Optics Communications 87 (1992) 99 -104 North-Holland
Optical morphological image processing with acoustooptic devices Ravindra A. Athale Electrical and Computer Engineering Department. George Mason University, Fairfax, I~4 22030, USA
Joseph N. Mait and Dennis W. Prather US Army Har(v Diamond Laboratories, 2800 Powder Mill Road, Adelphi, MD 20783, USA
Received 7 March 1991 : revised manuscript received 12 September 1991
An optical morphological image processor is described and demonstrated in which structuring elements are generated using an acoustooptic device in the Fourier plane of a coherent optical correlator. The size and shape of the structuring element can be modified easily and rapidly by changing the drive signal to the acoustooptic device. Space-bandwidth limitations on the system due to the use of an acoustooptic device are discussed and results of erosion and dilation experiments are presented.
F o r performing shape analysis, morphological image processing represents a viable alternative to Fourier-based linear image processing [l ]. Morphological operations are set operations defined between an input object and a smaller object referred to as a structuring element; the two most f u n d a m e n tal operations are those o f erosion and dilation. The erosion o f a binary object by a binary structuring element reduces the contours of the object, whereas dilation increases them. Although defined as set operations, erosions and dilations can be i m p l e m e n t e d as a convolution between object and structuring element followed by a simple b i n a r y threshold: a low ( n e a r zero) threshold for dilation and for erosion, a high threshold a p p r o x i m a t e l y equal to the area o f the structuring element. The complex operations necessary for shape extraction and analysis, such as openings, closings, and patterns spectra generation, can be synthesized using successive c o m b i n a t i o n s o f erosions and dilations. Several optical systems using this a p p r o a c h have recently been p r o p o s e d for i m p l e m e n t i n g erosions and dilations [ 2 - 6 ] . The systems differ only in the m a n n e r in which the structuring element is generated. Realization o f a circularly s y m m e t r i c structuring element is achieved in refs.  and  by utilizing the point spread function o f a defocussed imaging system. The structuring element discussed
in refs.  is generated using a complex, holographically recorded F o u r i e r plane filter and in ref.  a shadow casting system is d e m o n s t r a t e d in which the structuring element is i m p l e m e n t e d by a two-dimensional array of individually m o d u l a t e d light sources. A similar array o f light sources is described in ref.  as part o f a multi-channel correlator for implementing morphological transforms. Each o f these systems, however, has limitations. A r b i t r a r y structuring elements can not be realized nor changed dynamically using a system point spread function. The p r o g r a m m a b i l i t y o f the approach discussed in ref.  is limited due to a lack of suitable real-time holographic recording materials. The system can be made p r o g r a m m a b l e through the use o f a magneto-optic spatial light m o d u l a t o r ( M O S L M ) in the F o u r i e r plane. Such m o d u l a t o r s have exhibited update rates from I000 to 5000 frames per second, but allowed only for the display o f binary and ternary distributions. The shadow casting system o f ref.  is based on geometrical optics and hence is limited to small image sizes and structuring elements. Although the optical processor described in ref.  is flexible and easily p r o g r a m m a b l e , it is also limited to small sized structuring elements because the space-bandwidth of the optical system must be equal to the product o f the object and structuring element space-bandwidths.
0030-4018/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
To overcome the limitations of programmability and space-bandwidth, the system represented in fig, 1 is proposed. The system relies upon an acoustooptic (AO) Bragg cell in thc Fourier plane of a coherent optical correlator to generate the desired strucluring clemcnl. The Bragg cell essentially functions as a spalial lighl modulator (SLM), which provides lhe desired programmability. However, the Bragg cell does not suffer flom the limited space-bandwidth and limited amplitude and phase modulation of other current SLM technologies, such as the binary MOSLM. Analysis of the Bragg cell implementation of a one-dimensional structuring clement follows. The dcsired structuring element is realized by driving the AO device with a modulaled high frequency carrier: .(t)=a(t)
The grating generated by thc temporal frequency u v, functions as a holographic spatial carrier. Thus, if F ( u ) is the Fourier transform of the desired structuring element.l(x), given the linear relationship belween spatial frequency and time m a Bragg cell, then a(t)=
j l"(t)l .
0(1) =arglF(1)', .
To insure proper overlap in the image plane when the input object is displayed on a pixelated SLM, it is necessary for the structuring element to be discrete:
a,,exp(i#,,) 5(x-nM.vo) ,
:1 ~ ' . j
where ,% is the ccnter-lo-center pixel spacing of the SLM and .,~1 is the magnification of the optical system. The magnitudes a,, and phases 0,, represent the desired structuring clement. The corresponding spatial frequency function is therefore given by \2
y~ a,, cxp ( iO,, ) exp ( - i27rnMxo u ) . 11 = \ ' i
(4) and the temporal frequency function by .\2
where v,, = :I1.\-,, ! / ) J ~ .
V is the acoustic velocity of the AO cell, 2 is the wavelength of light, and ,1~ is the focal length of the second lens in fig. 1. A simple change in the subcarrier frequency uh affects the scale of the structuring elements without affecting its form, which is a property useful in calculating pattern spectra. If the magnitudes a,, are specified, using diffraclive optical element ( D O E ) design techniques, the phases 0,, can be determined such that high diffraction efficiency is obtained. In other coherent optical correlators the phase of the point spread function is
BraggCell I~,eam ~t-xpandcr
fl -'~"' @
tie Nel.aser InputImage
~F Amplilicr I
Fig. I. Morphologicalprocessorusingan acoustooptiecellin the Fourierplaneto generatethe desiredstrucluringelement. 100
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critical and hence cannot be set to an arbitrary value. in the present case, however, because there exists a Doppler frequency shift between the replicated images, it is necessary to sum incoherently the images in the output. The incoherent superposition thus allows us the freedom to set the phase values arbitrarily, which we have done so as to achieve high diffraction efficiency. The incoherent superposition also removes the time varying linear phase shift that is introduced by the translating Fourier grating structure. It is known that DOEs having unity magnitude are capable of generating responses with high diffraction efficiency and similar results can be obtained by imposing a phase-only constraint, i.e., [ F ( t ) [ = 1, on designs for this architecture. The techniques used in this work to calculate the phases 0,, were developed for the generation of high diffraction efficiency spot arrays using Fourier phase-only gratings [ 7,8 ]. One algorithm uses the fact that deviations from the phase-only condition in the Fourier plane correspond to intermodulation terms in the power spectrum of the structuring element [ 7 ]. Through the adjustment of the phases 0,, it is possible to reduce the power in the intermodulation terms and thereby realize a phase-only grating that realizes the desired structuring element with high diffraction efficiency. The phases corresponding to the upper bound on diffraction efficiency for phase-only spot array generators  have also been used. A discrete 9-spot structuring element generated by a TeO_~ AO cell ( I S O M E T model OPT-1 ) is shown in fig. 2a. (The image has been contrast reversed to enhance viewing. ) The AO grating frequency uAo is 45 MHz and the subcarrier frequency Vh is 1 MHz. The line scan presented in fig. 2b indicates the uniformity of the spot array. Structuring elements having from 2 to 11 spots have also been generated with similar uniformity. Although Bragg cell generation of a discrete array of spots has already been demonstrated , it has not previously been applied to the implementation of morphological operations as indicated by fig. 3. Fig. 3a is the image of a binary object produced at the first diffracted order by an unmodulated 45 M H z carrier. Figs. 3b-3e are the results of eroding and dilating the object by 2- and 3-spot structuring elements. The thresholding of the output image was
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performed by an electronic post processor. It should be mentioned that the object was input to the system using a phototransparency and not a SLM. The object is, however, similar in structure to that generated by a SLM: it is 7.5 mm square and its highest frequency is approximately I line p a i r / m m . Incorporation of a SLM into the system is planned and will allow consecutive operations to be implemented, as is necessary for openings and closings. The results presented here indicate the ability of the system to perform the fundamental operations of erosion and dilation. For both 2- and 3-spot structuring elements, the spacing between spots is equal to period of the highest frequency which, for the system parameters given, corresponds to vh= 1.016 MHz: x 0 = 0 . 9 3 mm; f~= 1000 m m and ~ - - 3 0 0 ram, which yields M = I/3; 2 = 6 3 2 . 8 nm; and V = 6 1 7 m/s. At this spacing, the 2-spot structuring element produces perfectly overlayed images in the fourth row and perfectly interlaced images in the third. The signal power used to drive the AO cell was measured to be 1.7 mW. The property of the erosion operation to eliminate features narrower than the structuring element can be seen clearly in figs. 3b and 3d. In fig. 3b note that the third row of frequencies is removed entirely, whereas in fig. 3d the second and third rows are removed. The opposite effect i~evident in figs. 3b and 3d where these rows have been completely filled in. Although the results are presented only for a onedimensional structuring element, two-dimensional structuring elements can be implemented in a time sequential fashion using two AO devices oriented orthogonally to each other in the Fourier plane. Such devices are commercially available in a single crystal configuration with transducers mounted on the orthogonal faces of the crystal . If both transducers are driven simultaneously, a point spread function is generated that is given by the outer product o f the individually generated point spread functions. An arbitrary structuring element can be synthesized as the superposition of multiple outer products. Further, since the frame time of the AO device is on the order of microseconds, morphological operations can be implemented at tens of kilohertz frame rates, which will ultimately be limited by the frame rate of the detector array. As mentioned above, a Bragg cell offers more 101
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S p a t i a l Units
Fig. 2. (a) Nine spot structuring element generated by the AO cell (contrast reversed). (b) Line scan of the structuring element. s p a c e - b a n d w i d t h ( S B W ) than other available SLM technologies. The operation of the Bragg cell as either a thick of thin diffractive element does, however, affect the size and SBW o f the input object and the structuring element that can be realized. Regardless o f the SBW o f an object, the effect on the object by a thin grating in the F o u r i e r plane, e.g., film or a conventional SLM, is to induce a shift in the object's location in the output plane. If it is necessary to use a spatial carrier to separate undiffracted light from higher diffractive orders, to insure that the entire input object is a p p r o p r i a t e l y shifted off-axis, the SBW o f the Fourier plane filter must be p r o p o r t i o n a l to the sum of the SBWs of the input object and the desired filter response: SBWg~,i,,~ ~c SBWobjcct + SBW~,p . . . . 102
On the other hand, due to Bragg matching conditions, a thick grating placed in the Fourier plane is capable o f inducing a shift only for plane waves oriented perpendicular to the grating vector. To produce the c o n t i n u u m o f shifts that are necessary te shift an entire input object requires a large number of thick gratings in the Fourier plane. As a consequence, the SBW o f a thick Fourier plane filter musl be p r o p o r t i o n a l to the product o f the SBWs o f the input object and desired filter response: SBWgrating 3( SBEobje,,t "SBW~,.sp. . . . -
Acoustooptic operation lies between these two extremes. Large t i m e - b a n d w i d t h product devices can be p r o d u c e d by utilizing anisotropic diffraction to
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Fig. 3. (a) Image of a periodic object in the first diffracted order in output plane of the processor. (b) Erosion and (c) dilation of the object by a two spot structuring element. (d) and (e) are as in (b) and (c) except a three spot structuring element is used. increase the range o f input angles and carrier frequencies for which the Bragg condition is satisfied. T i m e - b a n d w i d t h products in excess o f 4000 are available. A t r a d e o f f between the SBW o f the structuring element and the SBW o f the input image for a given device can be achieved by adjusting the focal length o f the F o u r i e r transform lens in the processor. When placed in the F o u r i e r plane o f an optical system+ the AO device must respond to the spectrum of plane waves p r o d u c e d by the input object. However, current designs for AO device transducers are optimized for operation as a scanner and hence are designed to respond to only single plane wave optical
inputs. Thus, i m p r o v e d performance may be obtained by modifying transducer design. Morphological operations on images can be performed by combining optical correlators with simple electronic nonlinear operations on the output image. The simple binary nature o f the structuring elements suggests that an acoustooptic device driven by an arbitrary waveform generator can generate the desired F o u r i e r plane filters easily and rapidly. Results of simple erosion and dilation experiments have been presented, as well as an analysis o f the space-bandwidth limitations o f the AO morphological processor based on Bragg matching limitations. 103
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Support of Professor Athale by Harry Diamond Laboratories and the Army Research Office under the Summer Faculty Research in Engineering Program is gratefully acknowledged. Several useful discussions with Dr. John Pellegrino are also gratefully acknowledged.
References [ 1 ] P. Maragos, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA (1985). [ 2 ] K.S. O'Neil and W.T. Rhodes, in: Hybrid image processing, eds. D.P. Casasenl and A. Tescher, Proc. SPIE 638 (1986) 41.
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 J.M. Hereford and W.T. Rhodes, Opt. Eng. 27 (1988) 274.  E.C. Botha and D. Casasent, Opt. Eng. 28 (1989) 501. [ 5 ] Y. Li, A. Kostrzewski, D.H. Kim and G. Eichmann, Optics LeH. 14 (1989) 981. [61G. Lohman and K.-H. Brenner, in: Optics in complex syslems, eds. F. Lanzl, H.-J. Prcuss and G. Weigelt, Proc. SPIE 1319 (1990) 161.  H.P. Herzig, D. Prongu¢ and R. D~indliker, Japan. J. Appl. Phys. 29 (1990) L1307.  U. Krackhardt, J.N. Marl and N. Streibl, Upper bound on the diffraction efficiency of phase-only fan-out elements, Appl. Optics, accepted for publication.  E. Tervonen, J. Turunen and A. Friberg, in: Optics in complex systems, eds. F. Lamsl, H.-J. Preuss and G. Weigelt. Proc. SPIE 1319 (1990) 288. [ 10] Available from Brimrose Corp., Baltimore MD.