Polarization-Encoded Optical Shadow-Casting Logic Units: Design

Polarization-encoded optical shadow-casting logic units: design Mohammad A. Karim, Abdul Ahad S. Awwal, and Abdallah K. Cherri

A general design algorithm is presented for the multioutput polarization-encoded optical shadow-casting scheme. A set of POSC equations is obtained from the truth table of the desired logic unit and is solved in terms of four possible pixel characteristics (transparent, opaque, vertically polarized, and horizontally polarized) and four possible source characteristics (off, unpolarized, vertically polarized, and horizontally polarized). To demonstrate its feasibility, the algorithm is used to determine the input pixel characteristics of a full adder and a full subtracter.

I.

Introduction

Recent optical computing research has concentrated primary effort toward realizing logic components.' Basic optical logic elements or optical gates are expected to perform high-speed combinational logic operations in parallel. Memory elements, on the other hand, are usually nonlinear devices for which speed is basically constrained by material relaxation times, cavityround-trip times, etc.2 3 Such nonlinear devices are normally expected to function as bistable devices. Use of such nonlinear devices in combinational logic operations, therefore, slows down the whole process. For the fastest computation, combinational logic must produce an output as soon as the inputs are made available. Thus linear elements are a better choice for building combinational logic circuitry, digital or optical. The lensless shadow-casting method4 -7 has a great advantage in speed of operation. Since all of the operations are linear, the computation speed is limited only by the speed with which light travels from the input plane to the output plane. With a fixed coded input, this system operates with the highest possible speed. The lensless shadow-casting system consists of spatially encoded 2-D binary patterns as the inputs. These coded inputs are placed in close contact at the input plane, and the overlapped coded pattern is illu-

The authors are with University of Dayton, Dayton, Ohio 454690001. Received 17 November 1986. 0003-6935/87/142720-06$02.00/0. © 1987 Optical Society of America. 2720

APPLIEDOPTICS / Vol. 26, No. 14 / 15July 1987

minated by a set of LEDs. A decoding mask is thereafter used to spatially filter and detect the logical output at the output plane. By changing the input LED pattern a variety of logical operations may be realized. In another method,8 instead of changing the input LED pattern, the output mask is switched to obtain different binary logic operations. In the optical shadow-casting method the input pixel elements are binary, e.g., either transparent or opaque. The remaining design variables include on and off states of the LED sources. This limits the number of output operations to only sixteen. Also the number of inputs that can be handled at the same time is limited by the fact that only two output light levels, transparent and opaque, can be distinguished separately. This limitation disallows the synthesis of a binary full adder. However, the use of polarization encoding9"10 increases the degrees of freedom for the choice of coding, LED arrangement, and output decoding mask. In this paper a systematic algorithm is presented for designing complex arithmetic logic units using such a polarization-encoded optical shadow-casting (POSC) scheme. II.

Algorithm Development

In the POSC method logical inputs and LED sources are both coded by the direction of polarization. Consider only two input variables A and B. For the sake of illustration, we choose a square-shaped arrangement of four LED sources, where one of the four LEDs is off, two adjacent LEDs are unpolarized and on, and the fourth LED is vertically polarized and on. Each square pixel of inputs A and B are segmented into four equal quadrants, and each of the four pixel quadrants are represented by both a sense of polarization (vertical and horizontal) and also a transparent/opaque cod-

Table1. A POSCexample. A

LED

A=0

w

-.

T

F T T

T

ITPIT

optical shadow-casting (POSC) sys-

Code

(cnramic pxelhown

V

O H HV T

'X111

H

LW II_

VV FY

A polarization-encoded

Output

AAB

2

EDs

Fig. 1.

B

V

6

_1

E0XH

| E[5 X IT

I

IHI

X 12

HoH] ,

tem.

ing characteristics. For performing logical operations coded inputs A and B overlap with each other as shown

in Fig. 1, and this corresponds to spatial domain filtering.

Since no lens or spatial frequency converter is

used, this cannot be termed as a frequency-domain filtering process. The overlapped code generates different output functions as determined by the LED arrangement as shown in Table I. The four possible input codes are represented by T, F, V, and H, respectively, for transparent, opaque, vertically polarized, and horizontally polarized codes. The LED arrangement causes each overlapped pixel to produce an output pixel pattern consisting of nine equal-sized micropixels.

Comparing the overlapped code and the LED ar-

particular arithmetic logic unit, i.e., a dedicated hardware circuit for performing only one type of operation

like that of an adder or subtracter. To aid the formulation of general POSC design algorithm, the basic overlap (indicated by A) operation is introduced via the followingset of rules: (a) The overlap of transparent code and an input code leaves the input code unchanged, while the overlap of opaque code destroys all input code resulting in an opaque output. (b) The overlap of orthogonal codes" results in opaque output. F is found to be orthogonal to all variables including (c) The overlap of any one of the codes with

itself.

itself results in the same code. Consequently,

rangement one would find that an overlapped pixel

quadrant code appears as the central output micropixel at the mask opening only if there exists an unpolarized LED in the same corner. For example, when A = 1 and B = 0, the vertically polarized pixel quadrant in the upper right corner is projected at the center of the decoding mask by the unpolarized LED at the upper right corner of the light source arrangement. The decoding mask is placed at the output to detect the output. It is possible to use four different masks, horizontally polarized (H), vertically polarized (V), mixed polarized (VH or HV), and True (T) mask, giving up to four different outputs. It may be noted that the output using mixed mask is detected using a detector whosethreshold exceeds 50%of the maximum detectable light intensity at the central output micropixel. The four outputs are seen to correspond to four

different logical operations: fH=

A B

fu = B.

fVH=fHv=A+B,

fT= A+B.

(la) (lb)

(1c)

(id)

Now we shall move on to see how one may generate

x A T=x

(2a)

x AF=F

(2b)

x A x =x

(2c)

H A V= V AH=F

(2d)

represents a total of twelve overlap results where x =

(T, F, H, V). It is to be noted that (a) F and T, and (b) H and V are complementary (where the complement operation is represented by a bar overhead). The complement pairs are also orthogonal since their overlap produces opaque output. However, while all complementary pairs are orthogonal all orthogonal pairs are not complementary. We attempt to describe the general design procedure next. The steps for designing a particular optical logic unit using POSC scheme are comparable with those for designing a digital combinational circuit. The design steps in purely digital systems involve determining Boolean logic expression(s) and the corresponding logic circuit necessary for realizing the functional characteristics of the desired unit. In comparison, the POSC design scheme involves determining the encoding patterns of the inputs that will actually produce the desired operation. The steps of the algorithm are as follows:

each quadrant can have either T, or F, or H, or V code) corresponding to a maximum of four different condi-

Step 1. The truth table is characterized. Step 2. The input pixel pattern is represented by an n X n spatial matrix in generalized terms.

tions for each LED sources, unpolarized, off, vertically polarized, and horizontally polarized, for designing a

output columns of truth table.

an input pixel code consisting of four quadrants (where

Step 3. An output mask is chosen for each of the

15 July 1987 / Vol. 26, No. 14 / APPLIEDOPTICS

2721

Step 4. The truth table rows are grouped according to the same output conditions, and a sequence (steps 5-7) is followed so that the conditions requiring the most outputs to be logical 1 is considered before the others (this is opposite to Quine-McClusky's tabular reductions where the smaller groups are formed first). The motivation for such an order is to satisfy the more complicated constraint conditions first. Step 5. The desired output (logical 1 or 0) from the truth table is projected backward from the output mask to the overlap pattern, so that in terms of output coding the overlap pixel pattern can be determined. For n = 2, the particular output may occupy any one of four quadrants. This gives a choice of up to four conditions depending on whether the corresponding code occupies a particular quadrant. Step 6. The POSC logicequations involving all input variables for similar output conditions are obtained for that particular pixel position. Step 7. Optimized selection is made in determining pixel quadrant characteristics to satisfy maximum truth table conditions with the minimum number of inputs involved. During the pixel pattern determination process, two POSC equations from two groups are simultaneously considered, if possible, so that they are complementary, either totally or partially. The complementary input variables take the same value as the output, while the noncomplementary input variables are assigned T codes. In case a condition cannot be satisfied, a new set of variables is chosen to fulfill the POSC logic equations. Steps 6 and 7 are repeated until satisfactory input codes have been determined. The design being considered involves determining the elements of an n X n spatial matrix. However, more degrees of freedom are present in regard to the choice of the input LED pattern and the decoding mask. In the design, for simplicity, the input LED pattern shall be kept fixed. For simpler logic units this poses no problem. But for realizing very complex logic units, truth tables may be segmented into several smaller truth tables according to different outputs, where one or more outputs may be designed separately corresponding to one particular LED arrangement. To demonstrate the design steps involved in the general algorithm the example of a full adder and a full subtracter 2 are considered respectively in the next two sections. Ill.

Condition

A

B

C

S

C'

1

0

0

0

0

0

2

1

1

1

1

1

3

0

0

1

1

0

4

0

1

0

1

0

5

1

0

0

1

0

6

0

1

1

0

1

7

1

0

1

0

1

0

1

Number

8 _- _ _- -_-_

1 -_-_

-_ _ -_ _ _-_

1 -_ -_ _ _ - _ _-_ _-

0 _-_-

_-_ _-

_-_ _ _-_ _-

-_ _-

_ _ _ _- - _ _- _ _ _- _ _-

_- _-

_- _ _ _- _ _-

-_ _-

Table II is completely satisfied where sum and carryout are, respectively, represented by S and C'. The truth table is segmented and organized in a way so that similar output conditions appear in a particular group. For simplicity, four unpolarized LEDs are chosen to be on, and the output is decoded by a mask with openings at the central micropixel. A vertically polarized mask is used to detect the sum output, while the horizontally polarized mask is used to detect the carry output. The horizontally or vertically polarized input code from the input pixel quadrant is projected at the mask center whenever an LED is on at the correspondingly identical corner of LED arrangement. Thus to have a logical 1 (or logical 0) at the output plane, a logical 1 (or logical 0) must be present in at least one of

the four quadrants in the overlap code. The design procedure then begins by arbitrarily assigning one quadrant in the overlap code. If we want, for example, a V to appear at the upper left corner in the overlap code, the POSC logic equation all A b

Ac

=

V can

be used to relate the corresponding input pixel quadrants. Such equations will be used for determining the input pixel characteristics. Our output mask is such that an opaque code at the central micropixel of decoding mask would result in a logical 0.

Full Adder Design

Let A, B and C be the three input variables, addend, augend, and carry-in, respectively. For simplicity, the variables are represented by a 2 X 2 spatial matrix so that its elements would provide the input pixel characteristics. For example, A

all [a 21

a

(3)

a 2 2]

can be used to represent a logical 1 in A input. B and C are also represented similarly by 2 X 2 matrices. The

design process involves determining the matrix elements so that the full adder truth table as shown in 2722

Table 11. Full adder truth table.

APPLIEDOPTICS / Vol. 26, No. 14 / 15 July 1987

Condition 1 of Table II reveals that O1 = 012 = 021 = F, and condition 2 reveals that Of, = Vand 021 = H, where 0 represents the overlap matrix. It may be mentioned that 012 and 022 for condition 2 can take any possible coding. Consequently, POSC logicequations for conditions 1 and 2 result into the following two sets of four equations: = 022

Set 1: all

A bl A

=

F

(4a)

a12 A b12 A C12 = F,

(4b)

a2 A b21 A C2 1 = F,

(4c)

a22 A b22 A C22= F.

(4d)

AC11 = V,

(5a)

d,

(5b)

= F, b12 = T, and c12 = H. Consequently, b12 has been changed from Vto T, and a12 has been changed from T to F. Note that this change does not cause any prob-

a2 A b2 A 21 = H,

(5c)

lem since Eqs. (4b) and (5b) are still satisfied. larly conditions 5 and 7, respectively, give

d,

(5d)

Set 2: all A b

a12

A b 2 A C12=

a 22 A b 22 A C22 =

a 22 A b22 A C22 = V

(7a)

a22 A b22 A C22 = H.

(7b)

where d is a don't-care code. We begin with set 2, as

this would be relatively harder to satisfy. Note that, if an element ij} of any one of the three matrices A, B and C is chosen to be T, than aij A bij A cij = F. To satisfy Eqs. (2a) and (5a) any one of the three 1111input pixel quadrants has to be a V. One of the remaining pixel quadrants would have to be a T, while the third one could be either T or V. We would choose T for the

third pixel quadrant for the time being, and it could be changed to V at a later stage if it becomes necessary. Thus the chosen quadrant codes become all = bl = T. and c1l = V. This choice also satisfies Eq. (4a) of set 1.

To satisfy Eqs. (2a) and (5c) any one of the three 211 input pixel quadrants must be an H, the second pixel quadrant must be a T, while the third pixel quadrant could be either a T or H. Consequently we choose a21 = b2l = H, and c21 = T. This particular choice is found to satisfy Eq. (4c) of set 1 as well. Since the two

remaining set 2 POSC equations involve d code, the corresponding set 1 conditions are examined first. To satisfy Eqs. (4b) and (4d) and at the same time Eqs. (2b) and (2d), either at least two of the corresponding input pixel quadrants must be complementary, or any one of the corresponding input pixel quadrants must be an F. In other words, any two of the corresponding

Like before, the two common literals are assigned T code, and c22 is set H to satisfy Eqs. (7a) and (7b). Thus a22 = 22 = T, and C2 2 = H, and this latest choice is also found to satisfy all the previously discussed conditions. By this time all the input pixel quadrants have been selected, even though there are two more truth table conditions to be satisfied. The input pixel quadrants {121and {221already contain unique codes from the latest iteration so that it will be very hard to satisfy any other conditions involving them. For example, for the 1121input pixel quadrant a 1 2 = b12 = T and C12 = H conditions must be met to satisfy Eqs. (6a) and (6b), even though the truth table conditions 3 and 8, respectively, provide

that case either one of the corresponding input pixel quadrants 1221should be an F, or any two of the corre-

sponding input pixel quadrants should be orthogonal. We choose a22 = H, b22 = F, and c22 = V to satisfy both Eqs. (4d) and (5d). However, the choices for pixel quadrants 121and 1221could be skipped without any loss of generality in the design process.

The minterms corresponding to full adder truth table conditions (3), (4), and (5) have two complemented

input literals, while the corresponding sum and carry codes at the mask are, respectively, Vand F. Similarly the minterms corresponding to conditions (6), (7), and (8) also have only one complemented literal so that the

sum and carry codes at the mask are, respectively, F and H. The conditions 4 and 6 provide POSC logic equations a12 A b

2

A C12 = V,

(6a)

H

(6b)

a12 A b12 A C12 =

These two equations are seen to have complemented output. Moreover, two variables, namely, a12 and b12, are common in both equations. Therefore, these two literals must be equal to T. The third variable c12 can only be H. Therefore, Eqs. (6a) and (6b) result into a12

a12 A b1 2 A C12

V,

(8a)

a12 A b12 A C 12 =

H

(8b)

Equation (8a) is violated by a12 = F, and Eq. (8b) is violated by b12 = T. Consequently, attempt is made to modify the other two pixel quadrants, 1111and 1211. POSC logic equations are written, respectively, for these two pixel quadrants:

input pixel quadrants must be orthogonal. We select a1 2 = T, b12 = V, and C12 = H to satisfy the conditions of Eq. (4b). Consequently, Eq. (5b) is also satisfied with d = F. In Eq. (5d), also, d can be set equal to F. In

Simi-

An examination

a21 A b 21 A C2 1 = V,

(9a)

all A b1l A cFl = H.

(9b)

of the above two equations reveals

that both of these are already satisfied by our latest iteration choices: al = bl = C21 = T, c11 = V,and a 21 = b2l= H. The complete coding choice for the full adder input pixels are, respectively, AT F

= [T T]

C=[T

]

(0

where sum and carry are, respectively, obtained using vertically and horizontally polarized detector masks. It should be noted that corresponding to all conditions having the same output, the output logic is distributed over different overlapped pixel quadrants resulting in additional degrees of freedom so that the choices of variables become independent.

It is of vital

importance in the design to group together the conditions which can be simultaneously

satisfied.

Some-

times additional flexibility is obtained when one condition happens to be the complement of another. For example, the two input/output conditions 3 and 8 are said to be complements of each other. It is possible that the solution of one could simultaneously satisfy the other condition. The full adder design could have been begun in a different manner as well. Step 4 of the design process could be simplified by treating the more complex condition into two or more simpler condi15 July 1987 / Vol. 26, No. 14 / APPLIEDOPTICS

2723

tions. For example, outputs for condition 2 can be

treated as two separate output conditions: (a) S = 1, C' = d; and (b) S = d, C' = 1. Consequently, for example,

conditions

(1) 2 and 8; (2) 2 and 3; (3) 4 and 6;

and (4) 5 and 7 can be treated in any order of preference to produce the same result of Eq. (10). The

choice of pixel pattern as shown in Eq. (10) is, however,

not unique. For example, the choice A = [H HV]

T

V] B =[H H

T

C=[T

H]

v H

Table Ill.

Full subtracter design.

I

X

Y

Z

D

B

I

1

1

l

1

1

2

0

0

1

1

1

3

0

1

0

1

I

4

0

0

0

0

0

5

1

0

1

0

0

6

I

I

0

0

0

7

0

1

1

0

1

W

8

1

0

0

1

0

T

(11)

also satisfies the full adder truth table. It is interesting to note that two pairs of the eight input conditions are complementary in nature. They are, respectively,

IF]IF

(a) 4 and 7, and (b) 5 and 6. The four corresponding

POSC equations are, respectively, a1 2 A b1 2 A C12 = V,

(12a)

a12 A

12

(12b)

a2 2 A

22 A C22 =

A C12 = H VI

(12c)

a22 A b22 A C2 2 = H.

(12d)

Equations (12a)-(12d) provide a unique choice of variables: a2 = b22 = cl 2 = 22 = H and a2 2 = b2 = V. Note that conditions (a) 2 and 3 and (b) 2 and 8 are also

complementary, but only partially. They respectively provide a11 A b11 A l=

IHIVI

LU

column of Table III. The content of the remaining quadrants are, however, unimportant for our consideration. The first three conditions actually call for six POSC equations. For B = D = 1 output a V and an H mask are placed after the overlapped code. Correspondingly, the overlap pixel quadrants 11}and 21}are, respectively, V and H to satisfy condition 1. Since conditions 2 and 3 also require that B = D = 1, the corresponding polarized codes are placed this time in different locations so that it is possible to obtain complementary equations as well. Consider two of these six equations:

H,

(13a)

V,

(13b)

a21 A b21 A C21= V

(13c)

a21 A b21 A C21= H.

(13d)

a11 A b11 A C11 = V,

(14a)

To satisfy Eqs. (13a) and (13b), cl is set to T while all and bl, can both be only H. Again to satisfy Eqs. (13c)

a11 A b11 A Cl = H.

(14b)

a,

A b1 A

=

and (13d), a 2 l and b2 l can both be T while c21 can only be V.

Finally, the full adder truth table condition 1 is also met by the pattern of Eq. (11), since in two of the pixel quadrants, {11}and 21}at least one is a T code, while

the remaining pixel quadrants have complementary codes. Similarly, by grouping conditions (a) 2 and 3, (b) 2 and 7, (c) 4 and 8, and (d) 5 and 6, one could easily

arrive at an input pixel pattern that is similar to the one used in Ref. 10. This completes the full adder design. We shall next consider a full subtracter design. IV.

Full Subtracter Design

We start by defining the truth table of the subtracter, as shown in Table III, where X, Y Z, D, and B are, respectively, minuend, subtrahend, borrow-in, difference, and borrow-out. A vertically polarized mask is used to detect D, while a horizontally polarized mask is used to detect B. The truth table is grouped in to three groups:

(a) 1, 2, and 3; (b) 4, 5, and 6; and (c) 7 and 8.

Note that the pair in the last group is complementary. Correspondingly, at least one or more overlap pixel quadrants are arbitrarily assumed as shown in the last 2724

APPLIEDOPTICS / Vol. 26, No. 14 / 15 July 1987

These two equations are partially complementary. So we choose b = T so that all = cl = V is an obvious choice. Similarly, a21 A b21 A C21= H,

(15a)

a2 A b 2 1 A C21 = V

(15b)

results into C21 = T and a 2 = b2l = H, while the remaining two equations a1 2 A b12 A C12 = H,

(16a)

a1 2 A b1 2 A C12 = V

(16b)

result into a12 = F; and b12 = C12 = V. Next consider the POSC equations corresponding to conditions 7 and 8:

a22 A b22 A C2 2

H,

(17a)

a2 2 A b 22 A C22 = V,

(17b)

=

which are complementary. The obvious solution is a22 = V, and b22 = C22 = H. Complementary solution at pixel quadrant 221ensures that all other conditions, except 7 and 8 produce F output. The other three pixel quadrants 1111,1121,and 211,with the already chosen codes, produce F as per conditions 4, 5, and 6.

This completes the design of POSC full subtracter. The input pixel patterns, therefore, becomes 'A =[V F]

V.

B =[T

V

V

(18)

Discussion

The method described in this paper is very systematic and general, and it may be easily extended to determine input pixel patterns for any binary combinational truth table. It may be noted that the properties of only orthogonal variables may be used to design

a trinary combinational unit. However, to detect trinary outputs (logical 0, 1, and 2) the decoding mask would have to be changed. For a larger truth table where there are more conditions to be satisfied, a com-

puter program may be written in terms of binary logic to determine the required input pixel pattern. Future work could be directed towards identifying optimum grouping preferences in POSC design for cost reduction and ease of fabrication. The disadvantages of the POSC method include diffraction effects and the time it takes to encode the inputs. It is, however, possible to eliminate the problem of diffraction by adjusting pixel size,13 and the encoding-time problem could be

References

1. R. Normandin, "All-optical, Fiber-Optic Modulator and Logic Gate Using Nonlinear Refraction and Absorption," Opt. Lett. 11,751 (1986). 2. H. M. Gibbs, and S. L. McCall, and T. N. C. Venkatesan, "Differential Gain and Bistability Using a Sodium Filled Fabry-Perot Interferometer," Phys. Rev. Lett. 37, 1135 (1976). 3. G. R. Olbright, N. Peyghambarian, H. M. Gibbs, H. A. Macleod, and F. V. Milligen, "Microsecond Room Temperature Optical Bistability and Crosstalk Studies in ZnS and ZnSe Interference

Filters with Visible Light and Milliwatt Powers," Appl. Phys. Lett. 45, 1031 (1984). 4. J. Tanida and Y. Ichioka, "Optical Logic Array Processor Using Shadowgrams," J. Opt. Soc. Am. 73, 800 (1983). 5. Y. Ichioka and J. Tanida, "Optical Parallel Logic Gates Using a Shadow-Casting System for Optical Digital Computing," Proc. IEEE. 72, 787 (1984). 6. J. Tanida and Y. Ichioka, "Optical-Logic-Array Processor Using Shadowgrams. II. Optical Parallel Digital Image Processing," J. Opt. Soc. Am. A. 2, 1237 (1985). 7. J. Tanida and Y. Ichioka, "Optical-Logic-Array Processor Using

Shadowgrams. III. Parallel Neighborhood Operations and An Architecture of An Optical Digital-Computing System," J. Opt. Soc. Am. A 2, 1245 (1985). 8. T. Yatagai, "Optical Space-Variant Logic Gate Array Based on Spatial Encoding Technique," Opt. Lett. 11, 260 (1986).

9. J. Tanida and Y. Ichioka, "OPALS: Optical Parallel Array Logic

corrected by making use of spatial light modulators.14

System," Appl. Opt. 25, 1565 (1986). 10. Y. Li, G. Eichmann, and R. R. Alfano, "Optical Computing Using Hybrid Encoding Shadow Casting," Appl. Opt. 25, 2636 (1986).

The authors would like to thank Steven Cartwright and Steven C. Gustafson of The University of Dayton Research Institute and the reviewers for going through this manuscript and making some extremely useful

11. J.D. Gaskill, "Linear Systems, Fourier Transforms, and Optics

comments.

Two of the authors (AASA and AC) would

like to thank the Department of Electrical Engineering of The University of Dayton, for providing graduate research support.

(Wiley, New York, 1978). 12. E. L. Johnson and M. A. Karim, Digital Design: A Pragmatic Approach (PWS, Boston, 1987). 13. R. Arrathoon and S. Kozaitis, "Shadow Casting for Multiplevalued Associative Logic," Optic. Eng. 25, 29 (1986). 14. W. E. Ross, D. Psaltis, and R. H. Anderson, "Two-Dimensional

Magneto-Optic Spatial Light Modulator for Signal Processing," Proc. Soc. Photo-Opt. Instrum. Eng. 341, 191 (1982).

EMIL WOLF ELECTED TO HONORARY MEMBERSHIP IN OPTICAL SOCIETY OF AMERICA Emil Wolf, professor of physics and professor of optics at the University of Rochester, has been elected an Honorary Member of the Optical Society of America in recognition of his Wolf, "preeminent service in the advancement of optics." who has been involved in the field for nearly 40 years, is known primarily for his work in electromagnetic theory and physical optics, especially diffraction and the theory of partial coherence. An OSA fellow and former Society president, Wolf is also the recipient of this year's Max Born Award for work dealing with the theory of partial coherence in the spacefrequency domain, scattering and inverse scattering, phase conjugation, radiation, and radiometry. After completing his studies at the University of Bristol and the University of Edinburgh, Wolf began his career at Cambridge University as a research assistant, then became Max Born's research assistant at the University of Edinburgh. Later, Wolf and Born wrote PRINCIPLES OF OPTICS, one of the Now in its sixth edition, it has been translated into Chinese, Japanese, and Russian, and a In addition to Taiwanese edition has also been published. best-known optics textbooks.

nearly 200 published papers, Wolf is editor OPTICS, a series that began in 1961, with He is also a member lished since then. Editorial Board of Optics Communications

of PROGRESS IN 24 volumes pubof the Advisory and the Editorial

Board of Advances in Optoelectronics. A native of Prague, Czechoslovakia, Wolf has taught at the University of Rochester since 1961, except for one term as

visiting professor at the University of California at Berkeley and another at the University of Toronto. As of 1 July he will be the Wolf was Wilson Professor of Optical Physics at Rochester. the 1977 recipient of the Frederic Ives Medal, the Optical Society's highest award for overall distinction in optics. Beyond honors bestowed by the Society, he received the Franklin Institute's Albert A. Michelson Medal in 1980, is a fellow of the American Physical Society, the British Institute of Physics, and the Franklin Institute. Wolf's election to honorary membership in the Optical Society of America will be formally acknowledged in a presentation be held in '87-to at the Society's annual meeting-Optics

Rochester, 19-23 October. 15 July 1987 / Vol. 26, No. 14 / APPLIEDOPTICS

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