Acousto-optic tunable filter sidelobe analysis andreduction with telecentric confocal optics

Dennis R. Suhre and Neelam Gupta

The acousto-optic tunable filter (AOTF) has optical sidelobes that are due to the acoustic field producedby the transducer. These sidelobes were analyzed by wave-vector phase matching between the optical andacoustic fields, which correlated with measurements made with a TeO2 AOTF. A white-light point sourcewas filtered and imaged, showing reasonably large and slowly decreasing sidelobes covering a largespectral range. This effect reduces the image quality of an AOTF system by producing faint secondaryimages of bright objects. The image quality can be improved with a telecentric confocal optical arrange-ment in which the angular shift of the sidelobes is greatly reduced, producing a much sharper image. Thiseffect was also demonstrated experimentally with the point source. © 2005 Optical Society of America

OCIS codes: 220.1000, 230.1040.

1. Introduction

Acousto-optic tunable filters (AOTFs) are electronicdevices that use the interaction of acoustic and opti-cal waves in acousto-optic crystals. They are used fora number of single-point applications, such asspectroscopy,1–5 laser tuning,6,7 and optical multi-plexing.8,9 The acousto-optic material TeO2 has gen-erally been used in the visible, and Tl3AsSe3 in theinfrared. They can produce high-speed filtering withaccess times of a few microseconds, and, for single-point applications, sidelobes are generally not an is-sue.

AOTFs can also be used for spectral imaging,10–14

for which sidelobes tend to reduce the image quality.The AOTF has a number of aberrations, such asscene shift, in which the entire scene is uniformlyshifted in angle as a function of the selected wave-length and is due to dispersion. One can compensatefor this effect by placing a wedge on the output face ofthe AOTF,15 thus using the natural dispersion of thewedge. Another aberration is image blur, which isfundamentally related to the AOTF diffraction pro-cess16 and displaces the image position slightly ac-

cording to wavelength. Because of the wavelengthspread of the AOTF bandpass, a blurred image willresult, and the blur distribution is determined by theacoustic field pattern. Inasmuch as a transducer gen-erally produces an acoustic field with sidelobes, theresultant image blur will also have structure, result-ing in image sidelobes and ghost images of brightobjects within the image. These image sidelobes aretherefore a direct manifestation of the image bluraberration.

It was recently shown that telecentric confocal op-tics can compensate for AOTF aberrations17 by re-ducing the angular shift produced by them. It doesnot require dispersion, as does wedge compensation,and can operate with any type of AOTF. By improv-ing the image quality, telecentric confocal optics per-mits pixel-limited images with large camera arrays.This improvement of image quality includes reduc-tion of the ghost images produced by bright images,as is demonstrated in this paper.

2. Analysis of AOTF Sidelobes

The design equations for an AOTF18 can be used toanalyze the sidelobes with the aid of the wave-vectordiagram shown in Fig. 1. The input light phase prop-agates at an angle �i to the optical axis of the acousto-optic crystal, as shown for a positive uniaxial crystalthat has a larger extraordinary index of refraction.This beam is diffracted by an acoustic beam propa-gating at �a into the first-order output beam propa-gating at �d to the optic axis. Phase matching of theoptical and acoustic beams requires that

D. R. Suhre (dsuhre@andrew.cmu.edu) is with the Carnegie Mel-lon University, 700 Technology Drive, Pittsburgh, Pennsylvania15219-3124. N. Gupta is with the U.S. Army Research Laboratory,2800 Powder Mill Road, Adelphi, Maryland 20783-1197.

Received 8 December 2004; revised manuscript received 21 April2005; accepted 22 April 2005.

0003-6935/05/275797-05$15.00/0© 2005 Optical Society of America

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kd � ka � ki, (1)

where ki is the incident wave vector, ka is the acousticwave vector, and kd is the diffracted wave vector. Themagnitudes of the wave vectors are given by

|ki| � 2�ni��0, |kd| � 2�nd��0, |ka| � 2���,

(2)

where ni is the incident optical index of refraction, nd

is defined below, �0 is the vacuum optical wavelength,and � is the acoustic wavelength. The interaction isassumed for simplicity to occur in a plane through theoptical axis, and the input is also taken as an ordi-nary ray. The phase-matching condition can then beexpressed by use of the law of cosines as

�02��2 � no

2 � nd2 � 2nond cos �, (3)

where � � ��i � �d� is the Bragg diffraction anglebetween the input and output beams. Ordinary indexof refraction no corresponds to the incident beam, andnd is the extraordinary index of refraction of the inputbeam at �d, which is given by

nd � (cos2 �d�no2 � sin2 �d�ne

2)�1�2, (4)

where ne is the extraordinary index of refraction, giv-ing a birefringence of n � |ne � no|. The values ofthe refractive indices for TeO2 as a function of wave-length can be obtained from the literature.19

AOTFs are designed under noncritical phasematching,20 in which the power flow ray directions ofthe incident and diffracted beams are equal, whichproduces the largest angular acceptance. This is truefor either an extraordinary or an ordinary input,where the two beams are collinear because of walk-off, and tangents drawn to the wave-vector surfacesat the intersections of the incident and diffracted

wave vectors will be parallel. With this restriction,both the diffracted and the acoustic wave vectors areuniquely determined once the input wave vector ischosen. However, neither the input nor the acousticbeams are completely plane waves, so a spread ofoutput wave vectors will result. It is this spread thatproduces blurring and sidelobe images with an AOTFsystem.

The dependence of the angular spread of the opticaland acoustic beams is well known for acousto-opticdevices,21 and generally the acoustic spread must begreater than the optical spread for efficient interac-tion. Figure 2 illustrates the origins of a spread in theoutput beam, where two wavelengths at a fixed inputangle are phase matched. This match requires aspread in the acoustic field, which will always existfor a finite geometry. With a uniform rectangulartransducer, the angular dependence of the acousticfield intensity is given by

Ia sinc2[�(� � �0)Li��], (5)

where � is the angle between the input optical andacoustic beams, �0 is the value of � for maximumefficiency, Li is the interaction length, and sinc x� sin x�x. In the small-signal approximation, the dif-fracted optical intensity will be linearly related to theproduct of the input and acoustic intensities, so theintensity of the sidelobes can be obtained from therelationship between � and �. This relationship isgiven from trigonometry as

sin � � (�0��nd)sin �. (6)

Equations (3) and (6) can be used to eliminate theoptical wavelength dependence, with the acousticwavelength fixed and corresponding to a given fre-quency applied to the transducer. Once the relation-ship between � and � is established, the relationshipbetween � and �0 can also be determined, and theintensity of the optical output as a function of � willbe determined by the acoustic intensity as a functionof �. In the small-signal approximation, the opticalintensity from Bragg scattering will be directly pro-portional to the acoustic and input optical intensities.

Fig. 1. Wave-vector diagram for positive uniaxial crystals such asTeO2.

Fig. 2. Wave-vector diagram illustrating a spread in the dif-fracted beam for a fixed input ray that is caused by a spread in theacoustic beam.

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3. Sidelobe Image Modeling and Measurements

A TeO2 AOTF with a 15 mm square aperture and5 mm long transducer was used to measure sidelobeimages from a point white-light source. The responseof this AOTF to a He–Ne laser beam is shown in Fig.3, which we obtained by varying the applied fre-quency and converting to the corresponding wave-length. This AOTF was designed with �a � 96° to theoptical axis of the crystal, and, under the paralleltangents condition, there is only one set of wave vec-tors at 632.8 nm that will give the peak response forthe measured frequency of 68.48 MHz. All the AOTFparameters, with the exception of the resolution,which depends on the transducer length, are thenuniquely defined. The measured resolution width cor-responded well to the calculated resolution for thetransducer length, as did the calculated wave-vectorangle compared to the design parameters. The re-sponse also closely followed a sinc2 x pattern, as pre-dicted for an AOTF with a rectangular transducer.

The AOTF frequency was adjusted to respond at620 nm, and a Watec Model WAT-902A camera with a25 mm focal length lens was used to image the diffractedbeam generated by the AOTF. The source was a high-intensity lamp apertured to less than a millimeter andplaced far enough away that the image occupied a frac-tion of a pixel spacing, which was 9.8 �m in the AOTFinteraction plane direction. No additional optical ele-ments were used, other than a series of calibratedneutral-density filters placed in front of the AOTF toincrease the dynamic range of the camera by preventingsaturation. An image of the point source is shown in Fig.4, and it illustrates the many sidelobe images that appearon either side of the central spot along the AOTF inter-action plane direction.

A series of images was obtained with the neutral-density filters, and the images were recorded and theintensity along a line centered on the row of spots wasread at each pixel. The data from the images were thenscaled with respect to the neutral-density attenuationand pieced together to form an intensity recording ofthe sidelobe spots over many orders of magnitude. Thedata are plotted in Fig. 5, for which they were normal-ized. The periodicity is not uniform, as can also be seendirectly from the image, and the intensity drops offroughly as a sinc2 x pattern, which can be expected

from the use of a rectangular transducer. The acousticsidelobes are responsible for the sidelobe images, asdemonstrated by the agreement with theory. For thisplot, the AOTF design parameters determined at632.8 nm as discussed above were used, and there isgood agreement in both intensity and periodicity be-tween theory and measurements. The figure also illus-trates the high quality of the AOTF, which allowed formeasurements over such a large dynamic range with-out being limited by homogeneity effects. This AOTFwas used in designing a telecentric confocal spectropo-larimetric imager.22

The optical wavelengths that correspond to the po-sition of the sidelobe images were also calculated, andthey are plotted in Fig. 6. The optical wavelengthrange was large; it covered the entire visible range.This wavelength range occurs over an angular shift ofthe output beam of less than 2°, which may seemsmall, but it is actually approximately half of themaximum angular separation of the input and outputbeams. As the acoustic frequency is constant, theoptical wave vectors would have to change by approx-

Fig. 3. Response of the TeO2 AOTF used for measurements to a632.8 nm He–Ne laser.

Fig. 4. Image of a diffracted AOTF image of a white-light pointsource, showing sidelobe images.

Fig. 5. Measured normalized AOTF sidelobe image intensity ofpoint source compared with theory.

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imately a factor of 2 to vary the separation angle bythis amount, consistent with the large wavelengthrange.

4. Telecentric System Image Analysis andMeasurements

A telecentric confocal optical AOTF system is shownin Fig. 7, and it has apertures at the object and imagefocal planes and is therefore telecentric for both ob-ject and image space. After interacting in the AOTF,the first-order diffracted beam is deflected by the dif-fraction angle and is separated from the zero-orderbeam by this amount. The output lens images thebeams, and the diffracted beam is projected throughthe output aperture, while the zero-order beam isblocked. The input aperture is adjusted such that theacceptance angle of the AOTF matches the inputf-number. When the acceptance angle exceeds thediffraction angle, the aperture must be limited to thediffraction angle. The output aperture is also ad-justed such that f2�D2 � f1�D1, where f1 and f2 are theinput and output lens focal lengths and D1 and D2 arethe input and output aperture diameters. This ad-justment of the output aperture allows the entireinput beam to be transmitted though the output ap-erture, while the zero-order beam is blocked. Theinput and output focal lengths and aperture diame-

ters can also be selected to provide a telescopicchange in the field angles such that the field of viewcan be matched to that of a camera system followingthe telecentric confocal system.

With this arrangement, the focused ray bundle willalways have the same angular extent for all fieldangles, providing a constant input angular spread,and uniform performance of the AOTF at all fieldangles. It also greatly reduces AOTF aberrations be-cause the angular effects of the aberrations are oc-curring on a small-diameter focused beam and, whenthe beam is expanded to its much larger output di-ameter, the angular aberrations are reduced by theratio of the focused and output beam diameters. Thiscan be a large effect, and the aberrations will gener-ally be negligible.

Images were obtained of the point source with thetelecentric confocal system, as shown in Fig. 8, andthey appeared rounded, with little sidelobe structure,although several faint diffraction spokes could beseen emanating from the image and are indicative ofthe blades of the adjustable apertures of the system.Images were recorded with a series of neutral-densityfilters, and the scaled data are plotted in Fig. 9 for theAOTF interaction direction. Also shown is an Airydiffraction pattern that has a 2.3 mrad angularspread at the first null, which is �44% larger thanthe diffraction spread expected from the confocal out-put aperture at a wavelength of 620 nm. A compara-ble elongation of the image in the AOTF interactiondirection can also be observed, indicating diffraction-limited imaging in the transverse direction but withsome spreading in the interaction direction.

The spreading of the diffraction pattern can be ex-plained by the AOTF sidelobes, which are still

Fig. 6. Calculated optical wavelengths corresponding to the side-lobe images of the collimated AOTF.

Fig. 7. Telecentric confocal optical arrange used to reduce side-lobe images.

Fig. 8. Image of a point source with a confocal system, showing alarge reduction of AOTF sidelobes.

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present with the confocal optics but are greatly re-duced in angular extent. The maximum reductionoccurs with the AOTF at the confocal center,17 wherethe sidelobes will be produced at the minimum dif-fraction limited diameter, and, after beam expansionwith the confocal optics, the angular extent of thesidelobes will be reduced by approximately a factor of60, which will compress all the sidelobes shown inFig. 5 to �0.5 mrad. This angular spreading couldaccount for the extended beam diameter in the AOTFinteraction direction, along with a blurring of thesidelobes of the expected Airy diffraction pattern.

5. Discussion

It was shown that sidelobe structure and ghost im-ages result when an AOTF is used in imaging white-light scenes and that the effect can be correlated inboth angle and intensity with simple geometricalphase-matching conditions and acoustic diffraction.The resultant optical sidelobes are asymmetrical,with a higher periodicity at shorter wavelengths. Thewavelength range of the sidelobes can be significant,covering the entire visible range. The intensity of thesidelobes follows that of the acoustic field, givingfairly high sidelobes with a sinc2 acoustic intensitypattern for the rectangular transducer that is typi-cally used.

In the past, acoustic field apodization to reduce theoptical sidelobes was attempted,20 which requiredcomplex phased transducer arrays, whereas thepresent solution is to use simple telecentric confocaloptics. The intensity of the AOTF sidelobes is notchanged with the optics, but the sidelobes are eitherblocked with apertures or contained within the an-gular image resolution. The telecentric confocal op-tics can then give either pixel or diffraction-limitedresolution. The use of telecentric confocal optics willallow an AOTF imaging system to achieve the max-imum possible image size, as determined by theAOTF’s aperture size and the f-number of the Bragginteraction.

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Fig. 9. Normalized intensity pattern produced by telecentric con-focal optics.

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