acousto-optic supermultispectral imaging

Acousto-optic supermultispectral imaging

Guan-Hong Gao and Zhong Lin

An assumption of supermultispectral imaging is presented. The focal point is to encode an objectbetween spatial and spectral information with a tunable bandpass filter, which is called the spatial-spectral encoder. Theoretical and experimental results have verified that the assumption is correct. Asupermultispectral imaging system that uses an acousto-optic tunable filter as the encoder was based onthe assumption. Approximately 5 nm of spectral resolution with 100 x 100 of the two-dimensional instantfield of view was obtained in the visible range. The most fascinating features may be that the spectralresolution is insensitive to the field of view and effective optical aperture and that the system has nomechanical moving parts.

Key words: Color image processing, multispectral imaging, acousto-optics.

Introduction

A typical multispectral imaging system with highspectral resolution uses the grating or prism as itsdispersive component, which determines that themaximum instant field of view of such a system is onedimensional. A mechanical scanning part is neededfor imaging, which will make the system complex andsensitive to vibrations.

Some researchers have presented new methods formultispectral imaging. Itoh et al. 1 described an inter-ferometric method that unifies the principles of inco-herent holography and Fourier spectroscopy. Theyreferred to the multispectral imaging that has spec-tral resolution as high as their spatial resolution assupermultispectral imaging. This technique can beused to collect the spectral and spatial informationsimultaneously and obtain the multispectral imagesfrom interferometric data through three-dimensionalFourier transformation. Although the number ofcalculations needed is large, this technique can beused for supermultispectral imaging applications.The rapidly growing computer technology may en-hance this application.

Carroll et al.2 reviewed spectral agility systems andtheir filtering devices. Spectral agility capitalizes onthe uniqueness of the spectral characteristics ofbackgrounds and targets in the sensor's field of viewin order to maximize the capability to perform detec-

The authors are with the National Laboratory of Optical Tech-niques, Department of Optical Engineering, Zhejiang University,Hangzhou 310027, China.

Received 1 April 1992.0003-6935/93/173081-06$06.00/0.t© 1993 Optical Society of America.

tion, discrimination, and tracking. But the instantfield of view and optical aperture have not particu-larly been considered at present, and no single tech-nique of spectral agility promising ideal performancehas yet been developed.

In the research reported in Refs. 3 and 4 theacousto-optic tunable filter5 6 (AOTF) was simplyused as a tunable filter placed in the imaging plane.We can conveniently use the systems to obtain mul-tispectral images by tuning the ultrasound frequencyin an acousto-optic crystal. If, however, we want toensure high spectral resolution, a small field of viewand optical aperture of the system must be imposed,which would be a fetal weakness in application.

In this paper an assumption of supermultispectralimaging is presented and verified. A system basedon the assumption, without any mechanical movingparts, is developed. This system uses the AOTF asits optical processor, and the method of optical process-ing used in this system is different from the methodsintroduced in Refs. 3 and 4. The experimental re-sults will also be demonstrated.

Principle of the Assumption

Most optical instruments collect spectral informationand spatial information separately. An acousto-optic supermultispectral imaging system that cancollect the above two types of information simulta-neously is illustrated in Fig. 1.

An object is placed in front of the focal plane of theobjective L1. Light from an arbitrary point of theobject is sent parallel to the beam in a correspondingdirection. Points A and B correspond to spatialdirections kA and kB, respectively. An optical tun-

10 June 1993 / Vol. 32, No. 17 / APPLIED OPTICS 3081

F- f I fa I f 2 d

Fig. 1. Schematic of the acousto-optic supermultispectral imag-ing system.

able bandpass filter that is a specially designed AOTFis placed between two objectives, L1 and L2.

If the angle of incidence ki is given, then thefiltering function T(ki) of the AOTF will be deter-mined only by the acoustic frequency fa:

T(ki) = function(X - X(k, fa))' (1)

where X,(ki, fa) is the central wavelength of the band-pass of the AOTF and X, depends on ki and fa. For acertain value of fa, an arbitrary pixel in the plane ofthe encoded image is nearly monochromatic. But Xof the pixel A' and that of B' are different, and thespectral bandwidth of every pixel is determined by theminimum bandwidth of the AOTF at the angle ofincidence ki. Consequently, the spatial points on theobject, the spatial directions ki, the pixels in theencoded image, and the wavelength X, are associatedin a certain relationship for a given frequency fa.

This relationship may be referred to as spatial-spectral encoding, and such a filter may be called aspatial-spectral encoder (SSE). When we tune fa,each spatial point on the object will be spectrallyscanned simultaneously but at a different startingwavelength. If the encoding relationship (rule) isknown and unique and certain (meaning that for eacharbitrary assigned spatial point A, its pixel A' isunique and the filtering wavelength XA dependence offa is monotropic in a certain regime), we can recon-

001]

Fig. 3. Wave vector geometry when Ki, Kd, K, and the optic axisare in the same plane.

struct (decode) multispectral images from the en-coded images in the sequentially tuning acousticfrequency fa. The tunable bandpass filter, whichmust satisfy the conditions mentioned above, wouldbe suitable as the SSE. We need to investigate theproperties of the SSE in three-dimensional space toverify the reliability of the principle. Because theAOTF was used in our experiment, the followinganalysis is made with respect to the AOTF. Anyavailable tunable bandpass filter, such as an electro-optic tunable filter, with the above optical featureswould be able to be used as the SSE.

Three-Dimensional Filtering Characteristic of theAcousto-Optic Tunable Filter

Most AOTF's are based on anomalous Bragg diffrac-tion. Dixon7 derived the tuning expressions of anom-alous Bragg diffraction in anisotropic media fromenergy and pseudomomentum conservation:

K = Kd + Ka,

Vi Vd ± fa, (2)

Fig. 2. Wave vector geometry in a positive uniaxial crystal whenthe incident light is extraordinarily polarized.

t

SFig. 4. General wave vector geometry when the incident light isextraordinarily polarized. K, is parallel to the plane z-t.

3082 APPLIED OPTICS / Vol. 32, No. 17 / 10 June 1993

where the subscripts i, d, and a denote the incidentlight, diffracted light, and ultrasound, respectively,and K is a wave vector. For the optical frequency, vis much bigger than fa; therefore vi is approximatelyequal to d; the choice of sign is determined by thepolarization of the incident light. The tuning expres-sions can be written as7

sin 0 = 2n1 V [fa + 9+ (ni2 - nd2)j, (3a)

ssin 02 = 2 _V fa

V 2 (n2 - fd2)]

where the choice of sign is determined by the direc-tion of the wave vectors.

In some cases, the incident light is of three-dimensional space, such as the situation in Fig. 1, oris not parallel to the plane consisting of the acousticwave vector Ka and the optic axis [001]. Figure 4shows the three-dimensional wave vector geometry.

Assume that the directional vectors of the inci-dent and diffracted light are (cos aj, cos pi, cosyi)and (cos ad, cos d, CpS 'Yd) in the s, t, z coordinatesystem, respectively; ka denotes the unit wave vectorof Ka. Using Figure 5, we can derive simultaneousequations about the angles (ai, A, 'Yi, af, P EdYd), ultra-sonic frequency fa, and the light wavelength X. Theline AP is the extension of ka. There are

OA2 + 0p2 - AP2

2(OA)(OP)

cos2 pi + (cos ot, + cos y, tan Oa)2 + 1 - (cos Yi/cos Oa)2

2[cos 2 pi + (cos (xi + cos yi tan Oa)2]1/2

where V is the acoustic phase velocity in the mediumand X is the free-space optical wavelength. Thedefinitions of the incident angle 01 and the diffractedangle 02 are shown in Fig. 2.

For the most uses of the acousto-optic devices, lightis incident upon these devices at a certain angle.The incident waye vectors of the light and the ultra-sound are commonly designed in the plane containedin the optic axis of the crystal. In this case, the wavevectors can be constructed as shown in Fig. 3.

OP Ikal = 1,

OM = cos (Xi,ON = cos Pi,OR = cos yi,

AP = cos yi/cos Oa.

OA = [cos2 pi + (cos a, + COS

In the same way, we can obtain

d Cos2 Pd + (COS atd + cos Yd tan Oa)2 +COS Od = 2[cos 2 Pd + (COS ad + COS Yd

1 - (COS d/COS Oa)2

tan Oa)2]1/2

Theangle expressions of the wave vector are

01 = +(90° - Oa + i0),

02 = +(90O - Oa + d)-

(4a)

(4b)

The more practical expressions may be written as

-COS(0a - Oi)

X

f2ni(i)V(0a) of + A (X2 [ni2(0 1) - nd 2(Od) I,

+COS(0a - Od)

A I X _ ) [n12(0 ) -2fld(0d)V(Oa) a1a f 2

(5a)

nd2(Od) |, (5b)

t

StFig. 5. Three-dimensional wave vector geometry.


Yi tan Oa)2]1/2,

(6b)

Cos i' =

For three-dimensional wave vector geometry, Eqs.(4) are replaced by

01 = +(90 - 0. + 0i'), (7a)

02 = +(90 - a + 0Od')- (7b)

Substituting Eqs. (6) and (7) into Eqs. (3), we canwrite the general tuning expressions of the anoma-lous Bragg diffraction in anisotropic media as

Verification

Numerical Calculation

We calculated the three-dimensional filtering loci ofthe TeO2 AOTF from Eqs. (8).

Assume that a monochromatic object whose wave-length is X is the input image of the system shown asFig. 1. The change of the output image, that is, theacousto-optic diffracted image, with tuning ultrasonic

+COS{0 - COS-[cos 2 pi + (cos a-i + cos yi tan Oa)2 + 1 - (cos y,/cos Oa)2

2[cos2 pi + (cos a, + cos _y, tan 0.)2]l/2

2nX()V(0 0 ) (f0 + 172(0) [ni 2(a) - nd2(ad)]}

; lrcos , COS-' C2d + (COS ad + COS Yd tan 0")2 + 1 - (cos yd/cos Oa)211tcos{0a - cos [cos2 Pd 2[cos2 Pd + (COS atd + COS Yd tan 0a)

2]1/2

X(d( | Vf0 X 2 [nt2(ai) - '],2nd(ad)V(0a) {fa 2172(0) nd(a)J

n i (a 1i)cos Pi = nd(aXd)COS Pd, (8c)

cos2 a + cos2 + cos2 y = 1. (8d)

We can transform Eqs. (8) into the expressionsabout the polar angle 0 and the azimuth angle + withthe use of the formulas tan 4 = cos y/cos P and 0 = a.

Given the incident light direction (cos ai, cos pi,cos Yi), ultrasonic incident angle 0a, and frequency fain an acousto-optic crystal, we cannot analyticallysolve for the diffracted light wavelength anddirection (cos ad, COS Pd, cos Yd) from Eqs. (8). There-fore, numerical calculation is the only method.

e0

80

26

10

I;=514.5nm o.

f= 17. 2M z

f= 9 .6rAM

f= 6 .SMEHZ

10

f=a4.7MHz

1 0 0 2 0 0

A=700 nim

f=7 9 .8MH z

f=6 2.8MHz

f=4 8.0MHz

f=2 2.9MH z

frequency fa is shown in Fig. 6. In fact, for a single fathe diffracted area of the monochromatic object is acurved strip. This strip is shifted in the polar direc-tion by tuning fa. The width of the strip is deter-mined by the angular aperture of the AOTF and thefocus of objective L2. Figure 6 shows the situationfor extraordinarily polarized incident light, and thecurved tendency of the loci for the ordinarily polar-ized incident light is identical to Fig. 6. However, ifthe object is made with complex light, the situationfor diffraction is shown in Fig. 7.

Numerically calculating the results shows that foran arbitrarily assigned spatial point on a definite,monochromatic object, the diffracted strip movesmonotropically with fa in a certain regime. If theobject is white, the result is equated to a compound ofthe diffracted strip of each monochromatic object, andthese strips do not overlie one another. Also, thesestrips shift with ultrasonic frequency fa, but theimage that contains spatial information does notmove. Strictly speaking, tiny movements exist.

806 c i 00 260-80°Fig. 6. (a) For a 514.5-nm monochromatic object, the diffractedtrack in the ultrasonic frequency f when the incident light isextraordinarily polarized and the incident angle of the ultrasoundOa is 90°. (b) For a 700-nm monochromatic object, the diffractedtrack in the ultrasonic frequency fa when the incident light isextraordinarily polarized and the incident angle of the ultrasoundO is 90°.

(a) (b)Fig. 7. Variance of the encoded image with the ultrasonic frequen-cy: (a) white object, (b) encoded images at different frequencies fa.


21

(8a)

(8b)

Experimental Verification

Different monochromatic targets were used as theinput images. Their encoded images were detectedby a 50 x 50 SPD area array and were then trans-ferred to a computer. Figure 8 shows the decodedimages that were sampled by the SPD and thenoutput by the computer for the monochromatic target.The images from left to right correspond to thediffracted images of the monochromatic target in thedifferent ultrasonic frequencies, and the horizontalcoordinate corresponds to the polar direction of theAOTF. The substantial change in the diffractedarea with tuning ultrasonic frequency is directlycorrelated with the numerical calculation. As a re-sult, the conditions of the SSE are satisfied for theAOTF.

Experimental Results of Acousto-OpticSupermultispectral Imaging

The arrangement of the acousto-optic supermultispec-tral imaging is fitted with the TeO2 AOTF as its SSE.8The specifications of the specially designed AOTFwith the acousto-optic crystal (TeO2) are

0i = 15°-35°; Oa = 900;Effective optical aperture: 9 mm x 12 mm;Ultrasonic frequency of operation: 30-120 MHz;Spectral half-bandwidth from 400-800 nm: 2.5-7

nm;Efficiency of diffraction for the extraordinarily po-

larized light in 632.8 nm: 96%.

The spatial-spectral decoding library is the key tothe system. Therefore the encoding rule of thesystem must be detected first. In practice, the decod-ing library was built by using the experimentalmethod. The supermultispectral images were de-

No. 1.I.No. 5

.

HE

A.3=-:

*_>-

's-A.=.sA

.s;

No . 9.san,.r

..X

.-

J-Fig. 8. Decoded images sampledmonochromatic target.

700nm

633nm

AK '

580nm

680nm

620nm

560nm

660nm

600nm

550nm

640nm

590nm

540nm

Fig. 9. Supermultispectral images of the simulated target illumi-nated with monochromatic light at 632.8 and 640 nm.

coded from 100 encoded images, which were sampledby the SPD area array. The spectral resolutionpower of the system is approximately 5 nm in thevisible range. Figures 9 and 10 illustrate the super-multispectral images of the differently simulatedtargets. The simulated target in Fig. 9 was a simplepattern that was illuminated with two monochro-matic light sources at 632.8 and 640 nm. The samepattern was illuminated with two monochromaticlight sources at 632.8 and 550 nm. Figure 10 showsthe results after decoding. Obviously, the decodingresults are correct.

The SSE method solves the problem of differentincident beams corresponding to different diffractedspectra. The advantage of this acousto-optic super-multispectral imaging is that the spectral resolutionis insensitive to the field of view and the effectiveoptical aperture. Previously multispectral imagingapplications of the AOTF had to limit the field andaperture of a system, which would be one quantityless than presented in this paper. Because supermul-

700nm

633nm

; r ;AAI

580nm

by the SPD area array for the

680nm

620nm

560nm

660nm

600nm

550nm

To r.

640nm

590nm

540nm

Fig. 10. Supermultispectral images of the simulated target illumi-nated with monochromatic light at 632.8 nm and 550 nm.


tispectral images contain information of high spectralresolution, which is vital for identifying targets anddiscriminating between targets and background withmetameric color, this technique can be applied inmilitary reconnaissance, remote sensing, astrophys-ics, industry, and the like.

This project was supported by the Research Foun-dation of the National Defence, Science & TechniqueCommittee of China, as well as by the ResearchFoundation of the Ministry of the Education ofChina.

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Supermultispectral imaging," Appl. Opt. 29, 1625-1630 (1990).2. J. E. Carroll, C. R. Smith, and R. Rodgers, "Spectral agility:

rationale and concept," in Infrared Systems and ComponentsIII, R. L. Caswell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1050, 74-87 (1989).

3. I. Kurtz, "Rapid scanning fluorescence spectroscopy using anAOTF," Rev. Sci. Instrum. 58, 1996-2003 (1987).

4. T. S. Chao, J. Yu, L.-J. Cheng, and J. Lambert, "AOTF imagingspectrometer for NASA applications," in Optical Information-Processing and Architectures II, B. Javidi, ed., Proc. Soc.Photo-Opt. Instrum. Eng. 1347, 655-663 (1990).

5. S. E. Harris and R. W. Wallance, "Acousto-optic tunable filter,"J. Opt. Soc. Am. 59, 744-747 (1969).

6. I. C. Chang, "Noncollinear acousto-optic filter with large angu-lar aperture," Appl. Phys. Lett. 25, 370-372 (1974).

7. R. W. Dixon, "Acoustic diffraction of light in anisotropicmedia," IEEE J. Quantum Electron. QE-3, 85-93 (1967).

8. G.-H. Gao and Z. Lin, "Fast multispectral imaging apparatus,"Chinese Patent 91105118.X (23 July 1991).


acousto-optic supermultispectral imaging

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