Self-induced Thermal Distortion Effects on Target Image Quality

Frederick G. Gebhardt

Experimental results are reported that show the effects of the self-induced thermal lens due to a highpower laser beam on imaging or tracking systems viewing along the same propagation path. The thermaldistortion effects of a wind are simulated with a low power ( < 3-W) CO2 laser beam propagating througha cell of liquid CS2 moving across the beam. The resulting image distortion includes a warping effectanalogous to the deflection of the C02 beam, together with a pronounced demagnification of the centralportion of the object. An active optical tracker is simulated with a He-Ne laser beam propagatingcollinearly with the C02 beam. The He-Ne beam pattern returned from a specular target is distortedand sharply confined to the outline of the crescent shaped CO2 beam. Simple ray optics models are usedto provide qualitative explanations for the experimental results.

The propagation of high power cw CO2 laser beamsin the atmosphere can lead to thermally self-inducedbending, spreading, and distortion effects due to theabsorption of the laser radiation by CO2 and H2O.-'These nonlinear propagation effects can severelyreduce the effective beam intensity4 and thus limithigh power CO2 laser applications. For the manycases, however, where thermal distortion effects onbeam intensity and deflection are small, e.g., at highaltitudes or with high wind, platform or slewingvelocities, it is of interest to determine the effects ofthe high power laser beam on tracking or imagingsystems viewing along the same propagation path.

In this letter, the results of several laboratorysimulation experiments are presented, showing thethermal distortion effects of a transverse wind onpassive image quality, as well as the propagation of alow power, collinear He-Ne laser beam. The resultsindicate that the image distortion effects can be sub-stantial even when the high power CO2 beam bendingand blooming effects are small. Although the imagedistortion exhibits a warping effect analogous to thedeflection of the high power beam, the most pronouncedeffect is the demagnification of the central portion of theobject. The experiment with the low power He-Nelaser beam propagating collinearly with the CO2beam in the moving, absorbing medium simulates acommon aperture active tracking system. The He-Nebeam, which is smaller than the CO2 beam, is deflectedand spread at the target similar to, but to a lesserextent than, the CO2 beam. The He-Ne beam reflected

The author is with United Aircraft Research Laboratories,East Hartford, Connecticut 06108.

Received 22 November 1971.

from the target surface is further spread and distorted,but the patterns observed at the receiver-transmitteraperture are sharply confined to the crescent regiondefined by the CO2 beam. Qualitative explanations ofthese results are given based on simple ray opticsmodels.

The self-induced thermal lens effects of a transversewind were simulated by moving a 5-cm diam, 2.5-cmlong glass cell containing CS2 across the cw CO2 laserbeam.3 The cell was equipped with NaCl windows ateach end and -sealed with silicone rubber gaskets.The 20-W CO2 laser used in the experiments wasstabilized to compensate for power variations due tovibrations and thermal drift, and the TEAfoo modeoutput beam was well collimated over the 2.5-cmabsorbing pathlength. The laser beam diameter wasapproximately 3 mm between the 1/e intensity points,and the laser beam intensity at the cell input wasvaried from -10 W/cm 2 to 40 W/cm 2 with a variableattenuator. 5 The velocity of the moving cell wasvaried in the range from 1.5 mm/sec to 3 mm/sec.

The arrangement for the collinear He-Ne laser beamexperiment is shown in Fig. 1. A Ge window ARcoated for 10.6 ,u was used to transmit simultaneouslythe CO2 laser beam and reflect collinearly the He-Nelaser beam through the moving CS2 cell. The He-Nelaser beam power was less than 1 mW, and the approxi-mately 1-mm diam beam was centered within the C02beam as indicated in Fig. 1. The distortion of thecombined CO2 and He-Ne laser beams was observed ona uv irradiated phosphor screen, approximately 2.5 cmfrom the end of the cell.

Examples of the distorted beam patterns are shownin the lower part of Fig. 1. The CO2 beam patternsappear dark as a result of the thermal quenching ofthe fluorescence of the phosphor, and the He-Nebeam patterns appear as the lighter spots. The

June 1972 / Vol. 11, No. 6 / APPLIED OPTICS 1419

Ge WINDOW ARI-/2.5 cm H-I COATED FOR 10.6M

/ hf~~I~k~f~ fV : ta IIIHeNe LASER BEAM

BEAM PATTERNS 2.5 cm FROM CELL

- WIND

HeNe HeNe AND C 2

N = 0 N = 0.6

strength of the thermal lens effect due to a wind (for acollimated beam) is conveniently expressed in terms ofthe dimensionless parameter 3

N (-dn/dT)2Pz ( _ [1 - exp(-az)(7rnopcpva3 az

where no, dn/dT, p, c, v, and a are, respectively, therefractive index, index change with respect to tempera-ture, density, specific heat at constant pressure, velocityand absorption coefficient of the medium; a is the l/ebeam radius, P is the incident laser beam power, andz is the pathlength. The values of N shown in Fig. 1were calculated using the known properties of CS2(no = 1.63, dn/dT = -0.79 X 10-3 0 C-; P = 1.26,g cm-'; and c = 0.95 J/g 0C), together with themeasured values for P,a,v, and az. [To account for theadditional air path beyond the CS2 cell we use the totalpathlength for z in the first factor in Eq. (1) andreplace az with at, where t is the cell length, in thebraced term. This is a reasonable approximationwhen at is large, and in this case at 2. ] The param-eter N, together with the Fresnel number defined bythe source beam size and pathlength, have been shownto be sufficient for specifying the beam distortion,deflection, and reduction in peak intensity for a widevariety of conditions. 3' 4' 6

For the N = 0 case in Fig. 1, the CO2 beam wasblocked, and only the undistorted He-Ne beam isshown. For the cases of N = 0.6 and 1.0 the CO2laser beam assumes the characteristic crescent shapewith the peak intensity shifted -0.7 and 0.9 times thebeam radius, respectively, into the flow. The He-Ne

Fig. 1. Thermal distortion ef-fects on collinear He-Ne laser

beam 2.5 cm from CS2 cell.

HeNe AND CO 2

N = 1.0

beam, which is also deflected into the flow and distorted,remains inside the crescent pattern of the CO2 beam.Since the He-Ne beam is smaller than the CO2 beamits behavior approximates that of the central ray of theCO2 beam which, within the limits of perturbationtheory3 is only deflected by the amount (N/2)a, whilethe shift in the peak intensity is greater and given by(3N/2)a. The distorted He-Ne beam pattern ap-pearing inside the dark crescent pattern of the CO2beam thus confirms the theoretical prediction that theshift in peak intensity does not follow the central raybut instead is greater. It is interesting also to note thatthe He-Ne beam, although becoming spread transverseto the wind, assumes an elliptical rather than a crescentshape.

In Fig. 2, the experimental arrangement is shownwith the He-Ne beam reflected from a specular target,which in this case is an AR coated Ge window, placednormal to the axis of the undistorted beam. Thereflected He-Ne beam is photographed with a camerafocused at the cell entrance window, and the distortedpatterns are shown for various values of N in the lowerpart of Fig. 2. Although the distorted He-Ne beampatterns show the spreading and bending similar tothat observed at the target, the sharp outer edges of thepatterns suggest that the reflected beam is trapped orconfined within the crescent region defined by theCO2 beam.

In Fig. 3, a simple ray-optics model for the distortionof the collinear He-Ne beam is shown. The He-Nebeam is deflected by the prismlike index gradient thatis also bending the CO2 beam. The deflection of the

1420 APPLIED OPTICS / Vol. 11, No. 6 / June 1972

CO 2

LASER BEAM

IT' %0 v 1 I" - ' - 2 - " " "

Ge WINDOWS ARCOATED FOR 10.6tL

-2. 5cm-']

ICO2 LASER

BEAM

CAMERA

FOCUSED ONCELL ENTRANCE

HeNeLASER BEAM

REFLECTED HeNe BEAM PATTERNS AT CELL ENTRANCE

---- WIND

N = 0 N = 0.4

Fig. 2. Distorted He-Ne laserbeam patterns observed at CS2cell entrance window after re-flection from a specular target.

N = 0.8 N = 1.2

smaller He-Ne beam is less than that of the CO2 beamfor the reasons given above; and, after reflection at thetarget, the beam is incident on the region through whichthe CO2 beam passes. As indicated in Fig. 3, the CO2beam is narrowed by the focusing action of the thermallens; and this results in a rather abrupt discontinuityin the refractive index. The portion T of the He-Nebeam that is refracted by this index discontinuity isdirected away from the transmitter axis while thereflected rays R remain confined within the regiondefined by the CO2 beam. Although the index dis-continuity is small (An/no -2.8 X 10 3N), the reflectioncoefficient at the boundary can be large since a (Fig. 3)is a small angle.

To examine the thermal distortion effects of wind onpassive imaging the experimental arrangement shownin Fig. 4 was used. Various two-dimensional objectswere placed approximately 2.5 cm from the CS2 celland centered in the region occupied by the undistortedCO2 beam. The objects were viewed through themoving CS2 cell along the propagation path of the CO2laser beam. A Ge window AR coated for 10.6 jL wasused to transmit the CO2 beam and as a mirror toreflect the visible image into the camera focused onthe objected plane. The patterns were illuminatedwith white light and consisted of the United AircraftCorporation symbol, numbers from an IBM card, anda uniform grid pattern with 1-mm spacing. With theCO2 laser beam blocked to prevent heating the liquidCS2 is clear with good optical quality as shown by theundistorted images in Fig. 4, for the cases of N = 0.

With the C02 beam passing through the movingliquid cell the images are distorted as shown in Fig. 4for the values of N = 0.4 and 1. [Here we have usedthe cell length for z in evaluating N with Eq. (1), since

HeNe BEAM

I _ _ _

--C0 2 BEAM

WIND

S

SPECULAR ARGE

I.'

T I//

T. / @A

I RT I 4

4-l

II

Fig. 3. Ray optics model for thermal distortion of collineartracking beam.

June 1972 / Vol. 11, No. 6 / APPLIED OPTICS 1421

v OVING CS 2CELL

- '§.:1::-.4

_ ,. . . I

I", �-_

OBJECT PLANEGe WINDOWAR COATED FOR 10.6 g

R BEAM

CAMERA FOCUSEDON OBJECT PLANE

Fig. 4. Thermal distortion ef-fects on passive imaging.

N = 0

N=0I

m=1.0 N = 0.4

N = .0 N = 0. 4

this is actually the pathlength of the distributed thermallens. ]

The directions of the flow simulating a wind areindicated by the arrows beside the distorted images.The thermal lens effect is seen to cause a bending of theimages in the flow direction that is opposite to thebending of the CO2 beam itself. In addition, thedistorted images exhibit a pronounced demagnificationof the detail in the central portion of the objects. Forexample, with N = 0.4 and 1 the images are demagnifiedapproximately by the factors of 2 and 4, respectively.For the images in Fig. 4, surrounded by the darkbackground, the field of view of the camera was re-stricted by placing a circular aperture slightly largerthan the CO2 beam diameter at the entrance windowof the CS2 cell.

To discuss the image distortion effects, we use thesimple ray-optics model shown in Fig. 5. It is con-venient to distinguish between the refractive indexdistributions associated with the thermal lens whichare along and across the flow or wind direction. Par-allel with the wind, i.e., along the x-direction, thetemperature change is proportional to the integral ofthe intensity, which produces the decreasing refractiveindex profile shown in Fig. 5. This is equivalent to aprism which, of course, leads to the familiar bending ofthe CO2 beam upstream in the wind. Rays passingthrough this prism from the central part of the imageare also deflected into the wind as shown in the sketch.Since the rays appear to be coming from a point down-stream in the object, this produces in the distortedimage the observed bending in the downstream directionas indicated in Fig. 5. Along the y-direction, which isperpendicular to the wind, the temperature is pro-

portional to the intensity, and hence the symmetrical,negative-lenslike refractive index profile shown in Fig. 5is produced. It is this distributed negative lens thataccounts for the pronounced demagnification observedin the distorted images.

The magnitudes of the prism and negative lenseffects under small distortion conditions are con-

PARALLEL WITH WIND

I

inI x1~

PERPENDICULARTO WIND

I

:02 BEAM \n/2Iy

�zcIj

X x _ OBJECT

o x -

Fig. 5. Ray optics model for thermal distortion of passiveimages.

1422 APPLIED OPTICS / Vol. 11, No. 6 / June 1972

N = 0

a

N = 0

N = 0.4 N = u.4

1

N = 1.0

I V'.'0_Al

't""I,I12" -

III

F-�::7-

veniently related to the distortion parameter N thatwas defined in Eq. (1). From the perturbation analysisin Ref. 3, the total decrease in the refractive indexAn along the flow or wind direction due to absorptionheating by a collimated Gaussian laser beam, canbe written as

An/no = (-\/r/2)(az/f(az)(a2/z2)N,

(An/no) V~r(a2/z2)N,

f - [z/(\1rnoN)J; N << 1,

and

h - (/2no); N << 1.(2)

where

fA-gz) fi 1 exp(-az)]J 3f~ a z ) = p a Z j 3This change in refractive index, together with theCO2 laser beam diameter, roughly define the indexgradient and hence the strength of the distributedwind-prism effect.

The distributed negative lens along the y-directioncan be expressed approximately by the quadraticrefractive index profile

[n(Oy)/n(O,O)J 1 + 2(y'/b'), (4)

where

n(0,0) = no[l- 2(An/no)], (5)

and

1/b2 = (1/4a2 )(An/no). (6)

The focal length f and distance h of the principal planesfrom the input and output planes of such a distributedlens of length z are, respectively, 7

f= -{b/[2no sinh 2(z/b)]}, (7)

and

h = (b/2no) tanh(z/b).

With these expressions an approximate analysis of thedemagnification effects can be made in terms of thevalues of N that will be encountered under atmosphericpropagation conditions.

In summary, we have shown the nature of the thermallens effects of wind on passive imaging and a lowpower visible tracking beam as simulated with theHe-Ne laser beam. It is interesting to note thatsignificant image distortion effects occur even forsmall values of N where the deflection and intensityreduction of the CO2 beam are relatively small. Thiscan be accounted for, at least in part, by the largerrefractive index of CS2 relative to air. The distortedimages viewed through the propagation path of thehigh power laser beam exhibit a deflection downstreamthat is opposite to the bending of the CO2 beam. Inaddition, there is a pronounced demagnification of thedetail in the central portion of the distorted image.The collinear He-Ne laser beam is deflected and dis-torted at the target similar to the CO2 beam. On reflec-tion from a specular target, which is normal to thetransmitter axis, part of the beam is refracted awayfrom the transmitter axis and lost. The portion of thereturn beam arriving back at the transmitter is reflectedby the thermally induced index gradient in such a wayas to confine the beam to the boundary of the distortedCO2 beam. Qualitative discussions of the experimentalresults have been given in terms of simple ray-opticsmodels. An approach for the quantitative evaluationof the image distortion data has also been describedthat makes use of the distortion parameter N based onthe available theory for the thermal lens effects due toa wind. 3,4

The author is pleased to acknowledge helpful discus-sions with D. C. Smith and the skillful technicalassistance of A. Guardiani.

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For the parameters of the present experiment, withN = 0.4, z = 2.5 cm, and az = 2.1, we obtain f =-0.74 cm, and h = 0.68 cm. It should be pointed outthat the large refractive index of CS2 (no = 1.63)relative to air decreases the focal length of the thermallens as shown by Eq. (7). Thus, the demagnification anddistortion effects here are stronger than those thatwould be obtained for a comparable value of N in theatmosphere.

For atmospheric propagation over ranges z <<10 km, az is much less than 1, and the expressions forAn, f, and h then become, respectively,

References

1. D. C. Smith, IEEE J. Quantum Electron QE-5, 600 (1969).2. J. Wallace and M. Camac, J. Opt. Soc. Am. 60, 1587 (1970).3. F. G. Gebhardt and D. C. Smith, IEEE J. Quantum Electron.

QE-7, 63 (1971).4. United Aircraft Research Laboratories Report-K921004-4,

"Investigation of Self-Induced Thermal Effects of C2 LaserRadiation Propagating in Absorbing Gases," F. G. Gebhardtand D. C. Smith (July 1971).

5. F. G. Gebhardt, J. H. McCoy, and D. C. Smith, IEEE J.Quantum Electron. QE-5, 471 (1969).

6. F. G. Gebhardt and D. C. Smith, Appl. Opt. 11, 244 (1972).7. H. Kogelnik, Bell Syst. Tech. J., 44, 455 (1965).

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