DE19627632A1 - Electronic optical computer arrangement - Google Patents

Abstract

An electronic-optical computing arrangement in which a device for coding of an input vector (Z) is provided as a first coding means (SLM), and in which in the surface zones for the respective vector dimension (Z1...Z5) the associated component value is shown as a bright-dark distribution (S1...S5). At least one filter is provided as a first filter device (FM) for functional evaluation of the coded input vector (z), with surface zones (Z1...Z5) unambiguously corresp. to the values and dimensions of the input vectors, and with a dark-bright distribution being used to express the functional dependency between a component value of a vector dimension and the associated functional value. A detection device (D) is used for detecting the integral brightness of the light emanating from an illumination device (BEL), after passing through the first coding device and the first functional filter device, and as an output shaping device a facility is provided for electronically transforming the light intensity into an output signal.

Description

The invention relates to an electronically optical re Chenanordnung especially for performing neural or fuzzy calculations using radial basis functions.

Realizations for fuzzy controllers and neural networks are known in many different ways from the field of technology. Often digital computers with simulators, or dedicated processors used. Neural networks, as well Neuro-fuzzy computer using radial basis function are explained in the prior art [1]. Optical Reality compared to the standard solutions have the theoretical Advantage that they work faster and that light beam len parallelize easily, which leads to Reali a high degree based on optical solutions of parallelizability, which does not have a ho hen technical effort required. High speed applications Applications of laser technologies are e.g. B. as a laser printer knows. There is particularly room for lighting computer applications Liche light modulators (SLM) proved suitable, which in State of the art are described under [2] with examples. Other such electronic optical computers are from the State of the art not known.

The object underlying the invention is a optoelectronic network with which both fuzzy Computers as well as neural networks using radial Basic functions can be implemented.

This object is achieved according to the features of patent claim 1 solved.  

Further developments of the invention result from the dependent Claims.

A particular advantage of the arrangement according to the invention is that it is only by using the filter a response to incoming light rays is a result for example, a neural network on input size aims. This makes the arrangement according to the invention special quick and can be used where the practice is high speed demands. By the beam according to the invention division of the light beam after passing through it coding means according to the invention can have any number of radial Apply basic functions in the function filter means simultaneously be tested. The limits are only in the area of Technology through the possibilities of dividing a light beam, as well as the evaluation of the integral brightness Passing through the coding means and the function filter with given in the detectors.

Each individual dimension of an is particularly advantageous gear vector in a strip-shaped area of the first Co diermittel coded, which corresponding strip-shaped Areas assigned in the first function filter means are. This type of optical arrangement requires, if too still the same size for the coding means and the functi onsfiltermittel is chosen, no extensive optical Measures to map a coded input vector to be able to make the appropriate function filter means nen. A maximum can be particularly advantageous as bright or be coded as dark, which is only for the Auswer tion of the light intensity in the detector got to. Suitable detectors from the prior art be selected which are inexpensive and which one corresponding detection behavior with regard to the expected the light intensity difference in the arrangement according to the invention exhibit. The arrangement of the functions in the form of  Stripes on the functional filter media and the individual Vector dimensions in the form of slots on the corresponding the strip also has the advantage that it is available space on the corresponding coding means and filters is optimally used.

They are preferably transferred from the computer to the input vector functions to be used in the form of gray value gradients in the Functional filter means coded. Read such gray value gradients They are easy to manufacture and can be used for example partially stored in an exposed slide. To make it easier to evaluate the light intensity measurement solution in the detector, but it can also be provided be that the functions to be used are in discrete gray values tabulations in the corresponding function filter means be placed, as this is at the exit at the light ink Gradual gradations in the measurement of the Light intensity after passing through the first coding medium and the first functional filter means result.

Preferably, in the arrangement according to the invention Initial shaping means designed so that the light intensities are reshaped in such a way that they are an intermediate result from the corresponding mathematical equation for the opti equation (see equation part equation (10) and equation (11)).

The starting molds in which it is particularly advantageous inventive arrangement designed so that they more Intermediate results in the mathematical calculation of the off initial values from the input value in the form of additional multi Consider the complications and additions (see equation section Equations (12) and (13)).

Be particularly advantageous in the arrangement according to the invention for the simulation of a neural network radial basis  functions in the form of bells that correspond to the Gaussian shape used because these are well suited for overlaying are largely analyzed in practice, and easy as gray value distributions in the function filter means let put.

The arrangement according to the invention can be particularly advantageous also as a fuzzy calculator using a radial basis functions according to [1, page 185] and from the equation section Apply equation (17). Can be particularly advantageous the application of the arrangement according to the invention as a fuzzy Calculator the defuzzification in the initial form stage perform that when applying equation (12) for Ge weighting factors wI the location of the identified focal points of the original puzzle sets are taken.

Are particularly advantageous in the arrangement according to the invention Standardization levels are provided, which all input and Standardize or denormalize output variables so that the signal processing not of the orders of magnitude and absolute depends on the individual sizes to be processed.

Are particularly advantageous in the arrangement according to the invention as light intensity reducing agents, for example spatial light modulators provided, since these are in the Practice particularly well suited and variable in operation their filter properties are configurable.

In the following, the invention is based on figures purifies.

Fig. 1 shows an example of an inventive electro nic optical computer arrangement,

Fig. 2 shows an example of a first encoding means,

Fig. 3 shows a first example of a means of Funktionsfiltermit,

Fig. 4 illustrates the functional score in accordance with the methods of the invention.

Numbers of equations in the description refer there for equations numbered accordingly in the equation part, which follows the description of the figures.

In Fig. 1 an example of an electro-optical computing arrangement according to the invention is given. An input vector Z is given, for example, via a feed 10 in an input stage IN which, for example, carries out coding and normalization of the input vector. For example, the first coding means SLM is controlled via a signal line 20 . In the first coding means SLM, the individual dimensions of the input vector Z are preferably coded separately in areas. A five-dimensional vector is shown schematically here, but any number of dimensional vectors can be imagined and coded. For example, the amount of the value of each dimension of the vector is standardized for coding and then arranged according to its standardized size as a slot in the first coding means on an associated strip-shaped surface. Spatial light modulators can preferably be used for the first coding means, since they have already proven themselves for optical computer applications and their light transmission properties are constantly reconfigurable. But there are also conceivable liquid crystal matrixes, which are controlled accordingly, and other corresponding closure mechanisms, which are known to those skilled in the art from practice. These first coding means are illuminated, for example, from a lighting means BEL which emits a uniform light beam LS. After passing through the first coding means, this light beam strikes, for example, optical imaging means OAM, which can be implemented, for example, in the form of a lens matrix. There, the light beam LS is divided into four sub-light beams LS5 to LS20, for example.

A particularly important property occurs in this process the arrangement according to the invention to the day namely pension parallelizability. For parallel processing of the input vector Z is therefore single according to the invention Lich the image of the first coding means required in Parallelize the shape of a light beam. The limits for the parallelization according to the arrangement according to the invention are therefore only to be multiplied by optical arrangements light rays and through the detection system intensity measuring detectors in the inventions limited arrangement according to the invention.

According to a further feature of the invention, the functio nal evaluation of the coded input vector using Functional filter means performed on which the split light rays LS5 to LS20. The functi Onsfiltermittel are with FM5 to FM20 according to the incident Images in the light beams LS5 to LS20. For any evaluation of an input vector Z by a radial Ba According to the invention, the disfunction is, for example, min such a function filter means FM is required. In the individual function filter means are then, as later will be explained, the individual functions in kor areas corresponding to the coding areas of the Co depositing agent. The functional evaluation of the one gangsvektor Z in the function filter means is for example wise by reducing the light intensity of the light inks the individual light beams LS5 to LS20. The integral brightnesses of the corresponding light rays is then after passing through the function filter medium by detectors D5 to D20, which in their designation the light rays and the functional filter media speak, detected.  

Subsequently, according to the mathematical description of the electronic optical computer in an output form in sub-units 50 and 60, for example, the signals of the measured light intensities LI5 to LI20 are formed in accordance with equations (10) and (11) in the equation part to provide intermediate results form. These intermediate results of the converted light intensity signals are multiplied by constants kappa1 to kappa4 for example in multiplication stages MS1 to MS4 according to equation (12) in order to obtain a second intermediate result. The first intermediate results from the multiplication stages MS1 to MS4 are then preferably fed to a summation stage SUM20, in which they are summed up to form a signal B. Furthermore, they are preferably supplied to multiplication stages M1 to M4, in which they are multiplied by weighting factors w1 to w4, in order to form a second intermediate result, which is subsequently added up, for example, in a summation stage SUM10 and is supplied to a division stage DIV10 as signal A. . The first sub-result B and the second sub-result A are then divided in a division stage DIV10, resulting in the output signal O. In the explanation of FIG. 1, it should be borne in mind that this is merely an exemplary embodiment of an electronic optical computer according to the invention. If the person skilled in the art has once understood the principle according to the invention to carry out the functional evaluation of an input vector by coding and by attenuating light rays, he can also construct other arrangements which include this principle according to the invention and which may include other means, for example lighting means or Use filter media as described in Fig. 1. Application requirements can also make it possible to dispense with individual components of the arrangement.

Fig. 2 shows an example of a coding of an input vector in a first coding medium used according to the invention. For example, a spatial light modulator SLM, as shown in [2], is used as the first coding means. However, other closure mechanisms are also conceivable which can be divided into transparent and non-transparent areas, such as liquid crystal closures, or mechanical closures. When selecting a suitable first coding means, however, it must be taken into account in what number and with what speed and in what dimension the vectors arrive at the input IN of the electronic optical computer. Accordingly, it must be taken into account that the coding to be carried out and the setting of the first coding means must be able to be carried out at a specific speed. In Fig. 1, the coding of a five-dimensional input vector Z with the dimensions Z₁ to Z₅ is shown as a game. Preferably, who codes the quantities of the input vector standardized in the first coding means so that the absolute amounts play no role in the evaluation by the computer. The coding of the individual values, which are assigned to the respective vector dimensions, takes place, for example, in dimension D in the form of strip-shaped areas in the first coding means. As can be seen, the first coding means is largely opaque in this case. However, it is also conceivable that an inverse representation is selected in comparison with this. The vector components of the individual dimensions Z₁ to Z₅ are co dated in the form of through slots S1 to S5. The number of vector dimensions corresponds here to M, for example, which was chosen to be 5 here. However, the method according to the invention should not only be limited to vectors of dimension 5 . It is immediately clear to see that vectors with a different number of dimensions can be encoded by the arrangement according to the invention in one of the most encoding means. The number of loading areas and the size of the coding means must then be selected accordingly. The location and arrangement, as well as the shape of the individual areas for coding the individual vector dimensions Z₁ to Z₅ is not decisive for the implementation of the invention. For the coding of the input vector in the arrangement according to the invention, only a clear assignment of the vector dimensions to corresponding areas in the first coding means is to be specified. For example, it is also conceivable that circular, concentrically arranged areas are selected which can be added to the individual vector dimensions. The individual values for the respective vector dimension would then be given, for example, by pie-like segments, which could be derived, for example, by normalizing the values in the form of angles. This type of division would have the advantage that a coding could be chosen which would allow a particularly finely graduated coding of a certain dimension, for example by arranging it in the outer ring of a concentric circular field. Thus, for example, the influence of a certain sub-function, which plays a special role in the rational basic function, could also be taken into account particularly precisely with regard to its influence on the result.

The dimension of the first filter means is selected here as D, for example, and the light, which is emitted by a laser, for example, passes through the coding slots S1 to S5. The individual vector components of the vector Z are preferably coded between 0 and 1. A vector Z = (0.6, 0.4, 0, 0.7, 0.4) ^{T is} shown here in FIG. 2, for example. For this variant of the first coding means according to the invention, the permeability of rectangular coding slots results, for example, in: Equation (4). Here rect [x] = 1 if | x | <½ and rect [x] = 0 in other cases. Preferably, each stripe which is assigned to a vector dimension is mostly impermeable except for a narrow slit which is arranged at y = Dz _j with a width δ. The light bundle passing through this first coding means is preferably fed to the function filter means, which are described in FIG. 3, by optical imaging means OAM, as already described in FIG. 1. The optical imaging means represent, for example, a field of lenses, but can also be implemented in the form of prisms or mirrors.

Fig. 3 gives an example of a functional filter means for use in an electronic optical Re arrangement according to the invention. According to the invention, it is provided that the image of the first coding means, in which the input vector Z was coded in any suitable manner in the form of permeability and non-permeability points, is fed to a function filter means, designated FM5 to FM20 in FIG. 1. According to the invention, it is further provided that such a functional filter means FM be provided for each radial basic function, which is necessary, for example, for the evaluation of an input vector by a neural network. An image of the first coding means, which was generated by the optical imaging means OAM, is preferably fed to each such functional filter means. It should preferably be noted that the detectors for the decrease in light intensity should be calibrated and that the optical deflection means should be of the highest possible quality by providing the same light intensity to each functional filter means.

For example, five partial functions FK1 to FK5 are combined to form a radial basic function in function filter means FM. It should be noted here that the imaging properties of the optical imaging means must preferably be such that they map corresponding areas for coding the vector dimensions to the corresponding areas in which the coded subfunctions FK are located. In some cases it may be necessary to choose the dimension D of the function filter means FM differently than the dimension D of the first coding means. In this case, the optical imaging properties must be adapted to this size increase or decrease. This statement applies analogously if the individual vector dimensions are coded differently in the function filter means, or if they have circular regions or diagonal stripe-shaped regions. As can be seen, a partial function FK1 of the radial basic function, which is represented by the function filter means FM in FIG. 3, has a maximum M1 at 0.75, while a partial function FK2 has a maximum M2 at 0.4. Here, for example, bell-shaped functions have been selected which have an intensity curve I1 in the case of FK1 and an intensity curve I2 in the case of FK2. The intensity profiles of the sub-functions FK3 to FK5 are not shown, but are preferably of a similar nature to that shown. As can be seen, the base width of the bells varies between the smallest subfunction FK1 and the widest subfunction FK4. The attenuation intensity of the respective sub-functions has been implemented here in a discrete form. Such a discrete area is given, for example, for partial function FK2 with A2 and for partial function FK4 with A4. The discretization of the bell-shaped curves in grayscale levels has the advantage that when evaluating the remaining light intensity after passage of the light beam through the first coding means and the first function filter means in the form of intensity levels can be evaluated, so that the detector gradual graded light intensities receives which are easier to identify. In the exemplary embodiment according to the invention according to FIG. 1, N = 4 is selected as the number of radial basic functions. The number of functional filter means is correspondingly 4 . The partial functions FK1 to FK5 to be used for the evaluation of the individual vector dimensions of the input vector Z are arranged in corresponding areas of the function filter means to which the coded information of the corresponding vector dimensions meet. Depending on the functions FK1 to FK5 to be evaluated in the function filter means FM, it may be more favorable to use an inverse position compared to FIG. 3 if this can be expected to result in a better measurement result in the detection of the change in light intensity in the detector . In the case of Fig. 3, the functional filter means is mainly permeable. The translucency of the i-th functional filter means is given by equation (5). The MIN operator used in this equation selects the smallest of its arguments. α is a constant. In the strip-like design of the area in question for the respective vector dimensions in the first function filter means and in the first coding means, for example, the gray value curve for a respective function and its corresponding vector dimension μ _{i, j} is centered vertically. This is illustrated with the intensity profiles I1 and I2 in FIG. 3. For example, the curve on both sides of the maximum falls in grayscale squared with the distance to the maximum. This drop is shown in FIG. 3 as an increase in brightness. According to the arrangement according to the invention, the light intensity, which can be measured for example on detectors D5 to D20, results from equation (6). It is assumed that δ «σ _ÿ D and that K stands for the unknown constants. The general basic functions are given by equation (1) and the normalized basic functions by equation (2). While normalized Gaussian basis functions can be given by equation (3).

Fig. 4 shows the evaluation according to the invention of an input vector which has been modulated in a light beam by first coding means and is to be evaluated by first function filter means for each radial basic function. Fig. 4 shows a superimposition of the images of Fig. 2 and Fig. 3. According to the invention, an input vector according to the arrangement according to the invention is to be evaluated in this way in an electronic computer. As can be seen, in this example the function FK1 does not lead to a weakening of the light bundle of the function value for the vector dimension Z1, which was coded in the form of a light slot S1. However, the light bundle part with the functional value of the vector dimension Z2, which was coded in the form of a light slot S2, strikes the area A2 of the partial function FK2 of the radial basic function. According to the gray value gradation of the function FK2, the light of the slot S2 is thus attenuated in the area A2 when it passes through the function filter means according to the gray value of the partial function FK2. The subfunction FK3 does not influence the function value of the vector of dimension Z3, because, as can be seen, the coding slot of the function value S3 lies next to the subfunction FK3 and the full intensity of the light slot S3 is let through by the function filter means FM. For the vector dimension Z4 and its component, which was coded in a light slot S4, the same applies as for the vector dimension Z2. This light slot, in the form of an image of the first coding means which had encoded the vector Z, strikes a gray value area A4 of the subfunction FK4, the radial basic function. According to the arrangement according to the invention, the light of the light slot S4 is reduced in intensity by the gray scale gradation of the function FK4 in the area A4. The same applies to the vector dimension Z5 and the components, which was coded in the form of a light slot S5, as for the vector dimension Z3. This means that the light from the light slot S5 is not weakened by the partial function FK5, since it strikes a completely transparent area of the functional filter means.

After passing through the light emanating from the lighting means BEL and passing through the first coding means SLM and the respective function filter means FM, the respective light intensity is to be measured in the form of light intensity values LI5 to LI20. For this purpose, the integral light intensity according to equation (7) is preferably determined by the detectors D5 to D20 shown in FIG. 1. For this purpose, equation (8) is assumed as a prerequisite, so that equation (9) results. Referring to FIG. 1, for example in con nection with the light intensity values LI5 to LI20 in the component 50 is a multiplication by 1 / (2Kα) which results in Equation (10). The inverse exponential function is preferably applied to this intermediate result in component 60 of FIG. 1, which leads to equation (11). Further multiplications with kappai and wI lead to equation (12). The desired output value of the system is obtained after equations (13) after summations and divisions. Since the constant K can be determined by measuring the light intensity from a detector, but the beam does not pass through the first coding means and the first function filter means. In order to make a precise statement when measuring the light intensities by the detectors, this process should preferably be carried out for the calibration of the corresponding detectors.

In summary it can be said that through the inventions arrangement according to the invention a very quick evaluation of a is possible by means of lighting technology measures, whereby only additive and multiplicative links are required. The invent Arrangement according to the invention has the great advantage that it a high degree of inherent through the optical components ter has parallelizability. The optically coded on gangsvector can by simple lens matrices or Mirror arrangements can be duplicated and by radial Basic functions in the form of function filter means in parallel be rated.

In some cases it can be useful to include the function filter tel so that these through the optical computer can be set variably, which means that exactly as with the first coding means, spatial light modulators for  the functional filter means can be used. In this way can other radial Ba functions can be set. For example be the case if the computer has a single input vector is to be evaluated by several neural networks, which are characterized by different radial basic functions terized, or if between the use of the Rech nerswitched as a neural network and as a fuzzy controller should be tet.  

Equation part

Reference

[1] "Neural Networks in Automation Technology" S. Hafner (ed.), R. Oldenbourg Verlag, Munich, 1994, pp. 159-192;
[2] "Optical Signal Processing" J. Horner, Academic Press, INC., 1987, pp. 478-495;

Claims (10)

1. electronically optical computing arrangement,

• a) in which the first coding means (SLM) are provided for coding an input vector (Z), in which the associated component value in the form of a light-dark distribution (S₁ ,..., S₅) is shown and / or coded, whereby the intensity of the light transmitted through the coding medium is changed, with each dimension (Z₁,... Z₅) and each value having a defined area (S₁,. ., S₅) of the coding means (SLM) is assigned,
• b) in which at least one filter is provided as the first function filter means (FM), for the functional evaluation of the coded input vector (z), which in its surface distribution with respect to values and dimensions of input vectors clearly corresponds to the first coding means corresponding area areas (Z₁ ,... Z₅), wherein a function value to be generated for each vector dimension and component is realized in that the functional dependency between a component value serving as a function argument of a vector dimension and the associated function value by a light-dark distribution in one of the vector dimension assigned surface area is specified, which corresponds to the course of the function and which changes the intensity of light shining through the function filter means,
• c) where illuminants (BEL) are provided for homogeneous illumination of the first coding means (SLM),
• d) in which optical imaging means (OAM) are provided for imaging the illuminated first coding means (SLM) onto a respective first function filter means (FM),
• e) the detection means (D) are provided for detecting the integral brightness of the light coming from the illuminant (BEL) after passing through the first coding means and the first functional filter means in the form of a light intensity,
• f) in which means for electronically transforming the light intensity into an output signal are provided as the output shaping means
• g) and at least the first coding means (SLM), the optical imaging means (OAM) and the first functional filter means (FM) are arranged optically so that the light from the illuminants (BEL) passes through them one after the other.

2. Arrangement according to claim 1, in which the surface area in first coding means (SLM) for a respective vector dimension (Z₁,..., Z₅) a strip is provided, which is between minimum and maximum value to be encoded, in which is a discrete value in the form of a rectangular area ches (S₁,... S₅) at the place corresponding to its value in Stripe is encoded, where for a maximum value which is selected as very light or very dark as coding. 3. Arrangement according to claim 2, in which the surface area in first filter means for a respective vector dimension Strip is provided, which is between minimal and maximum value to be encoded, in which a as Filter function (FK₁,..., FK₅) serving bell curve (I) in the form one that changes its gray value continuously or discreetly Band is realized, the width of the bell curve ei corresponds to an area from the area and their values are coded light or dark as in claim 2. 4. Arrangement according to one of the preceding claims, in which the initial shaping means ( 50 , 60 , MS, M SUM, DIV) are designed so that a respective light intensity value (LI5,..., LI20) is divided by a first constant and an inverse exponential function is applied to the result of this division. 5. Arrangement according to claim 4, wherein the starting molding means are designed so that a respective light intensity value to form a first intermediate result with a two multiplied th individual light beam constant (kappa) and the first intermediate result to form a second Intermediate result with a third individual beam len constant (w) is multiplied, after which ei the first partial result (b) the first intermediate results be added up and to form a second partial result nisses (a) the second interim results are summed up and to form the initial value (o) the second by the first intermediate result is divided. 6. Arrangement according to one of the preceding claims, in which the computer is designed as a neural network by as Filter functions (FK₁,..., FK₅) in the first function filter average (FM) radial basic functions in the form of Gaussian distribution lungs (I) can be used. 7. Arrangement according to one of claims 1 to 5, wherein the Computer is designed as a fuzzy computer by using as a filter functions in the first filter means the input Fuzzy sets are used and the De fuzzification carried out according to the focus method becomes. 8. Arrangement according to claim 7 and in particular claim 5, at defuzzification using the focus method is performed by the third light beam individual Kon was the main focus of the respective output fuzzy set is chosen. 9. Arrangement according to one of the preceding claims, in which Means for normalizing the sizes used are provided.   10. Arrangement according to one of the preceding claims, in which as a co-reducing the intensity of light tel (SLM, FM) a spatial light modulator is provided.