REFRACTIVE INDEX MEASUREMENTS OF MAGNESIUM OXIDE, … · 2020. 4. 2. · REFRACTIVE INDEX MEASUREMENTS OF MAGNESIUM OXIDE, SAPPHIRE, ... this work, including the students who have

REFRACTIVE INDEX MEASUREMENTSOF MAGNESIUM OXIDE, SAPPHIRE, AND

AMTIR-1 AT CRYOGENIC TEMPERATURES

Item Type text; Thesis-Reproduction (electronic)

Authors Nofziger, Michael James

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

Download date 06/05/2021 19:50:22

Link to Item http://hdl.handle.net/10150/291228

http://hdl.handle.net/10150/291228

INFORMATION TO USERS

This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the

quality of the material submitted.

The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction.

1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity.

2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame.

3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of "sectioning" the material has been followed. It is customary to begin filming at the upper left hand corner of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete.

4. For illustrations that cannot be satisfactorily reproduced by xerographic means, photographic prints can be purchased at additional cost and inserted into your xerographic copy. These prints are available upon request from the Dissertations Customer Services Department.

5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed.

Uni

International 300 N. Zeeb Road Ann Arbor, Ml 48106

1325276

Nofziger, Michael James

REFRACTIVE INDEX MEASUREMENTS OF MAGNESIUM OXIDE, SAPPHIRE, AND AMTIR-1 AT CRYOGENIC TEMPERATURES

The University of Arizona M.S. 1985

University Microfilms

International 300 N. Zeeb Road, Ann Arbor, Ml 48106

PLEASE NOTE:

In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V

1. Glossy photographs or pages

2. Colored illustrations, paper or print

3. Photographs with dark background

4. Illustrations are poor copy

5. Pages with black marks, not original copy

6. Print shows through as there is text on both sides of page

7. Indistinct, broken or small print on several pages \J

8. Print exceeds margin requirements

9. Tightly bound copy with print lost in spine

10. Computer printout pages with indistinct print

11. Page(s) lacking when material received, and not available from school or author.

12. Page(s) seem to be missing in numbering only as text follows.

13. Two pages numbered . Text follows.

14. Curling and wrinkled pages

15. Dissertation contains pages with print at a slant, filmed as received

16. Other

University Microfilms

International

REFRACTIVE INDEX MEASUREMENTS OF MgO,

SAPPHIRE, AND AMTIR-1 AT CRYOGENIC TEMPERATURES

by

Michael James Nofziger

A Thesis Submitted to the Faculty of the

COMMITTEE ON OPTICAL SCIENCES (GRADUATE)

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

19 8 5

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers

under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of

this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of

scholarship. In all other instances, however, permission must be obtained from the author.

2hLL̂ JL£L SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

HUt.,,.. L W. L. WOLFE' 'Date

Professor of Optical Sciences

DEDICATION

Dedicated, with love, to my family.

Their constant support gives me the courage to persevere.

iii

ACKNOWLEDGMENT

Many people have contributed to the successful completion of

this work, including the students who have worked on this project in the

past. Without their fine efforts this would have been a much more

difficult task.

A special thank you needs to be extended to those most closely

associated with this thesis. Professor W. L. Wolfe, advisor and friend,

has taught and guided me through as much personal growth as a knowledge

of optics. What more can one ask of a teacher? His confidence in me at

the start of this project was a Christmas gift never to be forgotten.

An equal thanks goes out to Dr. Jim Palmer, Jerry DeBell, and

Lang Brod. When mechanical and experimental problems arose, they always

had a solution. The real "nuts and bolts" success of the measurements

was achieved only as a result of their professional guidance.

Among the numerous students who offered suggestions, one in

particular gave more of his time and knowledge than could ever have been

expected. To my friend and consulting handyman, Chris Thompson, I say

thank you.

Countless hours have been spent on this manuscript by Anne

Damon, Kathy Seeley, and Bill Wolfe. They have gone above and beyond

their call of duty to help complete the job. Thank you.

Finally, but most importantly, is the gratitude I owe to my

fiancee, Judy. The completion of this thesis is a direct result of her

iv

V

constant love and support. May I be able to return the same in our

lives together.

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS viii

LIST OF TABLES ix

ABSTRACT xi

1. INTRODUCTION ' 1

2. EXPERIMENTAL PROCEDURE 3

Method of Perpendicular Incidence 3 Test Setup 5

System Alignment 8 He-Ne Coalignment 8 System Signal-to-Noise Ratio (SNR) 10

Test Procedures 10 Monochromator Calibration ........................ 11 Prism Apex Angle 11

Prism Alignment 14 Beam Profile 14 Window Correction 16 Data Measurement 17

3. RESULTS 18

Data Reduction Procedures 18 Magnesium Oxide Results 20

Comparison with Other Measurement 27 Sapphire Results 27

Comparison with Other Measurements 32 AMTIR-1 Results 32

Comparison with Other Measurements 44

4. ERROR ANALYSIS 60

Random Errors 60 Systematic Errors 61

Calculation of (Ad)p 64 Combined Errors 66

Temperature Coefficient 66 System Repeatability 7 2

Short-term Precision 72 Long-term Precision 74

vi

vii

TABLE OF CONTENTS—Continued

Page

APPENDIX A: PRISM SPECIFICATIONS 75

APPENDIX B: SYSTEM ALIGNMENT 77

APPENDIX C: He-Ne COALIGNMENT 80

APPENDIX D: SYSTEM SNR 82

APPENDIX E: PRISM ALIGNMENT ERROR ANALYSIS 86

REFERENCES 93

LIST OF ILLUSTRATIONS

Figure Page

1. Method of Perpendicular Incidence 4

2. Test Setup Layout Drawing 6

3. Prism Alignment Axes 9

4. Beam Profile 15

5. MgO (300K) n(x) 21

6. MgO (77K) n(x) 22

7. MgO n(T) 28

8. NBS vs UA MgO (300K) n(x) 30

9. Sapphire (300K) n0 (X) and ne (X) i . 33

10. Sapphire (77K), nQ (X), and ne (X) 34

11. Sapphire n0(T) * 39

12. Sapphire ne(T) 40

13. NBS vs UA Sapphire (300K) nQ (X) 42

14. AMTIR-1 (230K, 300K, 328K), n(X) 45

15. AMTIR-1 n(T) at 8 pm 52

16. AMTIR-1 n(T) at 10 urn 53

17. AMTIR vs UA AMTIR-1 (300K) n(x) 56

18. dn/dT Error Analysis 71

19. Prism Specifications 76

20. Prism/Dewar Alignment 79

viii

LIST OF TABLES

Table Page

1. System Components 7

2. Monochromator Calibration 12

3. Prism Apex Angle 13

4. Typical Notebook Entry 19

5. Sellmeier Fit for MgO at 300K 23

6. Herzberger Fit for MgO at 300K 24

7. Sellmeier Fit for MgO at 77K 25

8. Herzberger Fit for MgO at 77K - . 26

9. MgO : n(T) at 3.5 ym 29

10. NBS vs UA Data : MgO at 300K 31

11. Sellmeier Fit for Sapphire (nQ) at 300K 35

12. Herzberger Fit for Sapphire (nQ) at 300K 36

13. Sellmeier Fit for Sapphire (ne) at 300K 37

14. Herzberger Fit for Sapphire (ne) at 300K 38

15. Sapphire : n0(T) and ne(T) at 3.5 urn 41

16. NBS vs UA Data : Sapphire at 300K 43

17. Sellmeier Fit for AMTIR at 230K 46

18. Herzberger Fit for AMTIR at 230K 47


20. Herzberger Fit for AMTIR at 300K 49


ix

X

ige

51

54

55

58

59

62

63

65

67

68

69

73

85

LIST OF TABLES—Continued

Herzberger Fit for AMTIR at 328K . . .

AMTIR-1 : n(T) at 8 p

AMTIR-1 : n(T) at 10 um

AM vs UA Data : AMTIR-1 at 300K

AM vs UA Data : AMTIR-1 dn/dT values

Error Analysis

Description of Symbols

Variables for Error Analysis

Combined Errors: MgO at 300K

Combined Errors: Sapphire n0 at 300K

Combined Errors: AMTIR-1 at 300K . . .

System Repeatability

Variables Used in SNR Calculation

ABSTRACT

The measurement of the index of refraction of three infrared

transmitting materials, magnesium oxide, sapphire, and AMTIR-l, is

described in this thesis. The index of refraction of each material was

measured both as a function of wavelength and temperature.

Experimental data were taken over wavelength ranges of 2 to 5 jam and 7

to 12 ym, while the temperature varied over a range of 80 to 350K. A

desired accuracy in the index of five parts in the fourth decimal place

was generally achieved. Also described are the equipment, alignment and

measurement procedures, results, and a complete summary of the sources

and magnitudes of errors.

xi

CHAPTER 1

INTRODUCTION

Infrared optical systems typically utilize transmissive elements

in at least one or more of the sub-system assemblies. Cryogenic cooling

of these elements is frequently required to reduce self-emission and

increase the system signal-to-noise ratio. In the design of these

system elements one needs to know accurately both the index of

refraction and dn/dT, the change in index with temperature.

Unfortunately, for all but the most commonly used infrared materials,

the index of refraction and associated dn/dT are either not known

accurately enough or have never been measured. The research program

described in this thesis provides the infrared design engineer with a

source of obtaining index of refraction and dn/dT data for previously

unmeasured materials.

Many techniques have been devised to measure a material's index

of refraction. The method of perpendicular incidence, as described here,

provides for quick yet accurate measurements on samples over a

temperature range of 4K to at least 500K.

The index of refraction and associated dn/dT of three materials

have been measured at various infrared wavelengths and temperatures.

Data are presented for magnesium oxide (MgO) and sapphire over a

wavelength region of 2 to 5 p and a temperature range of 80K to 300K.

In addition, a Ge-As-Se type glass known as AMTIR-1 has been measured.

1

2

Data are presented over a wavelength region of 7 to 12 ym and a

temperature range of 170K to 350K.

Error analyses are presented for all three materials. In each case

the systematic and random errors are about 2x10"*, less than our

desired goal of SxlO-11. A two-term Sellmeier equation and a Herzberger

equation were fit to the data for each material. The results of this

curve fitting as well as comparison to published data are also,

presented.

CHAPTER 2

EXPERIMENTAL PROCEDURE

Many methods exist for measuring the index of refraction. Piatt

(1976) has compiled an excellent reference list on the subject. Most

methods are well-suited for room temperature measurements at visible or

infrared wavelengths. In particular, the minimum deviation technique

provides sixth decimal place accuracy over the visible portion of the

spectrum. However, for measuring the index and dn/dT of samples at

cryogenic temperatures, the required use of vacuum dewars prohibits easy

sample alignment. Any technique involving changes in sample position

during the measurements becomes difficult.

Method of Perpendicular Incidence

This method of measuring the index of refraction, introduced by

Piatt (1976) and more recently developed by Swedberg (1979), represents

a relatively easy yet accurate means of measuring samples at cryogenic

temperatures.

Swedberg provides detailed descriptions of the method and

equipment; because this work essentially parallels his, only a brief

summary of each will be given here.

The method of perpendicular incidence is illustrated in Figure 1.

The sample material with index n( A,T) is cut in the shape of a right-

triangular prism having apex angle a. A collimated beam of light is

3

REFERENCE BEAM

n ( A , T )

n's i n(a+d)

Fig. 1. Method of Perpendicular Incidence.

5

incident normal to the first surface of the prism; as a result, this

method has also been referred to as the autocollimation technique. The

incident beam is purposely made to be larger than the prism.

Approximately 30 percent of this beam is undeviated, providing a

reference beam with which to measure d, the prism's angle of deviation.

The remaining portion of the incident beam enters the prism through the

first surface. No refraction occurs here because the beam is at normal

incidence to this surface. Travelling parallel to the base of the prism,

the beam is refracted at the second surface. Applying Snell's Law at

this surface, the index of refraction of the prism material may be

expressed simply as

n'sin(a+d) n sin(a)

_ _ sin(a+d) ° " sin(a) (1)

where n' has been set equal to 1 for a prism sample in a vacuum. In

principle, the index of refraction is determined by measuring the prism's

apex angle a and the angle of deviation d.

Test Setup

The optical system used in these measurements has been designed

specifically for the method of perpendicular incidence. The system

provides a well collimated beam normal to the first surface of the

prism and a detection system to measure the prism's angle of deviation.

Figure 2 shows a layout of the optics, while Table 1 lists a brief

description of each of the components. More detailed information on

this same optical system may be found in Swedberg's thesis (1979).

PRISM DEWAR ASSEMBLY

[INFERENCE BEAM-

DETECTOR DEMAR ASSEMBLY-

M7<

ANGULAR REAOOl/r

ROTARY TAB I F

ORDKR-BI.OCKI NO FILTER.

SOURCE

CHOPPER

COLLIHATINC MIRROR

PRISM OP MATERIAL UNDER TEST

JARRELL-ASII MONOC11ROMATOR-

L.ASEP/ BEAM EXPANDER-

Test Setup Layout Drawing.

L = lens, M = mirror.

7

Table 1. System Components

Element Description

Ml Flat, first-surface mirror

Thermal source Ceramic rod (1/8 in. diam x 1 in. long) Temperature around 1250°C

Cut-on infrared filter at 6.5 ym

Princeton Applied Research optical chopper

(Model No. 125A) modulation frequency at 170 Hz

6 in. diam, F/4 parabolic mirror

Flat, first-surface mirrors mounted on the monochromator

Filter

Chopper

M2

M3, M4

Monochromator

M5

M6

Prism dewar

assembly

Rotary table

M7

M8

Detector

Detection electronics

Temperature sensor and controller

Jarrell Ash, 0.25 m Ebert-type (Model 82-420) 5 ym blaze (1/d = 148 mm-1) grating was used for 2-5 ym measurements 10 ym blaze (1/d =» 50 mm-1) grating was used for the 7-12 ym measurements

3 in. diam, F/4 off-axis parabolic mirror

Flat, first-surface mirror (relocatable out-of-

beam path)

Double-chamber dewar with KRS-5 windows (dewar

designed for liquid helium)

Genevoise Rotary Table, Type 1-4

angular readout to 1 arc sec

4 in. diam, F/4 off-axis parabolic mirror

Flat, first-surface mirror

2-5 ym: 0.010 in. diam InSb photodiode 7-12 ym: HgCdTe photoconductor

Detector Preamp Princeton Applied Research lock-in amplifier

Si diode sensors: Lakeshore Cryotronics Model DT-500CV-DRC Controller: Lakeshore Cryotronics Model DRT-7C

8

System Alignment

Proper alignment of the optical system may be described by two

separate alignment procedures: (1) alignment of the optics used to

provide a collimated beam at the prism, and (2) alignment of the prism

so this collimated beam is normal to the prismas first surface. These

two steps form the essence of the method of perpendicular incidence.

Swedberg (1979) has provided a good discussion of how to achieve this

alignment. Appendix B of this thesis contains step-by-step procedures

used to align the system for these measurements.

He-Ne Coalignment

As outlined in Appendix B, the alignment of the incident beam

normal to the prism's first surface is achieved using an autocollimation

technique. Figure 3 shows the three degrees of freedom used in prism

alignment. Rotations of the prism about the alpha and beta axes change

the angle of reflectance of the incident beam off the first surface.

When the prism's first surface is adjusted normal to the incident beam,

the reflected portion will be imaged by mirror M5 directly back onto the

exit aperture. This may be observed by placing a microscope near the

exit aperture and looking at the reflected image.

In principle, this autocollimation technique appears simple; in

practice, it can become quite difficult. Problems arise because the

radiance at the exit aperture is low and transmission of the KRS-5

window is poor over the visible spectrum. The situation is much worse

for prism materials whose Fresnel surface reflectance is only 4 to 5

percent (materials with a low index of refraction over the visible

9

A1 pha Ax i s

D i hedra1

Edge Gamma Ax i s

Beta Ax i s

Fig. 3. Prism Alignment Axes.

10

spectrum). A solution, found by Swedberg (1979) and used in these

measurements, involves the replacement of the thermal source with a He-

Ne laser beam. This beam is focused to provide a real image at the

location of the (removed) thermal source. The reflected image is now

visible even for prism materials which reflect only a few percent of the

incident beam. Details of this He-Ne co-alignment are given in

Appendix C.

System Signal-to-Noise Ratio (SNR)

The instrument described in this thesis is adaptable for making

index of refraction measurements over a wide range of wavelengths and

temperatures (Piatt, et al.; Wolfe, DeBell, Palmer, 1980). Changing the

wavelength region typically implies using a different detector having the

proper spectral response. Once the detector is installed, the entire

system is aligned according to the procedures already given and a signal

is detected. At this point, a comparison of the measured and calculated

signal-to-noise ratios can be useful to determine if the alignment is

optimal and if the detector is functioning properly. The details for

calculating the overall system signal-to-noise ratio are given in

Appendix D.

Test Procedures

In addition to aligning the optical system, there are other

procedures which must be carried out before data are actually taken.

This section gives a description of each.

Monochromator Calibration

Initial calibration of the monochromator was carried out using

the green line of a mercury source. An easier method, used for this

work, replaced the mercury source with the co-aligned He-Ne laser.

Calibration of wavelength vs dial number on the monochromator was done

by rotating the grating through several orders, noting the dial number

each time. This was done for both the 5 urn and 10 pm blazed gratings

used in the measurements. A linear least-squares fit to the data was

carried out in each case, with a correlation coefficient of 0.999 being

typical. Table 2 presents data and values of fit for a calibration

representative of both gratings. Also calculated is a root-mean-squared

(rms) value for the estimated error in monochromator calibration. This

represents the average error between the actual wavelength (the

multiple orders of 0.6328 um) and the calculated wavelength (from the

linear fit) at each of the dial numbers noted during the calibration.

This value of will be used later in the error analysis.

Prism Apex Angle

It was shown in equation (1) that calculating the index of

refraction involves knowing the vertex angle a of the prism to be

measured. The vertex angles of each of the three prisms were measured

using a Wild No. 79 Precision Spectrometer. Several different readings

were taken for each prism. The average values and standard deviations

of the measurements are listed in Table 3. It is worth noting that no

error is introduced into the values of index if the prism has a pyramidal

angle. (This angle is present if the three planes containing the prism

12

Table 2. Monochromator Calibration

Order Actual Calculated Difference Number Wavelength Wavelength x 1000

1 0.6328 0.63257 -0.2230 2 1.2656 1.26553 -0.0690 3 1.8984 1.89824 -0.1504 4 2.5312 2.53906 -0.2313 5 3.1640 3.16392 -0.0774 6 3.7968 3.79687 +0.0764

7 4.4296 4.42959 -0.0044 8 5.0624 5.06231 -0.0853 9 5.6952 5.69503 -0.1662

10 6.3280 6.32798 -0.0123 11 6.6908 6.69607 -0.0932 12 7.5936 7.59342 -0.1740

13 8.2264 8.22637 -0.0202 14 8.8592 8.85909 -0.1011 15 9.4920 9.49181 -0.1819

16 10.1248 10.12477 -0.0281 17 10.7576- 10.75749 -0.1089 18 11.3904 11.39021 -0.1898 19 12.0232 12.02316 -0.0360 20 12.6560 12.65580 -0.1168

21 13.2888 13.28860 -0.1977

22 13.9216 13.92155 -0.0438 23 14.5544 14.55427 -0.1247

RMS T0TAL= 0.1300

13

Table 3. Prism Apex Angle

Material Number of Average Standard Readings Deviation

deg min sec deg min sec

Magnesium Oxide 10 31 00 13 .6 00 00 0.8

Sapphire 10 31 00 13 .1 00 00 1.4

AMTIR-1 3 15 54 18 .9 00 00 0.3

14

faces intersect in a point.) Proper alignment of the prism by rotation

about the gamma axis (Appendix B) orients the dihedral edge (Figure 3) in

a vertical direction, regardless of whether there is pyramidal angle

present or not.

Prism Alignment

Prism alignment was carried out using the autocollimation

technique already described. In the process of measuring dn/dT, however,

it was discovered that cooling and warming of the prism sample dewar

changed the alignment of the prism. To check this, the dewar was cooled

to 77K while the position of the retroreflected image (back onto the

exit aperture) was tracked. The change in prism alignment was

predominantly about the alpha axis (see Figure 3) and was estimated to

be 0.98 milliradians. Even though this in itself seems insignificant, the

error introduced in the absolute value of index is unacceptably high (see

the "Error Analysis" section). The solution was to use the

autocollimation technique and realign the prism after every change in

sample temperature during dn/dT measurements.

Beam Profile

The intensity profiles of both the reference and deviated beams

were carefully measured prior to taking a set of data or after

realigning the optics. A typical beam intensity profile of a properly

aligned system is shown in Figure 4. In determining absolute values of

the index, the overall accuracy is determined in part by the degree of

symmetry of each of the beam profiles. One of the goals of the

alignment process is to make the beam profiles as symmetric as possible.

15

<nU>

7

n

+

+

2

+

+

+

+ +

+

+

9

0

+

ROTARY TABLE POSITION (relat ive scale)

Fig. 4. Beam Profile.

16

Window Correction

Measurements made at cryogenic temperatures require the use of

windows on the evacuated prism sample dewar. The three KRS-5 windows

used for this each have wedged surfaces. Even though the windows were

mounted on the dewar with the wedges in the vertical direction, Swedberg

(1979) had measured a residual horizontal component. This introduces a

systematic error in the measurements. In addition, the deviated beam

does not enter the exit window at normal incidence. Unwanted refraction

occurs through this window and another systematic error is introduced.

Swedberg (1979) provides a more detailed description of these two

sources of error.

The procedure to eliminate this combination of errors in the

measurements is as follows. With none of the three windows in place,

the system was carefully aligned and the index of refraction was

measured as a function of wavelength at room temperature. All three

windows were installed, the dewar was evacuated, and again the system

was carefully aligned. The index of refraction was measured at the same

wavelengths and temperature. A difference was observed between the

sets of indices, constant to a few parts in the fourth decimal place.

An average of these differences was calculated and this number was then

used to correct any set of data for which windows were used on the

dewar.

17

Data Measurement

Data were taken under two different sets of conditions. In the

first, the temperature of the sample was held constant and the index

was measured as a function of wavelength, i.e., n(x). This is referred

to as a wavelength run. In the second, a wavelength was chosen and held

constant while the index was measured as a function of sample

temperature, i.e, n(T). This is referred to as a temperature run. The

change in index with a change in temperature, dn/dT, is calculated by

finding the slope of the n(T) curve at a given temperature. The curve

representing n(T) may or may not be linear; if not, then dn/dT will be a

function of temperature and not a constant.

A cross-check of dn/dT is essentially built into the measurement

process. By making a wavelength run at various temperatures, dn/dT (as

a function of wavelength) may be determined independent of the value

obtained from the temperature run.

The actual process of taking data involves measuring the prism's

angle of deviation, d, with respect to the reference beam (see Figure 1).

After having mapped out both beam profiles to insure symmetry, the

process is to locate the center of each beam. Due to the slit function

of the monochromator, the beam profiles are broadened and the center

may be difficult to locate directly. An easier method is to locate the

85 percent points of the beam profile and take the average to find the

center. The angle of deviation, d, is simply the difference between the

centers of the reference and deviated beams.

CHAPTER 3

RESULTS

The results of measurements of n( x ) and n(T) for magnesium

oxide, sapphire, and AMTIR-l are presented. Techniques used for data

reduction are first discussed, followed by the data and a comparison

with results from the literature.

Data Reduction Procedures

The actual process of taking data, although simple in approach,

turned out to be quite tedious in practice. After aligning the system as

outlined in the last chapter, wavelength and temperature runs were made

for each material.

A wavelength run was done by first setting the monochromator to

the desired wavelength. The rotary table was then used to rotate the

detection system to locate the 85 percent points of each beam profile.

Each angular position (in degrees, minutes, seconds) was recorded and the

temperatures directly above and below the prism were also noted. Table

4 shows a typical entry into the notebook. The four angles were

converted to decimal degrees and then averaged to find the beam centers.

The angles of the centers were subtracted to give the deviation angle,

d, and equation (1) was used to calculate the index. This reduction was

done quickly using a hand calculator. By doing it after every change in

wavelength, bad data points became apparent immediately.

18

Table 4. Typical Notebook Entry.

Material: Magnesium Oxide

REF. o i i , — o i //

Dev. QBA* o / 'f — * t ft

T ToP

T &PiS£

d n

2. o

1

o 3? 5"S" ' o Ljtj s~i

1

l<? "35" 2/ J to 01 2i •z°it ZW 29. to So r /• 7® ??o

3.c 1

1 1

1 5~. ( J

1

1

1

1

1

20

A curve-fitting program published by Swedberg (1979) was used to

fit the n(X) data to both a two-term Sellmeier equation and a Herzberger

equation. The measured indices, the indices calculated from the

equations, and the differences are presented.

A temperature run was done in basically the same way as a

wavelength run, except the wavelength was held constant and the

temperature of the sample varied. Data were taken and reduced in the

manner just described. Sample temperature was changed using the

Lakeshore Cryotronic heater controller. Sufficient time was allowed

after each temperature change for the prism sample to reach the new

equilibrium temperature. The temperature gradient across the prism was

never greater than 2K.

For the three materials measured, the index of refraction was

plotted as a function of temperature. For AMTIR-l it appeared as if the

data closely followed a straight line. A linear least-squares fit to

the data was done to determine the dn/dT coefficient. The deviations

from a straight line for the other two materials are. discussed later in

the Temperature Coefficient section.

The following data are listed without error bars. An error

analysis, presented in the next chapter, provides a detailed calculation

and listing of the separate errors.

Magnesium Oxide Results

The refractive index as a function of wavelength, n( x ) , was

measured for magnesium oxide. A wavelength run was done from 2 to 5 pm

for sample temperatures of 300K (room temperature) and 77K (liquid

3 4 MAUELENGTH <nicroneters)

Fig. 5. MgO (300K) n(X).

22

I N D E X

0

F

R

E F R a c T I 0

H

1.72_

1.71

1.70

1.69

1.68

1.67

1.66

1.65

1.64

1.63

* *

-t

*

* *

*

*

I I I I >

3 4 WAVELENGTH (nicroneters)

Fig. 6. MgO (77K) n(A)

Table 5. Sellmeier Fit for MgO at 300K

UAUELENGTH MEASURED CALCULATED DIFFERENCE <UM> INDEX INDEX

2.0 1.70880 1.70889 -0.00009 2.1 1.70734 1.70739 -0.00005 2.2 1.70587 1.78584 0.00003 2.3 1.70431 1.70426 0.00005 2.4 1.70271 1.70262 0.00009 2.5 1.70101 1.70094 0.00007 2.6 1.69926 1.69920 0.00006 2.7 1.69750 1.69741 0.00009 2.8 1.69560 1.69556 0.00004 2.9 1.69372 1.69364 0.00008 3.0 1.69168 1.69167 0.00001 3.1 1.68967 1.68963 0.00004 3.2 1.68758 1.68752 0.00006 3.3 1.68537 1.68534 0.00003 3.4 1.68311 1.68309 0.00002 3.5 1.68081 1.68078 0.00003 3.6 1.67840 1.67839 0.00001 3.7 1.67593 1.67592 0.00001 3.8 1.67336 1.67338 -0.00002 3.9 1.67077 1.67076 0.00001 4.0 1.66808 1.66807 0.00001 4.1 1.66528 1.66529 -0.00001 4.2 1.66268 1.66243 0.00025 4.3 1.65932 1.65949 -0.00017 4.4 1.65648 1 •65647 0.00001 4.5 1.65337 1.o533b 0.00001 4.6 1.65020 1.65016 0.00004 4.7 1.64691 1.64687 0.00004 4.8 1.64358 1.64349 0.00009 4.9 1.64012 1.64002 0.00010 5.8 1.63663 1.63646 0.00017

ROOT MEAN SQUARE DIFFERENCE3 1.424156603E-5

COEFFICIENTS OF THE FORMULA

Al=l.95438519646 A2=4.66452641279 U1=0.0168154985595 U2=»444.923611359

Table 6. Herzberger Fit for MgO at 300K

HAUELENGTH MEASURED CALCULATED DIFFERENI (un> INDEX INDEX

2.0 1.70880 1.70880 0.00000 2.1 1.70734 1.70736 -0.00002 2.2 1.70587 1.70586 0.00001 2.3 1.70431 1.70430 0.000Q1 2.4 1.70271 1.70269 0.00002 2.5 1.70101 1.70101 0.00000 2.6 1.69926 1.69928 -0.00002 2.7 1.69750 1.69748 0.00002 2.8 1.69560 1.69563 -0.00003 2.9 1.69372 1.69371 0.00001 3.0 1.69168 1.69172 -0.00004 3.1 1.68967 1.68967 0.00000 3.2 1.68758 1.68756 0.00002 3.3 1.68537 1.68537 0.00000 3.4 1.68311 1.68312 -0.00001 3.5 1.68081 1.68080 0.00001 3.6 1.67840 1.67840 0.00000 3.7 1.67593 1.67593 0.00000 3.8 1.67336 1.67339 -0.00003 3.? 1.67077 1.67077 0.00000 4.0 1.66808 1.66807 0.00001 4.1 1.66528 1.66529 -0.00001 4.2 1.66268 1.66244 0.00024 4.3 1.65932 1.65950 -0.00018 4.4 1.65648 1.65649 -0.00001 4.5 1.65337 1.65339 -0.00002 4.6 1.65020 1.65020 0.00000 4.7 1.64691 1.64693 -0.00002 4.8 1.64358 1.64358 0.00000 4.9 1.64012 1.64013 -0.00001 5.0 1.63663 1.63660 0.00003

ROOT MEAN SQUARE DIFFERENCE" 1.021974922E-

COEFFICIEHTS OF THE FORMULA

A«1.71842051314 D=-0.0030329773527 B*0.0149027044262 E=-1.051138757E-5 C=-0.0169470306715

Table 7. Sellmeier Fit for MgO at 77K.

MAUELENGTH MEASURED CALCULATED DIFFERENl <UM> INDEX INDEX

2.0 1.707t4 1.70739 -0.00025 2.1 1.70576 1.70585 -0.00009 2.2 1.70435 1.70427 0.00008 2.3 1.70280 1.70266 0.00014 2.4 1.70116 1.70101 0.00015 2.5 1.69942 1.69931 0.80011 2.6 1.69764 1.69756 0.CU008 2.7 1.69591 1.69575 0.00016 2.8 1.69391 1.69389 0.00002 2.9 1.69208 1.69197 0.00011 3.0 1.69008 1.68998 0.00010 3.1 1.68800 1.68793 0.00007 3.2 1.68588 1.68582 0.00006 3.3 1.68370 1.68364 0.00006 3.4 1.68142 1.68138 0.00004 3.5 1.67909 1.67906 0.00003 3.6 1.67665 1.67666 -0.00001 3.7 1.67417 1.67419 -0.00002 3.8 1.67162 1.67165 -0.00003 3.9 1.66897 1.66902 -0.00005 4.0 1.66627 1.66632 -0.00005 4. 1 1.66347 1.66354 -0.00007 4.2 1.66087 1.66067 0.00020 4.3 1.65750 1.65772 -0.00022 4.4 1.65467 1.65468 -0.00001 4.5 1.65157 1.65156 0.00001 4.6 1.64835 1.64835 0.00000 4.7 1.64510 1.64504 0.00006 4.8 1.64178 1.64165 0.00013 4.9 1.63838 1.63816 0.00022 5.0 1.63486 1.63457 0.00029

ROOT MEAN SQUARE DIFFERENCE* 2.166125959E-5


Al«l.94740252201 U1=0.0199465938176

A2=4.15008386479 U2=400.091773703

Table 8. Herzberger Fit for MgO at 77K

HAUELENGTH MEASURED CALCULATED DIFFERENCE <un) INDEX INDEX

2.0 1.70714 1.70717 -0.00003 2.1 1.70576 1.70577 -0.00001 2.2 1.70435 1.70430 0.00005 2.3 1.70280 1.70275 0.00005 2.4 1.70116 1.70113 0.00003 2.5 1.69942 1.69945 -0.00003 2.6 1.69764 1.69770 -0.00006 2.7 1.69591 1.69589 0.00002 2.8 1.69391 1.69402 -0.00011 2.9 1.69208 1.69208 0.00000 3.0 1.69008 1.69008 0.00000 3.1 1.68800 1.68801 -0.00001 3.2 1.68588 1.68587 0.00001 3.3 1.68370 1.68367 0.00003 3.4 1.68142 1.68140 0.00002 3.5 1.67909 1.67906 0.00003 3.6 1.67665 1.67665 0.00000 3.7 1.67417 1.67417 0.00000 3.8 1.67162 1.67161 0.00001 3.9 1.66897 1.66898 -0.00001 4.0 1.66627 1.6662? 0.00000 4.1 1.66347 1.66349 -0.00002 4.2 1.66087 1.66063 0.00024 4.3 1.65750 1.65769 -0.00019 4.4 1.65467 1.65468 -0.00001 4.5 1.65157 1.65158 -0.00001 4.6 1.64835 1.64840 -0.00005 4.7 1.64510 1.64513 -0.00003 4.8 1.64178 1.64178 0.00000 4.9 1.63838 1.63835 0.00003 5.0 1.63486 1.63483 0.00003

ROOT MEAN SQUARE DIFFERENCE* 1.147062802E-5


A»l.7166703965 D=-0.00306729781252 0=0.0193441942796 E®-9.416368853E-6 C=-0.0307656552071

27

nitrogen). Measurements were made every 0.1 um in wavelength. The data

are presented in Figures 5 and 6 and Tables 5,6, 7 and 8.

The refractive index as a function of temperature, n(T), was

measured for magnesium oxide. A temperature run was done at a constant

wavelength of 3.5 um for sample temperatures of 80K to 290K.

Measurements were made approximately every 25K. A plot of the

refractive index vs temperature is shown in Figure 7. Table 9 lists the

values of index and the corresponding sample temperatures.

Comparison with Other Measurements

The index of refraction of magnesium oxide has previously been

measured by NBS (Stephens and Malitson, 1952; Strong and Brice, 1935).

Data were taken for samples only at or near room temperature, over

visible and near-infrared wavelengths. Figure 8 and Table 10 show a

comparison of the 300K data reported by Stephens and Malitson (1952) and

the 300K data given in this thesis. To provide a more readable graph,

only some of the data from this thesis (Table 5) have been plotted. An

excellent agreement between the two sets of data is clearly seen.

Sapphire Results

The anisotropic crystalline structure of sapphire causes optical

birefringence. Depending on the orientation of the crystal with respect

to the incident electromagnetic field, one of two indices of refraction

may be measured. The sample of sapphire that was measured had its

optical axis contained in the plane of the first surface of the prism.

As a result, both the ordinary and extraordinary indices of refraction

could be measured without reorientation of the prism sample.

28

<n<T>-"n<80> >£1E4

18

16

14

12

18

8

6

•Jv -h

80 100 120 140 160 180 200 220 240 260 280 360 TEMPERATURE <K>

Fig. 7. MgO n(T).

Table 9. MgO : n(T) at 3.5 um

29

Temperature Measured (K) Index

80 1.68144

85 1.68146

90 1.68145

98 1.68146

106 1.68149

110 1.68157

121 1.68167

151 1.68182

177 1.68200

203 1.68219

226 1.68245

251 1.68277

276 1.68304

292 1.68323

Note: The above data have not been corrected for the effects of the dewar windows. However, the correction is constant with temperature and does not affect dn/dT, the slope of the curve.

30

I N

D E X

0

F

R E F R A C T I 0

H

1.72

1.71

1.70

1.69

1.68

1.67

1.66

1.65

1.64

1.63

1.62 1 1 1 i i I I I • j * * * 1 * • » * • » • • * * * * » • •

1.5 2 3 4 5

WAUELEHGTH <nicroneters>

• * • * * • * • * • * • •

Fig. 8. NBS vs UA MgO (300K) n(X). * = data, + = NBS data.

Table 10. NBS vs UA Data : MgO at 300K

31

X(jim) n(UA) n(NBS) An(UA-NBS)

2.0 1.70880 1.70852 +0.00028

2.5 1.70101 1.70079 +0.00022

3.0 1.69168 1.69161 +0.00007

3.5 1.68081 1.68076 +0.00005

4.0 1.66808 1.66809 -0.00001

4.5 1.65337 1.65347 -0.00010

5.0 1.63663 1.63673 -0.00010

n(UA) n(NBS)

= measured experimental data

= values from NBS curve-fit equation

32

A wavelength run was done from 2 to 5 pm to measure the

ordinary index, nQ(X), and the extraordinary index, ne(x). Data were

taken for sample temperatures of 300K and 77K, at every 0.1 um in

wavelength. The data are presented in Figures 9 and 10 and Tables 11

through 14.

The refractive indices as functions of temperature, nQ(T) and

ne(T), were measured as well. A temperature run was done at a constant

wavelength of 3.5 ym for sample temperatures of 80K to 294K.

Measurements were made at ten different temperatures over this range.

A plot of nQ vs temperature is shown in Figure 11, and ne vs temperature

in Figure 12. Table 15 lists the values of n0 and ne measured at the

corresponding sample temperatures.


The refractive indices of sapphire have been measured at visible

wavelengths and room temperature by Jeppesen (1958). Data for the

ordinary index were extended to the near-infrared spectral region by

Malitson, Murphy, and Rodney (1958) and Malitson (1962) for samples at

room temperature. A comparison of the nQ data at 300K reported by

Maltison (1962) and the nQ data at 300K given in this thesis is presented

in Figure 13 and Table 16. As with magnesium oxide, an excellent

agreement is observed between the two sets of room-temperature data.

AMTIR-1 Results

AMTIR is an acronym for Amorphous Material Transmitting Infrared

Radiation. Manufactured by Amorphous Materials, Inc., AMTIR-1 is a Ge-

As-Se type of infrared glass designed to transmit over both atmospheric

33

1-75

1 .70

1 .65

*****

**** *****

**** **:* **!* * ! * . o - R A Y

* * * e-RAY *1*

** *** ±

*** ***

** ** ** *

1 • 60' * * * ' * * * * * * • • * * * • • * * * • * * * * * * * * •

3 4 MAUELENGTH (nicroMeters>

Fig. 9. Sapphire (330K) nQ (A) and ng (A).

4

34

1.75

I N D E X

0

F

R E F R A C T I 0

N

* t • * *

t

1.70

1.65

t ** t £ .

* * * * * * *!**

* * ? * o - R A Y * ± * *

e-RAY * * * t

Kt

' * * *

**

* l ± * t

** *

1.60'* * i 1 ,

2 3 4 5

WAUELEHGTH (nicrometers)

Fig. 10. Sapphire (77K), nQ (A) and ng (A).

Table 11. Sellmeier Fit for Sapphire (nQ) at 300K

HAUELENGTH MEASURED CALCULATED DIFFERENCE <un> INDEX INDEX

2.9 1.73725 1.73791 -0.00066 2.1 1.73536 1.73551 -0.00015 2.2 1.73323 1.73309 0.00014 2.3 1.73082 1.73062 0.00020 2.4 1.72850 1.72810 0.00040 2.5 1.72593 1.72552 0.00041 2.6 1.72332 1.72287 0.00045 2.7 1.72061 1.72014 0.00047 2.8 1.71773 1.71732 0.00041 2.9 1.71487 1.71441 0.00046 3.0 1.71046 1.71140 -0.00094 3.1 1.70864 1.70828 0.00036 3.2 1.70539 1.70506 0.00033 3.3 1.70203 1.70172 0.00031 3.4 1.69852 1.69827 0.00025 3.5 1.69489 1.69469 0.00020 3.6 1.69101 1.69098 0.00003 3.7 1.68708 1.68714 -0.00006 3.8 1.68309 1.68316 -0.00007 3.9 1.67891 1.67904 -0.00013 4.0 1.67465 1.67477 -0.00012 4.1 1.67016 1.67034 -0.00018 4.2 1.66606 1.66576 0.00030 4.3 1.66066 1.66101 -0.00035 4.4 1.65605 1.65608 -0.00003 4.5 1.65103 1.65099 0.00005 4.6 1.64582 1.64569 0.00013 4.7 1.64038 1.64021 0.00017 4.8 1.63496 1.63453 0.00043 4.9 1.62928 1.62864 0.00064 5.9 1.62343 1.62253 0.00090



Al-2.05997409902 A2=2.63385602966 U1=0.0402780100594 U2=177.885878829

Table 12. Herzberger Fit for Sapphire (nQ) at 300K

NAUELENGTH MEASURED CALCULATED DIFFERENCE <un> INDEX INDEX

2.0 1.73725 1.73732 -0.00007 2.1 1.73536 1.73532 0.00004 2.2 1.73323 1.73316 0.00007 2.3 1.73082 1.73086 -0.00004 2.4 1.72850 1.72844 0.00006 2.5 1.72593 1.72590 0.00003 2.6 1.72332 1.72326 0.00006 2.7 1.72061 1.72052 0.00009 2.8 1.71773 1.71767 0.00006 2.9 1.71487 1.71472 0.00015 3.0 1.71046 1.71166 -0.00120 3.1 1.70864 1.70850 0.00014 3.2 1.70539 1.78522 0.00017 3.3 1.70203 1.70184 0.00019 3.4 1.69852 1.69833 0.00019 3.5 1.69489 1.69471 0.00018 3.6 1.69101 1.69097 0.00004 3.7 1.68708 1.68709 -0.00001 3.8 1.68309 1.68309 0.00000 3.9 1.67891 1.67895 -0.00004 4.9 1.67465 1.67467 -0.00002 4.1 1.67016 1.67025 -0.00009 4.2 1.66606 1.66568 0.00038 4.3 1.66066 1.66096 -0.00030 4.4 1.65605 1.65609 -0.00004 4.5 1.65103 1.65105 -0.00002 4. 6 1.64582 1.64586 -0.00004 4.7 1.64038 1.64049 -0.00011 4.8 1.63496 1.63495 0.00001 4.9 1.62928 1.62924 0.00004 5.0 1.62343 1.62334 0.00009

ROOT MEAN SQUARE DIFFERENCE® 4.469451364E-5


A« i.7465386602 D*-0.90411312848259 0=0.056796400994 E=-3.595372842E-5 C»-0.102339136788

Table 13. Sellmeier Fit for Sapphire (ne) at 300K

HAUELENGTH MEASURED CALCULATED DIFFERENCE <UM> INDEX INDEX

2.0 1.72954 1.72972 -0.00018 2.1 1.72752 1.72758 -0.00006 2.2 1.72545 1.72536 0.00009 2.3 1.72320 1.72306 0.00014 2.4 1.72074 1.72066 0.00008 2.5 1.71823 1.71817 0.00006 2.6 1.71564 1.71559 0.00005 2.7 1.71297 1.71290 0.00007 2.8 1.71015 1.71011 0.00904 2.9 1.70730 1.70722 0.00008 3.0 1.70427 1.70422 0.00005 3.1 1.70116 1.70110 0.00006 3.2 1.69795 1.69788 0.00007 3.3 1.69462 1.69454 0.00008 3.4 1.69116 1.69109 0.00007 3.5 1.68754 1.68751 0.00003 3.6 1.o8376 1.68381 -0.00005 3.7 1.67993 1.67999 -0.00006 3.8 1.67601 1.67605 -0.00004 3.9 1.67190 1.67197 -0.00007 4.0 1.66774 1.66776 -0.00002 4.1 1.66335 1.66342 -0.00007 4.2 1.65936 1.65894 0.00042 4.3 1.65409 1.65431 -0.00022 4.4 1.64959 1.64955 0.00004 4.5 1.64470 1.64464 0.00006 4.6 1.63964 1.63958 0.00006 4.7 1.63437 1.63436 0.00001 4.8 1.62910 1.62899 0.00011 4.9 1.62360 1.62346 0.00014 5.0 1.61793 1.61776 0.00017



Al*2.05133862591 'A2=6.0387957247 U1«0.0I21325438922 U2=371.914900274

Table 14. Herzberger Fit for Sapphire (ne) at 300K

HAUELENGTH MEASURED CALCULATED DIFFERENCE <uti> INDEX INDEX

2.0 1.72954 1.72956 -0.00002 2.1 1.72752 1.72754 -0.00002 2.2 1.72545 1.72540 0.00005 2.3 1.72320 1.72313 0.00007 2.4 1.72074 1.72076 -0.00002 2.5 1.71823 1.71827 -0.00004 2.6 1.71564 1.71568 -0.00004 2.7 1.71297 1.71299 -0.00002 2.8 1.71015 1.71019 -0.00004 2.9 1.70730 1.70728 0.00002 3.0 1.70427 1.70427 0.00000 3.1 1.70116 1.70115 0.00001 3.2 1.69795 1.69791 0.00004 3.3 1.69462 1.69456 0.00006 3.4 1.69116 1.69110 0.00006 3.5 1.68754 1.68752 0.00002 3.6 1•68376 1.68382 -0.00006 3.7 1.67993 1.67999 -0.00006 3.8 1.67601 1.67604 -0.00003 3.9 1.67190 1.67197 -0.00007 4.0 1.66774 1.66776 -0.00002 4.1 1.66335 1.66342 -0.00007 4.2 1.65936 1.65894 0.00042 4.3 1.65409 1.65433 -0.00024 4.4 1.64959 1.64958 0.00001 4.5 1.64470 1.64468 0.00002 4.6 1.63964 1.63963 0.00001 4.7 1.63437 1.63444 -0.00007 4.8 1.62910 1.62909 0.00001 4.9 1.62360 1.62359 0.00001 5.0 1.61793 1.61792 0.00001

ROOT HEAN SQUARE DIFFERENCE" 1.699808284E-5


A*l.74413385049 D=-0.00446991590245 B=0.0264199282485 E=-2.471157894E-5 C=-0.0466218640364

39

<no<T>-no<80)>*1E4

16

14

12

18

8

6

0

A

-»—i—i—h -4 h

80 100 120 140 160 180 200 220 240 260 280 300 TEMPERATURE <K>

Pig. 11. Sapphire nQ(T).

40

I N

D E X

0

F

R E F R A C T I 0

H

<ne <T>-ne <80))*1E4

18

16

14

12

18

8

4

2

0 *•**•' *

80 100 120 140 160 180 200 220 240 260 280 300 TEMPERATURE <K>

Fig. 12. Sapphire ne(T).

Table 15. Sapphire : nQ(T) and ng(T) at 3.5 ym

41

Temperature Measured Measured (K) Index ne Index n0

80.2 1.68909 1.69657

84.8 1.68909 1.69656

89.5 1.68909 1.69655

94.5 1.68911 1.69656

102.5 1.68915 1.69659

122.5 1.68925 1.69668

129.5 1.68929 1.69679

149.7 1.68938 1.69683

201.3 1.68973 1.69718

293.5 1.69076 1.69806

Note: The above data have not been corrected for the effects of the dewar windows. However, the correction is constant with temperature and

does not affect the dn/dT, the slope of the curve.

42

1.74

1.73

1.72

1.71

1.70

1.69

1.68

1.67

1.66

1.65

1.64

1.63

1.62

+*

*

.*

*

*

* ' 1 I I 1 1 ' ' 1 1 ' J f ' 1 ' • ' ̂ » ' ' • '

MAUELENGTH <nicroneters>

Fig. 13. NBS vs UA Sapphire (300K) nQ (X). * = UA nQ data,

+ = NBS n data. o

Table 16. NBS vs UA Data : Sapphire at 300K

A (um) n0 (UA) n0 (NBS) An (UA-NBS)

2.0 1.73725 1.73773 -0.00048

2.5 1.72593 1.72609 -0.00016

3.0 1.71056 1.71224 -0.00178

3.5 1.69489 1.69534 -0.00045

4.0 1.67465 1.67524 -0.00059

4.5 1.65103 1.65159 -0.00056

5.0 1.62343 1.62397 -0.00054

n (UA) = measured experimental data

n (NBS) = values from NBS curve-fit equation

44

windows (3 to 5 vim and 8 to 12 yin) as well as the YAG laser wavelength

of 1.064 ym.

A sample in the form of a prism was obtained for measurements.

A wavelength run was carried out from 7 to 12 ym for sample

temperatures of 230K (-43°C), 300K (room temperature), and 328K (+55°C).

Measurements were made every 0.1 pm in wavelength. The data are

presented in Figure 14 and Tables 17 through 22.

As with the other samples, the index of refraction vs

temperature, n(T), was measured. Two temperature runs were done at

constant wavelengths of 8 and 10 ym for sample temperatures ranging

from 170K to 350K. Fourteen data points were taken over this

temperature range. A plot of n(T) at 8 ym is given in Figure 15 and n(T)

at 10 ym is shown in Figure 16.

Lists of the indices and corresponding temperatures at the two

wavelengths appear in Tables 23 and 24. For each set of n(T) data, a

least-squares linear fit was done to calculate dn/dT. The results and

coefficients of fit are also given. In each case, dn/dT was found to be

76 x lO-^C-1.


The only previously available source of refractive index data

for AMTIR-1 is that published by Amorphous Materials, Inc. (1983). They

have used the minimum deviation technique to measure the room

temperature refractive index from 1 to 14 ym. Values for dn/dT were

also measured over a temperature range of 25°C to 65°C at 1.15, 3.39,

and 10.6 ym in wavelength.

45

INOEX

2.51000r

1 *•*<?*< m

e o Ul >

•5

« u

u. 41

(J

2.48000

***U

****** x?v *****. ^*o*t

. 328 K

300 K

s 230 K

a 9 10 11 12

WAVELENGTH (u)

Fig. 14. AMTIR-1 (230K, 300K, 328K) , n(X).

Table 17. Sellmeier Fit for AMTIR at 230K

HAUELENGTH MEASURED CALCULATED DIFFERENCE (an) INDEX INDEX

7.9 2.49921 2.49^46 -0.00025 7.1 2.49902 2.49916 -0.00014 7.2 2.49860 2.49886 -0.00026 7.3 2.49840 2.49857 -0.00017 7.4 2.49836 2.49829 0.00007 7.5 2.49778 2.49801 -0.00023 7.6 2.49785 2.49773 0.00012 7.7 2.49765 2.49746 0.00019 7.8 2.49737 2.49719 0.00018 7.9 2.49715 2.49692 0.00023 8.0 2.49687 2.49666 0.00021 8.1 2.49664 2.49639 0.00025 8.2 2.49636 2.49613 0.00023 8.3 2.49606 2.49586 0.00020 8.4 2.49579 2.49560 0.00019 8.5 2.49553 2.49534 0.00019 8.6 2.49525 2.49507 0.00018 8.7 2.49496 2.49481 0.00015 8.8 2.49466 2.49454 0.00012 8.9 2.49442 2.49428 0.00014 9.0 2.49402 2.49401 0.00001 9.1 2.49381 2.49374 0.00007 9.2 2.49352 2.49347 0.00005 9.3 2.49321 2.49319 0.00002 9.4 2.49294 2.49291 0.00003 9.5 2.49259 2.49263 -0,00004 9.6 2.49231 2.49234 -0.00003 9.7 2.49202 2.49205 -0.00003 9.8 2.49171 2.49175 -0.00004 9.9 2.49134 2.49145 -0.00011 10.0 2.49097 2.49114 -0.00017 10.1 2.49067 2.49083 -0.00016 10.2 2.49037 2.49051 -0.00014 10.3 2.49002 2.49018 -0.00016 10.4 2.48972 2.48985 -0.00013 10.5 2.48937 2.48951 -0.00014 10.6 2.48906 2.48915 -0.00009 10.7 2.48866 2.48879 -0.00013 10.8 2.48825 2.48842 -0.00017 10.9 2.48784 2.48804 -0.00020 11.0 2.48746 2.48764 -0.00018 11.1 2.48720 2.48724 -0.00004 11.2 2.48682 2.48682 0.00000 11.3 2.48638 2.48638 0.00000 11.4 2.48596 2.48593 0.00003 11.5 2.48554 2.48547 0.00007 11.6 2.48529 2.48499 0.00030 11.7 2.48475 2.48448 0.00027 11.8 2.48441 2.48396 0.00045 11.9 2.48395 2.48342 0.00053 12.0 2.48343 2.48285 0.00058

ROOT HEAH SQUARE DIFFERENCE3 2.7 85060643E-5


Al=5.22571012898 U1=0.330659293792

A2=0.0613323313319 U2=264.67358834

Table 18. Herzberger Fit for AMUR at 230K

UAUELENGTH MEASURED CALCULATED DIFFERENCE <un> INDEX INDEX

7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 . 8 8.1 8.2 8.3 8.4 8.5 8 . 6 8.7 8 . 8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

10.0 10 .1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 1 1 . 1 1 1 . 2 11.3 11.4 11.5 1 1 . 6 11.7 1 1 . 8 11.9 1 2 . 0

2.49921 2.49902 2.49860 2.49840 2.49836 2.49778 2.49785 2.49765 2.49737 2.49715 2.49687 2.49664 2.49636 2.49606 2.49579 2.49553 2.49525 2.49496 2.49466 2.49442 2.49402 2.49381 2.49352 2.49321 2.49294 2.49259 2.49231 2.49202 2.49171 2.49134 2.49097 2.49067 2.49037 2.49002 2.48972 2.48937 2.48906 2.48866 2.48825 2.48784 2.48746 2.48720 2.48682 2.48638 2.48596 2.48554 2.48529 2.48475 2.48441 2.48395 2.48343

2.49913 2.49893 2.49872 2.49850 2.49828 2.49805 2.49782 2.49758 2.49734 2.49709 2.49684 2.49658 2.49632 2.49666 2.49579 2.49552 2.49524 2.49497 2.49468 2.49440 2.49411 2.49382 2.49352 2.49323 2.49292 2.49262 2.49231 2.49200 2.49168 2.49136 2.49103 2.49070 2.49037 2.49003 2.48969 2.48934 2.48899 2.48863 2.48827 2.48790 2.48753 2.48715 2.48677 2.48638 2.48599 2.48559 2.48519 2.48477 2.48436 2.48393 2.48350

0.00008 0.00009

-0.00012 -0.00010 0.00008 -0.00027 0.00003 0.00007 0.00003 0.00006 0.00003 0.00006 0.00004 0.00000 0.00000 0.00001 0.00001

-0.00001 -0.00002 0.00002

-0.00009 -0.00001

0.00000 -0.00002 0.00002 -0.00003

0.00000 0.00002 0.00003 -0.00002 -0.00006 -0.00003 0.00000 -0.00001 0.00003 0.00003 0.00007 0.00003 -0.00002 -0.00006 -0.00007 0.00005 0.00005 0.00000

-0.00003 -0.00005 0.00010 -0.00002 0.00005 0.00002 -0.00007



A=2.49439374217 B=0.647967078296 C=-12.5684088088

D=-4.768709281E-5 E=-3.817914938E-7

48

Table 19. Sellmeier Fit for AMUR at 300K

WAUELENGTH MEASURED CALCULATED DIFFERENCE <un> INDEX INDEX

7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 9.9 8 . 1 8.2 8.3 8.4 8.5 8 . 6 8.7 8 . 8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 19.0 19.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 1 1 . 1 1 1 . 2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 1 2 . 0

2.50506 2.50470 2.50429 2.50412 2.50405 2.50351 2.50357 2.50334 2.50302 2.50277 2.50259 2.50232 2.50201 2.50176 2.50149 2.50118 2.50090 2.50061 2.50029 2.50006 2.49976 2.49949 2.49915 2.49877 2.49848 2.49819 2.49784 2.49754 2.49724 2.49690 2.49666 2.49621 2.49587 2.49555 2.49518 2.49490 2.49453 2.49412 2.49376 2.49338 2.49303 2.49262 2.49226 2.49184 2.49148 2.49104 2.49068 2.49026 2.48979 2.48941 2.48907

2.50551 2.50512 2.50475 2.50440 2.50405 2.50371 2.50339 2.50307 2.59277 2.50247 2.50218 2.50189 2.50161 2.50134 2.501O7 2.50081 2.50055 2.50029 2.50004 2.49979 2.49954 2.49929 2.49905 2.49880 2.49855 2.49831 2.49305 2.49780 2.49754 2.49728 2.49702 2.49674 2.49646 2.49617 2.49586 2.49555 2.49521 2.49486 2.49449 2.49410 2.49367 2.49321 2.49270 2.49215 2.49153 2.49084 2.49006 2.48916 2.48812 2.48687 2.48537

-0.00045 -0.00042 -0.00046 -0.00028

0.00000 -0.00020

0.00018 0.00027 0.00025 0.00030 0.00041 0.00043 0.00040 0.00042 0.00042 0.00037 0.00035 0.00032 0.00025 0.00927 0.00022 0.00020 0.00010 -0.00003 -0.00007 -0.00012 -0.00021 -0.00026 -0.00030 -0.00038 -0.00036 -0.00053 -0.00059 -0.00062 -0.00068 -0.00065 -0.00068 -0.00074 -0.00073 -0.00072 -0.00064 -0.00059 -0.00044 -0.00031 -0.00005

0.00020 0.00062 0.00110 0.00167 0.00254 0.0037O


COEFFICIEHTS OF THE FORMULA

Al=5.21978984951 U1=0.574085835591

A2=0.00983376568743 U2=166.25768891

Table 20. Herzberger Fit for AMTIR at 300K

MAUELENGTH MEASURED CALCULATED DIFFERENCE <un) INDEX INDEX

7.0 2.50506 2.50490 0.00016 7.1 2.50470 2.50468 0.00002 7.2 2.50429 2.50445 -0.00016 7.3 2.50412 2.50422 -0.00010 7.4 2.50405 2.50399 0.00006 7.5 2.50351 2.50375 -0.00024 7.6 2.50357 2.50351 0.00006 7.7 2.50334 2.50326 0.00008 7.8 2.50302 2.50302 0.00000 7.9 2.50277 2.50277 0.00000 8.0 2.50259 2.50251 0.00008 8.1 2.50232 2.50225 0.00007 8.2 2.50201 2.50199 0.00002 8.3 2.50176 2.50172 0.00004 8.4 2.50149 2.50145 0.00004 8.5 2.50118 2.50118 0.00000 8.6 2.50090 2.50090 0.00000 8.7 2.50061 2.50062 -0.00001 8.8 2.50029 2.50033 -0.00004 8.9 2.50006 2.50004 0.00002 9.0 2.49976 2.49975 0.00001 9.1 2.49949 2.49945 0.00004 9.2 2.49915 2.49915 0.00000 9.3 2.49877 2.49884 -0.00007 9.4 2.49848 2.49853 -0.00005 9.5 2.49819 2.49822 -0.00803 9.6 2.49784 2.49790 -0.00006 9.7 2.49754 2.49757 -0.00003 9.8 2.49724 2.49725 -0.00001 9.9 2.49690 2.49692 -0.00002

18.0 2.49666 2.49658 0.00008 18.1 2.49621 2.49624 -0.00003 10.2 2.49587 2.49590 -0.00003 10.3 2.49555 2.49555 0.00000 10.4 2.49518 2.49520 -0.00002 10.5 2.49490 2.49484 0.00006 10.6 2.49453 2.49448 0.00005 10.7 2.49412 2.49412 0.00000 10.8 2.49376 2.49375 0.00001 10.9 2.49338 2.49338 0.00000 11.0 2.49303 2.49300 0.00003 11.1 2.49262 2.49262 0.00000 11.2 2.49226 2.49224 0.00002 11.3 2.49184 2.49185 -0.00001 11.4 2.49148 2.49146 0.00002 11.5 2.49104 2.49106 -0.00002" 11.6 2.49068 2.49066 0.00002 11.7 2.49026 2.49026 0.00000 11.8 2.48979 2.48985 -0.00006 11.9 2.48941 2.48944 -0.00003 12.0 2.48907 2.48903 0.00004



A=2.51671869904 D=-l.84483594E-4 B=-0.218392136146 E=9.514793892E-9 C=3.98731608444

Table 21. Sellmeier Fit for AMTIR at 328K

MAUELENGTH MEASURED CALCULATED DIFFERENCE <un>

7.9 7.1 7 .2 7 .3 7 .4 7 .5 7 .6 7 .7 7.8 7.9 8.9 8.1 8 . 2 8.3 8.4 8.5 8 .6 8.7 8 . 8 8.9 9.8 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 19.9 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 11.9 1 1 . 1 11.2 11.3 11.4 11.5 11.6 11.7 1 1 . 8 11.9 12.0



INDEX INDEX

2. 59753 2. 51093 -0. 00250 2. 59739 2. 59936 -0. 00197 2. 59689 2. 50872 -0. 00192 2. 50649 2. 50810 -0. 00161 2. 59644 2. 50751 -0. 00107 2. 59598 2. 50695 -0. 00097 2. 59598 2. 50641 -0. 00043 2. 59578 50589 -0. 00011 2. 50546 2! 50539 0. 00007 2. 50516 2. 50496 0. 00026 2. 50501 2. 50444 0. 00057 2. 50468 2. 50400 0. 00068 2. 50438 2. 50357 8. 00081 2. 50405 2. 50315 0. 00090 2. 50382 2. 50276 0. 00106 2. 50354 2. 50237 0. 00117 2. 58326 2. 50200 0. 00126 2. 50295 2. 50165 0. 00130 2. 50261 2. 50130 0. 00131 2. 50243 2. 50097 0. 00146 2. 50203 2. 50065 0. 00138 2. 50183 2. 50034 0. 00149 2. 50151 2. 50005 0. 00146 2. 50116 2. 49976 0. 00140 2. 50087 2. 49^48 0. 00139 2. 50058 2. 49921 0. 00137 2. 50025 2. 49895 0. 00130 2. 49991 2. 49870 0. 00121 2. 49964 2. 49946 9. 00118 2. 49926 2. 49823 9. 00103 2. 49888 2. 49801 9. 00087 2. 49859 2. 49780 0. 00079 2. 49827 2. 49760 0. 00067 2. 49795 2. 49741 0. 00054 2. 49756 2. 49724 0. 00032 2. 49726 2. 49709 0. 00017 2. 49686 2. 49697 -0. 00011 2. 49646 2. 49691 -0. 00045 2. 49612 2. 49700 -0. 00088 2. 49574 2. 49778 -0. 00204 2. 49541 2. 48883 0. 00658 2. 49499 2. 49453 0. 00046 2. 49466 2. 49490 -0. 00024 2. 49426 2. 49493 -0. 00067 2. 49387 2. 49488 -0. 00101 2. 49346 2. 49479 -9. 00133 2. 49306 0 . 49468 -0. 00162 2. 49271 2. 49457 -0.00186 2. 49236 2. 49445 -0. 00209 2. 49200 2. 49433 -0. 00233 2. 49154 2. 49421 -0. 00267

A1=5.18249059371 Ul=l.088694994

A2=-I.268093627E-4 U2al20.564074729

Table 22. Herzberger Fit for AMTIR at 328K

HAUELENGTH MEASURED CALCULATED DIFFERENCE (un) INDEX INDEX

7.0 2.50753 2.50748 0.00005 7.1 2.50739 2.50721 0.00018 7.2 2.50680 2.50695 -0.00015 7.3 2.50649 2.50669 -0.00020 7.4 2.50644 2.50643 0.00001 7.5 2.50598 2.50617 -0.00019 7.6 2.50598 2.50592 0.00006 7.7 2.50578 2.50566 0.00012 7.8 2.50546 2.50540 0.00006 7.9 2.50516 2.50515 0.00001 8.0 2.50501 2.50489 0.00012 8.1 2.50468 2.50462 0.00006 8.2 2.50438 2.50436 0.00002 8.3 2.50405 2.50409 -0.00004 8.4 2.50382 2.50382 0.00000 8.5 2.50354 2.50354 0.00000 8.6 2.50326 2.50326 0.00000 8.7 2.50295 . 2.50298 -0.00003 8.8 2.50261 2.50269 -0.00008 8.9 2.50243 2.50240 0.00003 9.0 2.50203 2.50211 -0.00008 9.1 2.50183 2.50181 0.00002 9.2 2.50151 2.50150 0.00001 9.3 2.50116 2.50120 -0.00004 9.4 2.50087 2.50089 -0.00002 9.5 2.50058 2.50057 0.00001 9.6 2.50025 2.50025 0.00000 9.7 2.49991 2.49993 -0.00002 9.8 2.49964 2.49960 0.00004 9.9 2.49926 2.49927 -0.00001 10.0 2.49888 2.49893 -0.00005 10.1 2.49859 2.49859 0.00000 10.2 2.49827 2.49825 0.00002 10.3 2.49795 2.49790 0.00005 10.4 2.49756 2.49755 0.00001 10.5 2.49726 2.49720 0.00006 10.6 2.49686 2.49684 0.00002 10.7 2.49646 2.49648 -0.00002 10.8 2.49612 2.49612 0.00000 10.9 2.49574 2.49575 -0.00001 11.0 2.49541 2.49538 0.00003 11.1 2.49499 2.49501 -0.O0002 11.2 2.49466 2.49464 0.00002 11.3 2.49426 2.49426 0.00000 11.4 2.49387 2.49388 -0.00001 11.5 2.49346 2.49350 -0.00004 11.6 2.49306 2.49311 -0.00005 11.7 2.49271 2.49273 -0.00002 11.8 2.49236 2.49234 0.00002 11.9 2.49200 2.49195 0.00005 12.0 2.49154 2.49155 -0.00081



A=2.53322308243 D=-2.963718118E-4 B=-l.01062327641 E=3.392131754E-7 C=20.621222699

52

<n<T)-n<179))*1E4

148

129

199

99

69

49

29

0 i .i

169 139 299 228 249 269 299 399 329 349 369 TEMPERATURE <K>

Fig. 15. AMTIR-l n (T) at 8 ym.

53

I H D E X

0

F

R E F R A

C T I 0 H

<n<T)-n<179)>S1E4

140 r

129

190

39

£0

40

29

9 '

160 139 299 229 240 2S9 289 399 329 349 369 TEMPERATURE <K>

Fig. 16. AMTIR-1 n(T) at 10 ym.

Table 23. AMTIR-1 : n(T) at 8 um

Temperature (K)

Measured Index

169.5 2.50104

179.5 2.50184

189.5 2.50228

199.5 2.50292

209.0 2.50391

219.5 2.50444

239.5 2.50611

259.0 2.50766

278.5 2.50925

299.0 2.51092

310.0 2.51160

323.5 2.51256

330.0 2.51317

Least-squares linear data slope = dn/dT - 76.4x10 °C' correlation coefficient = (

Table 24. AMTIR-1 : n(T) at 10 vm

Temperature Measured (K) Index

169.5 2.49532

178.5 2.49603

188.5 2.49653

198.5 2.49713

209.0 2.49816

219.5 2.49892

239.5 2.50018

259.0 2.50189

278.5 2.50350

299.0 2.50518

312.0 2.50583

324.0 2.50694

350.0 2.50902

Least squares linear data fit: slope = dn/dT = 76.3x10 °C-1

correlation coefficient = 0.9994

56

2.52 r

I H D E X

0

F

R E F R A C T I 0

N

2.50

2.48

* + *

$

+ *

* t

* + *

2.46 i i i i »

8 10

i i » 11 12

WAUELENGTH <ni c rone tars >

Fig. 17. AMTIR vs UA AMTIR-1 (300K) n(A). * = UA data, + = AMTIR data.

A graphical comparison of their data with the data presented in

this thesis is given in Figure 17. There is an apparent offset between

the two sets of data. Table 25 lists the index values and these

differences for six wavelengths. Our data are found to be lower than

the published data by an average value of -0.00084. While this value is

substantially higher than the calculated systematic error of 0.00050 for

these measurements (see Error Analysis chapter), it is well within the

batch-to-batch variation in index of 0.0030 reported by Amorphous

Materials, Inc. A material analysis was not available for the specific

sample measured. However, the offset in the compared data would seem

to indicate a slight variation in glass composition or structure as

compared to the sample measured by the manufacturer.

A comparison of the dn/dT data is given in Table 26. Good agreement

is observed, even though the data from the manufacturer covers the

temperature range of 25°C to 65°C only.

Table 25. AM vs UA Data : AMTIR-1 at 300K

(um) n(UA) n(AM) n(UA-AM)

7.0 2.50506 2.5057 -0.00064

8.0 2.50259 2.5034 -0.00081

9.0 2.49976 2.5005 -0.00074

10.0 2.49666 2.4976 -0.00094

11.0 2.49303 2.4936 -0.00057

12.0 2.48907 2.4904 -0.00133

Average difference = -0.00080 Standard deviation =» 0.00027

NOTE: AM stands for Amorphous Materials, Inc.

Table 26. AM vs UA Data : AMTIR-1 dn/dT values

Source Wavelength (jim) dn/dT x 10S/°C

AM 1.15 101.0

AM 3.39 77.0

UA 8.0 76.4

UA 10.0 76.3

AM 10.6 72.0

Note: AM stands for Amorphous Materials, Inc. The data reported by Amorphous Materials cover the temperature range from 25 to 65°C only.

CHAPTER 4

ERROR ANALYSIS

Any claim to having measured absolute values of refractive index

requires a thorough knowledge of all the experimental errors involved.

In fact, the ability to precisely understand and calculate the errors is

just as important as the experimental skills needed to make the

measurements. Swedberg (1979) has described in great detail the errors

associated with the method of perpendicular incidence. The equations he

derived will be used in this chapter to calculate the overall errors

associated with these measurements.

Various types of errors inherently limit the absolute accuracy

of any physical measurement. Included in this analysis are errors of

both a random and systematic nature. In addition, overall system

repeatability and errors due to prism misalignment and beam asymmetries

are discussed in some detail.

Random Errors

The random errors associated with this measurement process are

those which lead to a random deviation of the index from some true,

absolute value. If large enough, these errors can mask the true

functional relationship between index and wavelength or temperature.

This is most critical in determining whether or not dn/dT (the slope of

the n(T) curve) is linear or nonlinear with respect to temperature.

60

For these measurements, three random errors have been

identified. They arise from inaccuracies in: (1) measuring the deviation

angle of the prism, (2) setting the monochromator to an exact

wavelength, and (3) maintaining a constant prism temperature. The

equations describing these random errors and an explanation of the

symbols used are given in Tables 27 and 28, respectively.

Systematic Errors

The systematic errors associated with this measurement process

are those which lead to a constant deviation, or offset, of the index

from the absolute value. Although these errors leave the shape of the

n(x) and n(T) curves intact (adding only a constant term to the curves)

they are greater in magnitude and harder to minimize than the random

errors. Most of the experimental effort involved with calibration and

system alignment is aimed at reducing the systematic errors.

For these measurements, six systematic errors have been

identified. They result from inaccuracies in: (1) aligning the prism, (2)

measuring the prism apex angle, (3) refraction due to window wedge and a

vacuum-air interface at the dewar windows, (4) the finite spectral

bandwidth of the monochromator, (5) the calibration of the monochromator

dial vs wavelength, and (6) the measurement of the prism temperature.

The equations describing these systematic errors and an explanation of

the symbols used are given in Tables 27 and 28, respectively.

One additional systematic error could involve the rotary table

used to rotate the detector. If this rotation included a systematic

error in the drive mechanism, an error in measuring the prism deviation

Table 27. Error Analysis.

62

Source Equation

Deviation Angle

Wavelength

Temperature

Prism Alignment

Prism Apex Angle

Slit Width

Wavelength

Temperature

Random

An(dfc) fcdb - -f< Ud)b 3n

An(X^) = gj UX)d

An(Tp) = (AT)p

Systematic

4n(V " [iisW "n'],/! <4d)

[afcr -f - • An(a) cos(a)

sin(a) Aa

3n An(Xb) =» — (AX)b

An(Xc) =• — (AX)C

An(Tc) = § (AT)c

63

Table 28. Description of Symbols

Symbol Description

a Prism apex angle

Aa Error in measuring the prism apex angle

n Index of refraction (min. and max.)

3n/3T Slope of the n(T) curve (min. and max.)

3n/3X Slope of the n(X) curve (min. and max.)

(Ad)^ Total combined error in measuring the reference and deviated beam centers

(Ad)p Error in measuring the prism deviation angle due to prism alignment errors

( AT)C Calibration error of the temperature sensor

(AT)p Average fluctuation of the prism temperature

(AX)|j Monochromator bandwidth

(AX)C Monochromator calibration error

(AX)j Wavelength uncertainty due to the resolution

of the monochromator dial

64

angle and therefore an error in index would result. It is believed that

this error source is negligible, and the accuracy of rotation was not

verified experimentally. However, it is a possible source of error that

should be measured in future work.

Calculation of (Ad)p

The effect of prism misalignment about the alpha, beta, or gamma

axes (Figure 3) is to introduce a change, (Ad)p, in the deviation angle

measured between the reference and deviated beams. This in turn leads

to an error, An(dp), in the index. Proper calculation of (Ad)p requires

that rays be traced through the prism (in a three-dimensional sense) for

arbitrary rotations of the prism about its three axes. This was done

using the ACCOS ray-trace program.

The actual calculation of (Ad)p was carried out as follows. A

reference deviation angle was first calculated assuming the prism had no

tilt errors. Under this ideal condition the deviation angle was found by

applying Snell's Law at the second surface of the prism.

A real ray was then traced through the prism after the

appropriate amounts of rotation were introduced. The rotation, or tilt,

errors about each of the three prism axes were estimated experimentally

and are listed in Table 29. These errors were introduced by tilting the

prism using the TILT command in ACCOS. The combined effect of this

three-dimensional rotation is to change the prism deviation angle (i.e.,

the projection of the real ray on the horizontal detector plane of

rotation). These deviation angles appear in the ACCOS output as shown in

Appendix E.

Table 29. Variables for Error Analysis

Variable MgO Sapphire AMTIR-1

a 31.00378 31.00364 15.90526 deg

Aa 0.0042 0.0068 0.0012 mr

d (X min) 29.10806 29.79194 28.56333 deg

d (X max) 26.45681 25.73958 28.22000 deg

Ad (ref) 5.9 10.8 2.9 sec

Ad (dev) 5.9 10.8 2.9 sec

Aa 0.075 0.075 0.075 mr

A3 0.075 0.075 0.075 mr

AY 2.0 2.0 2.0 deg

n (min) 1.63663 1.61793 2.48907

n (max) 1.70880 1.72954 2.50506

(Ad)b 0.0572 0.1047 0.0291 mr

|(Ad)p| (X min) 0.149 0.149 0.157 mr

|(Ad)p| (X max) 0.147 0.146 0.157 mr

(AX)jj (bandwidth) 0.0261 0.0261 0.066 um

(AX)C (calibration error)

0.0001 0.0001 0.0006 Vim

(AX)j (min. scale division)

0.0008 0.0008 0.0023 ym

(AT)(j (sensor cal.) 2 2 2 K

(AT)p (stability) 2 2 2 K

3n/3T NA NA 0.000076 K-1

3n/3X (X min) -0.0146 -0.0202 -0.0036 um-1

3n/3X (X max) -0.0349 -0.0567 -0.0034 urn-1

66

Finally, (Ad)p was found by taking the difference in deviation

angle between the reference ray and the real ACCOS ray. These values

are listed in Table 29 for each prism.

Combined Errors

Using the assumption of Icenogle (1975) and Swedberg (1979), the

experimental errors are considered to be statistically independent. This

allows the total random and systematic errors to be calculated as the

root-sum-square (RSS) of the individual errors. The variables and

calculated errors for each of the prisms are shown in Tables 29-32.

Note that the systematic error due to the window wedge and vacuum-air

interface has not been calculated. This error was accounted for in the

data by the window correction procedure described in Chapter 2.

All of the total errors except two fall close to the desired

accuracy of SxlO-1'. These two are maximum systematic errors for

magnesium oxide and sapphire, which are both large due to the spectral

bandwidth error. This error itself is high due to a large slope dn/dx

for each material.

Temperature Coefficient

The procedure for making a temperature run was discussed in

Chapter 3. An assumption was made, based on information available, that

the changes in temperature did not cause mechanical movement inside the

dewar. This in turn could lead to changes in prism alignment.

Unfortunately, it wasn't until after the first two prisms were measured

that this assumption was discovered to be wrong. In fact, measurements

67

Table 30. Combined Errors: MgO at 300K

Random Errors:

Max. Min.

Deviation angle An(db) 0.000060 0.000053

Wavelength An(xd) 0.000028 0.000012

Temperature An(Tp) 0.000018 0.000018

RSS Total 0.000063 0.000057

Systematic Errors:

Prism alignment An(d p) 0.000192 0.000179

Prism apex angle An(a) -0.000008 -0.000007

Spectral bandwidth An( Xfc) -0.000911 -0.000381

Monochromator

calibration An(Xc) -0.000002 -0.000001

Temperature An(Tc) 0.000018 0.000018

RSS Total 0.000931 0.000421

Table 31. Combined Errors: Sapphire n0 at 300K

Random Errors:

Deviation angle

Wavelength

Temperature

Systematic Errors:

Prism alignment

Prism apex angle

Spectral bandwidth

Monochromator calibration

Temperature

Max. Min.

An(db) 0.000112 0.000092

An(Ad) 0.000045 0.000016

An(Tp) 0.000016 0.000016

RSS Total 0.000122 0.000095

An(d p) 0.000256 0.000121

• An(a) -0.001480 -0.000011

An(Ab) -0.001479 -0.000527

An(Xb) -0.000002 -0.000001

An(Tc) 0.000016 0.000016

RSS Total 0.001502 0.000541

Table 32. Combined Errors : AMTIR-1 at 300K

69

Random Errors:

Max. Min.

Deviation angle An(db) 0.000078 0.000077

Wavelength An(\d) 0.000008 0.000008

Temperature An(Tp) 0.000152 0.000152

RSS Total 0.000171 0.000171

Systematic Errors:

Prism alignment An(d p) 0.000558 0.000439

Prism apex angle An(a) 0.000008 0.000007

Spectral bandwidth An(xc) 0.000238 0.000224

Monochromator

calibration An(Xc) -0.000001 -0.000001

Temperature An(Tc) 0.000152 0.000152

RSS Total 0.000625 0.000516

dn/dT Error:

Random errors plus prism alignment An

RSS Total 0.000584 0.000471

showed considerable prism rotation, mainly around the alpha axis. This

appears to explain the deviations of n(T) from a straight line for

magnesium oxide and sapphire. The n(T) curve for AMTIR-1 was taken by

realigning the prism after each change in temperature. The higher

degree of linearity in the data points appears to reflect this

correction.

The error analysis for n(T) data follows that given by Swedberg.

The maximum RSS random error An is considered as an error bar at the

end points of the n(T) curve. This sets a limit (error) to the minimum

and maximum values of the slope, given by:

(dn/dT)max - dn/dT + T*i\

(dn/dT)min = dn/dT - (2)

The actual error in slope is therefore . A graphical explanation 2 ~

of this equation is shown in Figure 18.

One important change from Swedberg's definition of the RSS

random error An is to be noted. By having to realign the prism after

every temperature change, the error due to prism alignment now must be

considered as a random error. The expression for An becomes:

(An)2 = [An(db) ]2 + [An(Xd)]2 + [An(Tp)]2 + [An(dp)]2 (3)

For the AMTIR-1 prism, An(max.) = 0.000584. The error in dn/dT is

calculated to be =, +7.3 x K-1. 2 ~ M

71

I t l D E X

n2

n l

j j r ( m a x . )

5T (min->

1 i n e a r f i t t o t h e d a t a

T 1

H e i g h t o f e r r o r b a r s = 2 A n

T 2

T E M P E R A T U R E

Fig. 18. dn/dT Error Analysis.

72

System Repeatability

The combined effects of the random errors act to limit the

overall precision of the measurements. For this discussion, precision

may be thought of as the degree to which the same index value is

determined in a set of repeated measurements and conditions. The words

system repeatability and precision will therefore be used to mean the

same thing. Both a short-term and long-term precision have been

measured.

Short-term Precision

The short-term precision is that level of system repeatability

attainable during the time required for one wavelength run. This

precision was determined by first aligning the system and then making

repeated index measurements, alternating between two different

wavelengths. In this manner, the only uncertainties introduced by the

measurement process were those previously identified as the random

errors.

Five measurements at both 7 and 11 ym were made using the

AMTIR-1 prism. The standard deviation was calculated for each set of

index values and used as a measure of the precision. Results are shown

in Table 33. For each wavelength, the standard deviation is substantially

less than the RSS random error of 0.00017 calculated for AMTIR-1.

However, both standard deviations agree well with the deviation-angle

random error of 0.00007 calculated for AMTIR-1. The predicted

temperature random error of 0.00015 was not a factor in the measured

precision, indicating good temperature stability during the data-taking

Table 33. System Repeatability

Time of Measurement n(7 iim) n(12 um)

2:30 PM 2.50503

2:40 PM — 2.48902

2:45 PM 2.50506 —

2:49 PM — 2.48901

2:52 PM 2.50491 —

2:56 PM — 2.48894

3:00 PM 2.50507 —

3:04 PM — 2.48905

3:07 PM 2.50511 —

3:11 PM 2.48902

(7 um) = 0.00007

(12 um) - 0.00003

process. The short-term precision is therefore limited mainly by the

accuracy in measuring the deviation angle.

Long-term Precision

The long-term precision is that level of system repeatability

attainable from one day to the next. This precision was observed by

comparing index values taken on successive days, using the AMTIR-1 prism.

For the measurements made, the index at 11 and 12 pm changed by +0.00016

and +0.00022, respectively. Given that all factors affecting the

systematic errors remained constant, these changes should be accountable

by one of the random errors. In fact, both observed differences agree

well with the temperature random error of 0.00015 for AMTIR-1. This

temperature error was calculated assuming a change in prism temperature

of 2°C, a value well within the average daily temperature fluctuations

in the laboratory. The long-term precision is therefore limited by room

temperature stability, at least for prism materials where the

temperature error dominates the random errors. By measuring the

temperature fluctuation in a repeatable manner and knowing dn/dT, this

error may be corrected.

APPENDIX A

PRISM SPECIFICATIONS

75

.125 *.005

SURFACE I 5URFACE2

^0° ±20 ARC 5EC

see NOTE(2)

•SURFACE 3

.500 ±.005

0̂°

ARC SEC

UNIVERSITY OF ARIZONA OPTICAL SCIENCES CENTER

INFRARED LABORATORY

.000 ±.00E>

NOTES:

(1) Dimensions in inches (2) Apex angles ( in degrees)

MgO Sapphi re AMTIR-I

31.00 31 .00 15-90

MATERIAL: Ms°i Sapphire, AMTIR-1

SURFACE FLATNESS 1.2: ^ALLOWABLE CURVATURE

JjAFIGURE TOL. 3 -

(X=632.8 nmj

SURFACES MARKED "P" POLISHED ALL OTHERS f.ROUND

SURFACE QUALITY 1,2; 80/S0

3: 120/70 CHAMFER .020x45°, ALL EDGES

Fig. 19. Prism Specifications. c*

APPENDIX B

SYSTEM ALIGNMENT

Described in this appendix is a step-by-step procedure used to

align the optical system. Refer to Figure 2 in Chapter 2 to identify the

system components.

(1) Measure the height from the top of the table to the center

of the entrance slit.

(2) Adjust the center of the thermal source to this height.

(3) Install a pair of slits in the monochromator, each one

masked down to a 50 ym x 50 um hole centered in each of the slits.

(4) Adjust mirror M2 to focus the source onto the center of the

entrance slit.

(5) Rotate the grating to zero-order, and if necessary, align the

grating so the beam exits the monochromator at the center of the exit

slit.

(6) Adjust mirrors M4 and M5 to position the beam at the center

of the dewar entrance window.

(7) Install mirror M6 in the beam and adjust it until the beam

falls right beside the hole in the exit slit.

(8) Set up the 20x microscope to view the image. Translate

mirror M5 until best focus is achieved. If excessive astigmatism is

present, mirror M5 may not be in a proper off-axis position. When best

focus is obtained, the beam entering the dewar is collimated.

77

Refer to Figure 20 for the next section of prism alignment.

(9) Install the prism in the dewar, position the dewar on the

rotary table, and remove the three windows. Remove mirror M6.

(10) Use the adjusting screw (1) and the rotary table to position

the prism so the reflected beam falls back directly onto the hole in the

exit slit. If the reflected beam is too weak to see visually, use the

He-Ne beam as described in Appendix C. At this point the beam has been

autocollimated off the front surface of the prism.

(11) Rotate the grating to an infrared wavelength appropriate

for the prism being measured. Position the rotary table so the

reference beam falls on the detector.

(12) Adjust mirrors M7 and M8 to maximize the signal of the

reference beam.

(13) Position the rotary table so the deviated beam falls on the

detector. Use the adjusting screw (2) to maximize the signal of the

deviated beam. This step positions the prism dihedral edge vertical to

the plane of detector rotation, eliminating any effects due to prism

pyramid.

(14) Recheck step 10 to insure that the beam reflected off the

prism is still directly centered in the exit slit.

79

ADJUSTING SCREW (2)

DEV. BEAM

FIXED BALL PIVOT ADJUST I MR SCREW (1)

TOP VIEW

Fig. 20. Prism/Dewar Alignment.

APPENDIX C

He-Ne COALIGNMENT

This appendix describes a procedure used to coalign a He-Ne

laser beam to the thermal beam used for measurements. For prisms

having a low index of refraction over the visible spectrum, the beam

reflected off the first surface may be very difficult to see. The use

of a laser beam can make the autocollimatlon procedure much easier.

(1) Complete steps 1-8 in Appendix B.

(2) Remove the thermal source.

(3) Set up the laser, beam expander, and lens LI as shown in

Figure 2.

(4) Position lens LI so the focused laser spot falls in the

physical location normally occupied by the thermal source.

(5) Adjust mirror Ml so that mirror M2 focuses the laser beam at

the center of the entrance slit. Do not adjust mirror M2 in the

process. Lens LI should be chosen so the focused laser spot overfills

the opening in the entrance slit.

(6) Through an iterative process of tipping, tilting, and

translating mirror Ml, adjust the laser beam so it exits the

monochromator. Again, the opening in the exit slit should be overfilled.

(7) The prism alignment may now be carried out according to

steps 9 and 10 in Appendix R.

80

81

(8) Replace the thermal source and complete steps 11-13 in

Appendix B.

APPENDIX D

SYSTEM SNR

An expression for the overall signal-to-noise ratio (SNR) of the

system is derived in this section. By actually measuring the SNR and

comparing it to this calculated value, an indication of system

performance is obtained.

Certain assumptions are made for the calculation:

(1) The source is a blackbody source.

(2) The FHi of the beam input to the monochromator matches the

F/// of the monochromator.

(3) The spectral bandwidth of the monochromator is very small.

(4) The quantum efficiency of the detector is independent of

wavelength.

(5) The focused beam just fills the detector area. A description

of the variables used below may be found in Table D-l. The SNR at the

detector may be written as:

* 4»d • Dj

SNR - V (D-l) (Ad • B)*/*

The power on the detector, is calculated using the radiative transfer

equation:

T(system) • L,| ^ • A<j • A0 • cosQ^ • cosej

4>d - 1 s-i (D-2) •t n • 0

Assume that 0^ = e0 = 0 :

82

<|>d = |r(system) • l|>x • Aj • A0J/f02

83

(D-3)

The radiance of the source is calculated using the Planck equation:

s ® Le \ • A X = —75 e»A TT Xs

exp M-- r - l

A X (D-4)

where

2dW AX = —— • cos6

rm (D-5)

and

9 = arc sin [t] (D-6)

The overall system transmission may be written as:

t(system) =» r(filter) • t(chopper) • p(M2) • p(M3) • x(monochromator)

• p(M4) • p(M5) • t(window) • t(window) • p(M7)

• p(M8) • t(window) (D-7)

Combining (D-l), (D-3), and (D-4) gives:

[D* • x(system) • C, • A0 • (A^)1/2 • e • AX] SNR =

exp XT

- 1

(D-8)

f„2 ' (B)l/2 • Xs

As an example, the expected SNR for the HgCdTe detector system

may be calculated using equation (D-8). Consider a wavelength of 7.0 ym

and the following values:

T(system) = (0.9)(0.45)(0.9)(0.9)(0.5)(0.9)(0.9)(0.8)(0.8)(0.9)(0.9)(0.8)

= 0.06

C, = 3.74 x 10"12 W cm1

A# = 5.1 cm2

= 0.002 cm2

X = 7.0 ym

AX = 0.078 um

C2 = 14387.86 \im K

T - 1500 K

e = 0.8

F0 = 40.64 cm

B = 1 Hz

The calculated SNR is 6000. No experimental values were measured.

85

Table 34. Variables Used in SNR Calculation

Variable Description

active area of the detector

Aq area of the beam at mirror M7

B bandwidth of the electronics

Cj first radiation constant = 2irhc2

C2 second radiation constant = hc/k

d grating spacing between lines

D*^ figure-of-merit for particular detector in use

fm focal length of the monochromator

fQ focal length of mirror M7

Lse>x spectral radiance of the source

m order number of the grating

e emissivity of the source

w monochromator slit width

p reflection coefficient

t transmission coefficient

X wavelength selected by the monochromator

AX spectral bandwidth of the monochromator

(frj power (in watts) on the detector

Qd angle of the detector surface normal relative to the optic axis

90 angle of the mirror M7 surface normal relative to the optic axis

APPENDIX E

PRISM ALIGNMENT ERROR ANALYSIS

86

U 0 1G 0 00200 00300 00400 00500 00700 00800 00900 01000 OUOO 01200 01300 01400 01300 OloOO 01700 01300 01.350 01860 01900 02000 02100 02200 02300 02400 02500 02600 02700 02800 02900 03000

87

LSNS ACCQSV LI PRISM ERROR ANALYSIS LIC MGO 300K WV, 2 5 UNITS INCHES SCY FANG,10 TH,100C Al R TILT, .00429718" .00429713 2 ArR CV,0 TH . 423 GLASS MGO,1.7088a L.63662: TTLT,0 31.00378 0 oj,O. AIR RTILT,.0. 31.00378 0 CV.O. AIR' RTILTj .0(1429713' .00429713"2 EOS F0ff,0 Q .0, L R A Y , 0 0 1 PRXYZ ALL F08,0 0 0 2 RAY,0 0 2 PRXYZ ALL MODE AFOCAL OUTPUT CP LENO. EXIT

88

.TO 1ACCOS V 06/23/73 OSC AT TUCSON, AZ 11/23/34 10.05.03.

—LENS ACCOSV —LI PRISM ERROR ANALYSIS —LIC MGO 300K —WW, 2 5 —UNITS INCHES —SCY FANS, 10 —TH,1000 ——ATR —TtUr, .00429713' .0Q4297T.® Zl: —AIR —cv, a-—TH-', .425" —GLASS MGOVt • 7O880K: r. 6346& —TTLTra 3t-0037®. <J~ —CV, 0 —AIR —RTILT ,0 31 .0037ft a. . —CV, 0 —AIR ' —RT1 E.TY. 004297T3' .0a42*7rsrf2£ —e as

—Foa^a a a 1

—RAY,0 0 I

—PRXYZ ALL.

RAY AT WAUL. I - <YR-,XR> * C 0.00', CKOOX"'

SURF L

Y" o. oaoaaa--

X. cr.oaaaaa

r ~(r.!aaaaoo

YANG<DG> —.004443

XANG< OG) .004145

3 0.000000 -.OOOOl?'

avoaaaoa . aaaazL.

a . oooooo a.oooooo

-.002601 -.009347"

.002425 41.673223

4 -.000019 .000012 a .aooooo —.005147 30.649443

5 -.000019 .000012' a .oooooo - L.134744 30.650003

—F03.0 0 0 2 -

—FAY , 0 0 2

—»SXY2 ALL

"AY AT JAVL 2 - •: YP.XR) = C 'O .00 . 0 .00)

3UPF 0 . 0 0 0 0 0 0 0 .000000

(m

0.000000 YANG' Di3> - . 0 0 4445

3 o . o o o e o - .000020

0 .000000 .000022

0 . 0 0 0 0 C 0 0 .000000

- . 00271 —. UU32o4

,C0 2532 37.4oo?JJ

- - . o o o o2 ; . .3 0 00 1 3 0 .0000 00 - . 3 '3 4 ' ? : 3 2 : . 4.: : -

- . o o 0 0 2 c . 0 0 0 1 4 J 1 J ' J "J 2 _ . - 3 . . i

89

00100 LENS ACCOSV 00200 LI PRISM ERROR ANALYSIS 00300 LtC SAPPHIRE <NO> 300K 00400 WW,2. 3" 00500 UNITS INCHESL-00700 SCY FANG, 10. ooaaa m, 1000 oo9oa- AIR- . _ . atoatr TILT R. OA42S<7T S **.AC429!7R SRI OtiaO AIR*.--01.20(1" " CV.tt 01300 THi.AlS 0 L400- GLASS" SAPPHIRE;! .7372JE L.A2343P. 01300 TILTfd 31.003^4- a 01600 cu,a. 01700 AIR o i sao rttlt,a :a(i3S4 cr otasa - CWr® : ataaffr AXHT o T.90OR RTTTJ7 ,AO42S?RR«' .AIXV&TIAT Z 02JQ0Q EOS 02100 FOBvff & Or L 02200 RAY,a. a- I 02300 PRXYZ ALL 02400 FOB.O 0 0 2.. 02500 RAY ,0 0 2 02400 PRXYZ: ALL 02700 MODE AFOCAL 02300 OUTPUT CP 02900 LENa 03000 " EXET

1ACC0S V 0.5/23X73 QSC AT TUCSON, A2 11/23/34 13.19.38.

—LEMS ACCOSU —LI PRISM ERROR ANALYSIS —LIC SAPPHIRE <NO) 300K «WY,2 5 —UNITS INCHES —SCY FANG,.tQ. —TH r1000 —AIR —TILT, .00429718 .00429713; 2. -—AIR" —CV,0 —TH,.421 —GLASS SAPPHIRE,! . 73725-1.42343. —TILT,Or 31.003^4-a —CV,0 —AIR —RTILT.O 3t.00364 0 —CV ,0 —AIR —RTILT,-.0042971 & .00429713: Z. —EOS

—FOB,0 (J L

—RAY , 0 0" I

—PRXYZ ALL

RAY AT WAVL t - CYR,XR> * < 0.00,. 0-00)

SURF 1

Y o.oooooa

X a.aaaaao:

2" a;oaoaao

YANG<DG> —.004445

XANGCQG) .004145

2 3

0*.000000 -.000019

a. oiocooo .000021

ar.ooooaa 0 .000000

-.002558 -.009960

.002386 63.496423

4 -.000019 .000011 0.000000 -.005269 32.492733

5 -.000019 .00001Z 0 .000000 1.272291 32.472342

—FOB. 0 0 0 2

—PAY , 0 0 2

—PRXY Z ALL

RAY AT WAUL 2 - :yr,xr> = < o .00, 0.00)

SURF 7 0 .000000

X 0 .000000 0 .000000

YANI3< DG!> - . 004J.<13

•'AMG'' 0G: .00-11-i =

0.00 0 000 - . 0 00 0 20

0 .000000 .000022

0 .000000 0 .000000

-.002733 -.00310.5

. C0 25?3 z-6 . ~4?21 3

- - . 0 0 0 0 20 .000013 0 .000000 -. 34

- , 000 0 20 .0000 14 0.000000 .•? .s354l 25. "2'—c I

00100 00200 00300 00400 00500 00700 00300 00900 01000 01100 01200 01300 01400 01500 01600 01700 01300 oiasa 01360 0 1900 02000 02100 02200 02300 02400 02500 02600 02700 02300 02700 03000

91

LENS ACCOSV LI PRISM ERROR ANALYSIS LIC AMTIR-l 300K WW,7 12 UNITS INCHES" SCY FANS,10 THf1000

. AIR TILT, .00427718- . 004-2971 8- 2: AIR" CV,0 TH>.5 GLASS AMTIR:-£,Z.50306. Z.4390T TILT,0 15.90526 0 CV,0 AIR RTTLT, a IS.70526, 0-CUr0̂ AtRF' RTTtr, .004297tSv .0U429fttt;'£ EOS:-: . Fosya a ir R»Y,0-0 1 PRXYZ ALL Faa.ct O <T 2 RAY rtt. a 2 PRXYZ. ALL. MODE: A FOCAL OUTPUT CP-L£NO~ s<rr

92

iACCOS '-J 06/23/73 OSC AT TUCSON, AS 11/23/34 10.14.54.

—LENS ACCOSV —LI PRISM ERROR' ANALYSIS-—LIC AMTIR-L 30 OK —WV,7 12 —UNITS INCHES' —SCY FANG, 10 —TH.IOOO —AIR —TILT».a0429718' .00429718" 2 —AIR —CV,0 —TH, —GLASS. AMTlR-t>2:.50TO£ 2-4SW-—TTLT,a. 3..703Z6 0-—CV.O —AIR —RTTLT, 0 15.90326 0" —CV,0 —AIR —RTILT, .0042971® .00429719 2 —EOS.

—FOB,0 (J 0 t

—RAY, 0 Q t

—PRXYZ ALL

RAY AT UAOL 1 - <YR,XR) *- < 0.00,. Or.00)

SURF L

Y a.oooooo

X Q.aooaoa

z: o-iaaaaaa

YANGCDGi -.004445

XANG<DG> .004145

2 3

a.oaoaocr -.000015

O-.OOOOOOf .000015

o.ooaaaa: a.oooooo'

-.00177* -.006113

.001654-43.359600

4 -.000015 .000012 0.000000 -.00300? 27.434340

5 -.000013" .000013 0 .000000 1.038037 27.433931

—FOB. 0 0 0 2

—PAY.O 0 2

— ALL

SAY AT .iJAUL 2 - ' YR,XR) => < 0 .00, 0.00)

3URF V/"

0.00 00 00 0.000000 0 .000000 YANG': C'G"' - . 0 0 4443

•CANG-: DG' . 004 14 =

3 0 .000000 - . 0000 16

0 .000000 .000013

0 . oooooo 0.oooooo

-.oo;"So -.00e07«

.00 1io5 43.D1r 2;i

4 -. :• o o o i s .000012 0.00 0000 -.0 0 4901 2~ . ; =

-.000013 . 00001 3 0.000000 1.0 22545 27.0 91--: 3

REFERENCES

Amorphous Materials, Inc., 1983, AMTIR-1 Product Information, Garland,

Texas.

Icenogle, Harmon Weston, 1975, "The Refractive Index of Silicon, Germanium, and Lithium lodate as a Function of Temperature and Wavelength," MS Thesis, University of Arizona.

Jeppesen, Myron A., 1958, "Some Optical, Thermo-Optical, and Piezo-Optical Properties of Synthetic Sapphire," J. Opt. Soc. Am. 48,

629.

Malitson, Irving M., 1962, "Refraction and Dispersion of Synthetic

Sapphire," J. Opt. Soc. Am. 52, 1377.

Malitson, Irving M., Frederick V. Murphy, Jr., and William S. Rodney, 1958, "Refractive Index of Synthetic Sapphire," J. Opt. Soc. Am. 48, 72..

Piatt, Ben C., H. W. Icenogle, J. E. Harvey, R. Korniski, and William L. Wolfe, 1975, "Technique for Measuring the Refractive Index and its Change with Temperature in the Infrared," J. Opt. Soc. Am.

65, 1264.

Piatt, Benjamin Curtis, 1976, "Instruments for Measuring Properties of

Infrared Transmitting Optical Materials," Ph.D. Dissertation,

University of Arizona.

Stephens, Robert E., and Irving H. Malitson, 1952, "Index of Refraction of

Magnesium Oxide," J. Res. NBS, 49, 249.

Strong, John, and R. T. Brice, 1935, "Optical Properties of Magnesium Oxide," J. Opt. Soc. Am. 25, 207.

Swedberg, James Lee, 1979, "Measurements of the Refractive Index of Csl and CsBr at Cryogenic Temperatures," MS Thesis, University of Arizona.

Wolfe, William L., Arthur G. DeBell, and James M. Palmer, 1980, "Status of Cryogenic Refractive Index Measurements," Proc. SPIE 245.

93

Documents

REFRACTIVE INDEX MEASUREMENTS OF MAGNESIUM OXIDE, … · 2020. 4. 2. · REFRACTIVE INDEX MEASUREMENTS OF MAGNESIUM OXIDE, SAPPHIRE, ... this work, including the students who have