OPERATED BY UNION CARBIDE CORPORATION FOR THE UNITED STATES DEPARTMENT OF ENERGY

A Ray Tracing Package Through a Lens System and a

Spectrometer

B. Zurro P. W. King E. A. Lazarus

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Printed in the United States of America. Available from National Technical Infnrrnatinn Service

U .S. Department of Commerce 5285 Port Royal Road, Springfield, Virginia 22161

NTlS price codes-Printed Copy: A03; Microfiche A01

This report was prepared as an account of work sponsored by an agency of the UnitedStatesGovernment. Neither theunited StatesGovernment nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United StatesGovernment or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of theunited StatesGovernment or any agency thereof.

-

ORNL/TM-7168 Dist. Category UC-20 f

Contract No. W-7405-eng-26

FUSION ENERGY DIVISION

A RAY TRACING PACKAGE THROUGH A LENS SYSTEM AND A SPECTROMETER

* B. Zurro, P. W. King, and E. A. Lazarus

DISCLAIMER 1 .

This boor w a prepared as nn n c a u n ~ of w k ~ n y r r e d bv on sgencv of tho United State. Government. Neither the united Stater Gavernmenf mr anv sgcnw thermf. nor any of their emplovcer. makelsnv Wd,rDnlv, erD,eu Or i ~ ~ i e d , or a u u w I ~ I ~inbilicv or r=mnribilirv lor the a m r a w .

mmnleiene~ or vrefulnen of any informarion. eDDarmur. urducl. or prOCeu d M o d . or rep,enir ,hal its - U I ~ nol intrloge V , I V ~ ~ ~ I Y ormod rights. Refweme herein 10 arm rpRific mmmnc~.~ yoduct. procorr. nr bv trade name. t r d e m r k . menulaccurer. or otherwire. don MI m r i l y mnstitYte imply its endorrement. remmmendat~on. o! Iar(l,inp bv rho Unitmi

stater h r n m n t or thermf. The ~ i ew r snd opinions 01 authors erur€ssd herein do not nareorieflm thoreof the united Stare. t w e r n m n l or anv sgem ther-f.

. ~

Date Publ ished - March 1980

* Vistor from Junta de Energia Nuclear, Madrid, Spain.

NOT ICE This document contains information of a preliminary nature. It is subject to revision or correction and therefore does not represent a final report.

Prepared by the nAK R I D G E NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

for the. DEPARTMENT OF ENERGY

THIS PAGE

WAS INTENTIONALLY

LEFT BLANK

CONTENTS

......................................................... ABSTRACT v

.................................................. . 1 "INTRODUCTION

....... 2 . ALGEBRAIC RAY TRACING THROUGH A CENTERED OPTICAL SYSTEM 2

3 . GEOMETRIC RAY TRACING THROUGH A CZERNEY-TURNER .................................................. SPECTROMETER 5

.......................................... . 4 PROGRAM DESCRIPTIONS 7

4 . 1 SUBPROGRAMS .......................................... . 7

4 .2 INPUT .................................................... 7

4.3 OUTPUT ................................................... 9

4 . 4 APPLICATIONS ........................................ 9

REFERENCES ....................................................... 15 APPENDIX .......................................................... 17

iii

THIS PAGE

WAS INTENTIONALLY

L E F T B L A N K ,

ABSTRACT

To study the light collection optics of the ISX-B two-dimensional.

(2-D) Thomson scattering system, we have implemented in the Oak Ridge

National Laboratory (ORNL) Fusion Energy Division (FED) PDP-10 two

computer programs, LENS and SPECT, that trace rays through a lens system

and a spectrometer, respectively. The lens package follows the path of

any kind of ray (meridional or skew) through a centered optical system

formed by an arbitrary number of spherical surfaces. The spectrometer

package performs geometrical ray tracing through a Czerney-Turner spectro-

meter and can be easily modified for studying any other configuration.

Contained herein is a description of the procedures followed and a

listing of the computer programs.

1. INTRODUCTION

For luost of the optical problems that one has to face in a plasma

laboratory, the ray tracing packages available in computer libraries are

either too sophisticated for practical applications or not well documented.

Thus, difficulties are encountered when one tries to modify the packages

to satisfy the requirements of a particular application.

In this report we describe in some detail the ray tracing procedures

that we have implemented in the Oak Ridge National Laboratory (ORNL)

Fusion Energy Division (FED) PDP-10 and that apply to a collection lens

system and a Czerney-Turner spectrometer. These procedures have been

. implemented to study several aspects of the collection and focusing

properties of the ISX-B two-dimensional (2-D) Thomson scattering system,

but they are general enough to be used for any optical application

involving lenses and spectrometers.

The lens package follows the path of any kind of ray (meridional or

skew) through a centered optical system formed by an arbitrary number of

spherical surfaces. The spectrometer package performs a geometric ray

tracing through a Czerney-Turner spectrometer and can be easily modified

for studying any other configuration. These packages can be useful

tools for. (1) optimization and/or modification of a commercial system

and (2) design of new and original units. In the Appendix, we include a

listing of the codes with comments.

2. ALGEBRAIC RAY TRACING THROUGH A CENTERED OPTICAL SYSTEM

The multistation Thomson scattering system for the ISX-B tokamak

incorporates an £12 wide-angle 1ens.l To study the optical image that

this lens forms of a laser beam in a plasma, we have implemented a ray

tracing program in the PDP-10. This allows us to simulate the actual

conditions of the experiment and to view the optical image on the

Tektronix screen.

The present ray tracing code permits us to follow any kind of ray

(meridional or skew) through a centered optical system formed by an

arbitrary number of spherical surfaces. For each element we define a

three-dimensional (3-D) cartesian system (X, Y, Z), with Z along the

optical axis. The origin of the system is the intersection point of

each surface with this axis.

The elemental step of the ray tracing is to follow a ray from one

optical surface to the next one. Let us define the ray going from

surface s-1 to surface s by its direction cosines (2 m n 1 s-1' s-1' s-1 and its point of intersection with the surface s-1 (X s-l' Ys-l' zs-l);

all these data refer to the coordinate system of the surface s-1. We

will designate by p and p respectively, the refraction indices of s-1 s , the media before and after the optical surface s , hy p the inverse

rcldiuo of thc ourfacc, and by t the separation L t L v e r ~ ~ dcl jcr~ru~ S U L ~ ~ C ~ S .

With these assumptions it can be demonstrated2 that the direction

cosines of the ray upon leaving the surface s (R n ) and its S * %' s

intersection with s (Xc, YQ, Z ) are given by the expressions 3

R = s x Y Rs-l + Pc; p,

m = m + P s p s Y s , S s-1

n = n + Ps (p, Zs - !L) , S s-1

and

- Xs - Xs-1 + Rs-1 +s-l '

+ m + = Ys-1 s-l s-1 S

- zs - Z;-l + ns-l +s-l '

where

- - - z 1 Zs-1 ts-l '

- Ps - Us-l cos i - Us cos r S S '

T = A/(B - cos i ) , s-1 S

and

B = R + m + n - a) . (5) s-1 Ps Xs-l s-l Ps *s-1 s-1 (ps z:-l

The trigonometric~functions of the angles i and r (the incidence and S S

refraction angles at surface s) in the former expressions can be deduced

by the formulas

2 - 2 lJs-1 cos i = ( l ~ ~ - ~ s '.',_I sin2 iS)l/2 ,

and

The basic ray tracing step contained in the former expressions has

been implemented in subroutine RATRA (see Appendix). To extend this

elemental process to a whole optical system, one must know (1) the

inverse radius of the optical surfaces, (2) the refractive indices of

the media, and (35 the relative position of the various optical elements

(i.e., the separation between optical surfaces measured along the opti.c.al

axis).

Once the particular configuration of the optical system is f i x e d ,

we must define the initial rays coming from the object. One way of

doing this is to give the coordinates of an object point and the direction

cosines of the ray. To avoid the drawbacks of following rays that do

not go through the system, we will define the initial rays by choosing

two points, one in the object and another in the input pupil of the

system. By mapping thooc two arcas we can sLudy Llie path of any kind of

ray going through the system.

To s tudy t h e poss ib l e drawbacks of us ing a smal l monochromator a s .

t h e b a s i c u n i t f o r t h e ISX-B mu l t ipo in t Thomson s c a t t e r i n g system,

which w i l l use 1 5 of them, we have implemented i n t h e FED PDP-10 a

computer package t h a t performs geometr ic f a y t r a c i n g through a Czerney-

Turner monochromator. The b a s i c v e c t o r equat ions3 we have used permit a

formulat ion of t h e problem independent of t he coo rd ina t e system, and they

can be app l i ed t o any o t h e r type of spectrometer , even t o those t h a t

i nco rpora t e t h e very popular concave g r a t i n g .

The l i g h t input cone is def ined by f i x i n g two p o i n t s , one on t h e

inpu t s l i t and another on t h e phys i ca l mask placed on t h e f i r s t mi r ro r .

With a mapping of those a r e a s we can fo l low t h e pa th of a d i s c r e t e

number of r a y s e n t e r i n g the system.

The i n t e r s e c t i o n po in t P of a r ay (with d i r e c t i o n 7 ) wi th t h e M k f i r s t mi r ro r of r a d i u s R i s given hy

where P i s t h e .vector p o s i t i o n of t he i n i t i a l po in t of t h e ray on t h e 0

i n p u t s l i t . The r e f l e c t i o n of t h e ray a t t h e mi r ro r i s governed by t h e

v e c t o r equat ion

where II and a r e t h e inc iden t and r e f l e c t e d r ay u n i t v e c t o r s , respec- k t i v e l y , and an i s t h e s u r f a c e normal i n e i t h e r d i i e c t i o n .

A f t e r t h e r ay i s r e f l e c t e d a t t h e f i r s t mi r ro r , w e determine t h e

i n t e r s e c t i o n poin t P of the ' r ay wi th t h e d i f f r a c t i o n g r a t i n g p lane C-

given by

where 5 is t h e v e c t o r p o s i t i o n of a n a r b i t r a r y p o i n t i n t h e g r a t i n g

(e. g. , t h e c e n t e r ) and xl1 is t h e u n i t v e c t o r normal t o t h e g r a t i n g i n

e i t h e r d i r e c t i o n . A t t h i s s t a g e we check whether t h e r a y h i t s t h e

g r a t i n g o r no t . I f i t is n o t l o s t , t h e r a y w i l l be d i f f r a c t e d by t h e

g r a t i n g i n t h e d i r e c t i o n TL given by

where

- - b = e ; * a , ,

and

where R3 i s a.long t h e d i r e c t i o n of t h e r u l i n g , m is t h e d i f f r a c t i o n

o r d e r , h is t h e vacuum wavelength, d is t h e spacing of t h e r u l i n g s , and - - 9.2 (= R g x R1) i s p a r a l l e l t o t he g r a t i n g s u r f a c e a t r i g h t ang le s t o t h e

r u l i n g s . The v e c t o r R1 must po in t o u t of t h e g r a t i n g su r f ace .

W e d e a l w i t h t h e second mi r ro r i n a s i m i l a r way as t h e f i r s t one.

W e count t h e r a y s t h a t do n o t h i t t h e mi r ro r , and when t h i s happens we

start w i t h a new ray . F i n a l l y , t o determine t h e i n t e r s e c t i o n of t h e r ay

w i t h t h e image p l ane w e apply Eq. (9 ) . These i n t e r s e c t i o n p o i n t s form

t h e image of t h e i n p u t s l i t and a r e p l o t t e d on t h e Tektronix screen .

7

4. PROGRAM DESCRIPTIONS

4.1 SUBPROGRAMS

Both packages, LENS and SPECT, are written in single precision

FORTRAN IV. They run on the PDP-10 at ORNL's User Service Center. The

graphics are written in the ~ i s ~ l a ~ integrated Software System and Plotting Language (DISSPLA). The subprograms are listed below with

brief summaries of their functions.

LENS - Sets the data of the optical system, maps the object and input

pupil, drives subroutine RATRA, and plots the image on the Tektronix

screen.

RATRA - Follows the optical ray path from one optical surface to the

next one.

SPECT - Traces rays through a Czerney-Turner spectrometer and plots the

image on the Tektronix screen.

To execute both programs one must simply type

EX LENS, RATRA, @PUB:DISTEK (for the lens package)

and

EX SPECT, @PUB:DISTEK (for the spectrometer package) .

4.2 INPUT

The main data for running LENS (i.e., the optical surface inverse

radius, separation between surfaces, and refraction indices) are given

to the program by means of DATA statements. The data related to the

object (e.g., width and height of the laser beams) and to the image

(e.g., image plane position) are gjven through the Teletype.

SPECT uses a namelist input data file named TDTS, which is stored

in FOR13.DAT. This set of variables is descrllred iu Table 1.

Table 1. Spectrometer r a y t r a c i n g namel i s t i npu t

FORTRAN name D e f i n i t i o n Un i t s

XSI, ZSI Inpu t s l i t coord ina t e s mm

WSI, HIS

GSIZE

D

ALFA

R1, R2

SMASK

N 3

ALAM

DLA

N A

N 1 x N2 = number of p o i n t s on i n p u t s l i t ( f o r mapping)

Width and h e i g h t of t h e inpu t s l i t

Gra t ing s i z e

D i s t ance between grooves

Gra t ing ang le

Curva ture radius o f o b j e c t i v e , camera m i r r o r s

P o s i t i o n coord ina t e s of t h e ob j e c t i v e mi r ro r

P o s i t i o n coord ina t e s of t h e camera miriur

S i z e of t h e mask on both m i r r o r s

N 3 x N 3 = number of g r i d p o i n t s on t h e mask

I n i t i a l wavelength

Wavelength s t e p

Numbcr s f d i s c ~ e e e wavelengths

mm 13

uuu

nm

degrees

4 .3 OUTPUT

Graphics showing t h e image p o i n t s on t h e Tekt ronix s c r een a r e t h e

main ou tput of both p rog rams . The coo rd ina t e s of t h e image p o i n t s may

a l s o be typed by t h e Teletype.

4.4 APPLICATIONS

LENS and SPECT have been app l i ed t o model the 'wide-angle l e n s and

t h e monochromator HR-320 ( Ins t ruments SA, Inc . ) t h a t w i l l be i n s t a l l e d

i n t h e new ISX-B Thomson s c a t t e r i n g system; both components a r e sketched

i n F ig . 1.

Figure 2 shows t h e image s t r u c t u r e produced by t h e £12 l e n s f o r t h e

s c a t t e r e d l i g h t . The image i s seen a s i t w i l l be viewed by t h e f i b e r

o p t i c a l bundle t h a t w i l l r e l a y i t from t h e f o c a l p lane of t h e l e n s t o

t h e i npu t s l i t s of t h e spec t rometer , f o r t h r e e d i f f e r e n t p o s i t i o n s of

t h e bundle. The f i g u r e shows how s e n s i t i v e t h e q u a l i t y o f t h e image

c o l l e c t e d by t h e f i b e r gu ides i s t o t h e l o c a t i o n of t h e f i b e r gu ides .

We show i n F ig . 3 t h e image of t h e monochromator HR-320 inpu t s l i t

as obta ined by SPECT f o r f o u r d i f f e r e n t wavelengths. We have fol lowed

t h e samenumber of r a y s f o r a l l t h e wavelengths, b u t t h e number reaching

t h e image p l ane i s highe.r f o r t h e c e n t r a l p a r t of t h e f o c a l f i e l d due t o

t h e v i g n e t t i n g of t h e system. .We p l o t i n Fig. 4 t h e v i g n e t t i n g l o s s e s

(%) v s wavelength f o r t h i s monochromator when i t i s used a s a spec t ro-

graph i n a Thomson s c a t t e r i n g system.

ORNL-DWG 79-3424 FED

WIDE ANGLE LENS

SPECTROMETER CAMERA MIRROR IMAGE

_------I- F? t FIELD

'. -.\.

OBJtC; 1'IVL MIRROR

Fig. 1. Sketch of the optical systems modeled by LENS and SPECT.

ORNL-DWG 79-3425 FED

-.- -.- -.- -.- -.- -.- m.0

9.-

-.- -.- -.- -.- -.- ( I ) Z:Z

- I mm

SCALE

SCATTERED REGION CROSS-SECTION

Fig . 2. Op t i ca l images of t h e s c a t t e r i n g r eg ion . a s ob ta ined by r ay t r a c i n g through t h e f / 2 l e n s us ing a d i s c r e t e number of p o i n t s i n t h e o b j e c t , f o r t h r e e p o s i t i o n s of t h e f o c a l plane: (1) b e s t focus , (2) b e s t focus + 0.5 cm, and ( 3 ) b e s t focus - 0.5 cm.

ORNL-DWG 79-3427 FED

Fig. 3. Spectrometer ray tracing results showing the image of an infinitesimal narrow input slit for four wavelengths (700, 725, 750, and 775 rim); the 1200 grooves/mm grating was kept fixed.

Fig. 4 . Vigne t t ing l o s s e s (%) of t h e HR-320 f o r a p a r t i c u l a r con f igu ra t i on .

ORNL-DWG 79-3426 FED t o o

80

-

- GRATING INPUT SLIT - Q = 26.5 HEIGHT : 2 0 mm -

1200 g /mm WIDTH : 2.4mm - -

THIS PAGE

W A S INTENTIONALLY

LEFT BLANK

REFERENCES

1. N. Bretz , D. Dimock, V . Foote, D. Johnson, D. Lory, and E. Tolnas,

Pr ince ton Plasma Physics Laboratory Report PPPL-1356, Pr ince ton ,

New Je r sey (1977) . 2 . A. Cox, A System of OpticaZ Design, Focal P res s , New York, 1964.

3. J. W. Horwitz, Opt. Acta - 21, 169 (1974).

THIS PAGE

WAS INTENTIONALLY

LEFT BLANK

THIS PAGE

WAS INTENTIONALLY

LEFT BLANK

LEN 5

6 " ' " " d 'RAY TRACING PROGRAM THROUGH THE TDTS WIDE ANGLE LENS C

DIMENSION COSDI (50 ) ,XR(5*10 ) ,YR(5 ,10 ) ,ZR(5 .18 ) DIMENSION XP0(10000)~YP0(10000~cROG(10)~ENDR(10)~T~l0~

C c SEPARATION BETWEEN OPTICAL SURFACES - OBJECT AND IMAGE PLANE C ARE CONSIDERED AS OPTICAL SURFACES- C

ir .9

I& INVERSE OF SURFACE RADIUS ,?.

.- I- REFRACTION INDEX BETWEEN SURFACES C

KP. = 0 TYPE 9 3 .

9 3 FORMAT(2X-'FOCUS (24 .17 ) ' ) ACCEPT *s TE ( 7 TYPE 9

9 FORMAT(~X. ' BEAM D IMENS IONS (WIHDS B X l , BX2) HE IGHT BY' C

ACCEPT *a BX1 BX2, BY L

C - LASER BEAM M:qPPING d

DO 1 0 4 I 2 = l c 15 YMB=FLOATCI2-I)*BY/14. D.0 103 I I = 1 . 3 BX=BXl+(BX2-BXl)*YMB/6Y XM0=BX/2. -FLOAT( I I- 1) H(BX/2. K . 1

C C: INPUT PUPIL MAPPING C

D.0 2 8 0 1 ~ 1 . 5 D.0 3 0 0 J=1,8 RIc4.-FLOAT( I - 1 ) + 1 . TETA=FLOAT( J- 1 1 *45. XP=RI*COSD(TETA) YP=RI*SIMD(TETA) OP=SQRT( (XP-XMO) **2+(YP-YM0) *e+84.055**2)

C C INPUT RAY DIRECTION COSINES.THEY ARE DEFINED F I X I N G A POINT C THE OBJECT (XM0*YM0) AND A POINT ON THE INPUT PUPIL (XP,YP) C

EL= (XP->SMB.) /OP EM= (YP-YMB /OP EN=84.055/OP XM 1 -XMB YH 1 =YM0 ZM1=0. D.0 100 L11.7

RAY TRACING THROUGH AN OPTICAL SURFACE

(Xnl ,YMl*ZMl) COORDINATES OF THE RAY INTERSECTION WITH THE PREVIOUS OPTICAL SURFRCE ENM1 - REFRACTION INDEX OF THE OBJECT SPACE EN1 - # a IMRGE SPACE EL, EM. EN D IRECTION COS INES OF THE-.R~Y-- (X,Y,Z) COORDINATES OF THE RAY INTERSECTION WITH THE OPTIiXtL SURFRCE - - . . . . . - - CALL R A T R ( X H l ~ Y H 1 ~ Z M 1 ~ E L ~ E M ~ E N . R O ~ T ~ E N M 1 ~ E N l ~ X ~ Y ~ Z ~ XM 1 =X mi ow.

ZM 1 =Z CnNT INUE XR(I.J)=X XR( l .J)=Y ZR( I .J l=Z XPO (KP) EX YPO (KP) =Y KP=KP+l COSDI(K)=EN '

K=K+1 . CONTINUE CONTINUE GOT0 700

COSZ=COSZ/33, TYPE 550,COSZ

550 FORMAT(E12.5) 'TYPE 570, (COSDI(1). 101.33)

578 FllRYATc5E12.5) 500 CONTINUE 7 0 0 CONTINUE

GOT0 903 TYPE 749

749 FORMAT(/flX* 'X' 1 4 ~ . 'Y' 13X. '2') DO 750 Im1.5 I ' W E 800. (XR(I.J).YR(I.J).ZR(IeJ.)cJm1.8)

8 0 0 FORMAT(3X. E 12 m 4- 3% El2.4,3XL E 12 ,.4) 7 5 0 CON1 I NUE 903 CONTINUE 103 CONT I NU€ 1 0 4 CONTINUE

PAUSE 1508 TYPE 1550 1550 FORMBT(2X. X1 .= ' I

ACCEPT *, XI. X2 CALL TKTRN ( 12004 0 ) CALL BGNPL (- 1) CALL TITLE( ' IMAGESD*-100.'HORIZONTFIL'. 18e~ ' vERT IC f i L~a 100'

210..6.) ST=(X2-X1>.4.

CQLL GRAF(Xl,ST*X2.-5..5..28.) CALL MARKER ( 2 ) CALL SCLPIC(0 .1 ) CALL CURVE(XPO,YPO,KP,-I) CALL ENDPL(0) GOT0 1500 STOP END

RATRA

SUBROUTINE RATR(XMl,YMl,ZMl.EL,EM,EN,RO,T,ENMl,ENl,X,Y,Z) ZP=ZMl-T A = ( E L * R O * Y r I 1 - E M O ~ l ) ~ B='(EM*(RO*ZP-1.)-EN*RO*YMl)W C-(EN*RO*XMl-EL*(RO*ZP-l.))**2 SEN2= (A+B+C) /ENMl**2 COSIS=(ABS(ENM1**2 -SEN2*ENMi*M~~W.5 /ENMl

COSRS=(ABS(EN1**2-SEN2MNM1**2) )W.5 /ENl AB=2.*ZP-RO*(XM1**2+YM1**2+ZP*M) AC=EL*RO*XMl+EM*RO*YMl+EN*(RO*ZP- 1 . ) TAU=AB/(AC-ENMl*COSIS) P=ENMl*COS IS-EN l*COSRS X=XMl+EL*TAU YrYMl+EM*TAU Z=ZP+EN*TAU ELS=EL+P*RO*X EMS=EH+P*RO*Y ENS=EN+P*(RO*Z- 1 . ) EL=ELS EM=EMS EN =ENS RETURN END

SPECT

RAY TRACING PROGRAM THROUGH A CZERNY-TURNER'SPECTRONETER

COORD INATE SYSTEM:

X-AXIS : ALONG THE LONGITUDINAL AXIS 'OF THE SPECTROMETER AND PASSING THROUGH THE GRATING CENTER.

Z-AXIS : PASSING THROUGH THE CURVATURE CENTER OF THE OBJECTIVE MIRROR.

NAMELIST F I L E : FOR13.DAT

DATA :

INPUT S L I T .

X S I .ZSI - XDZ. COORDINATES OF AN INPUT S L I T POINT WSIDHIS - WIDTH AND HEIGHT OF THE INPUT S L I T N l .N2 - N~)EH'~-NUMBER OF POINTS O N THE INPUT S L I T

GRATING . GSIZE - S I Z E O F THE GRATING D - DISTRNCE BETWEEN GROOVES(NM) ALFA - ANGLE BETWEEN M E GRATING PLANE AND THE Z AXI.S(DEGREES1

MIRRORS.

R l c R 2 - CURVATURE RADIUS OF OBJECTIVE AND CAMERA MIRRORS XMV1,ZMVl - POSITION COORDINATES OF THE OBJECTIVE MIRROR XMV2cZMV2 - POSITION COORBINRTES OF THE CAMERA MIRROR SMASK - S I Z E OF THE MASK ON BOTH MIRRORS N3 - N3*NS NUMBER UF GRID POINTS ON THE MASK

WAVELENGTHS.

N 4 - NUMBER OF DISCRETE LRVEL. ALAM - I N I T I A L WAVEL. DL0 WAVEL. STEP tNMS

DIMENSION XES(7~17~8,8 .3)*YES(7c17*8c8,3) ,2ES(7,17~8,8~3) DIMENSION Y(25088) ,2(25000) NAMELIST/TDTS/XSI.ZSI.WIS,HIS,N~*N~~GSIZE~DDF~LFA~XGC~

2N4, RLAM. DLA. R 1 R2. XMVI . ZPlVl. XPlV2, Zmv;! , SMRSK. N3 3. XOS l 2 0 s

DO 2 0 0 J= l ,N2 YSI=-HIS/2.+DY*FLOAT(J-1) DO 3 0 0 K1=1,N3 XMB =XMV I

CALCULATES DIRECTION COSINES FOR INPUT L I G H T CONE

INTERSECTION F I R S T MIRROR AND DIRECTION COSINES AFTER REFLECTION

XSI-XSI-XCM1 ZSI=ZSI-ZCM1 A=EL*XS I+EM*YS I+EN*ZS I B=XSI**2+YSI**2+ZSI**2 XMl=XSI+(SQRT(A**2-B+RlW)-A)*EL ZMl=ZSI+(SORT(A**2-B+R1**2)-A)*EN YMl=YSI+(SQRT(R**2-B+R1**2)-A)*EM XMl=XMl+XCMl ZMl=ZMl+ZCMl ELN=(XMl-XCMl) /Rl EMN=YMl /R 1 ENN=(ZMl-ZCMl) /Rl A =EL*ELN+EM*EMN+EN*ENN ELS=EL-2.*A*ELN EMS=EM-2.*A*EMN ENSSEN-2.*A*ENN XSI=XSI+XCMl ZSI=ZSI+ZCNl

GRATING INTERSECTION AND DIFRRCTED DIRECTION

A=(XGC-XMl)*COSD(~LFA~-ZM1~IND(ALFA) B=ELS*COSD(ALFA)+ENS*SIND(ALFR) XGmXM l+AaELS.'B YG=YMl+A*EMS/B ZG=ZMl+A*ENS/B AL I =GS IZEnCOSD (ALFA) /2. AL I =ABS (AL I : AZG=ABS(ZG> AYG=ABS (YG) ZZG=ALI-AZG YYG=GSIZE/2.-AYG IF(YYGl61.61.62 IF(ZZG) 61.61,62 IRC=IRC+l GU'fU 63 A=ELS*SIND(ALFR)-ENS*COSD(ALFA)-RLAMB/D

EMS =B

INTERSECTION SECOND MIRROR AND REELECTION

A=ELS*XG+EMS*YG+ENS*ZG B=XG*@+YG*2+ZGW AB-SQRT(A*N-B+R2**2)-A xm=XG+AB*ELS YMZ!=YG+AB*EMS ZM2=ZG+AB*ENS XM2=XM2+XM2C. ZM2=ZH2+ZM2C AZ2=ABS(ZMV2-ZM2) AY2 CABS (YM2 IF(SMASK/2.-AZ2)64,65,65 I F (SMASK/2 .-AY2) 64,65,65

6 4 I M 2 w IM2-!1 GOT0 6 3

6 5 ELN=(XM2-XM2C)A?2 EMN=YM2/R2 '

ENN=(ZMZ-ZM2C) /R2 A=ELN*ELS+EMN*EMS+ENN*NS ELS=ELS-2.Wi*ELN Ekls=EPlS-2. *(rA*EPlN ENS=ENS-2.*A*ENN

C C CALCULATES IMAGE POINTS C

A=((XOS-XM2)*COSD(2.417)-(ZOS-ZM2)~1ND(2.417))~ 2(ELS*0.99911-ENS*0.042172)

XES(I.J.K1,K2,K3)=XM2+A)lELS YES(I,J,K~,K~.K~)PYM~+A*EMS ZES( I, J , K ~ , K ~ , K ~ ) P Z M ~ + A * E N S Y ( H > ~ Y E S ( I#J .K lcK2,K3) Z(M)-ZES(InJnKl,K2nK3)-f iBStZOS) M=M+l

6 3 CONTINUE 5 0 0 CONTINUE 400 CONTINUE 3 0 0 CONTINUE 2 0 0 CONTINUE 100 CONTINUE

TYPE 149,M, IRC* IM2 1 4 9 FORMAT(SX.3110) 296 T'T'PF 1JB 150 FORMAT(2X, ' 11,12,13,14,IS, IP '

ACCEPT 1 6 0 ~ I l ~ I 2 ~ I 3 ~ I 4 ~ I 5 ~ I P 160 FORMAT( I i . I2,4I 1)

ZQ-?TZ( T 1 a 12*13.14.15)-nBS(ZOS) TYPE 260,YES(Il,I2,13,14,15)~ZQ

2 6 0 FORMAT(SX, E 14.4,SX. E 14.4) IF ( IP .EQ.1 ) GOT0 2 9 0

1550 TYPE 1500 1500 FORMAT(2Xs'Zl .ZZ')

ACCEPT *, 2 1 22 PAUSE

C TEKTRON I X SCREEN PLOTTING .

CALL TKTRN ( 1200e0) CALL BGNPL (- 1) CALL TITLE ( ' IMAGES' ,- 100, 'HOR IZONTFIL' c 100c *VERT1CQLD

2100,10. e 6 . 1 ST=(Z2-Z1)/S. CALL GRAF(Zl.ST,Z2>-16..4.. 16. ) CAI-L MARKER (2 1 CALL SCI-PIC(G?. 1) CALL CLIRVE (Z , Y, M. - 1 C~II-L ENDPL (El> GOTU !550 . STi!F2 END

THIS PAGE

WAS INTENTIONALLY.

ILEFTBLANK

ORNLITM-7168 Dist. Category UC-20 f

INTERNAL DISTRIBUTION

1. P. W. King 10. Document Reference Section 2. E. Lazarus 11-12. Central Research Library 3. M. Murakami , 13. Fusion Energy Division 4. J. Sheffield Library 5. C. E. Thomas 14. Fusion Energy Division 6. R. E. Worsham Communications Center

7-8. Laboratory Records Department 15. ORNL Patent Office 9. Laboratory Records, ORNL-RC

EXTERNAL DISTRIBUTION

D. J. Anthony, Energy Systems and Technology Division, General Electric Company, 1 River Road, Bldg. 23, Room 290, Schenectady, NY 12345 J. Ayers, ORTEC, Inc., Midland Road, Oak Ridge, TN 37830 P. R. Bell, 132 Westlook Circle, Oak Ridge, TN 37830 J. F. Clarke, Office of Fusion Energy, Department of Energy, Washington, DC 20545 N. A. Davies, Tokamak Branch, Office of Fusion Energy, Department of Energy, Washington, DC 20545 S. 0. Dean, Office of Confinement Systems, Office of Fusion Enc.rgy, Department of Energy, Washington, DC 20545 H. K. Forsen, Exxon Nuclear Company, Inc., 777 106th Ave., NE, Bellevue, WA 98009 H. P. Furth, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08540 D. A. Gedckr, ORTEC, Inc., Midland Road, nak Ridge, 'EN 37830 R. W. Gould, California Institute of Technology, Mail Stop 116-81, Pasadena, CA 91125 C. C. Harris, Department of Nuclear Medicine, Duke University, Durham, NC 27706 E. G. Harris, Department of Physics, University of Tennessee, Knoxville, TN 37916 K. W. Hill, Princeton Plasma Physics T,aboratory, P.O. BOX' 451, Princeton, NJ 08540 R. L. Hirsch, Exxon Research and Engineering Cn., P.0, Box 101, Florham Park, NJ 07932 T. Hsu, Office of Confinement Systems, Office of Fusion Energy, Department of Energy, Washingt.nn., DC 20545 G. L. Jahns, General Atomic Co., P.O. Box 81608, San Diego, CA 92138 D. H. McNeill, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08540

J. Rice, Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139 R. H. Rohrer, Department of Physics, Emory University, Atlanta, GA 30322 M. M. Satterfield, The Nucleus, 461 Laboratory Road, Oak Ridge, TN 37830 R. J. Taylor, Center for Plasma Physics and Fusion Engineering, University of California, Los Angeles, CA 90024 S. von Goeler, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08540 B. Zurro, Junta de Energia Nuclear, Madrid, Spain Office of Assistant Manager, Energy Research and Development, DOE-ORO, Oak Ridge, TN 37830 Given distribution as shown in TID-4500, Magnetic Fusion Energy (Distribution Category UC-20 f, Experimental Plasma Physics)