12 U2+V2_n2COS26
2 2 1 1.

F2(u v -u v )
_1 3 2 2 3
and = tan -1
23 U2-U2+V2_v2
2 3 2 3

The constants are defined by

2u2 = C + (c2+d)2 and 2v2 = -c + (c2+d) (4)
2 2
where

c = n2(l-K2) n2sin2e and d ='4n4K2 ; (5)
2 2 1 1 2 2

2u2 = a + (a2+b)2 and 2v2 = -a + (a2+b),
3 3

where
a = n2(l-K2) n2sin2o and b = 4n4K2
3 3 1 1 3 3







It is assumed that the imaginary part of the complex refractive

index, n2K2, is less than 0.06. This corresponds to a maximum absorp-
4 -1 o
tion coefficient of 3.8x10 cm at 2000 A. Additional assumptions are

that 3n2K2 << 1 and n > 1.0; thus 3K2 << 1 and 4 << 1.
2 2 2 2 2

The expression (c2+d)2 given in Eqns. (4) was expanded in a Taylor

series about K = 0 applying the assumption K4 << 1 2K2. The

magnitudes of the first three terms of that series were compared, and

it was found that if n2 2 1.25, the third term could be ignored when

0 6e 600 and 3K2 << 1.
1 2

Thus,
(n2+n2sin2 1)
(C2+d)2 n n2sin28 + n2 2
2 1 1 n2-n2sin2e 2 2
2 1 1

Substituting this relationship into Eqns. (4) yields

n2n2sin2e (n2-n2sin2e )2
S2 + (6)
(n2-n2sin2e ) n2n2sin2e
21 1 2 1 1

and

n4K2
2 2
V2 = (7)
2 n2-n2sin2e
2 1 1

Equation (6) was further simplified to

U2 n2 n2 sin2e (8)
2 2 1 1

when n > 1.25, 0 < e 600, and 3K2 << 1. Equations (7) and (8)
2 1 2
are exact when e0 = 0 and their errors are less than 1% when

00 6 e < 600, ni = 1.0, n2 > 1.25 and n2K2 K 0.06.








The interfacial phase change o12 is then given by
12
2n cose n2K (n2-n2sin2eO )
tan tan x
tan-1 1 1 2 2 2 1 1 -1 X.
12 (n2-n2)-(n2n2in2e ) + n42
L 2 1 2 1 1 2 2J

The small angle approximations of cos x = 1.0, sin x = x, and

tan x = x are satisfied when x2 << 1, and they are in error by less

than 2% when 0 < e < 600, n = 1.0, n > 1.25, and n K < 0.06.
1 1 2 2 2
The resulting approximate relation for 012 is then given by
12

2n cose n2K (n2-n2sin2e )
1 1 2 2 2 1 1
S-(9)
12 (n2-n2)(n2-n2sin2o ) + n4K2
2 1 2 1 1 2 2

When 1% accuracy is desired for the approximation and n > 1.25 is
2
a necessary condition, then n < s 0.04 is the new restriction on the
2 2
imaginary part of the refractive index. Appendix 3 shows that for all

the film parameters encountered in this investigation, the error in the

small angle approximation for 41 was always less than 0.22%.
12
The periodicity of the fringes for semitransparent thin films is

now examined in terms of a perturbation on the period for nonabsorbing

thin films. The condition for extrema in nonabsorbing thin films is

sin(o +2u n ) = 0. This can be readily shown by setting v = 0 and
23 2 0
o = 0 in Eqn. (1) and solving dR/dn = 0. The conclusion that 1 can
12 12
be treated as a small angle is used in expanding cos(42 +2u nri ) as
23 2 12
the sum of two angles. Thus,

cos(4 +2u n+ ) = cos(4 +2u n) To sin(4 +2u n) (10)
23 2 12 23 2 12 23 2

The locations of the extrema for slightly absorbing films in terms of

the nondimensionalized film thickness, n, are assumed to be only








slightly displaced from that for a nonabsorbing film, no. It can then

be written that n = no + where e is considered to be a small quan-

tity. If Eqn. (10) is used for a semitransparent film in the vicinity

of the extrema, it reduces to

cos(( +2u n+ ) cos(p +2u n) $ + sin(2u e)
23 2 12 23 2 12 2

using sin( +2u n) = 0. Assuming that < sin(2u ) <<1 and that
23 2 0 12 2
Icos(2 +2u n) = 1 near an extremum,
23 2

cos(4 + 2u n+ ) = cos(q +2u n).
23 2 12 23 2

The first condition is shown in Appendix 3 to be valid.

Equation (1) can now be rewritten as

-4v2n -2v2n
p2 + p2 e + 2p p e cos(4 + 2u n)
12 23 12 23 23 2
-4v2n -2vn (11)
1+p2 p2 e + 2p p e 2 cos(q + 2u n)
12 23 12 23 23 2

in the vicinity of an extremum. Evaluation of dR/dn = 0 results in

the equation

2 -4V2 n -4v2n
(1 +p2 ) cos(@ +2u n) + (1-p2 e )sin(p +2u n)
u 23 23 2 23 23 2
2

V p
2 23 -2vn
-(p2 +l)e (12)
U p 12
2 12

When v is set equal to zero, as is the case for a nonabsorbing film,

the equation reduces to sin(2 +2u n) = 0, as was expected. Using the
23 2
relationships n = n + e, sin(3 +2u n ) = 0, and cos(3 +2u n ) = 1,
Eqn. (12) becomes23 2
Eqn. (12) becomes





13


V2 -4v (n +e) -4v (n +e)
+ (l+p2 e ) cos(2u e) (1-p2 e 2 sin(2u )
U 23 2 23 2
2

2 23 -2V ( +)
-- (p2 +l)e
U P 12
2 12
-4V2E -2V2
Assumptions are made that e 1 4V2 e, e 1 2V2 ,

and 2u2 is a small angle. The above equation then simplifies to

E -4v] I' -vo 4vo
E2 18Vu2p e 2 + 2 u 2(1-2 e ) v2(2p2 e 42
2 2 23 2 23 2 23

23 -2vn -4v20 23 -2v
+ (p2 + )e 2) -V] 1p2 + (p2 +l)e
P 12 2 23 P 12
12 12

An order of magnitude calculation revealed that for 1.25 s_ n 2.00,

0 < e s 60, and n K < 0.04, the e2 term in the equation was negli-
1 2 2
gible when compared to the e term, and in the coefficient of E, the

v2 term was negligible compared to the u2 term. The resulting equation
2 2
for the perturbation e is


-vv1+p2
-v 4+p2 e 2 P 23 (p2 +l)e 2 T1
2 23 P 12
-- _4V-no (13)
2u2( -p2 e 2 0)
2 23

The positive sign in Eqn. (13), cos( 23+2u n ) = +1, represents the
23 2 0
condition for a maximum when p is negative, and the negative sign,
23
cos( 23+2u 2 ) = -1, represents the condition for a minimum when p23
23 2 0 23
is positive provided that p is negative, I12 | s T/2, and 2 |3 < r/2.

The fringe period for a nonabsorbing film is Ano = T/U and the

actual locations of the extrema are given by no = (mir- )/2u where
0 23 2








m is an integer. Sample calculations using Eqn. (13) were made for

each type of ice investigated. The refractive index determined for
o 4
-1
each ice at 2400 A and a maximum extinction coefficient of 2.1x10 cm

were used. The calculations which gave the largest perturbation values

were for amorphous H 0 ice with e = 570. Those results are presented
2 1
in Table 1. The parameters used in calculating the values in Table 1

are given in the Notes. The ice was considered to be nonabsorbing for

the determination of u p and p ; however, a maximum extinction
2 12 23
coefficient was used to account for absorption and scattering in the

film. An estimate of the maximum extinction coefficient exhibited by

the ices investigated was used. It is interesting that the actual per-

turbation of the extrema approaches a constant value at very large film

thicknesses, and that the perturbation error is less than 1% of a per-

iod. The most important aspect of this calculation is the error

involved in measuring the fringe period for a semitransparent film com-

pared to a transparent film. It was determined experimentally that

errors in the period of less than 0.3% were not measurable. With this

in mind, it can be seen from Table 1 that periods measured from exper-

imental data would appear to have constant periods beyond the third max-

imum. It thus became a practice to determine the average fringe period

beyond the third interference maximum.

The approximations used in the derivation of Eqn. (13) are dis-

cussed in detail in Appendix 3. It was determined that all the assump-

tions are valid if the values for e are taken after the first three

maxima. This represents the same condition that was imposed by the

error in the fringe period discussed above.








Table 1


Perturbation Calculations for Position and


Period of Interference Extrema


-E
n -E n [%
0 0

2.833 0.1053 3.255
6.068 0.0738 2.282
9.302 0.0574 1.776
12.537 0.0477 1.475
15.772 0.0415 1.283
19.007 0.0374 1.155
22.242 0.0346 1.068
25.476 0.0326 1.008
28.711 0.0312 0.966
31.946 0.0303 0.936
35.180 0.0296 0.916
38.415 0.0291 0.901

1.216 -0.0315 -0.973
4.450 -0.0110 -0.340
7.685 0.0006 0.020
10,920 0.0084 0.260
14.155 0.0139 0.430
17.389 0.0178 0.552
20.624 0.0207 0.640
23.859 0.0228 0.704
27.094 0.0243 0.750
30.328 0.0253 0.783
33.563 0.0261 0.806
36.798 0.0266 0.823
40.033 0.0270 0.835

0.0280 0.865


a) These calculations were
o
at 2400 A with e = 57
i
b) n = 1.283; n K = 0.0;3
2 2 2


e -e
m-2 m
An [%]
0


0.973
0.506
0.301
0.192
0.128
0.087
0.060
0.042
0.029
0.021
0.015


-0.633
-0.360
-0.240
-0.170
-0.122
-0.088
-0.064
-0.046
-0.033
-0.024
-0.017
-0.012

0.000


made for amorphous H 0 ice
2

4 -1
=2.1x10 cm
Xt


c) n
3


= 1.296; n K = 1.543 (Optical constants of gold
o 27 3


at 2400 A

d) An = 3.2
0


35.


2
4
6
8
10
12
14
16
18
20
22
24

1
3
5
7
9
11
13
15
17
19
21
23
25


Maxima:












Minima:


Notes:








It should be emphasized that the sample calculation represents,

in effect, the worst possible case which could be encountered during

this investigation. All reductions in absorption or scattering can only

increase the accuracy of the period determination since E is directly

proportional to v Harrick22 and Ruiz-Urbieta et al.17 noticed the
2
lack of sensitivity of fringe location to film absorption in their

computer calculations. Their conclusions substantiate the above results

which were derived from general theoretical considerations. The fringe

period for a semitransparent film can now be used to determine the real

refractive index of the film.


Optical Constant Determination


Real Refractive Index

The fringe period for a semitransparent film has been shown to be

approximately equal to that for a transparent film, Ano = i/u Since

An = 2EAh/x the change in thickness over one period is Ah = X /2u .

Using Eqn. (8), Ah becomes

Ah = o (14)
2(n2-n2 sin2e )
2 1 1

Assuming that the cryodeposit grows at a constant rate, C, the period

of the fringe, At, is determined by At = Ah/C. Equation (14) may now

be written

C =o (15)
2At(n2-n2 sin2e )2
2 1 1

If the film is illuminated at two different angles of incidence,

a and e, simultaneously as it grows in thickness, the interference





17

fringes detected at their respective specular reflection angles exhibit

different periods of oscillation. Since the deposition rate is constant,

and Eqn. (15) is valid for both angles of incidence, C can be eliminated

using Eqn. (15) at a and 8. The resulting relationship is

Xo X0 (16)
2At (n2-n2 sin2a)2 2At (n2-n2 sin2g)2
1 2 1 2 2 1
where At and At are the interference fringe periods at a and 8,
1 2
respectively. Solving for n in Eqn. (16) yields

At 2
sin2a- (AT2) sin2
n n At (17)
1 2)2


Once a, 8, At At and n are known, Eqn. (17) can be solved for the
1 2 1
real refractive index of the film. Equation (15) can then be used to

determine the film thickness deposition rate. These same equations

were used by Tempelmeyer and Mills24 in evaluating the refractive index

of transparent CO cryodeposits.
2

Absorption Coefficient

Determination of large absorption coefficients for ice films at

wavelengths shorter than those used to investigate the real refractive

indices of ice films was made by Dressler and Schnepp;10 however, uncer-

tainties in their film thickness has led to possible order of magnitude

errors.12 It is the objective of this discussion to present a method

of determining the upper limits for the absorption coefficients for

water and ammonia ices with errors less than 10% without changing







the experimental configuration that was used for determining the real

refractive indices.

It is assumed that the condition required for a reflectivity

extremum of a semitransparent film to occur is cos(p +2u n) = 1.
23 2
This is based on qualitative assessment of Table 1. The mathematical

expression for the envelopes of the extrema can be approximated by
-4v n -2v 2n
p2 +p2 e + 21p p Ie
12 23 12 23
ext -4vn -2vn (18)
1 + p2 p2 e 2 + 21p p e 2
12 23 12 23

where the positive and negative signs are used for the envelopes of

the maxima, Rmax, and of the minima, Rmin, respectively. From an order

of magnitude calculation, the second term in the denominator was found

to be small in comparison to the sum of the other two terms and was

thus eliminated from the equation. If near normal incidence is used,

2v n can be approximated by Sh in Eqn. (18), where B is the extinction
2
coefficient of the film. The damping of the fringes, as represented

by Rx- Rmi can be used to determine B. The relationship for the

fringe amplitude is
-Bh -2Bh
41p p le (1-p2 -p2 e )
12 23 12 23
Rmax Rmin = -2Bh
1 4p2 p2 e
12 23

If the assumptions: 1-p2 p2 e-26h and 1 >>4p2 p2 e-2h are made,
12 23 12 23
the equation above reduces to
)- h
Rm Rmin 4p p 2(1-p2 )eh
ax min 12 23 12





19

Upon determining this relationship at two different film thicknesses

and taking the ratio of the two results, the extinction coefficient

can be found directly from the equation


1 (Rmax Rmin) h
h -h (R R. )I h
h2 1 Rmax min 2

Since the reflectivity is proportional to the detector signal, S,

this can be written as

1 In (Smax- Smin)!hil (19)
1 = Ln 7 (19)
h -h (S Sin) h
2 1 max min 2

provided the illuminating intensity remains constant from h to h .
1 2
The change in thickness, h -h is determined by maintaining a constant
2 1
film deposition rate, changing the illuminating wavelength of radiation

to one where the real refractive index has already been determined,

establishing the new fringe period, calculating the actual film depo-

sition rate, C, using Eqn. (15), and determining h -h = C(t -t ),
2 1 2 1
where t -t is the time necessary for the film to grow in thickness
2 1
from h to h
2 1
The error in the extinction coefficient, as determined by Eqn. (19),
5 -1
is less than 10% for 2 1.0x10O cm when the first and second maximum

locations are used for h and h A linear interpolation between
1 2
adjacent minima is used to establish Rmin at h and h A complete

error analysis of this approximate method is given in Appendix 3. This

extinction coefficient represents the upper limit for the value of the

absorption coefficient at that wavelength.












CHAPTER III
EXPERIMENTATION


Experimental Components

The experimental design is shown schematically in Fig. 2 and

photographically in Fig. 3. A brief explanation of the design and

purpose of the various experimental components follows with additional

details given in Appendix 1.


Light Source

The light source was a flow-through electrodeless hydrogen dis-

charge. Hydrogen pressures in the discharge were approximately
-3
10 torr. The spectral distribution (see Appendix 1) of the hydrogen

discharge makes it particularly well suited for application between
o o
1650 A and 3000 A where it exhibits a uniform continuum. The optics

of the monochromator were overfilled due to the close proximity of

the source to the entrance slit, and thus no additional condensing

optics were required. A MgF window separated the air-cooled high
2
temperature discharge from the monochromator vacuum space. This

light source proved to be a bright and stable radiation source for

application in these experiments.


Monochromator

A 0.3 m McPherson monochromator was used in conjunction with the

hydrogen discharge. Slit dimensions of 2000 pm in width and 5000 um

in height were necessary to insure the energy requirements of the


























Hydrogen light source
McPherson monochromator (0.3 m)
Six inch diffusion pump system
Light baffle system
MgF2 Rochon polarizer
Rotatable feedthrough
Flexible alignment coupling
Baseplate and collar (18" dia.
and 6" high)
Six inch diffusion pump system
Low voltage feedthrough


High voltage feedthrough
Port for ion gauge, thermocouple
gauge, and mass analyzer
MgF beamsplitter
UV enhanced mirror
Gold-coated sapphire substrate
Cryo-Tip
Photomultiplier tubes
Stainless steel bell jar (not
shown) seals to collar to


complete vacuum


system


Figure 2. Diagram of Experimental Apparatus



























Experimental Apparatus
A. McPherson monochromator E. Microwave generator for H
B. Light baffle system discharge 2
C. Experiment vacuum chamber F. Signal preamplifiers
D. Cryo-Tip control unit


Experimental Arrangement in Vacuum Chamber


A. Photomultiplier tubes C.
B. Oxygen-free, high-conductivity D.
copper,substrate holder E.


Cryo-Tip
MgF beamsplitter
UV enhanced mirror


Figure 3. Photographs of Experimental Apparatus








0
experiments would be met. The resolution was normally 53 A. The

beam emerging from the monochromator was an f/5.3 beam. A system of

stops was used to limit the beam divergence and size. Upon entering

the experiment chamber, the beam was approximately 6.4 mm in diameter

with a maximum total divergence of 0.50. A MgF window separated the
2
monochromator vacuum space from the vacuum space in the section

containing the light baffle system and the experiment chamber. A
-7
vacuum of 4.0x10 torr was produced in the monochromator by a six

inch diffusion pump which was equipped with a LN cryobaffle. An
2
ion gauge and a themocouple gauge were used to measure pressures in

the monochromator.


Experiment Chamber

An 18" diameter stainless steel bell jar and a matching collar

which was welded to a 3/4" thick base plate formed the experiment

chamber. There were eight ports into the chamber. Their functions

included: a port to admit the radiation coming from the monochromator,

a high-voltage feedthrough for the photomultiplier tubes, a low-voltage

feedthrough for the photomultiplier tube signals, a port for monitoring

pressure and a mass analyzer connection, a vacuum diffusion pump port,

a port for the cryorefrigerator unit, a roughing line connection, and

a cryopump connection. The position of the first six can be seen in

Fig. 2, and the roughing line connection can be seen on the side of

the bell jar in Fig. 3. A flexible bellows coupling was used between

the light baffle system and the chamber to permit alignment of the

light beam entering the chamber.

The experiment chamber was first evacuated with a six inch
-7
diffusion pump system to a pressure of 4.0xlO torr. A cryopump,









employing LN as the coolant, was then used to bring the chamber
2 -7
pressure to approximately 1.0x10 torr prior to the deposition of

an ice film. The chamber pressure was measured by an ionization

gauge, a thermocouple gauge, and an MKS Baratron capacitance manometer.

The inside of the chamber and all the optical mounts were painted with

a flat black paint, which exhibited low outgassing characteristics, to

reduce the amount of scattered light in the chamber.


Optical Components

Upon emerging from the monochromator, the size and divergence of

the light beam were defined by a system of stops. A rotatable MgF
2
Rochon polarizing prism was used to produce plane polarized radiation.

The unrefracted plane polarized beam was allowed to pass into the

experiment chamber while the refracted beam, which was polarized in a

plane 900 to the undeviated beam, was prevented from entering the

chamber by another system of stops.

A MgF window 1" in diameter and 2 mm thick was used as a beam-
2
splitter with an angle of incidence of 56'. The light reflected from

the beamsplitter was directed onto a UV enhanced mirror which reflected

it toward the cryosurface. An optically flat gold-coated sapphire

substrate was cooled to cryogenic temperatures for deposition of H 0
2
and NH ices. Sapphire was chosen because of its desirable thermal
3
conduction properties. Gold was selected for its moderately high UV

reflection properties and it inertness to the presence of water. Light

was incident on the substrate at two angles, 9.60 and 56.8. The

alignment procedure for establishing these angles is given in Appendix 2.

Radiation was reflected from the ice film onto the photocathodes of

two photomultiplier tubes (hereafter referred to as PMT's). Diffusing









elements were made from sandblasted MgF windows and were used in
2
front of the PMT's to produce a uniform illumination on the exposed

area of the photocathode. The illuminated area was limited by a 0.350"

diameter stop located directly in front of the sapphire window of the

PMT. Each PMT field of view was restricted so that stray scattered

light in the chamber would be undetected.

The photomultiplier tubes, EMR Model 541F-05M-18, are solar-

blind with sapphire windows. They exhibit good spectral response from
0 0
1400 A to 3000 A and have a maximum quantum efficiency of approximately

8%. High voltage was supplied to each PMT by a Fluke 0-6000 volt power

supply. The signal from each of the PMT's was processed by a Fairchild

solid-state preamplifier with a x10 gain and with the output filtered by

an RC circuit having a 10 sec time constant. A long time constant was

necessary because of the low signal to noise ratio which arose because

of low light levels in some parts of the spectrum. The PMT signal,

after amplification and filtering, was displayed on a digital voltmeter

and on a recorder.


Associated Instrumentation

An Air Products Cryo-Tip Heat Exhanger was used to produce the

cooling for the substrate on which the gas was to be deposited. It

can be controlled in temperature from 680K to 1100K within 0.10K and

from 1100K to 3000K within 0.50K. It was found, however, that during

deposition of hexagonal H 0 at 1550K, the temperature could be controlled
2
manually to only 1.50K. The cooling unit operates on a Joule-Thomson

cycle and has a maximum refrigeration capacity of 7 watts at 770K. A

mount made of oxygen-free, high-conductivity cooper was designed to

hold the gold-coated sapphire substrate on the tip of the cooling unit.









A copper-constantan thermocouple was soldered to the tip of the heat

exchanger to indicate the temperature of the Cryo-Tip-substrate system.

The temperature was determined from a potentiometer measurement of the

emf of the thermocouple. The cryosurface could be rotated, and a vernier

divided circle was used to measure the angular settings. This was

critical for optical alignment of the system.

Mass analysis of residual chamber gases and of the source gases

was accomplished by an Ultek Partial Pressure Analyzer (hereafter re-

ferred to as PPA). It had a charge to mass ratio capability from 2 to

100. Since it operated on the principle of a cycloidal mass analyzer,

the partial pressure of a constituent gas having a particular charge to

mass ratio could be read directly from the instrument in N pressure
2
units. Many of the results presented in the next section were determined

using this PPA.


Residual Gases and Source Gases
-6
After the experiment chamber was evacuated to a pressure of 1.0x10

torr by the diffusion pump system, the residual gas, as determined by

the PPA, contained H 0 as its most abundant constituent. The partial
2 -7
pressure of H 0 was 2.9x10 torr. This was 2.5 times higher than that
2 -8
of N The next most abundant species at partial pressures of 8.2x10
2
torr were OH, which was cracked from H 0, and C H at mass 43. The
2 37
detection of C H was probably due to the presence of acetone in the
37
residual gas. Acetone was used as a cleaning agent for all metal sur-

faces placed in the vacuum. The only other constituents having a
-8 -8
significant partial pressure (between 4.0x10 torr and 5.0x10 torr)

were found at mass 41, mass 45 and mass 58. The first two could be









caused by a variety of sources, rotary pump oil, isopropyl alcohol

or vacuum grease. The last one is probably caused by acetone, which

has an atomic weight of 58.

With the LN cryopump in operation the residual gas pressure was
2
reduced 60%. There was a proportional reduction in the partial

pressures of H 0, OH, mass 41, mass 43, mass 45 and mass 58. The
2
partial pressure at mass 28, which is mostly due to N was reduced
2
approximately 25%. The most likely condensible gas at mass 28 was

probably the result of cracking acetone. It was determined that the

use of a cryopump to reduce the partial pressures of condensible

residual gases at 770K was imperative to insure that contaminant ices

represented a small proportion of the desired ice film. Presence of

a substantial amount of contaminant ice could drastically alter the

optical properties of the film and thus give misleading results.

The NH source gas was purchased from Air Products and Chemicals,
3
Inc. and was of ultrahigh purity (99.999%). A mass analysis using the

PPA revealed that the primary contaminant in the source gas was N
2
Nitrogen is a noncondensible gas at 770K when its partial pressure is

less than an atmosphere. No other contaminant could be readily identified

by the PPA as being present in the NH source gas.
3
Conductivity water which was produced by a commercial still

served as the source of water vapor. It was collected in a glass

vacuum trap which was first cleaned with chromic acid and leached with

hot water from the still. Immediately after collecting a sufficient

amount of hot distilled water, the trap was connected to a mechanical

vacuum pump which pumped on the water causing it to boil. This process









removed most of the dissolved gases from the water. A mass analysis

showed that compared to the partial pressure of water vapor the source

gas contained approximately 2.6% N 1.1% CO and 0.3% 0 Carbon
2 2 2
dioxide is the only contaminant gas which has a low equilibrium vapor

pressure at 770K. However, due to using a maximum source gas pressure
-5
in the chamber of 10 torr during ice film deposition, the corresponding
-7
maximum partial pressure of CO would be 10 torr. That pressure is
2
lower than the estimated equilibrium vapor pressure for CO ice at 770K.
2
The greatest contamination of the ice films was due to the residual

condensible gases in the experiment chamber, some of which could not

be identified, rather than contaminants associated with the source gases.

An experimental estimate of the deposition rate for the residual gas
0
during the growth of an ice film was determined to be 14 A/min. It

was also estimated that the NH ice films were from 93% to 99.3% pure.
3
Since the major condensible residual gas in the chamber was H 0, the
2
actual purity of the H 0 ice films was higher than those given for NH
2 3

Experimental Procedures

Determination of the refractive index and extinction coefficient

of a semitransparent film on an absorbing substrate, using the methods

described in Chapter 2, requires that the light reflected at two angles

be detected simultaneously as the film thickness changes at a constant

rate. The setup is shown in Fig. 4, and the signals from the photo-

multiplier tubes are illustrated in Fig. 5. Using the angles a and B

and the fringe periods, At and At Eqn. (17) can be solved for the
1 2
real refractive index. The extinction coefficient for a highly ab-

sorbing film is obtained by using the amplitude of the fringes at two

film thicknesses and the change in film thickness, which is obtained by













B
J

A K

56.80 ,
\ 9.60
C H
LI / H



E
G


D F






A. Perpendicularly polarized radiation
B. MgF beamsplitter
C. UV enhanced mirror
D. PMT 6157
E. Stop to limit illuminated area on PMT
F. V-block mounts for PMT's
G. PMT 9553
H. Diffusing element and stop to limit field
of view and area illuminated on PMT
I. Ice film
J. Gold-coated sapphire substrate
K. Cryo-Tip


Figure 4. Experimental Arrangement for Refractive Index and
Extinction Coefficient Determinations













-.r-
s= -


LO -
r- C-



4-
. S.-
fO


m > 6
F-


At 1


Time

m > 6
F- At -


/ I B = 56.80




LO (C
,r3-


LO S-





Time


Examples of PMT signals used in determining the real refractive index
for ice films that are slightly absorbing.


m = 2


ca = 9.60


m=4


- -


S -S I
max min h
I 1 I


S -S I
max min h


t t. "
1 Time 2

Example of PMT signal used in determining the extinction coefficient
for ice films that are highly absorbing.[h -h =(t -t )xDep. Rate]
2 1 2 1




Figure 5. Typical Photomultiplier Signals used in Refractive Index
and Extinction Coefficient Determinations


r-- r




'- S3


o1 (0









first determining the deposition rate at a nonabsorbing wavelength,

to solve Eqn. (19). A detailed discussion of the procedure used in

conducting these experiments follows.

After the mechanical vacuum pumps had evacuated the experiment

chamber and monochromator to pressures less than 5 pHg, the vacuum

diffusion pump systems were started. Their cryobaffles were filled

with LN after the pressures in both the chamber and monochromator
2 -6 -6
were between 1.0x10 torr and 2.0x10 torr. The ion gauges were de-
-6
gassed, and the pressures dropped into the 10 torr range in approxi-

mately 18 min after the diffusion pumps were turned on. The pressure
-7
in the monochromator continued to slowly decrease to approximately 4.0x10

torr after 1 1/2 hours. The experiment chamber reached a pressure of
-7
6.0x10 torr after an hour of diffusion pump operation.

Hydrogen was bled through the light source cavity at a pressure of

1000 pHg to insure that there were no contaminant gases to cause unstable

spectral features in the light source. The Cryo-Tip was purged with low

pressure nitrogen (approximately 150 psig) to prevent condensible gases,

such as water, from causing blockage by freezing when the Cryo-Tip was

cooled down to LN temperatures.
2
The source gas lines were connected to both the experiment

chamber and a mechanical vacuum pump. There were shutoff valves on

each line. The source gas lines were evacuated by the mechanical

vacuum pump to a pressure of approximately 1 pHg. A purging of the gas

lines for 1/2 hour at a pressure of 1500 pHg always proceeded admitting

the gas into the chamber. This prevented contamination of the source

gas by residual gas in the lines.










Liquid nitrogen was fed into the cryopump to reduce the chamber
-7 -7
pressure from 6.0x10 torr to 1.0x10 torr over a 45 min period.

During that time, the light source was started so that a stable

discharge would be produced by the time the chamber pressure reached
-7
1.0x10 torr. The input power of the stable light source was approxi-

mately 85 watts while the reverse power was usually less than 10 watts.

The photomultiplier tubes were operated most of the time at their

maximum voltages (3600 volts for tube 6157 and 3900 volts for tube

9553). As a result, a 30 min warmup period was required so that the

dark current for each tube had time to decrease to a minimum level.

The desired wavelength was dialed into the monochromator, and the

slits were opened to 2000 pm in width (the height was fixed at 5000 um).

Maximum sensitivity settings on the dual channel chart recorder were

selected to conform to the signal levels from the PMT's. Tube 6157 was

at near normal incidence and a xlO amplifier was used to increase the

sensitivity of the recorder for that tube.

Cryo-Tip cool-down was initiated with a N supply pressure of
2
1500 psig. The only major difference between the procedures for

forming the amorphous phases of H 0 and NH ices and the hexagonal
2 3
phase of H 0 ice was the temperature of the Cryo-Tip during ice de-
2
position. For the amorphous phases of H 0 and NH ices the temperature
2 3
of the Cryo-Tip was approximately 770K and for the hexagonal phase of

H 0 ice the temperature was nominally 1550K 1.50K. Obtaining a
2
stable temperature of 155K required sensitive control of the supply

pressure to the Cryo-Tip. This was used to match the cooling capacity

to the heat load which was caused primarily by the deposition of the

ice film. Only small temperature changes could be tolerated during










hexagonal H 0 ice deposition due to the rapidly changing equilibrium
2
vapor pressure of the ice with temperature. Thus, a change in

temperature of more than 5K would cause an appreciable change in

the real refractive index of the ice.

Once the Cryo-Tip was stablilized at the desired temperature,

gas deposition was begun. The chamber was allowed to remain open to

the diffusion pump system so there would be no increase in the

concentration of contaminant gases during deposition of the ice

films. With the source lines still being purged, the valve to the

experiment chamber was opened until the chamber pressure was increased
-6
to approximately 0.5x10 torr less than the desired deposition

pressure. The valve through which the gas was being pumped by the

mechanical pump controlled the backpressure of the source gas. This

was closed until the chamber pressure increased to the desired value.

All further pressure adjustments were accomplished by manipulating

the backpressure valve. This method of differentially pumping the

source gas prevented a pressure surge when the valve to the experi-

ment chamber was opened initially, and made it possible to control

the backpressure of the source gas which in turn resulted in good

control of the deposition pressure. An output signal from the ion

gauge control unit was displayed on a chart recorder during each

experiment. Pressure control was normally within 0.5% of the

desired deposition pressure. The optimum deposition pressure was

dictated by several factors: the wavelength of light used, the

refractive index of the film, the system time constant, and

contamination of the film by condensible residual gases in the

chamber. The film was to be deposited as fast as possible to









decrease the contamination of the film. The time constant of the

system was required to be long to increase the signal to noise ratio

when low light levels were encountered this was true much of the

time. The wavelength of the radiation that was used and the re-

fractive index of the film at that wavelength also helped to deter-

mine the fringe period, e.g., the shorter the wavelength and the

larger the refractive index, the shorter the fringe period becomes.

The optimum fringe period was a compromise between the above factors

and was taken as approximately 1 min. Trial experiments were run for

each film to establish a chamber deposition pressure which would

yield the optimum fringe period.

Depending on the scattering and absorption properties of the ice

film, two to four sets of interference fringes at different wavelengths

were recorded during the deposition of one ice film. Amorphous NH and
3
hexagonal H 0 ices were so highly scattering that in the near-normal
2
incidence case only approximately 12 periods could be readily detected

in a spectral region where there was no absorption. For these ices,

usually two wavelengths were examined during each experiment with an

average of six periods at each wavelength. It was learned by experience

that at least six periods were necessary to insure an accurate determi-

nation of the fringe period. Amorphous H 0 ice was the least scattering
2
of the ices investigated so that as many as four wavelengths could be

examined during the growth of one ice film.

When an extinction coefficient was to be determined, the same

procedure outlined above was followed with only one difference. Since
5 -1
in a region of high absorption, e.g., approximately 2.0x10 cm only

about two highly damped fringes were detectable, the real refractive










index could not be determined. Because it was necessary to know the

change in thickness of the film so that the extinction coefficient

could be calculated by Eqn. (19), the wavelength was changed, while

the chamber pressure was held constant, to one where the refractive

index had been previously determined. Using the fringe period and

refractive index at that wavelength the deposition rate could be

determined using Eqn. (15). The change in film thickness could be

readily determined once the deposition rate was known.

In preparation for the next experiment, the PMT's source gas,

Cryo-Tip and cryopump were turned off, and the chamber gate-valve was

closed. Since the Cryo-Tip and ice film would take an average of

3 1/2 hours to warmup to room temperature in a vacuum, dry N gas
2
was admitted into the chamber until the pressure was approximately

3/4 atm. This pressure was used so that 0-ring seals in the chamber

would not be broken. At this high pressure the Cryo-Tip warmed up to

above 10C in less than 25 min. The chamber was then roughed out

with a mechanical vacuum pump to approximately 20 pHg in 15 min at

which time the gate-valve was opened. The diffusion pump again
-6
lowered the chamber pressure into the 10 torr range prior to the

growth of a new film.













CHAPTER IV
UV OPTICAL CONSTANTS


Amorphous Water Ice

The results of the determination of the real refractive index

for amorphous water ice are given in Fig. 6 and in Table 2. All the

experimental data plotted in Fig. 6 are average values of the re-

fractive indices obtained at each wavelength, and the error bars re-

present the standard deviation from the average values.

The experimental values of the refractive index for amorphous

H 0 ice in the visible region of the spectrum, as established by
2 23
Seiber et al., are also shown in Fig. 6. An extrapolation of

their values to ultraviolet wavelengths agrees well with the experi-

mental values determined in this investigation. Also plotted in that

figure are the refractive indices for amorphous H 0 ice determined by
11 2
Daniels using an electron energy-degradation experiment. Daniels'

values are expected to be the least accurate when the absorption of

the film becomes small, as is the case when the wavelength is greater
o
then 1700 A. For comparison, the theoretical refractive indices for
28
hexagonal H 0 ice given by Greenberg are also shown. The differences
2
in the refractive indices between Greenberg's values and the experi-

mental results are primarily due to the difference in the densities
between the two ice phases. The refractive index, n, increases with

greater density, p, assuming that the polarizability of the molecules

are the same in the two phases. The Lorentz-Lorenz equation relating





1.50


1.45 -



m
1.40





1 .35





1.30





1.25 I I III
1200 1400 1600 1800 2000 2200 2400 2600 2800 3000


3200 3400 3600 3800 4000 4200 4400


Wavelength (


Figure 6. Refractive Index of Amorphous Water Ice










Table 2


Wavelength

3200


3100

3000

2900

2800

2750

2600

2500

2400

2300

2200

2100

2050

2000

1900


1800


1750

1700


1650

1610


Real Refractive Index of Amorphous Water Ice

Refractive Index Average Standard
Measurements Refractive Index Deviation

1.2647 1.2751 1.2672
1.2744 1.2710 1.2705 0.0040

1.2781 1.2781

1.2692 1.2692

1.2752 1.2752

1.2710 1.2710

1.2758 1.2758

1.2698 1.2698

1.2841 1.2818 1.2830

1.2832 1.2832

1.2897 1.2812 1.2854

1.2922 1.2922

1.3085 1.2913 1.3088 1.3029 0.0082

1.3146 1.2993 1.3213 1.3117 0.0092

1.3313 1.3245 1.3233 1.3264 0.0035

1.3380 1.3265 1.3110
1.3214 1.3427 1.3279 0.0114

1.3601 1.3796 1.3338
1.3771 1.3626 0.0183

1.3991 1.3730 1.3860

1.3796 1.3751 1.3670
1.3917 1.3784 0.0089

1.4900 1.4146 1.4523

1.4955 1.4421 1.4665
1.4929 1.4956 1.4488
1.4317 1.4675 0.0253









2 2
this dependency is (n 1) / (n + 2) p. This relationship only

applies at wavelengths that are far removed from the wavelength regions
23
where the material absorbs. Seiber et al. established, in the visible

region of the spectrum, that the density ratio, p /p for amorphous,
A H
p and hexagonal, p ice was 0.884. Determination of this density
A H
ratio using the Lorentz-Lorenz relationship becomes less accurate as

the wavelength becomes shorter. This is because the absorption onset
o
for H 0 ice is at 1800 A, as is indicated by the molar absorption
2 10
coefficient curve shown in Fig. 7. The molar absorption coefficients

for water vapor are also plotted in that figure.

An important observation can be made by comparing Figs. 6 and 7.

The refractive index of the amorphous ice is seen to increase quickly
o
shortward of 2400 A and yet the absorption in the ice does not begin
0
until 1800 A. This may be an important factor in some planetary cloud

modeling investigations because a change in the refractive index, e.g.,

An = 0.05, of a spherical particle with no change in the absorption

coefficient can significantly alter the light scattering characteristics

of the particle.

The experimental errors involved in establishing the refractive

index using Eqn. (17) are due to: the nonmonochromaticity of the
o 0
radiation (53 A resolution was used at all wavelengths except 1610 A
o
where the light source was very bright so that a 16 A resolution

could be used), the change in the refractive index of the film over

the wavelength interval, the divergence of the beam, error in measuring

the fringe periods, error in maintaining a constant film deposition

rate, and error in the angle of incidence. All of the experimental

errors except those due to angle of incidence are readily evaluated by






40





4







-----"
10










EU



.r--
ci 3


S10


5-\




.-,
o

c 2


Water Vapor
-o










10


0
1400 1500 1600 1700 1800
o
Wavelength ( A )


Figure 7. Molar Absorption Coefficients for Water Ices
and Water Vaporio









examining the standard deviation exhibited by independent -determina-

tion of the refractive index at the same wavelength. It was found

(see Appendix 2) that the angles of incidence used in this investi-

gation were 9.60 0.20and 56.80 0.10. The error in the refractive

index resulting from an uncertainty in the angle of incidence was

determined to be less than the standard deviation of the refractive

indices (see Appendix 3), and thus the error bars used in Fig. 6 are

large enough to included all the experimental errors.

Ultraviolet absorption coefficients for amorphous H 0 ice are
2
given in Fig. 8. The results of the electron energy-degradation
11
experiments carried out by Daniels and the absorption coefficients
10
determined by Dressler and Schnepp are plotted in the figure
-1 -1 -1 3
(o[cm ] = e[a mole cm ]xp[gm/t]/M.W.,where p=0.917x10 gm/A and

M.W.=18 for H 0). Two determinations of the extinction coefficient
2 o o o
were made in this investigation at 1475 A, 1490 A and 1610 A, and

the average is shown on the graph. The positive error bar indicates

the theoretical error in using the approximate approach of Eqn.(19)

(see Appendix 3) and the negative error bar reveals the error between

the lowest extinction coefficient and the average value. It should

be emphasized that the extinction coefficient represents the upper

limit for the absorption coefficient at that wavelength. Due to
o
experiment limitations, 1475 A was the shortest wavelength which
0 o
could be investigated with reliable results. At 1475 A and 1490 A
o o
the wavelength resolution was 53 A. Only one wavelength, at 1610 A,

was investigated using narrow slit widths. As can be readily seen

in Fig. 8, the agreement between the extinction coefficient obtained
11
in this investigation and the absorption coefficients of Daniels is

















10 \






I \ -
E
U 1
4
10 -



S-
o
"G \ \






\ -
A Experimental Data
3 11



10 Daniels
\



10



S--- Dressler and Schnepp

4 Dressler and Schnepp's Values
a_ \






3at 1475
10 Daniels 1-










2
10
---* Dressler and Schnepp \

---* Dressler and Schnepp's Values
Normalized to Experimental Data
at 1475 a





1300 1400 1500 1600 1700
o
Wavelength ( A )

Figure 8. Absorption Coefficients for Amorphous Water Ice










extremely good. Dressier and Schnepp's values are larger by approxi-
o
mately a factor of two at 1475 A and smaller by approximately a factor
o
of two at 1610 A. Dressier and Schnepp's relative absorption coefficient
0
curve normalized at 1475 A to the upper limit for the absorption

coefficient established in this work is shown in Fig. 8. It is expected

that this new curve is a more accurate representation of the actual

absorption coefficient curve for amorphous H 0 ice than was given
2
previously by Dressier and Schnepp.


Hexagonal Water Ice

The real refractive indices for hexagonal water ice are shown in

Fig. 9 and are tabulated in Table 3. The average of the refractive

indices obtained at each wavelength is plotted, and the error bars

represent the standard deviation of those refractive indices.

There are no other known experimental values for the UV refractive
28
index of hexagonal H 0 ice. The theoretical curves of Greenberg and
29 2 29
Popova et al. are also plotted in Fig. 9. Popova et al. used a

Kramer-Kronig inversion technique employing the absorption coefficient
10
for hexagonal H 0 ice given by Dressier and Schnepp. The experimental
2
values of the refractive index do not strongly deviate from the curve
o o
reported by Greenberg between 2000 A and 2400 A, and yet there are

other definite, repeatable differences in the two curves. The experi-

mental values are consistently higher than Greenberg's curve and lower

than Popova's values. The major deviation from the theoretical values
0 0
reported by Greenberg is between 1610 A and 1800 A. In this wavelength

region the experimental data clearly show a definite increase in the
0
refractive index while Greenberg's values decrease shortward of 1800 A.







1.8



1.7 \ Experimental Data
1\ 28
\ Greenberg
29
1.6 \ Popova et al.
















1.2 I IIIIIII

1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
o
Wavelength ( A )


Figure 9. Refractive Index of Hexagonal Water Ice
















Table 3


Real Refractive Index of Hexagonal Water Ice


Wavelength


Refractive Index
Measurements


Average
Refractive Index


1.3452 1.3286 1.3344
1.3499 1.3479 1.3387


1.3515 1.3552
1.3449 1.3487

1.3796 1.3701
1.4041 1.3496

1.3638 1.3671
1.3953 1.3916


1.4414
1.4566
1.4500

1.5368
1.6268
1.6756


1.4782
1.4930
1.4276

1.5875
1.7566
1.7148


1.3583


1.3632


1.4136


1.5150
1.4195


1.7568
1.5934


Standard
Deviation


3200


2800


2400


2100


1800



1611


1.3408


1.3517


1.3733


1.3863



1.4602



1.6560


0.0076


0.0047


0.0182


0.0186



0.0308



0.0798








This increase in the refractive index could have a significant effect

on the modeling of hexagonal H 0 ice cloud reflectance properties.
2
All the errors in the determination of the refractive index for

hexagonal H 0 ice are the same as those discussed for amorphous H 0
2 2
ice.

Dressler and Schnepp's absorption coefficients for amorphous
o 5 -1
H 0 ice were consistently measured shortward of 1500 A to be 4.59x10 cm
2
while the values reported for hexagonal H 0 ice in the same range
5 -1 2 5 -1 10
were scattered between 2.95x10 cm and 4.59x10 cm Due to the

optical properties of the film and substrate, only very weak fringes
o
could be detected at 1490 A for hexagonal H 0 ice. A qualitative assess-
2
ment of the extinction coefficient revealed that it was on the order of
5 -1
1.0x10 cm It is felt that this value may have been underestimated

as much as a factor of two, but not more since the fringes did not give

the appearance of damping more rapidly than those for the amorphous H 0
5 -1 2
ice. An upper estimate for the absorption coefficient of 2x10 cm is

still less than half of the value given by Dressler and Schnepp for both
o
H 0 ice phases. At 1611 A, better fringe visibility allowed an accurate
2
calculation to be made of the extinction coefficient. It was determined
4 -1
to be 4.64x10 cm which is a factor of three higher than the value

given by the curve in Ref. 10. It is interesting to note, however, that

the actual data points established by Dressler and Schnepp at approximately
o 4 -1 4 -1
1600 A show 1.53x10 cm for amorphous water ice and 2.85x10 cm for

hexagonal water ice. This is the same trend found in this investigation

only Dressler and Schnepp's values are approximately a factor of two

smaller. Assuming that the maximum absorption coefficients reported by

Dressler and Schnepp for hexagonal H 0 ice are a factor of two too
2
large, the theoretical predictions of the index of refraction by









29
Popova et al. would be too large also. This is because the larger

the absorption coefficient is the more quickly the refractive index

increases as the wavelength decreases toward onset of absorption.

It follows then that a smaller absorption coefficient would decrease

this effect and better agreement would be obtained between the experi-

mental data and the values reported in Ref. 29.

Employing the Lorentz-Lorenz relation discussed in the previous

section, an estimate of the density ratio between amorphous and

hexagonal H 0 ices was made using the refractive indices determined for
2 o
each ice phase at 3200 A,p /p = 0.81 + 0.03. This is approximately
A H 23
8% less than the value established by Seiber et al. in the visible

region of the spectrum. This discrepancy is felt to be primarily due

to the error in using the Lorentz-Lorenz equation at a wavelength which
o
is within 1400 A from where H 0 ices start absorbing.
2

Amorphous Ammonia Ice

The real refractive index of amorphous ammonia ice as determined

in this investigation is presented in Fig. 10 and in Table 4. Again

the experimental data shown in the figure are the average values of

the refractive indices determined at each wavelength, and the error

bars are their standard deviation. A theoretical calculation of the

refractive index is also plotted in Fig. 10 for comparison.

The theoretical values for amorphous NH ice are based on calcula-
3
tions using Cauchy's formula and the Lorentz-Lorenz equation. Cauchy's

formula relates how the refractive index for a gas, n, changes with
-5
wavelength, A; n = 1.0 + A(1+B/X2). For NH gas A = 37.0x10 and
-3 30 3
B = 12.0x10 The Lorentz-Lorenz equation discussed previously can





1.9





1.8 T Experimental Data


U Theoretical Calculations


S1.7


S-o


- 1.6



*-- *
1.5





1.4 I I I I
1800 2000 2200 2400 2600 2800 3000 3200
o
Wavelength ( A )


Figure 10. Refractive Index of Amorphous Ammonia Ice









Table 4


Wavelength

3200


3100

3025

3000

2900

2800


2750

2600


2500


2400


2200

2100


2000


1950


1925


Real Refractive Index

Refractive Index
Measurements

1.4894 1.4814 1.4841
1.4849 1.4844

1.4982

1.5055

1.5077 1.4900

1.5331

1.5517 1.5295 1.5053
1.5646

1.5515 1.5395

1.5506 1.5365 1.5322
1.6060

1.5450 1.5473 1.5859
1.5757

1.5900 1.6115 1.6188
1.5811 1.5776

1.6784 1.6542

1.7216 1.6907 1.6908
1.6949 1.7119

1.7896 1.7887 1.7707
1.7302 1.8052

1.7840 1.7794 1.7990
1.8135

1.8079 1.8304 1.8085
1.9037 1.7832


of Amorphous Ammonia Ice

Average Standard
Refractive Index Deviation


1.4848 0.0026

1.4982

1.5055

1.4988

1.5331


1.5378 0.0226

1.5455


1.5563 0.0295


1.5635


1.5958 0.0165

1.6663


1.7020 0.0125


1.7769 0.0258


1.7940


1.8267 0.0413









be used to determine the refractive index for a solid, n when the
s
refractive index for the gas, n the density of the gas, p and the
g g
density of the solid, p are known, assuming that the polarizability
s
of the molecules are the same in both phases. Thus, n = {[(p /p ) C +
1/2 s g s
2.0] / [(p /p ) C 1.0]} where C = (n2 + 2.0) / (n2 1.0). For
g s -3 g g
NH p = 0.771x10 gm/ml and p = 0.817 gm/ml. It can be seen in
3 g s
Fig. 10 that the agreement between theoretical and experimental values
0 o
is quite good between 3000 A and 3200 A. The theoretical calculations

become more in error toward shorter wavelengths as the simplified

equation presented above becomes less accurate.

The only other known experimental determination of the refractive

index for NH ice was for the cubic phase at the sodium D wavelength
o 3 31
(5892 A) reported by Marcoux. He established the refractive index

to be n = 1.415 0.005. No meaningful comparison can be made between

this value and the experimental values presented in this investigation

for amorphous NH ice.
3
Examination of the molar absorption coefficients for amorphous NH
3
ice and NH gas given in Fig. 11 and the measured refractive indices
3
given in Fig. 10 also indicates that the refractive index changes

significantly with wavelength when there is little or no absorption by

the gas or ice. The determination of ammonia ice cloud reflectance

characteristics could depend a great deal on this information.

Two measurements of the extinction coefficient for amorphous NH
o 3
ice at 1760 A were made. The average extinction coefficient was found
5 -1
to be 2.46x10 cm This represents only 27% of the value of Dressler
10
and Schnepp's absorption coefficient. A measurement was made of the
o o
extinction coefficient at 1600 A with 21 A resolution to determine







10













10 II
h I






4


















SAmorphous Ammonia Ice \
S2\




s A Cubic Ammonia Ice I

~ Average Absorption Coefficient .
0














1200 1400 1600 1800 2000 2200

o
Wavelength ( A )
Figure 11. Molar Absorption Coefficients for Ammonia Ices and Ammonia
Gas0









whether the relative curve given in Ref. 10 was reasonable in light

of the NH gas absorption minimum there. The experiment revealed that
3
the absorption coefficient for the ice did not exhibit a large reduction

in absorption as the gas did. It also substantiated the value for the
0
extinction coefficient determined at 1760 A. Determination of the
0
extinction coefficient at wavelengths longward of 1760 A would not

have been conclusive because the absorption coefficient was changing

too rapidly with wavelength. Using the relative absorption curve
5 -1
reported by Dressler and Schnepp and normalizing it to 2.4x10 cm at
0
1760 A resulted in the curve presented in Fig. 12 (an ice density of
3
0.817x10 gm/A was used in the conversion of the NH molar absorption
3
coefficient). The normalized curve is expected to more accurately

represent the true absorption coefficients for amorphous NH ice than
3
that previously reported in Ref. 10.

















10 -









E
-.-- 4
10


4-


0
10
o-

o A Average of Experimental
: 3 Data at 1760 A
10


Dressier and Schnepp's
Absorption Coefficients
Normalized at 1760 A




2
10 I I I I
1400 1600 1800 2000 2200
o
Wavelength ( A )


Figure 12. Normalized Absorption Coefficient Curve for
Amorphous Ammonia Ice












CHAPTER V
CONCLUSIONS

Real refractive indices were determined for amorphous and hexagonal
o o
H 0 ices between 1611 A and 3200 A and for amorphous NH ice between
2 o o 3
1925 A and 3200 A. Extinction coefficients for amorphous H 0 ice and
o o 2
amorphous NH ice were established at 1475 A and 1760 A, respectively.
3
Amorphous H 0 ice exhibited a slowly increasing refractive index
2 o o
from 1.270 to 1.292 as the wavelength decreased from 3200 A to 2200 A.
o
Shortward of 2200 A the refractive index increased rapidly to 1.468 at
o
1611 A. This rapid increase in the refractive index longward of the
0
onset of absorption for amorphous H 0 ice at 1800 A could cause signifi-
2
cant changes in the nature of H 0 ice cloud or frost reflectances between
o o 2
1800 A and 2200 A. Application of these data to modeling H 0 ice clouds
2
or frosts may help to explain recent experimental reflectance curves
1
obtained for amorphous H 0 frost (see Fig. 13). An upper limit for
2
the absorption coefficient as established by the extinction coefficient
5 -1 o
was determined to be 1.96x10 cm at 1475 A. This is in agreement
11
with the value measured by Daniels and less than one-half the value
10
found by Dressler and Schnepp. Normalization of Dressier and Schnepp's
0
relative absorption curve to the above value at 1475 A results in a more

accurate representation of the absorption coefficients for amorphous H 0
2
ice.

The refractive index of hexagonal H 0 ice was found to have the
2 28
same general trend as the theoretical curve reported by Greenberg







100
90
80
70

60 -

50 -

40


30



20






u 10
9 -
8
7 Amorphous Water Frost
6

5

4 A Hexagonal Water Frost

3



2







1600 1800 2000 2200 2400 2600 2800
o
Wavelength ( A )


Figure 13. UV Reflectances of Water Frosts









0
longward of 1800 A, but the experimental values were always slightly
0
higher than the theoretical calculations. Also, shortward of 1800 A
28
Greenberg's values showed a decreasing trend while the experimentally

determined refractive index rapidly increased. This increasing re-

fractive index was more in agreement with the theoretical curve of
29
Popova et al. The experimental values slowly increased from 1.341
o o
at 3200 A to 1.403 at 2000 A, and they then rapidly increased to 1.656
0
at 1611 A. This rapid increase in the refractive index longward of
0
the onset of H 0 ice absorption at 1800 A may help explain some of
2
the pre-absorption features seen in the hexagonal H 0 frost reflectance
2
shown in Fig. 13. An upper limit of the absorption coefficient for
o
hexagonal H 0 ice established in this investigation at 1490 A is less
2 10
than one-half of the value given by Dressler and Schnepp.

Amorphous NH ice showed a steadily increasing refractive index
3 o o o o
from 1.485 at 3200 A to 1.596 at 2400 A. From 2400 A to 1925 A the

refractive index rapidly increased to 1.827. Amorphous NH frost does
3
not have prominent pre-absorption features as does amorphous and hexagonal

H 0 frosts (see Fig. 13 and 14), however, the rapidly changing refractive
2 o
index longward of the onset of absorption at 2200 A should still have an

influence on the resulting cloud or frost reflectance curves. Experi-
o o
mental refractive indices between 3000 A and 3200 A are in good agree-

ment with theoretical values calculated using Cauchy and Lorentz-Lorenz

relationships.
o
The extinction coefficient for amorphous NH ice at 1760 A was
5 -1 3
determined to be 2.46x10 cm This value was approximately one-
10
fourth of Dressler and Schnepp's estimate. The relative absorption
0
curve given in Ref. 10 was then normalized at 1760 A to the value given





57
100
90 -
80 ,-e
70 -
60 -
50 -

40 -
I
30
I

20 -



01

1u II
9 1
9
a 8
4--
7 7
6
5
SAmorphous Ammonia Frost
4 -


3 A Cubic Ammonia Frost



2





1 I I I I I
1600 1800 2000 2200 2400 2600 2800
o
Wavelength ( A )
1
Figure 14. UV Reflectance of Ammonia Frosts






58

above. This resulted in a better estimate of the absorption curve

for amorphous NH ice.
3
No success has been achieved in determining the refractive index

for cubic NH ice. The high equilibrium vapor pressure of NH ice
3 3
deposited above 1250K introduces many new experimental problems which

have not yet been solved.




































APPENDICES














APPENDIX I
DETAILS OF EXPERIMENTAL COMPONENTS


Light Source
32
The light source was based on an Evenson type microwave cavity.

A Scintillonics 2450 MHz microwave generator was used to power the gas

discharge. The discharge gas was H which was supplied at a pressure
2
between 500 pHg and 1500 uHg. Figure 15 shows the continuum and line

flux resulting from the discharge. The N contamination in the labora-
2
tory grade H caused much of the line structure in the spectrum from
o 2 o
2900 A to 3400 A.

A Tesla coil was used to initially excite the H discharge. Tuning
2
of the Evenson cavity with the H discharge in operation was effected by
2
adjusting a coupling slider and a tuning stub until a voltage standing

wave ratio of less than two was achieved with an input power of approxi-

mately 70 watts. The light source was stable in its output power and

spectrum over long periods of time after an initial warmup of one-half

hour.


Monochromator

The monochromator used was a 0.3 m McPherson Monochromator, Model

218. The features of this instrument are:

1. 0.3 m focal length
2. 1200 grooves per mm snap-in grating
3. f/5.3 exit beam o
4. maximum resolution of 0.6 A
5. independently adjustable slit dimensions












10 peak at ( 1610,16.2



8 o
S5 A Resolution


- -



4 4




2



0 I I I I I I I I I
1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400
o
Wavelength ( A )
33
Figure 15. Hydrogen Light Source,Spectral Distribution of Intensity









A 6" Norton oil diffusion pump system backed by a Duo-Seal 5.6 cfm

vacuum mechanical pump was employed to evacuate the monochromator to a
-7
pressure of 4.0x10 torr. A Chevron cryobaffle filled with LN was
2
used above the diffusion pump as a cold trap. The mechanical pump and

diffusion pump were separated by a Veeco coaxial foreline trap to

prevent backstreaming of the mechanical pump oil into the monochromator.

Experimental Chamber
-7
Chamber pressures of 1.0x10 torr were produced by a 6" Norton oil

diffusion pump system and a LN cryopump. A 10.6 cfm Duo-Seal mechanical
2
vacuum pump was used to back up the diffusion pump. A Chevron cryobaffle

and Veeco foreline trap were also employed as in the case of the monochro-

mator. An air-operated gate valve was utilized to safeguard the chamber

against backstreaming of mechanical pump oil due to a power failure.

A valve system allowed the chamber diffusion pump to be backed by

the 5.6 cfm pump while the 10.6 cfm pump was used to differentially

pump the source gas lines.

The oil used for both diffusion pumps was Dow Corning-705, and the

vacuum grease used exclusively was Apiezon L.

The LN cryopump consisted of a coil of stainless steel tubing
2
cooled to 77K. The residual chamber pressure was reduced by as much as

a factor of four by cryopumping of condensible gases.


Optical Components

A MgF Rochon polarizing prism with the dimensions 12 mm x 12 mm x
2
50 mm, was purchased from Continental Optical Corporation. The

divergence angle between the two diverging plane polarized beams which
o
the prism produces was specified to be 30 at 2000 A. Tests were conducted










using two Rochon prisms to determine the degree of plane polarization

of the exiting beams. It was found to be in excess of 99.97%. The

light which was detected when the prisms were cross-polarized may not

have been a result of inefficiency of the prisms but due to depolariza-

tion of portions of the beam by scattering from the edges of stops in

the system.

The gold-coated sapphire substrate used for the ice film deposition

had a surface polish of better than one microinch and was flat to less
0
than 10 wavelengths per square inch at 5892 A. Its dimensions were

1"x2"x0.040"thick, and it was manufactured by the Adolf Meller Company.













APPENDIX 2
ALIGNMENT PROCEDURES

A primary objective of the alignment was the accurate determina-

tion of the angles of incidence for the radiation onto the ice film.

Knowledge of these angles is critical to the calculation of the optical

constants for the ice.

The tops of both the monochromator and experiment chamber were

removed for access to internal optical components. A flashlight, which

was used for a light source, was directed by use of a mirror onto the

monochromator grating which was set to zero order. The grating re-

flected the light onto the telescope mirror in the monochromator which

in turn illuminated the exit slit. The dimensions of the exit slit were

2000 um in width and 5000 um in height. A system of stops which limits

the size and divergence of the light beam leaving the exit slit was

rigidly fixed to the monochromator. Provided that the light source is

positioned so the exit slit and stops are overfilled, the characteristics

of the beam entering the experiment chamber are completely determined by

the monochromator. A flexible coupling which connected the tube con-

taining the stops and the chamber allowed the direction of the beam

entering the chamber to be controlled by moving the monochromator.

Initially, the monochromator was positioned to direct the light

beam onto the center of the gold-coated sapphire substrate. Small

adjustments of the rotational position of the Cryo-Tip and monochro-

mator position were necessary to make the light beam reflect back onto

itself. The light beam was then considered to be at normal incidence.









The angular setting of the Cryo-Tip was indicated by a vernier

divided circle, which could be read to + 0.10. Establishment of the

horizontal divergence of the beam was accomplished by inserting a

razor into the beam just as the beam entered the chamber. With the

razor's edge in the vertical position, the Cryo-Tip was rotated to

determine at what angle the light reflected from the substrate could

not be seen on the razor as the razor was moved horizontally through

the beam. This established the condition where the most horizontally

diverging part on one side of the beam was made to be incident normal

to the reflecting surface (see Fig. 16A). This was done with the razor

on each side of the beam. The angular separation of the two Cryo-Tip

settings determined the horizontal divergence of the beam, and the

average of the Cryo-Tip settings was considered to be the angular

setting for normal incidence.

The vertical divergence of the beam was established by measuring

the maximum vertical displacement of the light beam reflected back onto

a horizontal razor as the razor was moved vertically through the beam.

The position of the razor's edge and reflecting substrate determined the

divergence angle of the beam in the vertical plane. Figure 16C illustrates

the technique.

The Cryo-Tip was rotated through 570 to the approximate position

it would assume during the experiments. The axis of rotation was con-

sidered to lie parallel to the plane of the substrate. A sample

calculation was made to determine the error in the beam's angle of

incidence if the Cryo-Tip were rotated 600 and the axis was 3' from

being parallel to the plane of the substrate. The error in the angle

of incidence as determined by the rotation of the Cryo-Tip was less than








normal incidence
position of substrate
vacuum chamber wall ,







razor
horizontal
divergence
half-angle
Top View

A.


vacuum chamber wall
MgFZ
beamsplitter


normal incidence position
of substrate


horizontal
divergence
half-angle


)! UV enhanced mirror

Top View

B.


vacuum chamber wall


8.375"

Side View

C.


Figure 16. Alignment Techniques


razor


substrate


I










0.10 of a degree, which is within the measurement accuracy of the

divided circle. It was concluded that since the proceeding example

was considered to be an extreme case, the angle of incidence of the

beam can be accurately determined by the Cryo-Tip angular settings.

A beamsplitter and UV enhanced mirror were placed into a

position which would direct a second light beam onto the center

of the reflecting substrate at near-normal incidence. A technique

similar to that given above for the first beam was used to establish

the horizontal and vertical beam divergences and the normal incidence

angular setting for the second beam. The method of determining the

horizontal beam divergence is illustrated in Fig. 16B.

The angles of incidence for the two beams were established by

taking the final angular setting of the Cryo-Tip and substracting

it from the normal incidence angular settings of the two beams. The

incidence angles were a = 9.60 and B = 56.80 with horizontal half-angle

divergences of 0.4 and 0.20,respectively. The vertical divergences

were +0.340 and -0.17 at a and 0.260 at B, where the positive and

negative signs designate divergence up and down, respectively.

Increasing beam divergence decreases the visibility of the fringes

and thus affects the ability to measure the average fringe periods, but

it does not change the average period, which is indicative of the

average angle of incidence for the beam.

The light which was incident on the substrate at the oblique angle

was estimated to be at least 90% perpendicularly polarized to the plane

of incidence. The slight depolarization of the plane polarized light

beam entering the chamber was due to the birefringent MgF beamsplitter.
2
The fringe periods are not affected by the polarization of the beam, but






68


the reflectivity of the ice film decreases with an increasing percentage

of parallel polarized light in the beam. It is therefore desirable to

have the incident light mostly perpendicularly polarized.

















APPENDIX 3
ERROR ANALYSIS


Perturbation Derivation

The approximations for u v and 1 derived in Chapter II
2 2 12
were evaluated to determine their maximum errors using the limitations

that n > 1.25, n K < 0.06, 0 < e < 600, and n = 1.0. As was noted
2 22 1- 1- 1
before, the expressions for u and v given in Eqns. (7) and (8),
2 2
respectively, are exact for the normal incidence case, e = 0,
1
regardless of the values for n K or n At e = 600 the approximate
2 2 1 1
equations for u and v have their greatest error, within the limitations
2 2
given above, for n = 1.25 and n K = 0.06. Even at these extreme values,
2 2 2
Eqns. (7) and (8) are in error by only 0.12% and 0.20%, respectively.

The approximation for c which is given in Eqn. (9), has a maximum
12
error of 1.49% at e = 0 and 1.39% at e = 600, when n = 1.25,
1 1 2
n K = 0.06, and n = 1.0. If the maximum value for n K can be re-
22 1 22
duced to 0.04, the error at e = 00 is reduced to 1.1%. The maximum
1
error for the small angle approximation of 1 occurs at e = 0.
12 1
When n = 1.25, n K = 0.06, and n = 1.0, the maximum error is 2.24%,
2 22 1
and if n K is reduced to 0.04, the maximum error becomes 1.00%. It is
22
reasonable to assume that all the approximate expressions derived for

u v and ( under the limitations stated above were of acceptable
2 2 12
accuracy to be employed in subsequent derivations.









The validity of the assumptions which were made in the derivation

of Eqn. (13) for e is now discussed in terms of the actual optical

constants of the ice films. The assumptions used were

a. 2u e is a small angle
2
1. cos(2u e) 1.
2
2. sin(2u e) = 2u e.
-4v e 2 2 -2v c
b. e 2 1 4v e (it follows that e 2 = 1-2v e)
2 2
c. Linearization of perturbation equation: 1 >> 18v J.
2
d. Elimination of v2 term in coefficient of E: 1>> 3(v /u )2.
2 2 2
e. 1 >> 1 sin(2u e ), and 1 is a small angle.
12 2 12 o
Evaluation of Eqn. (13) was made at 2400 A using the optical constants

of amorphous ammonia ice, NH -A, amorphous water ice, H 0-A, and hexagonal
3 2
water ice, H 0-H. Results similar to those found in Table 1 for H 0-A
2 2
were calculated for the other ices. The maximum values of E are used in

evaluating assumptions (a) to (d) for each ice. The results of these

calculations are presented in Table 5. It was assumed that the maximum
0
extinction coefficient caused by absorption or scattering at 2400 A was
4 -1
2.1xl0 cm (n K = 0.040).
2 2
Only assumptions (a.l) and (c) given above introduce errors of

greater than 1% to the determination of e in Eqn. (13), and their

largest error can be seen for H 0-A at e = 57. If the maximum e used
2 1
in the evaluation of the approximations was taken from the third maximum

of the reflectivity curves (see Table 1), the revised evaluations are

given under *H O-A in Table 5. The error in approximation (a.l) is
2
then less than 1% while that for (c) is 2.4%. This error in approximation

(c) is not significant and can be ignored for all practical purposes in

the determination ofe .









Table 5


n
2
e [deg]

u
2
V
2
S[rad]
23
E

2u e
2
sin(2u E)
2
cos(2u E)
2
18v2C I
3(v /u )2
2 2
1-4v E
2
-4v e
e 2


Notes: a)

b)

c)

d)

e)


Evaluation of Assumptions in Perturbation Derivation

NH -A H O-H H 0-A
3 2 2

1.5958 1.3733 1.2832


10

1.5863

0.0402

1.2653

-0.0302

-0.0958

-0.0957

1.0000

0.0097

0.0019

1.0049


57

1.3576

0.0470

1.0872

-0.0404

-0.1097

-0.1095

0.9940

0.0152

0.0036

1.0076


10

1.3623

0.0403

1.0883

-0.0527

-0.1436

-0.1431

0.9897

0.0170

0.0026

1.0085


1.0049 1.0076 1.0085


Wavelength used was 2400


57

1.0875

0.0505

0.8742

-0.0749

-0.1629

-0.1622

0.9868

0.0302

0.0065

1.0151


1.0152


10

1.2714

0.0404

1.0144

-0.0725

-0.1844

-0.1833

0.9830

0.0234

0.0030

1.0117


57

0.9712

0.0528

0.7804

-0.1053

-0.2045

-0.2031

0.9792

0.0445

0.0089

1.0222


*H 0-A
2

1.2832

57







-0.0574





0.9938

0.0242


1.0118 1.0225


n K = 0.0400 was used in determination of v
2 2 2 27
Gold at 2400 A has n = 1.296 and n K = 1.543.
3 3 3
Maximum E always occurred at the first maximum.

Maximum e used in *H 0-A was at the third maximum.
2









To evaluate the assumptions that 1 >>1 sin(2u E) and 4 is
12 2 12
a small angle, it was necessary to use the largest estimated absorption

coefficients for which the refractive index was established for the ices.

It can be readily seen from Table 6 that these assumptions are in error

by less than 1.2% for all the ice films.

It can be concluded that the evaluation of e using Eqn. (13) has

a maximum error of 4.4% when calculations are made for the ice films

examined in this investigation, and the errors decrease to less than

2.4% if E is taken beyond the third fringe maximum.

Real Refractive Index

The errors involved in using Eqn. (17) result from uncertainties in

establishing the average fringe periods and angles of incidence. Errors

in determination of the average fringe periods are indicated by the

standard deviation of the refractive indices measured at the same wave-

length in independent experiments of the same ice film. The other

major source of error in Eqn. (17) comes from the uncertainty in knowing

the angles of incidence of the light beams on the ice film. From the

discussion in Appendix 2, it is reasonable to assume that the average

angles of incidence for the light beams were 9.60 0.20 and 56.80 0.10.

The maximum errors in the refractive indices due to these angle of

incidence uncertainties are presented in Table 7. The calculations are

based on data at the extreme wavelengths where the refractive indices

were determined for each ice.










Table 6


Evaluation of Assumptions

NH -A
3
o
x[A] 1925

n 1.8267
2
n K 0.0696
2 2
n 1.302
3
n K 1.353


in Perturbation Derivation

H O-H H O-A
2 2

1611 1611

1.6560 1.4675

0.0590 0.0385

1.4315 1.4315

1.348 1.348


3 3
e [deg]
1
[rad]
12
sin4
12
tan4
12
cos4
12
Ssin(2u e)
12 2


lotes: a)

b)


10

0.0587

0.0587

0.0588

0.9983

0.0056


57

0.0364

0.0363

0.0364

0.9993

0.0037


10

0.0668

0.0667

0.0669

0.9978

0.0096


57

0.0426

0.0426

0.0426

0.9991

0.0069


10

0.0659

0.0659

0.0660

0.9978

0.0121


57

0.0441

0.0441

0.0441

0.9990

0.0089


Optical constants for gold were taken from Ref. 27.

The values of sin(2u e) were taken from Table 5.
2


N









Table 7


Error Analysis of the Refractive Index

Wavelength Refractive Index

Amorphous NH ice 3200 1.4848 0.0026
3 1925 1.8267 0.0034

Amorphous H 0 ice 3200 1.2705 0.0021
2 1580 1.4713 0.0026

Hexagonal H 0 ice 3200 1.3408 + 0.0023
2 1611 1.6560 0.0030


The uncertainties in the refractive indices are within the error bars

given in Figs. 6, 9 and 10, which were established by the standard

deviation of the data determined at each of the wavelengths. Thus, the

error in the refractive index is determined more by the inaccuracy

involved in measuring the average fringe period than in measurement of

the angles of incidence of the light beams.


Extinction Coefficient

Estimates of the extinction coefficients and refractive indices for

water ices in a spectral region of high absorption were used to calculate

theoretical reflectivity curves. A comparison was made between the

estimates of the extinction coefficients calculated by Eqn. (19) for

these curves and the actual extinction coefficients which were used to

generate them. It was observed that for a region of high absorption, i.e.,
5 -1
> 2.0x10 cm less than two fringe periods are detectable in the

reflectivity curve. The approximate calculation of B using Eqn. (19) is

less than -7% in error under those conditions. This result was based on

an analysis of a theoretical reflectivity curve which simulated an
o
amorphous water ice film illuminated by 1475 A light. In that calculation








11
n = 1.50 (from Daniels )n K = 0.234 (absorption coefficient of
2 5 -1 2 2
2.0x10 cm ), n = 1.293, and n K = 1.178 (optical constants of gold
o 27 3 3 3
at 1475 A ). This curve is shown in Fig. 17. The relative reflec-

tivity curve which was predicted by Dressier and Schnepp's absorption
5 -1
coefficient of 4.17x10 cm and the relative experimental curve obtained

in this investigation were normalized so that the reflectivities of their

first minimum and maximum were the same as the theoretical curve having
5 -1
S= 2.0x10 cm These normalized reflectivity curves are also presented

in Fig. 17. This was done to illustrate that the experimental curve

compares favorably to the theoretical curve for amorphous water ice.

There is, however, a considerable difference between the experimental

curve and the curve with the higher absorption coefficient. This sub-

stantiates the claims of Chapter IV that the absorption coefficients

determined by Dressler and Schnepp are higher than they should be.
O
A theoretical reflectivity curve for amorphous H 0 ice at 1611 A
2
was calculated using n = 1.468 (see Table 2), n K = 0.0445 (absorp-
2 4 -1 22
tion coefficient of 3.47x10 cm ), n = 1.432, and n K = 1.35 (optical
o 27 3 3 3
constants of gold at 1611 A ). An estimate of the absorption coeffi-

cient using Eqn. (19) indicated that the error was less than -8% when

the extrema beyond the third maximum were used. This procedure was followed
o
for evaluation of the extinction for amorphous H 0 ice at 1611 A.
2










11 --- B = 2.0x10 cm-
--a Experimental Data
10 -
SB = 4.17x105 cm-1
9





S- / \
8 \





51-
S\ I
1 -






0
0 200 400 600 800 1000 1200 1400
0
Film Thickness ( A )

o
Figure 17. Water Ice Film Reflectivity at 1475 A















BIBLIOGRAPHY

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of Amorphous-Cubic NH Frosts and Amorphous-Hexagonal H 0
3 o o 2
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0 o
"Spectra of Venus and Jupiter from 1800 A to 3200 A," J. Atmos.

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BIOGRAPHICAL SKETCH

Edward V. Browell was born February 6, 1947 in Indiana, Pennsylvania.

He graduated from Mainland Senior High School, Daytona Beach, Florida in

June, 1964. In September of that year, he entered Daytona Beach Junior

College. He was elected to the DBJC Hall of Fame and received an

Associate of Arts degree with High Honors in June, 1966. He transferred

to the University of Florida that September and earned a degree of

Bachelor of Science in Aerospace Engineering with High Honors in December,

1968. The following January he enrolled in the Graduate School of the

University of Florida and was awarded a National Science Foundation

Traineeship. Optics was his field of study, and in March of 1971

he received the Master of Science in Aerospace Engineering.

In June, 1971 he completed two years of Air Force ROTC training and

was designated a Distinguished Military Graduate. In the summer of 1973

he underwent his active duty training with the Air Force as a Lieutenant

at the AF Armament Lab, Eglin Air Force Base. For his work he was

awarded the USAF Meritorious Service Medal for Outstanding Achievement.

Since March, 1971 he has been pursuing the degree of Doctor of

Philosophy at the University of Florida. He has four published papers

which are based on a wide range of topics in applied optics. The

professional societies of which he is a member include Sigma Xi, Optical

Society of America, and American Institute of Physics.

Edward V. Browell is married to the former Judith Rae Good. He is

a member of Omicron Delta Kappa, Phi Kappa Phi, Tau Beta Pi, and other

honorary societies.








I certify that I have read this study and that, in my opinion,
it conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.




Roland C. Anderson, Chairman
Professor of Aerospace
Engineering



I certify that I have read this study and that, in my opinion,
it conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.

)/

Dehn is R. Keefer /
Associate Professor
Aerospace Engineering



I certify that I have read this study and that, in my opinion,
it conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.




Mark H. C1 rkson-
Professor of e ace/
Engineering



I certify that I have read this study and that, in my opinion,
it conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.




Alex E reen
Graduate Research Professor
in Physics and Astronomy







I certify that I have read this study and that, in my opinion,
it conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of DocLor of Philosophy.



Stanley S. Ballard
Professor of Physics




This dissertation was submitted to the Dean of the College of
Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.


June, 1974



Dean, College of Engineering


Dean, Graduate School