Thermal-blooming-induced low-order aberrations

Julian S. Nichols and Dennis C. Duneman

The low-order (focus and astigmatism) aberrations induced in a thermally bloomed medium with transverseflow were measured. The maximum focus OPD for a 10-cm aperture was measured to be -0.4 Ylm at an Irel_ 0.5. The maximum astigmatism OPD was measured to be -1.4 ,tm at an Irel 0.4. The low-order aberra-tions were dominant at Irel 0.4. For Irel 0.4, higher-order terms become more important. Using themeasured values of focus and astigmatism as inputs, a loop was closed around a deformable mirror to correctfor the measured aberrations. The presence of an iterative condition in which correction for thermal bloom-ing leads to a more severe condition of blooming, and so on, was observed. However the loop converged toa stable condition. The maximum increase in peak intensity on target achieved by closing the loops was30-40%.

I. Introduction

The feasibility of using adaptive optics to correct forthe effects of thermal blooming has been discussed onmany occasions.1 -7 The work can be divided into twobroad categories: outgoing wave systems and returnwave systems.5 In the outgoing wave systems, the effectof the thermal blooming on the outgoing beam is mea-sured or otherwise determined. In the return wavesystems, the effects on a return wave are measured orotherwise determined. Actual implementation of acorrective system results usually in an additional sub-breakout or categorizing. In one instance the aberra-tion is precalculated-assuming the system configura-tion and propagation conditions are known wellenough-and the precalculated results are used toprefigure an adaptive element so as to correct for theblooming effects. In the second instance a closed-loopcontrol system is used to correct for the thermalblooming in real time by sensing some characteristic ofthe beam-usually the intensity of the beam on target(outgoing wave system) or the intensity of the returnwave. This intensity maximization is usually accom-plished by incorporating a dithered outgoing beam anda hill climbing algorithm. In the closed-loop adaptivesingle parameter (CLASP) 7 system, the two approacheswere combined by precalculating a fixed figure in arelative sense which was imposed on an optical element

The authors are with U.S. Air Force Weapons Laboratory, KirtlandAir Force Base, New Mexico 87117.

Received 16 December 1983.

and then the amplitude was dithered to obtain maxi-mum on-target intensity.

Smith's8 review paper devotes a section to phasecompensation of thermal blooming. Pearson5 haspublished an excellent short paper in which he reviewsseveral papers and in which he reconciles many of theapparent contradictions in the results of efforts to cor-rect for thermal blooming using adaptive optics. Innone of the experiments are the induced aberrationsmeasured. Either the aberrations are estimated ana-lytically or the intensity profile is maximized using amultidither system.

In this paper an experiment is described in which theoutgoing CO2 beam blooms a medium and heats a tar-get. The return image beam from the heated targetobtained by using a shared aperture is examined by awave front analyzer to measure the focus and astigma-tism aberrations induced in a forced wind, thermallybloomed gaseous medium. Control loops are closedaround a deformable mirror to cancel the measuredaberrations.

Pearson5 and Bridges and Pearson1 have discussedthe possibility that coherent adaptive techniques(COAT), when used for correcting thermal blooming,can lead to a stronger thermal blooming condition whichrequires further corrections and so on. This degener-ative situation has been observed in the experimentreported here. Happily, the system converged to astable state.

On closing the loops, the overall improvement inbeam intensity on target is within the range discussedby Pearson.5

II. Experimental

The experimental configuration is shown in Fig. 1.The beam from the 200-W CO2 laser is expanded by the

2342 APPLIED OPTICS / Vol. 23, No. 14 / 15 July 1984

IIsa

54.Ban \IwlQDIDWIC a EGG

TILT\ 16i 38.I~ Tm IN, S- I I GWER

276i H CELL I ATM. o5.a

Fig. 1. Schematic of experimental arrangement.

first beam expander to accommodate the designed10-cm diam footprint of the deformable mirror. Thedeformable mirror is an edge actuated modal mirrordesigned to correct for focus and two axes of astigma-tism. 9 1 0 The second beam expander is inverted. It isused to compress the beam and to focus the beam on thetarget. The beam diameter as it enters the thermalblooming cell is 1 cm. The thermal blooming cell is asmall scale wind tunnel. The gas is ambient air at at-mospheric pressure which is doped with small quantitiesof Freon to increase the absorption. The wind is vari-able from stagnant to -2 m/sec. The blooming cell isdescribed in detail in Ref. 11. A portion of the CO2

beam is split off at the output of the thermal bloomingcell and sent to an IR scanner located in the focal plane.The scanner presents 3-D views of the beam intensity.Except for the small portion which is sent to the IRscanner, the beam is focused on the target which isheated to a red-and-white hot temperature. The targetis the tip of a water-cooled 0.20-cm diam copper wire.Thus the wire is not consumed and the target size re-mains constant throughout the period of data taking.The position of the target can be changed to compensatefor the beam bending caused by thermal blooming.The spectrum of radiation generated by the hot targetcontains a strong component of 3.5-4.1-,am wavelengthwhich is propagated back through the thermal bloomingcell to the deformable mirror and off the dichroic to thewave front analyzer. The wave front analyzer measurestwo axes of tilt, focus (P4 ), and two axes of astigmatism(P5 ,P6 ) at 3.5-4.1 Aum using three InSb detectors. Adetailed description of the wave front analyzer is givenin Ref. 12. The output from the two tilt channels in thewave front analyzer is used to close a loop around thetilt mirror so as to cancel any residual static tilt errorsor dynamic tilt inputs generated in the blooming cell orby other optical components. The closed-loop band-width (3 dB down) of the two tilt channels is -60 Hz.The focus channel output of the analyzer can be usedto close a loop around the deformable mirror to cancelany observed return wave focus aberrations. The twoastigmatism outputs from the analyzer can also be usedto close loops around the deformable mirror. Thebandwidth (3 dB down) of the closed loop P4 , P5, andP6 channels is -150 Hz.

To summarize: the CO2 beam is used to generatethermal blooming and to heat a target. The outgoingwave intensity profile is recorded by the IR scanner.The blackbody return wave front from the heated targetis analyzed by the wave front analyzer to determine theamount of focus and astigmatism aberrations present.

Electrical outputs of the analyzer, which are propor-tional to the aberrations, are used to close tilt loopsaround the tilt mirror and focus and astigmatism loopsaround the deformable mirror.

The experimental procedure was:(1) With the CO2 beam on and with no thermal

blooming (i.e, no Freon added to the ambient atmo-sphere) the target is heated. The deformable mirroris flat and the analyzer is adjusted to yield zero focusand astigmatism outputs. (Note that the tilt loops arealways closed.) The wind velocity is set to a specifiedvalue. The CO2 intensity profile is examined.

(2) Freon is introduced slowly into the cell until aspecified intensity of the CO2 beam is observed on thescanner. The ratio of this beam intensity to the in-tensity with no blooming is called Irel. With the focusand astigmatism loops open, the voltage outputs of thecalibrated analyzer yield directly the number of wavesof aberration induced for that particular bloomingcondition. Photographs of the CO2 intensity profile forthis blooming condition are taken.

(3) The focus and astigmatism loops are closed. Theanalyzer outputs drive the deformable mirror to com-pensate for the thermal-blooming-induced aberrationsuntil the analyzer outputs are zero. The CO2 beamprofile is photographed. By recording the voltage re-quired into each channel of the calibrated deformablemirror to zero the output of the analyzer, the amountof corrective aberration is obtained directly.

Ill. Data

Measured wave front aberration data, given in Fig.2, are focus (P 4 ) and two axes of astigmatism (P5 ,P6 ) inthe Zernike notation:

P 4 = K 4 (2r 2- 1),

P 5 = K 5r 2 cos2O,

P 6 = K 6r 2 sin2O.

(1)

(2)

(3)

The measured aberrations in units of wavelength at 4,um (X 4 ,m) are plotted vs Irel (Irel = ratio of the peak CO2beam intensity with thermal blooming to the peak CO2beam intensity with no blooming) with crosswind ve-locity v as a parameter.

All six curves in Fig. 2 are plotted to the same scaleto facilitate comparison. It is important to note thatin Fig. 2(a) the focus aberration was obtained from thewave front analyzer with the aberration loop open.This aberration represents the aberration induced forthat condition of thermal blooming which yields thecorresponding Irel. Figure 2(b) gives the aberration thatthe deformable mirror had to impose on the beam inorder to yield a zero output on the analyzer (i.e., the loopwas operating in a closed configuration). The fact thatthe aberration values in Fig. 2(a) and (b) are not equaland opposite is indicative of the condition hypothesizedin Refs. 1 and 5 in which a correction leads to another(more severe) blooming condition which leads to an-other correction and so on. A similar statement appliesto Figs. 2(c) and (d) for P5 aberration and to Figs. 2(e)and (f) for P6 aberration. Even though this nonlinear

15 July 1984 / Vol. 23, No. 14 / APPLIED OPTICS 2343

I r e II .9 .8 .7 .6 .5 .4 .3 .2 .1l ,,,,,, *I . '.

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Fig. 2. Measured wave front aberration data in units of wavelength at 4 Atm (X4,m) plotted vs Irel with crosswind velocity as a parameter:(a) open loop P 4 ; (b) closed loop P 4 ; (c) open loop P; (d) closed loop P 5 ; (e) open loop P6 ; (f) closed loop P 6.

effect is present, the system converged to a stable pointsuch that the final output of the analyzer in all threechannels was driven to zero.

For each data point shown in Fig. 2, a set of photo-graphs of the intensity of the outgoing CO2 beam wastaken. A sample set is shown in Fig. 3. A set consists

of a profile view and a 3-D view of the beam for the no-blooming condition, a comparable pair for the conditionof blooming but no correction (open loop), and a pairtaken after the loop has been closed and stabilized to acondition such that the analyzer output has been drivento zero.

2344 APPLIED OPTICS / Vol. 23, No. 14 / 15 July 1984

0

-.1

+.

0

- .3

- .4

-. 5

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(b)

(c)

Fig. 3. Intensity profile and 3-D view of the outgoing CO2 beam as

recorded on the EG&G IR scanner (Irei = 0.5, v = 37.4 cm/sec): (a)

no blooming; (b) open loop bloomed; (c) closed loop bloomed.

IV. Discussion

A. Applicability of Low-order AberrationMeasurements

The potential value of the aberration data presentedin Fig. 2 is dependent to a large extent on the followingquestion: "What portion of the total blooming-inducedaberrations can be attributed to the low orders P4 ,P5 ,P6

which the analyzer is capable of measuring?" Thisquestion has been discussed briefly in the literature. 8'1 3

However in those papers, the influence of the degree of

thermal blooming (i.e., corresponding Irel) for the resultspresented is not clear and the configuration is differentfrom that considered here. In the following discussionwe will try to get a handle on this question by examiningthe experimental results.

An expression for Irel based on the wave front aber-rations can be written

Irel _ exp[-(27rNx)2 1, (4)

where NX. is the number of wavelengths of aberrationpresent.

From Fig. 2 we have the number of waves of P4 ,P5,P6

at 4 Aum induced by the bloomed media. This is easilyconverted to waves at 10.6 Aum. If P4 , P5, and P6 are thedominant aberrations

N (JTp42 + NP5

2 + NP62 ),

Fig. 4. Irel calculated from the measured open-loop aberrations

plotted against the observed Irel.

where NP 4 = number of waves of P4 aberrations at 10.6

Aim and similarly for NP5 and NP6. Values for Irel,calculated from Eq. (4) using Eq. (5) and the measuredaberration data, are plotted against the observed Irel inFig. 4. The Irel calculated from the measured aberra-tions begins to deviate significantly from the ideal linewhen the observed Irel < 0.3-0.4. An assumption thatfor more severe blooming conditions (i.e., Irel < 0.3-0.4)higher-order aberrations are starting to become sig-nificant would account for this deviation. The behaviorof the curves in Fig. 2 for the open-loop case seems alsoto substantiate this assumption. In these figures we seethat both P5 and P6 show a leveling off or a saturationfor Irel < 0.4. The P4 curves in Fig. 2 actually show a

decrease in magnitude for Irel < 0.5. Thus even thoughthe degree of thermal blooming increases (as demon-strated by decreasing Irel) the number of waves ofP4 ,P5,P6 stays the same or decreases. This observationsuggests that higher-order terms are becoming moresignificant.

B. Nonlinear Effect

The nonlinear effect suggested by the data in Fig. 2was mentioned briefly in Sec. III. For each of the threeaberrations shown in Fig. 2, if one overlays the closed-loop curve and the open-loop curve, it is seen that fora given open-loop aberration, a larger closed-loop ab-erration is required to be imposed on the deformablemirror in order to return the output of the analyzer tozero. For Irel > 0.6 the effect is mild. For more severeblooming (smaller Irel) the effect becomes more pro-nounced.

If the value Nx in Eq. (5) is determined from theclosed-loop data and

Irel exp[-27rNX)2]

is plotted vs the observed Irel, the curve of Fig. 5 results.

The nonlinear effect becomes obvious here in that allpoints fall below the 450 line in a consistent, orderlyfashion. This shows graphically the more severe

15 July 1984 / Vol. 23, No. 14 / APPLIED OPTICS 2345

1.0

.86

(a)

-

. X

-W

eZ .4

.2

0

I

.6

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Fig. 5. Irel calculated from the measured closed-loop aberrationsplotted against the observed Irel.

X-u:15.6 cm/sec0u- 3

7.4 cm/secA-u62 cm/sec

.6

.5

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3

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.

1 .9 .8 .7 .6 .5 .4 .3 .2 . II rel

Fig. 6. Relative increase in beam intensity resulting from closed-loopoperation.

blooming condition generated by attempting to correctthe original condition. A translation of each data pointto the left until it intersects the 45° line yields an esti-mate of the equivalent open loop rel that results fromthe attempt to correct for the original Irel. (Howeverone must be cautious and observe the proscriptiondiscussed above in terms of higher-order terms beingintroduced for Irel < 0.3-0.4.)

C. Beam Intensity ImprovementFor each data point in Fig. 2 a set of photographs like

those shown in Fig. 3 was obtained. We define 1 =open-loop bloomed intensity, and IC = closed-loopbloomed intensity. Then an intensity improvementresulting from closing the P4 , P5, and P 6 loops can bedefined as

limp = * (6)Ia

I, and I, can be obtained from the photographs for eachdata point. The quality of the data from the IR scanner(i.e., the photographs) is not as high as that obtainedfrom the analyzer and the deformable mirror. Theamplitude variations were generally of the order of20-40%. The noise components responsible for thesevariations are probably largely due to (1) temporalvariations in the CO2 laser,, and (2) variations inducedby random turbulence in the thermal blooming cell.(Note that the dynamic tilt mirror largely canceled thesetilt effects as seen by the analyzer. No such tilt cor-rection was present in the IR scanner leg of the experi-mental setup.)

Iimp is plotted vs Irel in Fig. 6. The data points werederived from a visual time averaging of the IR scannerrather than from scaling a single photograph. Thescatter in the data, which seems to increase as theblooming becomes more severe, is bothersome. How-ever, one is probably safe in drawing some qualitativeconclusions.

(1) The degree of improvement increases as theblooming condition becomes more severe until Irel 0.4.This observation is consistent with data presentedabove which suggest that the low-order aberrations aredominant for Irg > 0.4.

(2) For Ire < 0.4 the degree of improvement de-creases. This behavior is consistent with previous ev-idence that for Irel < 0.4 higher-order aberrations-which we have no ability to correct in this experi-ment-become more important.

(3) The maximum improvement obtained was 30-40% (imp 0.30-0.40). This peak improvement occursat an Irel 0.3-0.4.

(4) The data in Fig. 6 have been plotted with windvelocity as a parameter. If one chooses, a weak argu-ment can be made for a dependence of Iimp on velocity.However, because of the scatter in the data, I believeeither more analytical effort and/or experimental datais desirable before making that plunge.

V. Conclusions

The low-order aberrations (focus and astigmatism)induced in a bloomed media located in the first 50% ofthe propagation path of a focused Gaussian 10.6-Aumlaser beam have been measured as a function Of Irel withcrosswind velocity as a parameter. The data suggestthat these low-order aberrations are dominant for an Irel> 0.4-0.3. For more severe blooming (Irel < 0.4-0.3)higher-order terms become important. These experi-mental results are consistent with the analytical resultsof Bradley and Herrmann13 and Nahrstedt 14

The control system used for the aberration correctionis faster (bandwidth > 200 Hz) than the response timeof the bloomed media15 (bandwidth < 100 Hz). Thecorrection for thermal blooming using this system leadsto a stronger blooming and so on. However, thisevolving situation converges to a stable condition.

The improvement in intensity on target obtainedwith a closed-loop system increased as Irel decreaseduntil the maximum improvement of 0.3-0.4 wasreached at an Irel 0.4. For lower Irel (more severe

2346 APPLIED OPTICS / Vol. 23, No. 14 / 15 July 1984

blooming) the improvement decreases. This decreasein Iimp for more severe blooming is attributed toequipment limitations (i.e., the inability to correct forhigher-order aberrations). The power into the bloomedmedium was constant at -125 W. The adaptive opticssystem corrected for focus and astigmatism only.

References1. W. Bridges and J. Pearson, "Thermal Blooming Compensation

Using Coherent Optical Adaptive Techniques (COAT)," Appl.Phys. Lett. 26, 539 (1975).

2. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M.

E. Pedinoff, "Coherent Optical Adaptive Techniques: Design

and Performance of an 18-Element Visible Multidither COATSystem," Appl. Opt. 15, 611 (1976).

3. C. A. Primmerman and D. G. Fouche, "Thermal-Blooming

Compensation: Experimental Observations Using a Deforma-

ble-Mirror System," Appl. Opt. 15, 990 (1976).

4. J. Herrmann, "Properties of Phase Conjugate Adaptive OpticalSystems," J. Opt. Soc. Am. 67, 290 (1977).

5. J. E. Pearson, "Thermal Blooming Compensation with Adaptive

Optics," Opt. Lett. 2, 7 (1978).

6. J. A. Fleck, Jr., and J. R. Morris, "Equivalent Thin Lens Modelfor Thermal Blooming Compensation," Appl. Opt. 17, 2575

(1978).7. C. A. Primmerman, F. B. Johnson, and I. Wigdor, "Thermal-

Blooming Compensation Using the CLASP System," Appl. Opt.

17, 2909 (1978).8. D. Smith, "High-Power Laser Propagation; Thermal Blooming,"

Proc. IEEE 65, 1679 (1977).

9. A. Fuschetto, "Three Actuator Deformable Water Cooled Mir-ror," Proc. Soc. Photo-Opt. Instrum. Eng. 179, 17 (1979).

10. J. Nichols and D. Duneman, "Performance Evaluation of anEdge-Actuated, Modal, Deformable Mirror," Opt. Eng. 22, 366(1983).

11. B. Pierce et al., "Design of a Thermal Blooming Cell for use in

Evaluating Adaptive Optics," Proc. Soc. Photo-Opt. Instrum.Eng. 179, 81 (1979).

12. J. S. Nichols and D. C. Duneman, "Edge Scan Wave-Front Ana-

lyzer for Low Order Aberrations," Appl. Opt. 22, 2836 (1983).

13. L. C. Bradley and J. Herrmann, "Phase Compensation forThermal Blooming," Appl. Opt. 13, 331 (1974).

14. D. Nahrstedt, "Image Distortion and Compensation in the

Presence of Thermal Blooming," Proc. Soc. Photo-Opt. Instrum.

Eng. 410, 150 (1983).15. J. S. Nichols and D. C. Duneman, "Frequency Response of a

Thermally Driven Atmosphere," Appl. Opt. 21, 421 (1982).

Richard Abrams

Hughes Aircraft Co.

Charles S. Ih

U. Delaware

S

OSA 1983

New Orleans

Photos: F. S. Harris, Jr.

H. John Caulfield

Aerodyne Research

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