Real-time optical correlation of 3-D scenes

Aaron D. Gara

A real-time correlation operation is performed on a 3-D object with a liquid crystal incoherent-to-coherentimage transducer. The character of the autocorrelation peak as a function of scene translation and rotationis described and an example presented of cross correlation with a second similar object.

1. Introduction

One of the most important recent advances in thefield of optical information processing has been thedevelopment of real time incoherent-to-coherent imagetransducers 1-5 (e.g., Titus tube, PROM, EALM, liquidcrystal light-valve, or the Ruticon). The availabilityof these devices is especially meaningful for practicalapplications of optical processing. Examples have beenreported in the literature on real-time processing of filmand video picture input data.6 '7 In this paper the useof a liquid crystal image transducer is described as thereal-time input to an optical correlator where the sceneis a known 3-D object. The results clearly demonstratethe potential of the system for automatically deter-mining the position and orientation of an object.

I. Correlation System

The optical correlation is performed with the ar-rangement of Fig. 1 which is essentially the matchedfilter configuration first described by Vander Lugt. 8 Acoherent reference beam from the mirror is used torecord a hologram of the Fourier transform of the objectas it is imaged onto the image transducer. This holo-gram is subsequently used as the matched filter for thatobject with the autocorrelation and cross-correlationsignals displayed with a TV system located in the outputplane.

A. Matched Filter Recording

The object is illuminated with a conventional tung-sten halogen projector bulb. Lens L1 forms an imageon a photoconducting layer at the input of the imagetransducer. The linearly polarized collimated read lightfrom a He-Ne laser is sent through a polarizing beamsplitter which reflects the vertical component (per-pendicular to the plane of the paper) and transmits the

The author is with General Motors Corporation, Research Labo-ratories, GM Technical Center, Warren, Michigan 48090.

Received 19 May 1976.

horizontal component. The vertical component entersthe output side of the image transducer and after re-flection emerges with a horizontal component whoseamplitude depends on the incoherent image light in-tensity. This horizontal component out of the imagetransducer passes through the polarizing beam splitterto the Fourier transform lens (L2). The coherent imagein the Fourier transform plane and the uniform inten-sity, collimated reference beam (both horizontally po-larized) interfere to form the matched filter. The ref-erence/object beam intensity ratio is controlled by thepolarization angle of the linearly polarized beam en-tering the beam splitter. The filters were recorded onAgfa 10E75 plates (1.3 mm thick). The plates are heldin a liquid gate filled with 0-type xylene and processedout of the gate. After processing the filters can beplaced back into the holder in the gate with little or noadjustments necessary. Since the exposure times wereshort ( 5o sec with a Y4-mw, 16-mm diam beam incidenton the beam splitter), the object need not be on a typicalvibration free holographic mounting.

B. Image Transducer

The image transducer used is the liquid crystal lightvalve developed by the Hughes Research Laboratories,Malibu, Calif. The detailed characteristics of this de-vice have been well documented in the literature.9Therefore, only a summary of its operation will be de-scribed. The device, as shown in cross section in Fig.2, is a number of thin film layers sandwiched betweentwo optical glass substrates. An ac voltage (typically3.5-5 V at 1-10 kHz) is primarily divided between thecadmium sulfide photoconducting and the liquid crystallayer.

The liquid crystal is a nematic type with positive di-electric anisotropy and homogeneously aligned with a450 twist. In the off state (no writing light) the readlight, which is linearly polarized, will emerge from theliquid crystal with its polarization state unchanged. Asthe intensity of the writing light increases, the voltageacross the liquid crystal increases causing the molecularorientation to both untwist and tilt toward the

January 1977 / Vol. 16, No. 1 / APPLIED OPTICS 149

OutputPlane

X__--

Coherent Readout Beam

IFourier Transform I Polarizing Beamsplitter

Plane i / V

- - -X/_ _' -0 - - - - S r - - -

'3 '2 : I ~~~~~~~~mageTransducer

II

/i1rror

riting Light Object

LI /

I ncoherentSource

Fig. 1. Diagram of the optical system for both recording the matchedfilter and obtaining the correlation output. The matched filter wasrecorded on photographic emulsion using the image on the image

transducer as the object for the filter.

PHOTOACTIVATED AC LIQUID CRYSTAL LIGHT VALVE

Fig. 2. The image transducer in cross section (not to scale).

Front View

Side View

Fig. 3. Front and side view of the object used for the correlationstudy.

homeotropic (perpendicular) alignment. The read lightwill exit the liquid crystal with a polarization componentperpendicular to its original polarization direction, theamplitude of which is proportional to the intensity ofthe writing light.

The performance characteristics of the Hughes lightvalve has been reported9 to be >100-1/mm resolution;>100-1 contrast ratio; 10-msec turn-on time and 15-msec turn-off time; and 0.3-ergs/cm2 input light sensi-tivity at threshold. The particular device used hereperforms near these specifications except for longerturn-on and turn-off times.

Ill. Results

The object (an electromechanical relay) used formaking the filter is shown in Fig. 3. It has bright anddull metal surfaces (an especially strong highlight isobtained from the round metal can) in addition to anarea of plastic material. The image on the transduceris a 7/1 demagnification of the object. The unfilteredimage recovered from the processor is shown in Fig. 4(a).Figure 4(b) is an overexposed picture of the intensitydistribution in the Fourier transform plane for thisobject. The beam ratio was set to be approximately 1to 1 at the spatial frequency distribution indicated bythe arrow (which corresponds to approximately 3 cy-cles/mm).

A. Autocorrelation

1. Sensitivity to TranslationThe autocorrelation output of the filter with the

original object imaged onto the panel is shown in Fig.5. The object is in the same position and orientationas when the filter was recorded. This output is sensedby a vidicon camera and displayed. A scan of the signalintensity along a vertical line which passes through thecenter of the autocorrelation peak is also displayed onthe monitor. The two vertical lines on either side of thesignal scan are reference lines for video signal calibra-tion. The scale in the figure corresponds to the objectspace scale. The width of the autocorrelation peak atone-half amplitude (after calibration) is 1.5 mm. (Thelinear dimensions of the object are approximately 50 X50 mm.)

The intensity profile of the autocorrelation peak wasrecorded for different object positions in the verticaldirection (normal to the axis of the correlator). Thesedata are shown in Fig. 6(a). The position of the imageon the image transducer at the 0-mm, 40-mm, and65-mm translation positions is given in Fig. 6(b). At 65mm, the image of the object on the transducer is almostcompletely out of the area illuminated by the coherentreadout beam.

A translation in any other direction perpendicular tothe optic axis produces similar results. However, it isclear from the Fourier transform intensity distributionthat the three metal legs produce a large contributionto the high frequency content of the transform, and astrong correlation will be obtained from this region ofthe object.

150 APPLIED OPTICS / Vol. 16, No. 1 / January 1977

Fig. 4. (a) Image of the object as seen at the outputof the optical processor (no filter in the Fourierplane). The circle is the diameter of the readoutbeam on the image transducer. (b) The intensitydistribution in the Fourier transform plane. Thematched filter was recorded with a uniform intensityreference beam approximately equal to the intensity

of the region indicated by the arrow.

(a) (b)

Fig. 5. The autocorrelation peak displayed on a TV monitor alongwith the signal from a vertical scan through the center of the corre-

lation peak.

The data show that, when properly oriented in angle,the lateral position of this object can be found. Thepositioning accuracy will depend on the sophisticationof the data reduction system. With visual examinationin a traveling microscope, the peak could easily be lo-cated to an accuracy of ±0.4 mm in object space coor-dinates. This corresponds to 1 part in 125 for thisparticular object.

2. Angular Orientation SensitivityThe strength of the autocorrelation as a function of

angular rotation of the object in a matched filter oper-ation will depend on the symmetry of the object. Thestructure of the object studied here has a partial sym-metry when the object is rotated by 900 and 1800 aboutthe optic axis. In the 900 orientation the correlation

peak is approximately 5% of the 0° value, and at 180°the peak is approximately 25% of the 0 position.Figure 7 shows the rate at which the correlation signalapproaches the maximum value near 00.10

B. Cross Correlation

In a practical application, the matched filter tech-nique for finding the position of an object must be ableto give a strong correlation for all objects of the sameclass and reject all other scene structures. To illustratethis, Fig. 8(b) is a second object of the same class.There are some differences in appearance between thisobject and the original object for which the matchedfilter was recorded. The bright metal can has a roughersurface and does not show the vertical line structure.Also, the three metal prongs near the bottom have darkstain areas. The cross-correlation peak from thematched filter using this object as the input is shown inFig. 8(a). (All other system parameters are the sameas those used for the autocorrelation results.)

Other objects, not of the same class, but havingcomparable over-all dimensions, were placed into theinput scene and resulted in no observed correlation withthe detector sensitivity level used above.

IV. Conclusions

The ability to provide automatically the angularorientation and position of a complex 3-D object in realtime is an important application for optical patternrecognition systems. The results of this study dem-onstrate that a coherent optical processor using amatched filter and a real-time incoherent-to-coherentimage transducer is a promising approach to this ap-plication.

The author is grateful to Alex Jacobson of HughesResearch Laboratories for his assistance in discussionsrelated to the operation of the liquid crystal light valve.R. A. Farrar and R. W. Lewis provided helpful sugges-tions and encouragement for this study.

January 1977 / Vol. 16, No. 1 / APPLIED OPTICS 151

Fig. 6. (a) The character of the autocorrelationpeak as a function of translational position of theobject. (b) The position of the image on the image

transducer for the object translation indicated.

Original Position-

15mm-25mm -40mm -50mm -60mm-65mm-

0

40mm

65mm

(a)

0 10

(b)

20 30

Fig. 7. The autocorrelation peak as a function of rotation of theobject about an axis parallel to the optic axis.

Fig. 8. The cross-correlation peak(a) for a second object (b) similarto the one used to record the

matched filter (c).

(a) (b) (C)

152 APPLIED OPTICS / Vol. 16, No. 1 / January 1977

References

1. J. Donjon et al., IEEE Trans. Electron Devices ED-20, 1037(1973).

2. J. Feinleib and D. S. Oliver, Appl. Opt. 11, 2752 (1972).3. W. J. Poppelbaum, M. Faiman, D. Casasent, and D. Sand, Proc.

IEEE 56, 1744 (1968).4. T. D. Beard, W. P. Bleha, and S. Y. Wong, Appl. Phys. Lett. 22,

90 (1973).5. N. K. Sheridon, IEEE Trans. Electron Devices ED-19, 1003

(1972).

6. P. Nisenson and R. Sprague, Appl. Opt. 14, 2602 (1975).7. D. Casasent, in Proc. 1975 IEEE International Optical Com-

puting Conference, Washington (1975). IEEE Catalog No.75CH0941-5C.

8. A. B. Vander Lugt, IEEE Trans. Inform. Theory IT-10, 2(1964).

9. A. Jacobson et al., Opt. Eng. 43, 217 (1975).10. The orientation sensitivity will of course depend on other system

parameters (see, e.g., A. B. Vander Lugt, Optical and Elec-trooptical Information Processing (MIT Press, Cambridge,Mass., 1965). A discussion of these effects for different objectstructures will be included in a future paper.

INDUSTRY HIRES MORE Ph.D SCIENTISTSAND ENGINEERS IN 1973-75 PERIOD

The number of industrially employed scientists andengineers with Ph.D. degrees increased from 50,000 toabout 66,000 between 1973 and 1975, according to arecent National Science Foundation report. As a result,the report said, one-quarter of all employed doctoralscientists and engineers were affiliated with businessand industry in 1975, compared with 22% in 1973.

Changes in the pattern of employment within othersectors such as education, hospitals, government, andnonprofit organizations were less significant. Educa-tional institutions continued to be the largest employersof Ph.D. graduates. In 1975 about 58% of the employeddoctoral scientists and engineers were in educationalinstitutions.

Data reflecting the 1975 status of the industrial seg-ment of the nation's scientific and engineering man-power resources are presented in the NSF's most recentScience Resources Studies Highlights: LargestIncrease in Employment of Doctoral Scientists andEngineers is in Industrial Sector: 1973-75. TheNSF Highlights identifies other changes that have oc-curred between 1973 and 1975:

The population of doctoral scientists and engineersgrew from 245,000 in 1973 to 278,000 in 1975, a 13% in-crease. During this period, the number of womenholding the Ph.D. in science and engineering increasedat a faster rate (23%) than men (12%).

The unemployment rate for doctoral scientists andengineers, which was 1.2% in 1973, was just under 1% in1975.

The proportion of employed doctoral scientists andengineers receiving Federal support in their work de-creased from 46% in 1973 to 43% in 1975. This decreaseis consistent with the pattern of Federal R&D fund-ing.

Copies of the Science Resources Studies High-lights (NSF 76-326) are available upon request fromNSF's Division of Science Resources Studies, 1800 GStreet, N.W., Washington, D.C. 20550.

January 1977 / Vol. 16, No. 1 / APPLIED OPTICS 153