INTRACAVITY ADAPTIVE OPTICS

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R. Freeman, J. Spinhirne, D. Anafi

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C9, s u p p z d m e n t a u n O 1 l , Tome 4 2 , n o v e m b r e 1 9 8 0 , p a g e C9-405

INTRACAVITY ADAPTIVE OPTICS

R.H. Freeman, J.M. Spinhirne and D. Anafi.

U n i t e d T e c h n o l o g i e s R e s e a r c h C e n t e r , O p t i c s a n d A p p l i e d T e c h n o Z o g y L a b o r a t o r y , P.O.

Box

2692, W e s t P a l m B e a c h , F l o r i d a 3 3 4 0 2 U.S.A.

Abstract.- A major consideration in most laser resonator designs for high power is to obtain the maximum far field irradiance on a target. Various design approaches have emerged in recent years to optimize the far-field irradiance by utilizing different resonator concepts for the purpose of obtai- ning the best mode control and near field beam quality. The different concepts utilize annular and compacted gain mediums, spatial filtering techniques, novel optical components and adaptive optics. This paper will describe recent results using intracavity adaptive optical techniques versus extracavity adaptive optical techniques. Experimental results will be provided which will show the correction capability for low order aberrations (tilt and astigmatism) commonly found in high energy la- sers. A comparison of several optimization control techniques using a multidither zonal COAT system will be discussed describing the effects of hardware limitations and considerations on the performance of the system.

I. INTRODUCTION interpretations for correcting these aberrations.

Correction of intracavity phasefront distor- This paper presents control algorithm and resona- tions using multidither zonal COAT systems has tor design considerations when utilizing a multi- been previously reported by several authors 1-3 dither COAT control system for astigmatism and demonstrating significant improvement in overall tilt (static, dynamic) correction.

resonator performance. Performance parameters

*

such as Beam Quality

,

far-field Power-in-the-

**

Bucket (FIB)

,

and total power are usually used in defining improvement in laser resonator performance, and are also used in the control algorithm. An extensive experimental and analytical study has been conducted at United Technologies Research Center to evaluate intra (ICAO) versus extra cavity (ECAO) phasefront correction for several low order aberrations (tilt, astigmatism, and defocus). This paper describes the experimental results and

*

BQ is defined as the ratio of the measured reciprocal percentage PIB which is normalize& by the reciprocal percentage PIE of a uniforv plane wave annular corresponding to the geometrically predicted resonator output.

**

PIB is the far-field power within the Airy disk of the outcoupled beam. The Airy disk dimen- sion is determined from the geometrically predicted near field intensity pattern of the resonator.

11. EXPERIMENTAL CONFIGURATION A. Laser Device

A schematic diagram of the Neq =

6.5,

positive branch, confocal, linear, unstable C02 resonator used in these experiments is shown in Figure 1.

ANNULAR OUTCOUPLED

BEAM

OUTPUT COUPLER MIRROR

i

DEFORMABLE ABERRATION

MIRROR GENERATOR

L - 1

Fig. 1 Sketch of Experimental Set-Up

There are two turning mirrors located within the cavity. Mirror M2 (the aberration generator) is

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t h e a s t i g m a t i s m and t i l t g e n e r a t o r used f o r t h e s e t e s t s . The o t h e r t u r n i n g m i r r o r (M2) i s t h e deformable m i r r o r f o r t h e i n t r a c a v i t y a d a p t i v e op- t i c s e x p e r i m e n t s and f o r t h e f l a t m i r r o r used f o r t h e e x t r a c a v i t y a d a p t i v e o p t i c s e x p e r i m e n t s . The e x t r a c a v i t y t u r n i n g m i r r o r (M3) i s t h e deformable m i r r o r used d u r i n g e x t r a c a v i t y c o r r e c t i o n and a p l a n e m i r r o r o t h e r w i s e . An i n t r a c a v i t y beam s p l i t t e r (3% r e f l e c t i v e ) i s l o c a t e d n e a r t h e o u t - p u t c o u p l i n g m i r r o r t o p r o v i d e a sample o f t h e i n t r a c a v i t y mode i n t e n s i t y p r o f i l e . A p i c t u r e o f t h e e x p e r i m e n t a l t e s t bed, i n c l u d i n g a l l diagnos- t i c equipment, i s shown i n F i g u r e 2. The g a i n medium used i n t h e s e experiments i s a 1 0 cm diam- e t e r , c o n v e c t i o n c o o l e d , c l o s e d c y c l e , CW C02

e l e c t r i c d i s c h a r g e .

CVM IR IR

DIFFUSER,

\

CAMERA M1 C$M CAMERA

s u r f a c e i n f l u e n c e f u n c t i o n , and t h e a c t u a t o r ex- c u r s i o n a m p l i t u d e s f o r t h i s m i r r o r a r e approxi- m a t e l y

2

1 3 microns f o r a p l a n o r e f e r e n c e p o s i t i o n . T h i s d i s p l a c e m e n t was found t o b e a t l e a s t 50% l a r g e r t h a n r e q u i r e d f o r c o r r e c t i o n of t h e a b e r - r a t i o n s i n t r o d u c e d . Zonal m u l t i d i t h e r h i l l - c l i m b i n g s e r v o tech- n i q u e s s i m i l a r t o t h o s e used i n v a r i o u s c o h e r e n t o p t i c a l a d a p t i v e t e c h n i q u e (COAT) s y s t e m s were used t o c o n t r o l t h e f i g u r e of t h e deformable mir-

r o r s . D e t a i l s of t h e p a r t i c u l a r c o n t r o l a l g o r i t h m s used a r e g i v e n i n t h e e x p e r i m e n t a l d a t a s e c t i o n of t h i s p a p e r . The r e s o n a t o r mode f o o t p r i n t s o n t h e d e f o r m a b l e m i r r o r f o r i n t r a c a v i t y and e x t r a c a v i t y l o c a - t i o n s a r e shown i n F i g u r e 3. For b o t h c a s e s , t h e a m p l i t u d e s o f t h e d i t h e r s were s e l e c t e d s o t h a t e a c h d i t h e r produced a p p r o x i m a t e l y t h e same r e t u r n s i g n a l t o t h e COAT e l e c t r o n i c s . Because of t h e o p t i c a l feedback p r o v i d e d by t h e r e s o n a t o r , i n t r a - c a v i t y a c t u a t o r s n e a r t h e o p t i c a x i s r e q u i r e v e r y low a m p l i t u d e d i t h e r s compared t o t h o s e n e a r t h e edge, and e x t r a c a v i t y a c t u a t o r s r e q u i r e s t i l l high- e r d i t h e r a m p l i t u d e s b e c a u s e of t h e s i n g l e p a s s n a t u r e of t h e c o r r e c t i o n .

ACTUATOR

F i g . 2 Photograph of Experimental R e s o n a t o r ₁ ₂ ₃

r

LOCATION 1 2 3

T e s t Apparatus

-.

,

,.

B. C a v i t y O p t i c s

9 10 11 12 13

:--

The deformable m i r r o r used is a c o n t i n u o u s

14

s u r f a c e d i s c r e t e a c t u a t o r m i r r o r 4 . The a c t u a t o r

'3

,_r:

.

%

'

l o c a t i o n s a r e i n a s q u a r e a r r a y o f 3.0 cm s p a c i n g , INTRACAVITY _EXTRACAVITY t h u s a l l o w i n g 1 6 a c t u a t o r s t o b e w i t h i n t h e mode

Fig. 3 Beam F o o t p r i n t on DM f o r ECAO & ICAO f o o t p r i n t . Each a c t u a t o r h a s a Gaussian l o c a l

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C . Performance D i a g n o s t i c s

Four d i a g n o s t i c measurements ( a s shown i n F i g u r e 4 ) were made t o c h a r a c t e r i z e t h e r e s o n a t o r performance. The r e s o n a t o r i n t r a c a v i t y mode i n - t e n s i t y p r o f i l e i s monitored by a s c a n n i n g IR cam- e r a u s i n g t h e sample p r o v i d e d by t h e i n t r a c a v i t y beam s p l i t t e r (S1). The o u t c o u p l e d beam i s d i v i d e d i n t o t h r e e beams by a ZnSe wedge beam s p l i t t e r t o p r o v i d e performance measurements ( a s d e s c r i b e d b e l o w ) , as w e l l as t o p r o v i d e f e e d b a c k s i g n a l s t o c o n t r o l t h e deformable m i r r o r .

The f i r s t sample of t h e o u t c o u p l e d beam is

f o c u s e d o n t o a n a p e r t u r e by a n 8 meter r a d i u s of c u r v a t u r e concave m i r r o r . The power t r a n s m i t t e d through t h i s a p e r t u r e ( u s u a l l y one A i r y d i s k i n d i a m e t e r ) i s s e n s e d by a HgCdTe d e t e c t o r . The d e t e c t o r o u t p u t s i g n a l is u s e d a s a feedback s i g - n a l f o r t h e COAT c o n t r o l e l e c t r o n i c s . DIFFUSER (D) POWER METER APERTURE

'-

'A'

B

POWER

y2

SI CVM FM

I I

/

I

LACTCD ' IR CAMERA

F i g . 4 Schematic Diagram o f E x p e r i m e n t a l Appara- t u s . A 13.6m r a d i u s convex m i r r o r (CVC) and a 19.6m r a d i u s concave m i r r o r (CCM) form t h e p o s i t i v e b r a n c h c o n f o c a l u n s t a b l e l i n e a r r e s o n a t o r w h i c h h a s two i n t r a c a v i t y f o l d i n g m i r r o r s , t h e deformable m i r r o r (MI), and t h e a b e r r a t i o n g e n e r a t o r (M2). The i n t r a c a v i t y mode i s sampled by a ZnSe s p l i t t e r (S1) monitored by a n IR camera. The o u t c o u p l e d beam i s i n c i d e n t on f o l d - i n g m i r r o r (FM) which i s t h e deformable m i r r o r d u r i n g e x t r a c a v i t y c o r r e c t i o n ex- p e r i m e n t s and i s t h e n s p l i t i n t o t h r e e beams f o r measurement o f power through a f a r - f i e l d a p e r t u r e (A) ( t h e COAT feed- b a c k s i g n a l ) , f a r - f i e l d i n t e n s i t y p r o f i l e u s i n g a n i n f r a r e d camera ( I ) , and t o t a l power ( P ) .

The second o u t c o u p l e d beam sample p a s s e s through a r e d u c i n g t e l e s c o p e t o e n l a r g e t h e f o c u s e d s p o t s i z e i n o r d e r t o m o n i t o r t h e f a r - f i e l d i n t e n - s i t y d i s t r i b u t i o n by a n IR s c a n n i n g camera.

The t h i r d o u t c o u p l e d beam sample i s i n c i d e n t on a n HgCdTe power m o n i t o r . T h i s t o t a l o u t p u t power s i g n a l i s r e c o r d e d on magnetic t a p e and may

a l s o s e r v e a s a n a d d i t i o n a l feedback s i g n a l f o r t h e COAT c o n t r o l e l e c t r o n i c s .

111. EXPERIMENTAL RESULTS

A. ICAO C o r r e c t i o n O p t i m i z a t i o n A l g o r i t h m I n a n i d e a l l a s e r s y s t e m w i t h a fundamental

R = 0 mode, t h e performance improvement w i t h i n

i n t r a c a v i t y a d a p t i v e o p t i c s i s e x p e c t e d t o b e near- l y i n d e p e n d e n t o f t h e c o n t r o l a l g o r i t h m 6 . I n o u r

TOTAL POWER HIGH VOLTAGE DlTHER FREQUENCY DETECTOR

AMPLIFIERS INPUT SYNTHESIZE (HgCdTe) LOW PASS

FILTERS AND GAIN ADJUST

COATDETECTOR APERTURE COAT DETECTOR (HgCdTe)

Fig. 5 C o n t r o l Loop Block Diagram (PIB Optimiza- t i o n )

e x p e r i m e n t s , however, a s i g n i f i c a n t d i f f e r e n c e was o b s e r v e d between c o n t r o l a l g o r i t h m s t h a t op-

t i m i z e Beam Q u a l i t y (BQ) o r Power-in-the-Bucket (PIB). The c o n t r o l l o o p f o r PIB o p t i m i z a t i o n as

shown i n F i g u r e 5 i s t h e u s u a l a l g o r i t h m f o r mul- 5

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c a n i n c r e a s e PIB by a combination of i n c r e a s i n g t h e o u t p u t power a n d / o r improving t h e BQ. The c o n t r o l l o o p f o r BQ o p t i m i z a t i o n i s shown by Fig- u r e 6. The p e r c e n t a g e PIB, o b t a i n e d b y a n a l o g

d i v i s i o n of t h e PIB by t h e t o t a l power ( P ) , i s used a s t h e c o n t r o l f e e d b a c k s i g n a l and is t h e q u a n t i t y maximized b y t h e COAT system.

I

DEFORMGLE

MIRROR

I

TOTAL POWER HIGH VOLTAGE DITHER FREQUENCY

F t & - d \ u - & ,

FILTERS AND

COAT DETECTOR APERTURE COAT DETECTOR (HgCdTe)

I

Fig. 6 C o n t r o l Loop Block Diagram (.BQ Optimiza- t i o n )

Astigmatism C o r r e c t i o n

E x p e r i m e n t a l r e s u l t s f o r i n t r a c a v i t y c o r r e c - t i o n of a s t i g m a t i s m u s i n g two c o r r e c t i o n a l g o r i t h m s a r e shown i n F i g u r e s 7 and 8. The changes i n t h e Beam Q u a l i t y upon l o o p c l o s u r e f o r b o t h c o n t r o l a l g o r i t h m s i s shown i n F i g u r e 7. A s u b s t a n t i a l BQ improvement u s i n g BQ o p t i m i z a t i o n is o b s e r v e d f a r a l l a m p l i t u d e s o f a s t i g m a t i s m . For PIB o p t i - m i z a t i o n , however, t h e r e a r e i n s t a n c e s where BQ d e g r a d a t i o n upon l o o p c l o s u r e o c c u r s implying o u t - p u t power i n c r e a s e i s t h e s i g n i f i c a n t f a c t o r i n improving PIB. C o n f i r m a t i o n of t h e importance of o u t p u t power i n c r e a s e f o r PIB o p t i m i z a t i o n i s shown i'n F i g u r e 8. For a l l a s t i g i n a t i s m s t r e n g t h s t h e r e i s a s u b s t a n t i a l power i n c r e a s e upon l o o p c l o s u r e . For BQ o p t i m i z a t i o n t h e r e i s no g e n e r a l t r e n d i n t h e b e h a v i o r of t h e o u t p u t power. I n some i n - s t a n c e s t h e r e i s a s i g n i f i c a n t d e c r e a s e i n o u t p u t power upon l o o p c l o s u r e a s i n d i c a t e d by t h e d a t a f o r a s t i g m a t i s m s t r e n g t h s of z e r o , and 0.20 waves. 0 OPEN LOOP

CLOSED LOOP - BQ OPTIMIZED CLOSED LOOP - PIE OPTIMIZED

ASTIGMATISM STRENGTH

(CENTER TO EDGE PHASE IN WAVES AT 10.6 pm) F i g . 7 C o n t r o l Algorithm Dependence o f Beam

Q u a l i t y During Astigmatism C o r r e c t i o n

0

OPEN LOOP

CLOSED LOOP - BO OPTIMIZED CLOSED LOOP - PIB OPTIMIZED

L ₀ _0.08 _0.12 _0.16 _0.20 _0.24 _0.28 ASTIGMATISM STRENGTH

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w i t h PIB c o n t r o l r e s u l t s i n t h e b e s t PIB improvement and a s u b s t a n t i a l power improvement upon l o o p c l o s u r e , b u t h a s poor BQ improvement. For BQ op- t i m i z e d I C A O , l i t t l e t o t a l power improvement (on t h e a v e r a g e ) i s o b s e r v e d ; however, t h e r e i s good BQ improvement. 2 0 1 8 1.6 1.4 1.2 1

.o

ECAO PIB ICAO BO

OPTIMIZED OPTIMIZED

F i g . 9 ECAO/ICAO (PIBIBQ) Comparison

-

Based on Average Performance f o r S t a t i c Astigmatism and Thermal D i s t o r t i o n C o r r e c t i o n S t u d i e s

B. D i s c u s s i o n of I n t r a c a v i t y R e s u l t s 6 As h a s b e e n shown by a n a l y t i c a l s t u d i e s

,

t h e R = 0 mode of a well-behaved r e s o n a t o r , s h o u l d

have b o t h t h e b e s t BQ and o u t p u t power and s h o u l d b e t h e mode which o p t i m i z e s b o t h BQ and PIB. T h e r e f o r e , r e s t o r a t i o n or' b o t h BQ and o u t p u t power s h o u l d b e accomplished d u r i n g c l o s e d l o o p opera- t i o n by r e t u r n i n g t h e r e s o n a t o r t o a n R = 0 mode.

The e x p e r i m e n t a l d a t a a p p e a r t o c o n t r a d i c t t h e a n a l y t i c a l l y p r e d i c t e d b e h a v i o r .

To d e t e r m i n e t h e r e a s o n s f o r t h e e x p e r i m e n t a l l y observed d i f f e r e n c e s i n BQ and PIB o p t i m i z a t i o n , t h e i n t r a c a v i t y mode s t r u c t u r e f o r t h e two caEes were c a r e f u l l y examined. F i g u r e 1 0 shows t h e un- p e r t u r b e d r e s c n a t o r i n t r a c a v i t y mode w i t h a n d w i t h -

NO DEFORMABLE DEFORMABLE

MIRROR INTRACAVITY MIRROR INTRACAVITY Fig. 1 0 I n t r a c a v i t y Mode S t r u c t u r e With and With-

o u t Deformable M i r r o r

o u t t h e d e f o r m a b l e m i r r o r i n t r a c a v i t y . Comparison

of t h e two modes shows improper l a s i n g on t h e lower l e f t s i d e of t h e r e s o n a t o r which c a n be a s s o c i a t e d w i t h a l o c a l i z e d f i g u r e e r r o r i n t h e deformable m i r r o r a s shown i n t h e i n t e r f e r o g r a m o f F i g u r e 11. There is a d i r e c t s p a t i a l c o r r e l a t i o n of t h e low i n t e n s i t y a r e a i n t h e open l o o p i n t r a c a v i t y mode and t h e d e f o r m a b l e m i r r o r l o c a l d i s t o r t i o n l o c a - t i o n . The s p a t i a l f r e q u e n c y o f t h e f i g u r e e r r o r is h i g h e r t h a n t h a t of m i r r o r r e s p o n s e and c a n n o t b e removed by a p p l i c a t i o n o f t h e c o n t r o l v o l t a g e s t o t h e a c t u a t o r s ; t h u s , t h e mode w i l l b e l o c a l l y a b e r r a t e d d u r i n g b o t h open and c l o s e d l o o p opera- t i o n 7 .

Because of t h e l o c a l i z e d n a t u r e of t h e f i g u r e e r r o r , t h e f u l l a p e r t u r e a b e r r a t i o n s a r e small (1125 of a wave) w h i l e t h e l o c a l i z e d phase t i l t produced by t h e f i g u r e e r r o r i s 65% of t h e Krupke

& sooy8 c r i t i c a l v a l u e . A s we w i l l show, t h e de- f o r m a b l e m i r r o r f i g u r e e r r o r i s a major f a c t o r i n t h e d i f f e r e n t r e s p o n s e s observed f o r t h e two con- t r o l a l g o r i t h m s .

BQ O p t i m i z a t i o n

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t o t a l power. The mode which would normally b e expected t o g i v e t h e b e s t BQ would be a n

R

= 0 mode however, t h e u n c o r r e c t a b l e f i g u r e e r r o r on t h e deformable m i r r o r i s s u f f i c i e n t t o degrade t h e mode s t r u c t u r e s o t h a t a new mode t h a t i s some l i n e a r

0.4 pm PHASE INTRODUCED IN , ,

.

. . . - - - OR PER GE - . . . . - - -

TYPICAL "FLAT" DEFORMABLE MIRROR FIGURE

OPEN LOOP 50 WATTS OUTPUT

CLOSED LOOP. BO OPTIMIZED CLOSED LOOP, PIE OPTIMIZED 50 WATTS OUTPUT 70 WATS OUTPUT

Fig. 11 Deformable Mirror F i g u r e I n f l u e n c e on Resonator Mode S t r u c t u r e

combination of t h e o r i g i n a l modes of t h e unperturbed r e s o n a t o r is now t h e lowest o r d e r mode. I n p a r t i - c u l a r , t h e r e may b e modes which have low i n t e n s i t i e s a t t h e r e g i o n of s e v e r e f i g u r e e r r o r s and would be- have s i m i l a r l y t o h i g h e r o r d e r modes of t h e unperturbed r e s o n a t o r . I n view of t h e p o s i t i o n of t h e l o c a l d i s t o r t i o n i n t h e deformable m i r r o r , one would expect an R = 1 mode with l o b e s on t h e l e f t and r i g h t t o be a s t a b l e mode f o r t h e r e s o n a t o r . How- e v e r , a n L = l mode h a s a n u l l on-axis i n t h e f a r - f i e l d and would t h u s not b e a s t a b l e mode under c l o s e d loop o p e r a t i o n . Experimental evidence i n - d i c a t e d t h a t , f o r some c a s e s , t h e c l o s e d loop in-

t r a c a v i t y mode s t r u c t u r e appears very s i m i l a r t o t h a t of a

R

= 1 mode ( s e e F i g u r e 11) f o r t h e c l o s e d l o o p i n t r a c a v i t y mode shape f o r BQ o p t i m i z a t i o n . I n t h i s c a s e i t was a l s o noted t h a t t h e o u t p u t power d i d n o t i n c r e a s e upon loop c l o s u r e , and i n some in- s t a n c e s a c t u a l l y decreased. F i g u r e 12 shows t h e

SINGLE AGA CAMERA FRAME SINGLE AGA CAMERA FRAME ( t

=

9.52 sec) 0.18 sec LATER

( t

=

9.70 sec)

Fig. 12 I n t r a c a v i t y Mode During Closed Loop Cor- r e c t i o n f o r Astigmatism, BQ Optimized ICAO

i n t r a c a v i t y mode p r o f i l e s f o r c l o s e d loop o p e r a t i o n a t two d i f f e r e n t times s e p a r a t e d by 0.18 s e c . Notice, t h a t t h e two single-lobed modes occur. The r e s o n a t o r a p p a r e n t l y s w i t c h e s from one mode t o t h e o t h e r i n a time s h o r t compared t o t h e adap- t i v e c o n t r o l bandwidth (30 Hz). The f a c t t h a t t h e mode s w i t c h e s from l e f t t o r i g h t i n d i c a t e s t h e r e

i s no r e a l advantage of one mode over t h e o t h e r , and t h e r e i s enough n o i s e i n t h e system t o i n i t i - a t e a change between t h e two modes. The modes show t h a t t h e system e l i m i n a t e s t h e n u l l on-axis i n t h e f a r - f i e l d and o p t i m i z e s t h e BQ simply by e l i m i n a t i n g one l o b e of t h e

R

= 1 mode. Because of t h e mode f l u c t u a t i o n from s i d e t o s i d e , t h e time averaged mode s t r u c t u r e ( a s shown i n Figure 11) would appear very s i m i l a r t o a s t a n d a r d L = 1

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PIB O p t i m i z a t i o n

The b e h a v i o r d e s c r i b e d f o r BQ o p t i m i z a t i o n does n o t o c c u r f o r PIB o p t i m i z a t i o n s i n c e a de- c r e a s e i n o u t p u t power would r e s u l t i n a d e c r e a s e i n Power-in-the-Bucket

.

The optimum mode f o r t h i s c o n t r o l w i l l b e any combination of h i g h e r o r d e r

modes t h a t w i l l i n c r e a s e t h e PIB. These modes w i l l have a p o o r e r beam q u a l i t y t h a n t h e BQ o p t i - mized mode.

F i g u r e 11 shows t h e c l o s e d l o o p i n t r a c a v i t y mode s t r u c t u r e f o r PIB o p t i m i z e d ICAO. Note t h a t t h e r e i s n o t much change i n t h e s t r u c t u r e compared t o open l o o p , b u t t h e r e i s a power i n c r e a s e . Com- p a r i s o n of t h e BQ and PIB o p t i m i z e d c a s e s i n Fig- u r e 11 shows t h e d r a m a t i c d i f f e r e n c e i n t h e mode s t r u c t u r e f o r t h e two c o n t r o l a l g o r i t h m .

F i g u r e 1 3 shows i n d i v i d u a l AGA camera frames f o r c l o s e d l o o p o p e r a t i o n , PIB o p t i m i z e d . There a r e s u b s t a n t i a l i n t e n s i t y v a r i a t i o n s from frame t o frame, b u t no l e f t t o r i g h t i n t e n s i t y r e d i s t r i - b u t i o n a s was s e e n f o r BQ o p t i m i z a t i o n i n F i g u r e 12, The s i g n i f i c a n c e o f t h e s e r e s u l t s w i l l be summarized i n t h e c o n c l u s i o n . a b i l i t i e s o f t h e s y s t e m was performed f o r t h r e e c a s e s : (1) a d d i t i o n of t h e s t a t i c t i l t a b e r r a t i o n p r i o r t o COAT s y s t e m l o o p c l o s u r e ; (2) d u x i n g l o o p c l o s u r e ; and (3) dynamic t i l t a b e r r a t i o n . T h i s was performed f o r t h r e e magnitudes (.22, .44, and

.66 waves) c e n t e r t o edge phase t i l t p e r t u r b a t i o n f o r t h e above t h r e e c a s e s .

G e n e r a l f e a t u r e s o f t h e d a t a which a r e n o t e d i n F i g u r e 1 4 a r e :

1)

The a b s e n c e of i n t r a c a v i t y mode i n t e n s i t y i n t h e lower c e n t e r p o r t i o n o f t h e mode f o r a l l a m p l i t u d e s of tilt. The d e v i a t i o n of t h e mode s t r u c t u r e from t h e i d e a l i s d u e t o t h e l o c a l i z e d f i g u r e e r r o r of t h e deformable m i r r o r p r e v i o u s l y d e s c r i b e d . 2) The s p r e a d i n g of t h e f a r - f i e l d i n t e n s i t y p a t t e r n f o r t h e a l i g n e d r e s o n a t o r upon l o o p c l o s u r e T h i s b e h a v i o r c a n b e a t t r i b u t e d t o t h e f a c t t h a t t h e COAT f e e d b a c k a p e r t u r e is l a r g e r t h a n t h e f a r - f i e l d A i r y d i s k . The h i l l - c l i m b i n g s e r v o c a n op- t i m i z e t h e power t h r u t h e a p e r t u r e by f o r c i n g t h e r e s o n a t o r t o o p e r a t e o n some mixed mode which i n - c l u d e s components of h i g h e r o r d e r modes. T h i e

FAR FIELD

INTRACAVITY ( t =4.04 sec) 0.37 sec LATER ( t = 4.41 sec) MODE

F i g . 1 3 I n t r a c a v i t y Mode During Closed Loop Cor- r e c t i o n f o r Astigmatism, PIB Optimized

ICAO _{OPEN LOOP} _{CLOSED LOOP}

NORM. POWER

=

1 .O NORM. POWER

=

1.24 S t a t i c T i l t C o r r e c t i o n

F i g . 1 4 S t a t i c T i l t ( B a s e l i n e Case) F a r - F i e l d and I n t r a c a v i t y Mode P a t t e r n s f o r Open C h a r a c t e r i z a t i o n o f t h e tilt c o r r e c t i o n cap-

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mixed mode w i l l n o t h a v e t h e same f a r - f i e l d performance a s t h e lower o r d e r mode.

The d a t a f o r b o t h methods o f s t a t i c t i l t cor- r e c t i o n a r e summarized i n F i g u r e 15. Near i d e n t i - c a l c o r r e c t i o n f o r b o t h methods i s observed f o r s m a l l t i l t a m p l i t u d e s a s shown by t h e b e h a v i o r of t h e o u t p u t power v e r s u s t i l t a n g l e . T h i s f i g u r e d r a m a t i c a l l y i l l u s t r a t e s t h e e f f e c t of t r a n s l a t i o n of t h e f a r - f i e l d produced by t h e i n t r a c a v i t y t i l t OUTPUT POWER

(NORMALIZED TO OPEN LOOP ALIGNED CASE)

8,

=CRITICAL TILT ANGLE = 0 170 mr

CONTINUOUSLY

CLOSED LOOP

OPEN LOOP

' CLOSED

WAVES WAVES WAVES

TILT (9,)

Fig. 1 5 S t a t i c T i l t T e s t o f Output Power v s . T i l t Angle (8,)

and t h e a b i l i t y of t h e a d a p t i v e o p t i c t o move t h e beam c e n t r o i d c l o s e t o t h e o r i g i n a l o p t i c a x i s . The l a c k of good c o r r e c t i o n a t 0.66 waves t i l t f o r l o o p c l o s u r e a f t e r t i l t i n t r o d u c t i o n i s caused by a lock-on problem w i t h t h e c o n t r o l a s w i l l b e d i s c u s s e d i n t h e f o l l o w i n g p a r a g r a p h s . The major f e a t u r e s o f a l l t h e s t a t i c t i l t d a t a c a n b e e x p l a i n e d i n t e r m s o f t h e l i m i t a t i o n s o f a p p l i c a t i o n o f h i l l - c l i m b i n g s e r v o t e c h n i q u e ? t o i n t r a c a v i t y a b e r r a t i o n c o r r e c t i o n . The poor c o r r e c t i o n f o r l a r g e a m p l i t u d e s o f t i l t when t h e t i l t was i n t r o d u c e d p r i o r t o l o o p c l o s u r e i s d i r e c t l y r e l a t e d t o t h e c o n t r o l algo- r i t h m . When t h e tilt a m p l i t u d e i s l a r g e enough t o t r a n s l a t e t h e peak o f t h e f i r s t r i n g - o f t h e f a r - f i e l d d i f f r a c t i o n p a t t e r n o n t o t h e c e n t e r o f t h e COAT d e t e c t o r a p e r t u r e (0.16 waves f o r t h e r e s o n a t o r under s t u d y ) t h e p o s s i b i l i t y e x i s t s f o r l o c a l maxima lock-on r e s u l t i n g from t h e 21IN am- b i g u i t y 9 problem. The l i k e l i h o o d of t h i s o c c u r i n g is reduced i f t h e COAT d e t e c t o r a p e r t u r e i s l a r g e r t h a n a n A i r y d i s k diameter1' a s demonstrated by t h e f a c t t h a t n e a r i d e n t i c a l performance o c c u r s f o r t h e c l o s e d l o o p and c o n t i n u o u s l y c l o s e d l o o p c a s e s f o r t i l t . c o r r e c t i o n a t 0.22 waves, a t i l t a m p l i t u d e l a r g e r t h a n t h e 0.16 waves r e q u i r e d t o c e n t e r a s i d e l o b e on t h e COAT d e t e c t o r a p e r t u r e . However, by r e d u c i n g t h e 2RN ambiguity problem by i n c r e a s i n g t h e COAT a p e r t u r e s i z e , one h a s a l s o s a c r i f i c e d optimum performance of t h e s y s t e m a t s m a l l t i l t a m p l i t u d e s a s shown by t h e beam spread- i n g upon l o o p c l o s u r e f o r t h e a l i g n e d r e s o n a t o r .

E l i m i n a t i o n of t h e 2IIN ambiguity problem in- h e r e n t i n m u l t i d i t h e r c o n t r o l a l g o r i t h m s h a s been

t h e s u b j e c t o f c o n s i d e r a b l e research1'. However, f o r t h e s e t e c h n i q u e s t o a p p l y t o t h e i n t r a c a v i t y u s e o f a d a p t i v e o p t i c s , t h e y must n o t o n l y b e a b l e t o d i s c e r n l o c a l maxima lock-on produced by t h e o u t p u t phase a b e r r a t i o n s ( t h e s o l e c o n c e r n when e x t r a c a v i t y c o r r e c t i o n i s performed), b u t must d e t e r m i n e t h e p o s s i b i l i t i e s of l o c a l maxima i n o u t -

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p a t t e r n s i d e l o b e lock-on. Dynamic T i l t C o r r e c t i o n

I n t h e dynamic t i l t s t u d y , t h e tilt was a p p l i e d s i n u s o i d a l l y a t t h e same amplitudes (peak-to-peak e x c u r s i o n s ) a s i n t h e s t a t i c case and a t two d i f - f e r e n t f r e q u e n c i e s (10 Hz and 30 Hz). The beam spread f o r t h e dynamic c a s e i s a l s o q u i t e s e v e r e . This may b e due t o t h e s i z e s of t h e COAT a p e r t u r e which w i l l allow some movement of t h e beam c e n t r o i d without a s e v e r e power l o s s a t t h e COAT d e t e c t o r .

A s shown i n Figure 16, t h e r e i s not t h e same i n c r e a s e i n t o t a l power t h a t was observed f o r t h e s t a t i c c a s e . This a g a i n i s a r e s u l t of t h e COAT d e t e c t o r a p e r t u r e s i z e being l a r g e r t h a n t h e beam c e n t r o i d , s i n c e t h e beam can move a c r o s s t h i s aper- t u r e i t does n o t produce a f i x e d mode and we do n o t s e e a s much power i n c r e a s e a s f o r s t a t i c t i l t cor- r e c t i o n . A s a r e s u l t of t h i s , t h e power i n an aper-

t u r e i n t h e beam c e n t r o i d i s d e c r e a s i n g with t h e i n c r e a s i n g of t i l t . Another reason f o r t h e poorer c o r r e c t i o n f o r dynamic t i l t i s t h a t t h e bandwidth of t h e e l e c t r o n i c c o n t r o l i s n o t s u f f i c i e n t .

OUTPUT POWER

(NORMALIZED TO OPEN LOOP ALIGNED CASE)

t

I rCLO$ED LOOP 10 HZ CLOSED LOOP

S

30 Hz

e

OPEN LOOP TILT ( Oc)

Fig. 16 Dynamic T i l t Output Power v s . T i l t Angle (ec)

I V . CONCLUSIONS

The l o c a l i z e d , h i g h s p a t i a l frequency f i g u r e e r r o r i n t h e defbrmable m i r r o r l e d t o a very im- p o r t a n t g e n e r a l conclusion r e g a r d i n g t h e r e l a t i v e

m e r i t s of BQ and PIB o p t i m i z a t i o n f o r ICAO c o r r e c - t i o n i n e i t h e r l i n e a r o r annular r e s o n a t o r s .

The r e l e v a n c e of t h e d e s c r i b e d r e s u l t s t o t h e High Energy Laser Community when t h e r e a r e s i g n i - f i c a n t l o c a l i z e d i n t r a c a v i t y a b e r r a t i o n s (such a s an o p t i c a l m i r r o r f i g u r e e r r o r , d e v i c e s t r u t s , g a i n medium d i s t o r t i o n s , h i g h c o a t i n g a b s o r p t i o n , axicon t i p e r r o r s , e t c . ) 1 2 , t h e r e can b e dramatic d i f f e r e n c e s i n t h e mode s t r u c t u r e f o r optimum BQ performance compared t o t h a t f o r optimum PIB performance. When they cannot b e c o r r e c t e d by t h e a d a p t i v e o p t i c because of a s p a t i a l frequency l i m i t a t i o n , a d i f f e r e n c e i n performance f o r t h e two c o n t r o l a l g o r i t h m s can b e expected. BQ o p t i - mization w i l l d r i v e toward a mode having low i n t e n - s i t y over t h e r e g i o n s of g r e a t e s t i n t r a c a v i t y a b e r r a t i o n t h u s reducing t h e i n f l u e n c e of t h a t

a b e r r a t i o n , b u t a l s o producing v o i d s i n t h e mode s t r u c t u r e . Although having good beam q u a l i t y , t h e s e modes would b e extremely u n d e s i r a b l e i n a

high power d e v i c e because i t does n o t maximize t h e power on t h e t a r g e t . Thus, PIB o p t i m i z a t i o n wouid be t h e more d e s i r a b l e c o n t r o l a l g o r i t h m under t h e s e circumstances w i t h t h e p o s s i b l e added re- quirement of e x t r a c a v i t y beam clean-up t o achieve good beam q u a l i t y .

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when t h e c o n t r o l l o o p i s c l o s e d a f t e r t i l t i s i n t r o d u c e d . Reasons: a) 2TtX ambiguity lock-on b) l o c a l maxima i n l a s e r performance r e s u l t - i n g from r e s o n a t o r mode c o m p e t i t i o n e f f e c t . i s more of a problem w i t h t i l t a b e r r a t i o n t h a n w i t h a s t i g m a t i s m because t i l t more s e v e r e l y d i s r u p t s t h e mode s t r u c t u r e of t h e r e s o n a t o r . T h e r e f o r e , we s u g g e s t t h a t a s e p a r a t e t i l t s e n s o r b e used t o p r o v i d e e r r o r s i g n a l f o r c o r r e c t i o n of t i l t and l e t t h e m u l t i d i t h e r COAT s y s t e m c o r r e c t f o r h i g h e r o r d e r a b e r r a t i o n s where i t performs much b e t t e r .

This work h a s been sponsored i n p a r t by t h e Defense Advanced Research P r o j e c t s Agency and t h e A i r Force Weapons Laboratory, and t h e United Technologies Research Center C o r p o r a t e sponsored r e s e a r c h program.

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