rwa mn mmmxowual cmoout oegm...tbouxscal i pot 3rcs.w-.1 rwa mn mmmxowual cmoout oegm cl dtm t. atom...

25
TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft L*a"x St014 0515

Upload: others

Post on 22-Jan-2021

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

TBOUXSCAL I POT 3RCS.W-.1

RWA mN mmmxOWUAL CMOOUT OEGM

cl Dtm T. Atom6.mw Lurs carpomP. Or Box 5063

Rap!ugso MY 14627

I USAIny Mbft L*a"x

St014 0515

Page 2: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

DISPOSITION INSTRUCTIONS

Of:S"iHOY THIS REPORT WHEN IT IS NO LONGER NEEDED. DO Nm·

PFf':Jrl:\: IT TO TH'E ORIGINATOR.

DISCLAiMER

f;-·!E FH>!DlNGS IN THIS REPORT ARE NOT TO BE CONSTRUED AS AN

DFF!ClAL DEPARTMENT OF THE ARMY POSITION UNLESS SO OESIG·

'4t.·n::D BY OTHER AUTHORIZED DOCUIYIENTS .

. ~o-r CONSTITUTE AN OFFICIAL iNDORSEMENT 0~ A:>:'flCVAL OF

n-lE UC:E OF SUCH COMMERCIAL HARDWARE Ofl SOFTWARE.

Page 3: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

UNCLASSIFIEDS1CURTY CLASSIFICAT#ON Or TWIS PAGE (Whse Date RAG4eed

REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

R.PO"t NUNSEN "I. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER

RR-CR-84-1 A7)Alql S34. TITLE (mid Subdue) V. TYPE OF REPORT & PERIOD COVERED

10.6 pam GRADIENT INDEX OPTICAL COMPONENT DESIGN _

6. PERFORMING ORG. REPORT NUMBER

1* AUTHORIi') S. CONTRACT OR GRANT NUMBER(s)

Duncan T. Moore

10. PERFOSWING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT. TASKAREA & WORK UNIT NUMBERS

Gradient Lens CorporationP. 0. Box 5053, River Campus StationRochester, NY 14627

11. CONTROLLING OFFICE NAME AND ADDMS 12. REPORT DATE

Coamander, US Army Missile Command November 1983ATTN: DRSMI-RPT Is. NUMBER OF PAGES

Redstone Arsenal, AL 35898 1714. MONITORING AGENCY NAME a ADDRES(It difreruit &am Cantrelfo Office) IS. SECURITY CLASS. (of thi repot)

UnclassifiedISM. °ECL ASSI FI CATION/OOWNGRADING

SCHEDULE

I. OISTRIUUTIOM STATEMENT (of Rddet A )

Approved for public release; distribution unlimited.

17. OISTRiUTION STATEMENT (Of M ebetw mWtmd I I 2000 ft dff.,mt I- Repot)-

I5 SUPPLEMENTARY NOTES

W KEY WORMS (Cog.m.eve -0 I 00 U He1eeemp Md #I*ndt& I bo& nmber)

Gradient indexZinc SulfideZinc SelenideLensesOptical desi.n

S, AMACr (1 1 ,111,11 -M - ,mNMW -. d1, OF MeeW ,M.i,)

Testing methods needed to determine the optical characteristics of zincselenide and zinc sulfide gradient index materials are evaluated. The methodsdescribed include measurements for homogeneity of the material, transmissionand regularity of the profile. In addition, the physical properties (i.e., theconcentration of selenium and sulphur versus the spatial coordinate) aredescribed.

-(continued)

OD, S Irn eW 1 Oes"L" UNCLASSIFIEDUWJRITy cPimCATON or "MI PAWE Mm 55 ~w

A,..

Page 4: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

m3cLAsIua~uMKOWNTY C&ANMSFION~S OF ThIS PA56E~ bM.ft

Three designs have been conducted to show the profile that -. needed for

saia and radial gradient lenses fbri c&afinwIsc seleiide ad sIn

sulf Ide. The problems of correcting the (aj.beratftio,,f an ogive surf a aredescribed and possible solutions to this pro eu are outlined. I'

I

I

V

5,V

iI

: I III I II I I I "- I a ;

Page 5: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

CONTENTS

Page

I . INTRODUCTION . . . . .. .. . .. . .. .. .. .. .. .. . .3

II. TESTING METHDS . ............... ........ 7

III. DESIGN OF 10.6 MICROMETER OPTICAL COMPONENTS .. .. ........ 7

IV. REQUIREMENTS OF AN AXIAL GRADIENT LENS BLANK. .. ......... 8

V. REQUIREMENTS OF A RADIAL GRADIENT SINGLE ELEMENT BLANK .. . . . 10

VI. DESIGN OF AN OGIVE CORRECTOR PLATE. .. .............. 11

REF ERENCES . . . . . . . . . . . .... .. .. .. .. .. .. .. . .16

'S GUIA&. L

Avail a~nd/orLAst Speclial

1!

Page 6: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

I . IETMOUCTICE

Four optical properties suet be measured in order to adequatelycharacterize zinc selenide/ziuc sulfide gradient index materials: (1) thetransmission of thematerial, (2) the base index of refraction, (3) the indexof refraction profile (variation of index of refraction with spatial co-ordinate), and (4) the uniformity of the gradient. In addition, one physicalproperty (the concentration of selenium and/or sulfur as' a function ofposition) must be measured. This latter measurement is necessary at thelaboratory stages to adequately describe the physical model which willeventually predict the index of refraction from compositional information.

While it is expected that the transmission of zinc selenide/zinc sulfidegradient Index materials will have transmission properties given by theaverage of the sulfide and selenide independently, it is necessary to verifythis. For example, the transmission of a sample which has 50 percent zincselenide and 50 percent zinc sulfide at a certain point is expected to havethe average transmittance of the two materials at that particular wavelength.However, because the combination materials cannot be deposited at the optimumrates, this combination is expected to have a somewhat lower transmission thanthis average. (It is well known that the ideal temperatures and pressures forthe two materials to create the best materials are not the same. Therefore, ata laboratory level, this transmission must be measured). In addition, a fewsamples should be manufactured which are not gradient index material but rathersimply combinations of the two materials so that the transmission of thesecan be measured to determine what the optimum conditions are.* For example,a series of samples which are homogeneous in nature consisting of approximately20 percent zinc selenide and 80 percent sulfide, 40;60, 60;40, 80;20, shouldbe manufactured. These will allow for a adequate determination of thetransmission of these materials and thus a prediction of the transmission of anindex of refraction gradient made of these two compositions.

The system for making such measurements Is quite straight-forward andshould consist simply of an infrared spectrophotometer. A number of suchinstruments are commercially manufactured. The measurements should be madebetween 0.5 micrometers and 12 micrometers. One additional problem may ariseconcerning the deposit of the gradient. For example, if a series of discretesteps are produced in the material, each with a slightly different index ofrefraction, then one would expect reflection from each of these boundarylayers. This will contribute to an effective loss in transmission which mustbe separated from the normal transmission errors in the bulk material. Thus,one would expect, In materials where step indices of refraction are used, toget a somewhat lower transmission than would be a continuous variation in indexof refraction.

The optical performance of a gradient index component is directly determinedby the uniformity of the index of refraction profile; that is, as a function ofthe aperture coordinate, the profile should be the ame along all lines.

3

X=mas

Page 7: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

However, it In weil known In the chemical vapor deposition method of zincselenide and zinc sulfide that the formation of small nucleation sites resultsIn a deposition of material in a non-uniform way. For examle, at anucleation site, more material will be deposited as a function of time and,thus, a bump will be formed. In the manufacture of homogeneous zinc selenideor zinc sulfide, this is not a problem since the material being depositedis of a uniform composition throughout the entire deposition time. However,since the deposited material is to be changed in a systematic way, once anucleation site is formed, the bump that results creates a surface of constantindex which has small perturbations on it. These perturbations result inwavefront error throughout the material. The effect will be to have awavefront which will be nominally spherical or plane, with perturbationssuperimposed upon it. To estimate the errors of these, let us consider thefollowing problem. Suppose, at som point in the material, a nucleation siteis formed which has a height above the normal deposition plane of 10micrometers. After the nucleation site has been formed, the layers depositedabove It are plane except for a 10 micrometer bump. This continues untilthe deposition has been completed. The surface is now polished plane and thelast deposited layer will be removed. A part of the index of refractionprofile which corresponds to a depth of 10 micrometers is exposed at a pointabove the nucleation site. If the index of refraction between the area abovethe nucleation and the normal material is 0.1 the optical path introduced bythis effect is 1.0 micrometer (that is, 1/10 of a wave at 10.6 micrometers).If the nucleation site causes a bump of 100 microns, with the same index ofrefraction variation, then the effect will be to create a one wavelengthoptical path variation. These local inhomogenieties have the same effect asgrinding and polishing errors in normal optical fabrication. Thus, they canbe interpreted and the tolerances can be determined in the same way that theseoptical path errprs are calculated. In normal optics used for high qualityimaging, it is usually necessary to maintain these errors through less thanX by four (i.e., an optical path error of 2.5 micrometers at 10.6). Thus, ifthe index profile over the depth varies by 0.01 it will be necessary to besure that the corresponding heights be less than 250 micrometers. Othercombinations of nucleation heights and index of refraction are, of course,possible. By reducing the index of refraction difference over the material,particularly near the surface, one can tolerate an increase In the height ofthese nucleation sites.

The measurement of the Index of refraction profile (i.e., the variationin index of refraction as a function of spatial coordinate) can be measuredin a number of ways. There are some unique problems in measuring a profilewhere the materials have a high index of refraction. Because it is possibleto generate Index of refraction variations of 0.2 in infrared materials (e.g.,in zinc selenide or in germanium) over depths of only a few millimeters, theslope of the index of refraction profile can be enormous. For example, anindex change of 0.2 over a distance of 1 millimeter creates a slope of 0.2M. -1.* This should be compared with the gradients manufactured in opticalglasses for visible use where a typical index of refractioy profile is 0.5over 5 millimeters. This results In a slope of 0.01 um. *The effect ofthis Is to camse probem with normal interferometrIc measurement techniques.In these techniques, two surfaces of the material are polished such that thegradient is parallel to the surf aces.* Thus, light propagates through the

Page 8: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

sample perpendicular to the gradient. The optical path introduced by sucha material is given by the product of the thickness of the polished sample andthe Index of refraction change (An). By taking this number and dividing bythe wavelength of light, one determines the number of interference fringesthat will be observed. For example, if the index change is 0.01 and the samplethickness is 2 millimeters, the optical path in such materials is 20 micro-meters. If the wavelength of the instant radiation is 0.05 micrometers, then40 interference fringes will be seen in a Mach-Zehnder interferometer (80 willbe observed in a Twyman-Green configuration). Thus, 40 fringes will be seenover a distance of 5 millimeters (the depth of the gradient) or 8 fringesper millimeter. Now consider an infrared material such as zinc selenide.In this case, the index change can be 0.2. Assuming a sample preparationthickness of 2 millimeters and a depth of 1 millimeter, the optical path inthis system is 400 micrometers and, at 10.6 microns, the number of fringeswill be 40. Thus, there will be 40 fringes over a thickness of 1 millimeter.This corresponds to a fringe spacing of 25 micrometers which is 2 1/2 timesthe wavelength of incident radiation. While this is not an unsolvableproblem, it does create a high fringe density and requires high performanceoptics to image the sample onto the detector plane.

Two solutions have been offered for this problem. The first is to usestandard interferometric techniques but to introduce a modulation with twofrequencies. The system, called a harmonic interferometer, has been describedelsewhere [1]. The results of the measurement of a zinc selenide/zincsulfide combination have been performed on this instrument (see Figure 1).However, in this situation, the sample thickness was reduced to about one-half of a millimeter in order to adequately reduce the fringe density.

The second solution is one which provides an index of refractionmeasurement by observing polarization changes at the surface. The system,called a phase lock ellipsometer, modulates the input polarization of abeam incident at an angle near the Brewster's angle. The polarization ofthe light changes. The results are accurate to about 0.01 in the currentsystem. With some improvements, this could be increased to 0.001. Thisonly results, however, in an accuracy of one hundredth of the indexvariation, whereas interferometric techniques result in measurements of theorder of 0.0001 of the index of refraction variation. However, it is notlimited in any way by the slope of the profile. The results of measurementsof this instrument are shown in Figure 2 [2). This latter technique suffersfrom one important effect; that is, it only measures the surface. This isan advantage when there are very thin layers, however, it is susceptibleto surface preparation methods and, thus, the use of it to measure absoluteindex of refraction is somewhat dubious. Since the surface is prepared inthe ame way, it is expected that this will provide at least an indicationof the index of refraction profile in very steep gradients.

The last optical property that- needs to be characterized is the baseindex of refraction. In interferoueter methods, only the index of refractionvariations are characterized and, thus, one never knows whether the referenceIndex of refraction in 1.5 or 2.5. While one may argue that some point inthe material is a baseline (e.g., one could assume that there is ahomogeneous composition of zinc selenide to deposit and, thus, the index of

5

Page 9: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

02WAVILUMH

1.0 .0 20 t.0OSSAM Wmm &DMPU km

Figure 1. Zinc-Selenide., Sulfide gradient.

rornm 1

02

11=*,-21 slusesae, Sai" A a41amt.

16

Page 10: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

refraction is known at that point), this is probably not adequate in

normal optical systems. Again, there are two possibilities. One is to usean nterferomutric technique which measures the absolute index of refraction

by Measuring the optical path difference as the sample is tilted in one armof a Yach-Zehnder interferometer. Knowing the thickness of the sample, itcan be show that a measurement of the absolute index of refraction can bemade (31. This measurement is currently available to about 0.001 and israther independent of the base index of refraction. The second techniqueir to use the phase lock ellipsometer to make such measurements. Currentlysuch measurements have been made to an accuracy of about 0.05 but they canbe Improved by an order of magnitude by a change in instrumentation. Thetwo techniques, taken in combination, give adequate results and are wellwithin the needs of the lens design. The index of refraction as a functionof wavelength is measured to about 0.005. There currently exists no methodby which a company can get these measurements made. Thus, this representsa research topic which must be solved to do gradient index as well ashomogeneous optics.

11. TESTING METHODS

One final measurement needs to be made in the laboratory stages.All models which predict the index of refraction of the function of spatialcoordinate are based on concentration of the various constituent parts. Forexample, by knowing the variation of selenium within the material, oneshould be able to predict the resulting index of refraction profile. Thisis necessary to the parameters of the lens design, which are normally givenin index of refraction versus spatial coordinate, can be translated intomaterials parameters. In order to correlate these two, it is necessary tomeasure the concentration of the materials. Thus, one would recommend that

microprobe analysis be done on the material to determine this data. Thereare a number of methods which could be applied. One of them is based onenergy dispersive techniques which are well suited to these samples. Ifthe samples are prepared so that the gradient is exposed, as it would befor Interferometric techniques, then a scanning electronmicroscope cansample vrious locations in the gradient and make a compositionalmeasurment. This technique is well known in optics and has been used tomeasure silver concentrations as a function of depth in optical materials.It zy be necessary, in order to give proper correlation, to make as manyas 10 to 15 sample measurements. This will assure direct correlation of indexof refraction with materials properties.

111. DESIGN OF 10.6 MICROMETER OPTICAL COMPONENTS

Two gradient index lens systems have been designed to specify the typeof las blanks that need to be produced using zinc selenide/zinc sulfidematals. Because an axial gradient and a radial gradient have differentffeets on the performance of a lens, the exact aberrations that are corrected

differ between the two designs. The underlying theme is the determinationof the profile of the index of refraction as a function of position in orderto write a series of specifications for a chemical vapor deposited zincaelemide/zine sulfide gradient index material.

7

Page 11: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

IV. REQUIRnWS OF AN AXIAL GRADIENT LENS BLANK

The design of axial gradient single element lenses corrected forspherical aberration and coma has been described [4]. The importantparameters for correcting spherical aberrations are the first curvatureof the lens and the value of the first coefficient of the index of refractionprofile. If the index of refraction is given by

N(z) - N woo + 1o z + ...

then the important parameter for aberration correction is the No1 coefficient.Further, it has been shown that this coefficient needs to be maintained overdistance equal to the sag of the surface (e.g., for a lens of aperture 50 umnand with a first curvature equal to 0.00714 mm-l, then this sag is equal to2.2 mim). After this distance, the profile may become homogeneous to take onany profile that is suitable to the other production parameters.

A number of single element gradient index components have been designedusing a base index of 2.24 corresponding to zinc sulfide and 2.43 correspondingto zinc selenide. It has beer. assumed that the diameter of the lens is 50 mm.Various focal lengths have been chosen. Table 1 gives a summary of thoseresults including the design parameters, the values of the curvature (cvl andcv2), the gradient depth that needs to be maintained, and the index change(An) that needs to be produced. It can be-seen that even in the situationwhere an f/l single lens element is designed, the value of the change ofindex is only 0.119 (i.e., only one half the capability of a zincselenide/zinc sulfide process). One would, therefore, expect that, at theboundary of the first surface, the composition is approximately 50% zincselenide/zinc sulfide and, in thi interior of the lens blank, 1001 zincsulfide in the homogeneous material. This would make the most costeffective lens.

It can further be shown that the coefficient NOl must be maintained toapproximately ± 3%. This variation depends substantially on the imagingcriteria that is established. In most processes, even those of diffusion,this is an easy coefficient to be maintained. However, variations outsideof this regime can be taken into account if it is reproducible. In thatzircumstance, the focal length of the lens can simply be scaled appropriately.Many other design configurations exist that can be used to compensate forquadratic coefficients of the index of refraction profile.

There are a number of expected problems with a zinc selenide/zincsulfide combination - one is the smoothness of the index of refractionprofile with depth. If a ripple surface or ripple index profile is created(due to steps in the processing), one would expect a Fresnel effect to becreated. If bumps are created, due to nucleation centers, one would expect:the same effect as pits in the lens system. Depending upon the size of theindex variation and its lateral and vertical extent, this may create anultimate problem for this process. New analytic tools will have to bedeveloped in order to handle these particular problems.

8

Page 12: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

DIAMETER -50 ZIM-HTBE1 RDETLNE

FO1A GRADIENTLENGTH F# Noo NoiL(MM-1) cvl(MO( ) CV2 DEPTH(MM) AN

200 MM 4 2.430 -.211x10-2 .0059 .0025 1.84 .0039

100 2 2.430 -.390xlcr2 .0126 .0061 3.93 .0154

62.5 1.25 2.430 -.122h101l .0145 .0037 4.53 .0553

50 1.0 2.430 -.295xl01l .0147 .0009 4.59 .1355

N(Z) - N0 0 + N0 1 Z

cvl - CURVATURE OF FIRST SURFACE

CV2 - CURVATUJRE OF SECOND SURFACE

same"-

Page 13: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

V. REQUIREMENTS OF A RADIAL GRADIENT SIN~GLE ELE14ENT BLANK

A number of radial gradient lenses have been designed both for thevisible and for the infrared [5, 6]. In the infrared, a two elementgermanium based gradient index system has been designed for use inreconnaissance application [7]. It has a full field of view of 42* and isdiffraction limited over nearly 0.8 of that field. The lens system isdiscussed elsewhere; however, this design is not currently manufacturable.Before such sophisticated lenses can be produced, it is necessary tomanufacture simpler systems. The simplest lens system is the radial gradientWood lens. In this system, the surfaces of the final lens element areplano and a radial gradient is introduced in the material with an axis ofsymmetry which becomes the optical element axis. The index of refractionin this system is represented by a polynomial in the radial coordinate

N(r) - N0 + N 0r2 + N2 r +

where N00 is the base index of refraction (nominally 2.3 for a zinc selenide/zinc sulfide combination), NlO is the quadratic coefficient in the index ofrefraction polynomial and contributes the power of the element; and N20 andhigher coefficients contribute to the aberration correction of the third,fifth and seventh order respectively. The power of such an element (i.e.,the reciprocal of the focal length) is given by the simple relationship-2Nl0t (where t is the thickness). This assumes that the focal length islarger than the thickness of the lens. An alternate form to determine thefocal length is -r 2 /2 tAn, where r is the radius of the component and An isthe index change from center to edge due to the quadratic component. Forexample, for a single element lens with a diameter of 50 mmand a thicknessof 10 mm. the focal length is given by the simple relationship of 31.25divided by the index change. The f number of this system is given by therelation -25/4OAn. Thus, the index change created critically determinesthe focal length and f number of the system. For example, for an indexchange of .05 the focal length of such a system is 625 urm and the f numberis 12.5. If the index change is 0.2 (the theoretical limit of the zincselenide/zinc sulfide process) then the focal length will become 156 and thef number is approximately 3. In order to construct faster systems than this,curved surfaces will be necessary to supplement the power due to the gradient.The other alternative is to increase the thickness of the lens but this hasthe disadvantage of increasing the weight of the component. Some verysimple examples are shown in Table 2 in which the base index and index ofrefraction polynomial have been described for systems in which the sphericalaberration is corrected. The dispersion of the gradient has been calculatedto minimize the chromatic aberration on the wavelength band of 8-12 microns.In Table 3, the equivalent parameters for a homogeneous single element lensof similar focal lengths are given. One sees that the spherical aberrationof such a Wood element is essentially reduced. The Petzval field curvature,which is a difficult aberration to correct in most lens systems, is reducedproportional to the index of refraction. However, the coma is substantiallylarger and, thus, the addition of curved surfaces on the lens system has theadvantage of not only increasing the power of the lens element but-will allowthe coina to be corrected.

10

Page 14: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

In Table 4, the tolerances for the f/3 single element radial gradient

component have been calculated and, in Figure 3, the ideal profile has been

plotted with the error bars superimposed on it. This is only one of an

infinity of solutions that could be manufactured but points the direction

for future manufacturing technologies. Other solutions will lead to other

focal lengths and to other f numbers. After these are manufactured, the

lns then can be redesigned. It is important, however, to make a lens

element of this type as it is a good representation and is relativelydifficult compared to the axial gradient.

The problems associated with errors to the nucleation sites and

radial-gradients are identical to those of the axial gradient. Again, if the

inhomogeneity variation occurs, one will see on the transmitted wavefront

small perturbations.

VI. DESIGN OF AN OGIVE CORRECTOR PLATE

After a number of attempts at correcting the first order properties of

an ogive surface, it has been concluded that, at least by conventionalgradient techniques, this is not possible. The reason can be seen fairlysimply. In the ogive system, the refracting surface is highly curved. This

steep curvature is a function of the aperture. For example, rays strikingnear the optical axis see a very strongly refracting surface, whereas those

out near the edge see, essentially, a plano window that is tilted at some verysteep angle. This results in the rays being transmitted at very different

angles. In the ideal situation, the light transmitted through the surfaceIs refracted at a constant angle as a function of aperture. Of course, inthe ideal situation, the ray, after refraction, would have the same angle asit did before and, thus, there would be no power introduced by it. This

variation of refraction as a function of aperture is essentially a first orderproblem and, as we have seen by the design of an axial gradient and those ofa radial gradient, this phenomenon will not be corrected by such gradients.It is, therefore, my conclusion that it is not possible, using a simple

axial or radial gradient, to correct the strong aberrations introduced by anogive surface.

Having spent considerable time analyzing this problem, it occurs to mathat there is a new system that might be investigated in the future - that is,the use of Fresnel gradient index optics. In this system, the refractingpower Is given in the same way as a Freanel system works - by a series oflittle facets but these facets are now created by index of refractionvariations. This has some advantage over shadows that would normally becrestat and can result in strong refraction as illustrated by the standardowarhead condenser lens in most overhead projectors. With this very simpleystem, it is possible to create strong refractions and by the use of

gradient index it might be simple to manufacture with very high quality.

U?

Page 15: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

OjF

Figure 3. Lndz of refraction Prof ile-f /3 wood laws.

12

Page 16: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

TABLE 2

RADIAL GRADIENT WOOD LENS

DIAMETER OF LENS: 50 =

Focal N1 (Ua 2) -(4 ) ThicknesscoatLength (in)1 2(m N 56

200 - 2.42 -0.25 x 10 0.173 x 108 10.0 0.156 -0.147

150 2.42 -0.33 x 10 0.398 x 108 10.0 0.206 -0.193

100 2.42 -0.50 x 10 1.378 x 10 8 10.0 0.312 -0.289

-3 -750 2.42- -1.00 x 10 1.088 x 10 10.0 0.625 -0.564

13

Page 17: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

TAML 3

ONFAISOK 01 OMGENOUS SINGLET ANID RADIAL GRADIENT SINGLET

f/3, f1 , 150 -

H.omogemeous Woodcv 1 0.00804

0cv2 0.00345

T 1 10.0 10.

R0 0 .6m) 2.403 2.403

RI0 -0.330 x 10-3

'20 +0.398 x 10-

'oo( - 13. ) 2.385 2.385

310 -0.335 x 10-3

N20 0.398 x 10-8

N00( - 8.2)n 2.416 2.416

1IO 0.330 x 10-3

' "20 0.398 xlO-8

IAeld Angle Spot Size (at 10.6m)

0.00 0.430m 0.012m

2.5" 0.600 x 0.500 0.420 x 0.210m

* 5.00 1.057 x 0.700n 0.571 x 0.466m

Spot Size (All wavelengths)

0.0" 0.900n 0.022m

2.5' 1.080 x 0.988= 0.601 z 0.210m5.0" 1.612 x 1.201"- 0.571 x 0.466

14

&MON

Page 18: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

TAIL 4

TOLERMN OF RADIAL GRADIET F01 WOOD LIS

f/3, fl - 150

Nomial Value Error Z Error

Noo 2.403 +0.030 1.252

110 -0.335 z o.os 1o- 4.5Z

120 0.398 a 10±- 8 +0.04 x 10- 10.01

X20

-- -- . i. l I I I I I I3

Page 19: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

REVuRICzs

1. J.J. Miceli, Infrared Gradient Index Optics: Materials. Fabrication andTestinm, Ph.D. Thesis, Usiwsty of Roebter, 1962.

2. N.J. Sullo, -a.,urmet _ of Ahso&ute Refractive Index Profiles in GradientIndex Materials Using Modulation Ellipsometry, M.S. Thesis, Universityof Rochester, 1982.

3. G.W. Johnson, Measurements of Strongly Refracting, Three DimensionalIndex Distributions, Ph.D. Thesis, University of Rochester, 1979.

4. D.T. Moore, "Design of a Single Element Gradient Index Collimator,"J. Opt. Soc. An., Vol 67, No. 9, p. 1137-44 1977.

5. P.O. McLaughlin et al., "Design of a Gradient Index Binocular Objective,"Proc. of the 06A 1980 International Lens Design Conference SPIE, Vol.237 p. 369-79 (1980).

6. L.G. Atkinson et al., "Design of a Gradient Index Photographic Objective,"Appl. Opt., Vol. 21, No. 6, p. 993-98 (1982).

7. D.T. Moore, Gradient Index Lens Research, Final Report, U.S. Army MissileCommand, Red-&Eone Asenal, labma, Contract No. DAA01-81-C-B042, 1982.

Page 20: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

DISTRIBUTIONNo. of

Com.dr. US Atuy Research OffiLee CopiesATTF: D3130-PH, Dr. R. Louts 5

Dr. S. D. Quenther1P.O0. lo 1L2211Resarch Triangle Park, NC 27709

US Army Research and Standardization Gr oup (Europe)ATN: DXU--RX/LTC D. R. Reinhard1Box 65m New York 09510

Cameander * US Army Materiel Development and Readiness CoMiandATI: Dr. *Jams Bender1

Dr. Gordon Bushey15001 Risenhower AvenueAlexandria, VA 22333

Eeadquarters, Department of the ArmyOffice of the DCS for Research, Developmsut and AcquisitionATN MAAAZ1Roam 3MA74, The PentagonWashington, DC 20301

UMIRoom 331079, The Pentagon1Washington, DC 20301

DirectorDefense Advanced -Research Projects Agency1400 Wilsom Boulevard1Arlington, VA 22209

ATTMs Dr. 0. anota.Deputy Assistant for Research (in Advanced Technology)Room 331067. The Pentagon1Wasiapton DC 20301

Director. Defense Admeed Research Projects Agency/STOATU:s Cmmnder T. I. Viomar1

3.1V. Wals 1140 Wilm BoalevardArulIgto, -VA 22209

Comnoer. US Army &Vtatim System Commadn3th ami We" seSreets

Naefterg U Army Ar NbiWlty 2@664=sb and DelmetLaboratory

Moffat 11.16, CA %M3

Page 21: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

Coamr, US Army Ilectrouics Research sod Dovelopmt ConnedAT79: DSI-TL-T9 Dr. Jacobs 1

DNLU-E, Uery 3. Sonatas 1Fort NMooouth, NJ 07703

Director, US Army light Vision LaboratoryATTN: John Johnson 1

John Deline 1Feter VamAtta 1

Fort Belvoir, VA 22060

CommnderUS Army Picatinny ArsenalDover, NJ 07801

CommanderUS Army Barry Diamond Laboratories2800 Powder Mill RoadAdelphi, MD 20783 1

Commander, US Army Foreign Science and Technology CenterATTN: W. S. AlcottFederal Office Building220 7th Street, NECharlottesville, VA 22901

ComnnderUS Amy Trainlng and Doctrine Coeand 1Fort Monroe, VA 22351

Director, Ballistic Missile Defense Advanced Technology CenterATTI: ATC-D 1

ATC-0 1ATC-l 1ATC-T 1

P. 0. Box 150Huntsville, AL 35806

Corn qer, US Naval Air System ComedMissile Guidance and Control Branch 1Usshiamgon, DC 20360

Chief of Sava esearchepartm t of the Navy

Vsshia~tem DC 20301 1

US Navel Air Develpmt CenterUmdaster, PA 15974

SCi rus Naval Ocemt System CenterCode 6003Dr. loper aliteoueGm Kaep CA 92152

_ 18

Page 22: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

Directorl. Naval Researb LaboratoryATM: Dave Rkaoolt1

Code 5570o T. GialborlainsWshngton, DC 203W

CMdero Rome Air Develal ment CenterUS Air ForceATTN: Jams Vailwki, luG 1Griff Is* Air Force Base, NY 13440

Comander, US Air Fore, AJOSRIU9ATTN: Dr. J. A. Neff1Building 410Bolling Air Force BaseWashington, DC 20332

CarnanderUS Air Force Avionics LaboratoryATTN: D. Rees

V. Schoonover1Dr. E. Champaign1Dr. J. Ryles1Gale Urban1David L. Flannery1

Wright Patterson Air Force Base, ORi 45433

Comander, AFATLUTATMh Charles Warren1Xglinu Air Force Base, FL 32544

lbvironmentel Research Inst itute of MichiganRadar end Optics DivisionATTN: Dr. A. Koa1

Dr. C. C. Alekeoff1Junes Upatnieks1

P0. Box 618Ann Arbor, MI 41807

IIT Research InstituteATTN: GACIAC10 West 35th Street1Chicago, IL 60616

Dr. 3. 0. Castle9601 San Gabriel, HEAlbuquerque, MM 87111

Dr.* Vincent J.* Corcoran2034 Freedom LaneFalls Church, VA 220431

Optical Science ConsultantsATM Dr. 0. L. Fried1IN 0. Box 366Towba Lis",. CA 926ft

Page 23: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

Comner, Center for Naval AnalysesATIV: Document Control11401 Wilson Boulevard

RAytheon CompanyAM: A. V. Jelalian1528 Boston Post RoadSudbury, NA 01776

Dr. J. W. GoodmanInformation Systems LaboratoryDepartment of Electrical Engineering1Stanford UniversityStanford, CA 94305

Eric G. Johnson, Jr.National Bureau of Standards325 S. BroadwayBoulder, CO 80302 1

M. VanderlindBattelle Columbus Labe505 Ring AveColumbus, 0R 43201

Dr. Nicholas GeorgeThe Institute of Optics 2University of RochesterRochester, MY 14627

Nawel Avionics Facilty 1Indianapolis, IN 46218

1e B. lotsHarris CorporationP.O0. Box 37 1mlbourms, nL 32901

Moert L. KurtzutA Corporation 18302 Vhitesburg Dr., 81untsville, AL 3560

J. ft. YyceItek Corporation 110 agmire loadLezinpom, a 02173

Dr. Dayid Ceseasent 1maw-eg-eHall" adiversityNinresage Nal. vDoom 106

?itsbwr. PA 15213

20

Page 24: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

K. G. Leib Research Department Grmnman Aerospace Corporation Beth~.3ge, NY 11714

Terry Turpin Department of Defense 9800 Snvage Road Fort George G. Heade, ND 20755

Dr. Stuart A. Collins Electrical Engineering Department Ohio State University 1320 Kennear Road Columbus, OH 43212

Mike Scnrborough, MS-19 Teledyne Brown Engineering Cummings Research P~rk Huntsville, AL 35807

1

1

1

1

AFEL 1 Hanscom A:tr Force Base, MD 01731

Dr. Arthur N. Chester 1 Dr. Donald H. Close 1 Thomns R. O'Meara 1 Dr. \·Iilfried 0. Eckhardt 1 ~ughes Research Laboratories 3011 ~alibu Canyon Road Malibu, CA 90265

TR\·i Defense and Space Systems Group One S;:,ace Park ATTN: Dr. Peter 0. Clark Redcndo Beach, CA 90278

~. J. Caulfield Aerodyne Research, Inc. Bedford Research Park Crosby Drive Bedford, MA 01730

US Army Materiel Systems Analysis Activi.ty ATTN: DRXSY-MP Aberdeen Proving Ground, MD 21005

US Army Night Vision Laboratory ATTN: DELNV-L, Dr. R. Buser FoLt Belvoir, VA 22060

21

1

1

1

1

Page 25: RWA mN mmmxOWUAL CMOOUT OEGM...TBOUXSCAL I POT 3RCS.W-.1 RWA mN mmmxOWUAL CMOOUT OEGM cl Dtm T. Atom 6.mw Lurs carpom P. Or Box 5063 Rap!ugso MY 14627 I USAIny Mbft …

UM31-LP, Mr. Voist1-~01-Y1ARN, Jerry IMagood 1-RE, W. Pittanf 1-RD 3-3.0 1-RR, Dr. E ar tuan 1

Dr. Bennett 1Dr. Christensen 100Dr. Duthie 1

-RPR 15-APT 1

Dr. Raymond L. TaylorCVD Incorporated 335 Industrial ParkwayWoburn, MA 01801

22