OPTICAL REVIEW Vol. 2, No. 3 (1995) 189-193

Real-Time Reconfigurable Interconnections for Parallel Optical Processing*

Neil MCARDLE and Mohammad R. TAGHIZADEH Department of physics, Heriot- Watt Un iversity, Edin b urgh EH14 4AS, scotland, U' K'

(Accepted March 31, 1995)

In this letter we describe the advantages of a dynamic optical interconnection system for parallel information processing applications. The system is based on a liquid crystal television which acts as a binary phase-only spatial light modulator. We describe example algorithms where reconfigurable interconnects would be useful and present results of several interconnection topologies which have been implemented.

Key words : optical computing, dynamic optical interconnections, parallel processing, Iiquid crystal spatial light modulators, phase-only modulation

1. Introduction

Optical interconnections are playing increasingly impor-

tant roles in communication systems and are expected to be employed in future information and image processing systerns. They have many advantages over electronic connections. These include the inherently parallel nature of light, the ability of optical beams to cross in free space

without crosstalk, and the high bandwidth of optical communication channels. In addition to these advantages, a degree of prograrnmability of the optical interconnec-tions can provide further benefits, mainly in the saving of

hardware but also improved performance and increased flexibility in algorithm design. An optical processing sys-tem needs to have many types of interconnection stages, iL

it consists of fixed interconnections. However, a single reconfigurable interconnection stage can replace them, providing a significant hardware saving.

We envisage a machine containing a module which can dynamically alter the interconnection topology . For exarn-

ple, this would allow the machine to select the best topol-

ogy for executing some image processing tasks, then select a nonlocal topology for executing algorithms such as fast

Fourier transforms (FFTS), then another topology for arithmetic processing. A machine with a fixed intercon-nection topology would be limited to executing only those algorithms which the topology allows, or alternatively to execute other algorithms but very inefHciently. In effect a

reconfigurable interconnection al]ows the "programming" of the hardware topology to suit the problem being solved,

instead of designing the algorithm to execute on the particular piece of hardware available, as is done at present.

Several reconfigurable interconnection systems have been demonstrated using a variety of devices including photorefractive materials, nematic and ferroelectric liquid

crystal spatial light modulators (SLMS), magneto-optic SLMs, and acousto-optic devices. See Ref. 1) and refer-ences therein for more details. In this paper we concen-trate on space-invariant optical interconnections using a nematic liquid crystal spatial light modulators (LCSLMS~

*Presented at the International Commission for Optics Topical Meeting, Kyoto, 1994.

obtained from a commercially available television projec-tor. These devices have been chosen primarily for their 10w cost, easy availability, and straightforward configura-

tion by interfacing of the drive electronics to personal computers. In addition they operate at low voltages and have low power consumption.

As one example consider a FFT algorithm. Figure l schematically shows a radix'2 Cooley-Tukey decimation in time algorithm. The algorithin shown here is for the one dimensional case of eight input signals (N=8). The number of interconnection stages is given by log2N, and in this case is three. For the purposes of this paper it is

only necessary to consider the interconnections between processing stages. We can perL0rm the required intercon-nection by a space'invariant optical method by imple-menting a Lan-out of three (i.e., up, down, and straight through), and masking the unwanted beam. Alternatively, arbitrary permutations of the channels can be performed by a space-invariant interconnection method. In this case the aperture of the interconnecting device must be split into many facets and a different phase structure displayed at each. However, since this system can handle a very low number of channels due to the relatively low resolution 0L liquid crystal (LC) panels, we have chosen to use the space-

invariant mode. In general, it is possible to obtain any desired permutation of the channels by cascading several space-invariant interconnection stages.

It is easy to see the potential savings in algorithms of this sort, where many fixed interconnection stages can be replaced by a single reconfigurable stage. The FFT is not the only algorithm which requires interconnection pat-terns of this sort and we are currently investigating the advantages of a dynarnic interconnection system for other algorithms including sorting and image processing.

2. Experimental System

The LC television panel used in the experiments is one of three panels obtained from a commercially available television projector manufactured by Seiko-Epson (VPJ 2000). Previous experiments have been performed using a similar panel manufactured by Citizenl'2) and with another model of the current panel.3) However, the current panel has a higher resolution and smaller pixel size than that

189

190 OPTICAL REVIEW Vol. 2, No. 3 (1995)

~ Fo fl """"""'--- F4 f2 --'--"' """" 2 F2

f3 -'---------------' -"----'---'---- F6 F1

f5 ---' -'- --' -" 2 -'--'-'--------- F5

~ ."• ••'''.•• .•• 2 ..""" """" 3 F3 f7 ""--'----"---" -"------'---'---- -"----'---'---- F7

Subtraction Multi plication

Fig. 1. Standard radix-2 decimation-in-time Cooley-Tukey FFT algorithm. Shown here for the case of N:=8 inputs. The three fixed interconnection stages can be replaced by a single reconfigurable

stage .

used in any previously reported experiments. The tele-vision projector has three such panels; one for each of the

red, green, and blue components of the image. The panels are twisted nematic devices and have been

designed for intensity modulation when placed between crossed polarizers. The plastic polarizers supplied with the

panels have been removed and replaced by high quality polarizers in rotation stages. The panels have physical dimensions of 26.9x20.2 mm2 and contain 480X440 pixels. The active area is 3lx31 ,clm2 with a center to center spacing of 56 ;Im and 46 /Im in the horizontal and vertical

directions, respectively. The LC Iayer has a thickness of 4.5~0.5pm and a birefringence of 0.091. The panel uses active matrix addressing and has a polycrystalline Si thin film transistor (TFT) circuit at each pixel. This addressing

scheme effectively holds the applied voltage across the pixel constant between successive frame scans, and is the preferred technique in most modern liquid crystal tele-vision displays. We have interfaced the projector to an IBM compatible computer and can display arbitrary pat-terns on the panel.

The pixel structure of the panels acts as a two-dimen-sional diffraction grating when the panel is illuminated by

coherent light. This structure causes absorption in the dead space between windows as well as losses into the higher diffraction orders. To effective clear aperture of the

panel is 37% but with Fresnel reflection losses and ab-sorption losses in the LC, we measured an absolute trans-mission of 28% directly after the panel. After spatial filtering the higher diffraction orders, the proportion of incident power left in the zero order was measured to be approximately 10%. To overcome these losses we have fixed a microlens array (MLA) to one of the panels in order

to focus all of the incident light through the pixel win-dows. The MLA is an array of 8-phase level diffractive lenses fabricated by reactive-ion etching in a I mm thick silica substrate. The focal length of the MLA is 1.1 mm (in glass) which is the thickness of the LC panel glass faces.

There is one lens for each pixel on the panel and the horizontal and vertical pitches match the pixel pitch. We have measured diffraction limited spot sizes and with the

MLA attached to the panel we have almost doubled the transmission of the panel from 28% to 51%. Even better

N. MCARDLE & M.R. TAGHIZADEH

performance is expected in future designs. The intercon-nection patterns implemented in this paper were obtained using an unmodified panel.

The panel is illuminated by a He-Ne laser with an operating wavelength of 632.8 nm as shown in the experi-mental set-up of Fig. 2. The linearly polarized light of the

laser is converted to circularly polarized light by the quarter wave plate (QWP). This ensures constant illumi-nation intensity at the panel for various angles of the polarizer P. The polarizer P and analyzer A are dichroic sheet polarizers sandwiched between glass plates. The output from the panel is spatially flltered in the Fourier plane of a lens to remove the unwanted higher diffraction orders. The zero order image is viewed by a CCD camera. The output from the CCD can be acquired by a frame grabber and analyzed on the computer which also controls the pattern to be displayed. The displayed pattern can be updated at video rates.

In our projector, as in most display applications, the panels are twisted nematic devices which are designed as intensity modulators. The LC molecules are aligned at the entrance and exit glass plates by a proprietary rubbing technique and are oriented at 90' to each other. So the LC material adopts a helical configuration. When illuminated by linearly polarized input light, the generally accepted view of their operation is that the orientation of the light

follows the twist of the molecules and exits the panel at 90'

relative to the input light. However when a voltage is applied perpendicular to the plates, the molecules tend to become aligned along the direction of the electric field and

in this configuration do not modulate the polarization of the input light. When the panel is placed between crossed polarizer and analyzer, the device modulates the intensity.

Several schernes have been proposed to obtain phase-only modulation without significant intensity modulation from twisted nematic devices. These schemes usually involve accurate setting of the bias voltage (controlled by the brightness setting) or operating the panel in a double-

pass conflguration so that the polarization rotation is cancelled out on the second pass. However due to limited adjustment of the bias voltage in our projector it is neces-

sary to adopt another technique.

HeNe P LC A

oWp

l

1

SF CCD

FRAME GRABBER

PC

MONITOR

Fig. 2. Experimental layout showing liquid crystal panel (LC) between polarizer (P) and analyzer (A). Other components include spatial filters (SF) and quarter wave plate (QWP).

OPTICAL REVIEW Vol. 2, No. 3 (1995)

The effect of LC panels on the polarization orientation described above is only true of thick LC Iayers. In general the output light is elliptically polarized.4) Analysis of the

twisted nematic panel by Jones calculus allows the detailed investigation of the polarization state of the output light.

As the voltage applied to the panel is increased, the azimuth angle of the ellipse rotates. The envelope of the ellipses is close to a straight line which means that nearly

phase-only modulation is achievable if an analyzer is aligned perpendicular to the envelope. ThereL0re by care-ful alignment of the polarizer and analyzer it is possible to

find a particular orientation where phase modulation with 10w intensity modulation occurs. In the panel used here the polarizer angle is 63' and the analyzer angle is 1" relative to the LC molecular director at the input face.

3. Design of Phase Structures and Results

In this section we describe some demonstrated intercon-nect patterns useful for various information processing algorithms and we compare the experimentally observed performance and efficiency to that predicted by theoretical calculations.

One of the simplest interconnection patterns to imple-ment is the fan out of a single bearn to two identical diffracted orders (1x2). The optimal diffractive element for

performing a fan-out to 2 is a binary-phase grating with the groove width equal to half a period and a phase delay of 7r tadians. If the grating period and focal length of the

Fourier transforming lens are chosen correctly, the spot spacing can be matched to the spacing of devices on the processing array to provide nearest neighbor or nonlocal interconnections in I dimension. This phase structure has a theoretical diffraction efficiency of 8/712 (81%) into the +1

and -1 orders. When the phase structure is written onto the LCSLM the output spots obtained are shown in Fig . 3(a). The measured diffraction e~iciency was found to be approximately 80% and the uniformity error was 6%. Approximately 20% of the power is diffracted into higher orders .

In binary-phase gratings phase depth values other than 7r rad are usually considered undesirable because signifi-cant power is left in the zero order. However if the phase depth is chosen such that the power in the +1, O, and -1 orders is equalized, then we obtain a fan-out to 3 (1x3) interconnect. As explained above, this interconnect pat-tern would be required for a space-invariant implementa-tion of the FFT and other algorithms. The required phase depth of the binary Ronchi-type grating was calculated to be 0.647z. The output spots generated by such a phase structure are shown in Fig. 3(b).

Perhaps the most commonly used interconnect pattern is the neighborhood interconnection which is used in a variety of low level image processing tasks such as noise removal. On a square array, the connections to the eight neighboring elements is commonly performed by either (i) fanning out to nearest neighbors in up, down, Ieft, and right directions, or (ii) fanning out to next-nearest-neigh-

bors in the four diagonal directions. The fan-out to next-

N. MCARDLE & M.R. TAGHIZADEH l 91

nearest-neighbors is achieved by simply crossing the solu-tion for the fan'out to 2 described previously, producing a

binary checkerboard phase pattern. This structure has a theoretical diffraction ef~ciency of (8/7z:2)2 and the spots

(a)

(b)

(C)

Fig. 3. Output spots for (a) Ix2 interconnection, (b) Ix3 intercon-nection required for FFT algorithm, (c) 1><:4 next-nearest neighbor

interconnection.

Table 1. Summary of theoretical and experimental performance of simple phase structures.

Interconnect

pattern

Theoretical diff raction

efliciency (%)

Measured diff raction

efficiency (%)

Measured unif ormity

error (%)

IX2 lx3 1><4 nearest

neighbor lx4 next-nearest

neighbor

87 86 65.7

65.7

~~ 80

~~ 81

~~ 60

~~60

6 7.4

9.5

7.2

192 OPTICAL REVIEW V•1. 2, No. 3 (1995)

(a)

(b )

Fig. 4. Binary phase structure for non-separable trapezoidal stripe" geometry design to generate a 4x4 spot array (a), and the spot array at the Fourier plane generated by this structure (b).

produced by this structure are shown in Fig. 3(c). By rotating the phase structure by 45' the nearest neighbor interconnection is performed. The theoretical and experi-mental diffraction efnciencies and uniformity errors of all

these structures are summarized in Table 1. Good agree-ment between theoretical and experimental results is achieved.

Damman gratings are commonly used to generate arrays of spots of equal intensity. However, so called nonseperable type phase structures exhibit higher ef~-ciency and better uniformity and we have generated arrays of spots by displaying trapezoidal stripe-geometry5) phase

N. MCARDLE & M.R. TAGHIZADEH

Table 2. Summary of theoretical and experimental performance of trapezoidal stripe-geometry phase structures for generating arrays of

equally intense spots.

Array size Measured Theoretical Measured

diffraction uniformity diff raction

efficiency (%) efflciency (%) error (%)

4X4 8X8

77 72

~~ 69

~~ 72

l0.7

32.9

structures on the LC panel. Figure 4(a) shows the phase pattern to generate a 4x4 array, and Fig. 4(b) shows the array of spots generated by this pattern. The diffraction efficiencies and uniformity errors for this and other arrays

is summarized in Table 2. Some work has been performed to study the limitation

of the interconnection obtainable from pixellated devices of the kind used here.2,6) In this paper we have demonstrat-

ed a fan-out of 16 with reasonable uniformity. However, larger fan-outs are achievable.

Compared to fixed computer generated hologram fan-out components, the relatively large uniformity errors are due to the fact that we are displaying pixellated versions of

the original phase structure designs. The uniformity errors

depend on how many pixels we choose to sample the original design. In the case of the 8x8 array, only two panel pixels were used in each stripe of the original phase

pattern (which contains 32 stripes in one period). Im-proved performance can be achieved by using more pixels to represent the phase structure. Also, we are working on a real-time optimization system which will adjust the transition points on the trapezoids depending on some merit function which is calculated from the actual optical

output. This should improve the performance taking into account the characteristics of the physical set-up. The relatively high zero order observed in some of the arrays was due to crosstalk between neighboring pixels. This has

the effect 0L producing a non-ideal sharp transition between the regions of zero phase and 7c phase modula-tion. Good agreement is achieved between theoretical and experimental diffraction efliciencies.

4. Conclusions

Since the devices are based on nematic LCs, the reconfiguration time is relatively slow. However, we envis-

age a machine which could contain such a reconfigurable stage to increase the flexibility in the number of algo-rithms which can be executed. In these cases it may not be necessary to change the interconnection topology in a time of the same order as the clock period. Several cycles

(from hundreds to thousands) may be executed with a given topology beL0re reconfiguration is necessary. How-ever, we accept that for a viable system the reconfiguration

time must be improved beyond the 20-30 ms currently achievable. To this end we are also investigating the use of Lerroelectric LC devices which are 2-3 orders of magni-tude faster.

We have described the advantages of a reconfigurable optical interconnection system in the context of parallel

OPTICAL REVIEW Vol. 2, No. 3 (1995)

optical computing. Using a commercially available LC television projection panel, in a phase-only modulation mode, a number of space-invariant fan-out arrays and interconnection topologies have been demonstrated. Mea' sured diffraction efiiciency and uniformity of the arrays are

close to theoretical predictions.

Acknowledgments

The authors thank Paul Blair and Nigel Watson for providing the phase pattern solutions for some of the interconnect topologies demonstrated here. This work was supported by the Science and Engineering Research Council (SERC) under the Scottish Collabo-rative Initiative in Optoelectronic Sciences (SCIOS) . The authors

would also Council.

Ref erences

N. MCARDLE & M.R. TAGHIZADEH

like to acknowledge generous support by the

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British

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4)