Method for carrying out a computing operation by means of holography

Abstract

The invention relates to a method (100) for carrying out a computing operation by means of holography, wherein in the method, an output data item is generated, by means of the computing operation, from a specified input data item of a multiplicity of possible input data items. The invention also relates to a transparent display device (200, 201, 202) for generating a two-dimensional transparent pattern for use as an optical processing scheme (320, 321) and / or as a holographic filter, in particular a Fourier hologram (302, 303), in the aforementioned method.

Description

[0001] Method for performing a calculation operation using holography

[0002] Description

[0003] The present invention relates to a method for performing a computational operation using holography and furthermore to a transparent display device for generating a two-dimensional transparent pattern for use as an optical processing scheme and / or as a holographic filter, in particular a Fourier hologram, in the above method.

[0004] State of the art

[0005] The technology of holography has long been known as state of the art. Holography is an optical technique for capturing and reproducing three-dimensional images, which are called holograms. Unlike conventional photographs, which only provide two-dimensional images, holograms also capture the depth and spatial appearance of the recorded object. Specifically, holograms record the intensity and phase of objects, whereas conventional photographs only capture intensity alternately.

[0006] A hologram is an image created using holography, a method for recording and reconstructing a wave field. The wave field can originate from any object and, unlike a photographic image, shows both the intensity and phase of the wave field at every point in the image. A hologram is typically created by illuminating the object to be recorded with coherent light.

[0007] Holography has a wide range of applications in various fields due to its ability to capture and reproduce three-dimensional images with depth and parallax. Some applications of holography include security applications, such as in banknotes, credit cards, passports, and identity cards to prevent counterfeiting; art and entertainment; medical imaging and scientific visualization; engineering and design; display technology, such as holographic displays; and education and training. DE 102020 210 935 B3 discloses a device and a method for reading holographically stored information, in particular for authentication, counterfeit detection, and data storage.

[0008] One object of the present invention is to improve upon the prior art. In particular, it is an object of the invention to provide a method for performing a computational operation which, firstly, offers an alternative to other types of data processing, especially computational methods, such as those using silicon chips. A further object of the invention is to provide a method for performing a computational operation which has an increased processing speed compared to the prior art. Furthermore, it is an object of the invention to provide a method of the aforementioned type in which the parallelism of the search operation is increased compared to the prior art. Finally, it is an object of the invention to provide a method of the aforementioned type which has improved interference immunity compared to the prior art.

[0009] This problem is solved by a method having the features of independent claim 1. Advantageous embodiments of the invention are specified in the dependent claims.

[0010] The method according to the invention serves to perform a computational operation using holography. Here, the method generates an output data from a predetermined input data set of a multitude of possible input data sets using the computational operation.

[0011] The method according to the invention advantageously achieves a significantly faster processing of a computational operation than in the prior art, for example by computers based on silicon chips. In particular, the use of holograms offers the advantage that all information stored in the hologram can be applied to the input data in parallel, thus enabling the parallel processing of an enormous amount of information.

[0012] The following terms will be explained:

[0013] A mathematical operation is understood as a special case of data processing that receives mathematical input data and outputs mathematical output data. In this context, data processing is understood as a procedure that receives input data and generates output data using a predefined transformation or algorithm.

[0014] The term "input date" refers to any date, which can be a digit, number, letter, or string. More generally, the input date can be any date containing information.

[0015] The term "output date" refers to any date, which can be a digit, number, letter, or string. More generally, the output date can be any date containing information. For arithmetic purposes, the output date is understood as a mathematical date that contains information or can correspond to a mathematical input.

[0016] If, for example, one considers an arithmetic operation of a NAND gate, an input value can be a binary representation of the two input bits, for example 00, 01, 10, or 11. The output value in this example is the NAND operation of the two input bits, which yields 1, 1, 1, and 0 for the aforementioned input values.

[0017] A key concept of the invention is that a computational operation can be processed significantly faster than in the prior art if a large number of possible input data are graphically represented, arranged in a two-dimensional plane at suitable, cleverly chosen positions, and this large number of graphically represented possible input data are filtered using a holographic filter that filters a predefined input data. In this case, an evaluation unit can determine, based on the resulting illuminated points and their positions, which of the possible input data are mathematically linked to the predefined input data.

[0018] A preferred embodiment of the method may further comprise the following steps: producing a holographic filter, in particular a Fourier hologram, based on a graphical representation of the specified input data; producing an optical processing scheme based on the arithmetic operation; illuminating an arrangement comprising the processing scheme and the holographic filter with light from a coherent light source, such that a distribution of at least one luminous point is created; and determining the output data based on the distribution of the at least one luminous point.

[0019] When the term holographic filter is mentioned below, it can be understood to refer in particular to a Fourier hologram.

[0020] This embodiment of the method is also referred to as the first embodiment.

[0021] In this context, illuminating the arrangement, which comprises a processing scheme and at least one holographic filter, until the distribution of the at least one luminous point is generated, but without the subsequent evaluation of the resulting distribution, is referred to as a step or processing step of the procedure. In this step, a computational operation is performed. The procedure can consist of a single step.

[0022] In this context, a holographic filter is understood to be an optical element based on holographic technology and used for the selective transmission or suppression of light. Unlike conventional optical filters, which are based on absorption or interference, holographic filters utilize the interference patterns of light to create specific optical properties. A holographic filter typically consists of a holographic material that records an interference pattern generated by the superposition of two or more light beams. By selecting the properties of these light beams, such as wavelength, polarization, or angle of incidence, the resulting interference pattern can be designed to achieve specific optical effects. For example, a holographic filter can transmit specific colors or wavelengths of light while blocking others.This can be useful for applications such as spectral filtering in spectroscopy, color filtering in photography, or light control in lighting technology.

[0023] Fourier holography is a technique for generating holograms based on the principles of the Fourier transform. This method is frequently used in holography to create high-quality and efficient holograms of complex three-dimensional objects. The fundamental principle of Fourier holography is that the interference pattern between the reference light beam and the light scattered or reflected by an object is recorded in the frequency domain. This interference pattern corresponds to the Fourier transform of the recorded object.

[0024] The graphical representation of the possible input data can be two-dimensional and contain at least one character and / or at least one symbol. For mathematical input data, the graphical representation can therefore include the digital characters 0 and 1, but also decimal characters or digits 0, 1, 2, ..., 9, or alternatively, hexadecimal characters 0, 1, ..., 9, a, b, c, d, e, and f. Alternatively or additionally, the graphical representation can be any mathematical representation of information. For input data of the search operation, the graphical representation can contain characters of the ASCII standard, the Unicode standard, or other characters that can encode information, e.g., Chinese characters.

[0025] The graphical representation of the possible input data is preferably unique, such that holographic filtering can distinguish each graphical representation of one possible input data from a graphical representation of another possible input data. This feature advantageously ensures that the output data is unique.

[0026] The holographic filter, in particular the Fourier hologram, can be designed and configured to filter spatial frequencies of the graphical representation of the given input data. This means that the holographic filter only allows the spatial frequencies of the graphical representation of the given input data to pass through and either blocks or filters out other spatial frequencies.

[0027] This feature advantageously ensures that, of the patterns contained in the possible input data which are sent through the holographic filter, only those patterns are allowed through which are identical or very similar to the pattern of the specified input data.

[0028] Using the NAND gate mentioned above as an example, the holographic filter filters out the spatial frequencies of a graphical representation of a given input data. This could, for example, be a graphical representation of input bit 01.

[0029] The optical processing scheme can be a two-dimensional transparent element that has a multitude of optical representations of the possible input data, each of which is arranged at a predetermined position of the transparent element.

[0030] Due to the predetermined position of each optical representation of the possible input data, the output date of the search operation or the calculation operation can advantageously be deduced by means of the subsequent filtering by the holographic filter and the evaluation of the light distribution after the holographic filter.

[0031] This can be clearly illustrated using the example of the NAND gate. The optical processing scheme can be a two-dimensional transparent element on which the four possible graphical representations of the input data 00, 01, 10, and 11 are arranged at different positions within the two-dimensional transparent element. Each graphical representation of the input data is characterized by two coordinates, for example, an X-coordinate and a Y-coordinate, measured from a corner of the transparent element. These coordinates converge on the center point of each representation.

[0032] In the next step, an arrangement comprising the processing scheme and the holographic filter is illuminated with light from a coherent light source, resulting in a distribution of at least one luminous point. This distribution of at least one luminous point can, for example, be arranged in an evaluation plane.

[0033] Preferably, the light first strikes the processing scheme and then the holographic filter. The pattern of the processing scheme is preferably transformed into the spatial frequency domain using a lens that performs a Fourier transform. The holographic filter then filters the resulting Fourier transform of the processing scheme. The holographic filter, which is based on a graphical representation of the given input data, thus only allows the Fourier-transformed pattern corresponding to the given input data to pass through. The filtered Fourier transform is then transformed back into spatial space using a lens. This ensures that a luminous point is only present at the position in the beam path that corresponds to the respective position of the given input data on the processing scheme.In a subsequent step, the release date is determined based on the distribution of at least one luminous dot.

[0034] In this case, the output date can be determined using an evaluation unit for evaluating the output date, which is executed and set up, based on a position or positions, preferably also based on an intensity, of the distribution of the at least one luminous point to decide what value the output date has.

[0035] By linking the position of a light point or a distribution of light points with, preferably, the intensity of the light point or an intensity distribution of the light points, the output date can advantageously be determined. This is due, among other things, to the fact that the positions of the possible input data on the optical processing scheme are known.

[0036] Preferably, the distribution of the at least one luminous point is arranged in the evaluation plane, so that the evaluation unit can preferably be arranged in this evaluation plane.

[0037] This will be illustrated using the example of the NAND gate. Since, when using a single frequency for the light from the coherent light source and assuming the optical processing scheme has each possible input value only once, a luminous spot is generated behind the holographic filter only at the position in the beam path that corresponds to the specified input value on the optical processing scheme, the position of the luminous spot—for example, in the evaluation plane where a detector for detecting the light is preferably located—can be used to determine the value of the output value. The evaluation unit can, for example, use the coordinates of the luminous spot to recognize whether the input value of the NAND gate was 00, 01, 10, or 11.For example, if the evaluation unit recognizes that the coordinates of the light point indicate that the input value was 00, it decides that the output data is the NAND gate of two 0-bits; thus, bit 1 is output. Alternatively, the evaluation can be simplified by a clever arrangement of the graphical representations of the input data on the optical processing scheme. With the NAND gate, the three input data values ​​00, 01, and 10 have a 1 as the output data, and only the input data value 11 yields a 0 as the output data. If the three input data values ​​00, 01, and 10 are arranged in one row and the input data value 11 is arranged in another row, the output data can be determined by evaluating a single coordinate—namely, the coordinate perpendicular to the two aforementioned rows.

[0038] Another preferred embodiment of the method may include the following steps: creating an optical processing scheme based on a graphical representation of the specified input data, creating a holographic filter, in particular a Fourier hologram, based on the search operation, illuminating an arrangement comprising the processing scheme and the holographic filter with light from a coherent light source, such that a distribution of at least one luminous point is produced, and determining the output data based on the distribution and / or intensity of the at least one luminous point.

[0039] This embodiment of the method is also referred to as the second embodiment.

[0040] The optical processing scheme can be a two-dimensional transparent element that displays a graphical representation of the input data, positioned at a predefined location within the transparent element. For example, in the case of a NAND gate, the transparent element of the optical processing scheme might display the input data "00" as a graphical representation.

[0041] In the step of producing a holographic filter, in particular a Fourier hologram, based on the computational operation, the holographic filter, in particular the Fourier hologram, can be designed and configured to filter spatial frequencies of a multitude of graphical representations of the possible input data, preferably all graphical representations of the possible input data. It is further preferred that the holographic filter, in particular the Fourier hologram, is generated using a graphical representation that includes a multitude, preferably all, graphical representations of the possible input data.

[0042] In the step of illuminating the arrangement comprising the processing scheme and the holographic filter with light from a coherent light source, according to the embodiment of the method described above, when using a single frequency for the light from the coherent light source and in the case that the optical processing scheme contains each possible input data only once, only a single luminous point is produced behind the holographic filter. However, according to the second embodiment of the method described herein, in the step of illuminating the arrangement comprising the processing scheme and the holographic filter with light from a coherent light source, when using a single frequency for the light from the coherent light source, several luminous points are produced behind the holographic filter, with a maximum number of luminous points equal to the number of possible input data.

[0043] This will again be illustrated using the example of the NAND gate. As mentioned above, the transparent element of the optical processing scheme, for example, has the input data 00 as a graphical representation. The holographic filter, in particular the Fourier hologram, was created using a graphical representation that includes all graphical representations of the possible input data, i.e., 00, 01, 10, and 11.

[0044] When the arrangement, which includes the processing scheme and the holographic filter, is illuminated with light from a coherent light source, several luminous points are created behind the holographic filter, with a maximum number of luminous points equal to the possible input data.

[0045] The final step of determining the issue date is more complex in the present embodiment of the method than in the embodiment of the method described above, since in the present case more than one luminous point is created for a single frequency of the light source.

[0046] For the example of the NAND gate with input date 00, the most intense or brightest luminous dot is the one that results from filtering the spatial frequencies of the graphical representations of input date 00. The luminous dots that result from filtering the spatial frequencies of the graphical representations of input dates 01 and 10 are less intense than the aforementioned luminous dot. The luminous dot that results from filtering the spatial frequencies of the graphical representation of input date 11 is the least intense, as the similarity between the graphical representation of input date 11 and the graphical representation of input date 00 is the least.

[0047] Therefore, it is possible to determine the output date by evaluating the distribution of the luminous points or the luminous pattern or light pattern, as well as the intensities of the luminous points or the intensity distribution. Since the luminous point resulting from the filtering of the spatial frequencies of the graphical representation of the input date 00 is the most intense or brightest, it can be concluded that the input date is 00 and therefore the output date must be 1.

[0048] The following explanations refer to the first embodiment of the method, unless explicit reference is made to the second embodiment of the method.

[0049] According to a further preferred embodiment, information can be encoded in an intensity, a wavelength and / or a polarization of the light of a graphical representation of an input data.

[0050] A graphical representation of input data can have more than two wavelengths. A holographic filter, in particular a Fourier hologram, can also be recorded with multiple wavelengths. Therefore, if two input data sets have the same graphical representation on the optical processing scheme but different wavelengths, a holographic filter, especially a Fourier hologram, recorded for only one wavelength, can discriminate between the two input data sets, thereby enabling information to be encoded in the wavelengths.

[0051] It is also possible for different input data to have the same graphical representation but differ in intensity. This advantageously allows more than one piece of information to be encoded in a single graphical representation of input data. For example, the intensity of an input data can have N different intensity levels, where N is a positive integer greater than two. Thus, N different pieces of information can be encoded in a single input data graphical representation.

[0052] Furthermore, it is conceivable that information can be encoded using light polarization. This makes it possible to use non-binary numbers represented by intensity. If information is encoded in a single wavelength of light, the coherent light source can emit at least two frequencies. In this case, the evaluation unit can analyze at least two frequencies.

[0053] The computational operation can have at least two steps, each of which includes the processing of an arrangement of a processing scheme and a holographic filter.

[0054] This advantageously allows for more complex calculations to be performed.

[0055] Each step can perform a calculation. Therefore, a step can also be described as partial data processing or a partial calculation. The sequence of at least two steps can be visually arranged sequentially.

[0056] It is preferred that an input date of a given step of at least two steps includes both the processing scheme of the given step and the output date of the preceding step.

[0057] According to another embodiment, the arrangement can comprise at least two holographic filters arranged in series. In this case, the at least two holographic filters are arranged in series following a processing scheme. Here, the input date of a holographic filter is the output date of the preceding holographic filter.

[0058] This has the advantage that, using this feature, two different search operations can be combined for a single, predefined input data point. First, the first calculation is performed, and then the second calculation is applied to the result of the first calculation.

[0059] The holographic filter and / or the optical processing scheme can be implemented using at least one switchable transparent display device. This advantageously allows different computational operations to be performed sequentially using the same device. The transparent display device can be a modulating display that modulates light from a light source shining through it.

[0060] The transparent display device can be implemented using a DLP® display or a display that has a photoactive material, such as an LCD display.

[0061] DLP® stands for Digital Light Processing and is a projection technology developed and trademarked by the US company Texas Instruments (TI). In this technology, images are created by modulating a digital image onto a light beam. The light beam is broken down into pixels by a rectangular array of movable micromirrors and then reflected pixel by pixel either into or out of the projection path. The core component of this technology, containing a mirror matrix and its control circuitry, is called a DMD, or Digital Micromirror Device.

[0062] By using a transparent display device, it is advantageously possible to electronically generate, in particular computer-generated, electronically store, electronically display, and / or quickly switch between the holographic filter and / or the optical processing scheme. This has the advantage that different holographic filters and / or optical processing schemes can be implemented using only one device.

[0063] The calculation operation can be a linear transformation, a matrix multiplication and / or an operation of differential calculus.

[0064] Linear transformations are well-known in mathematics. Examples of linear transformations include the translation, rotation, scaling, and reflection of vectors in space. Linear transformations are fundamental in many areas of mathematics and applied sciences, including linear algebra, functional analysis, physics, engineering, and computer science.

[0065] Matrix multiplications have many applications in various fields, such as computer graphics (e.g., to compute transformations like scaling, rotation, and translation of 3D objects), physics, machine learning, neural networks, graph theory, and economics. Matrix multiplication can be matrix multiplication of the general linear group GL(n,K). The general linear group GL(n,K) is a mathematical structure consisting of all invertible n x n matrices over a field K. K is preferably the field H of real numbers or the field C of complex numbers.

[0066] An operation in differential calculus can be, for example, a differential operator, such as an ordinary differential operator, a partial differential operator, and / or a functional operator.

[0067] The advantage of being able to perform linear transformations, matrix multiplication and / or differential calculus operations using an extremely fast optical method cannot be overstated.

[0068] This method can be used for search operations where the input date is a first string and the output date is a second string that meaningfully complements the first. This text completion is often offered by search engines for internet searches; it is also known as autocomplete. When a user types a search query, automated systems generate completions to execute the desired search query more quickly and save users time. For example, if a user types "today is" as the first string into the search engine, suggestions such as "day of," "my best day," "a good day to be happy," "Thursday," etc., could meaningfully complement the first string.

[0069] This method can be implemented, for example, using the first embodiment of the method mentioned above. Here, a holographic filter is created based on a graphical representation of the given input data, which in this case is the graphical representation of the words "today is".

[0070] The optical processing scheme can have a large number of text completions, potentially several thousand or even millions. These text completions are arranged in a matrix. For example, for the first string "today is," a text completion might be "today is Thursday" or "today is my best day." Since the form of the first string "today is" is part of the latter text completions "today is Thursday" or "today is my best day," and the holographic filter allows spatial frequencies of the graphical representation of "today is" to pass through, illuminated dots will appear after the holographic filter for those text completions in the processing scheme that contain the first string "today is." An evaluation unit can thus determine, based on the position of the illuminated dots, which text completions are part of the output date.

[0071] The method may include electronic, optical or electro-optical processing and / or transmission of information contained in the distribution of the at least one luminous point.

[0072] This advantageously ensures that the information contained in the distribution of the at least one luminous point can be further processed and transmitted flexibly, in particular optically, electronically or electro-optically.

[0073] The aforementioned feature can be implemented using a processing module. This step can occur after the illumination of the arrangement and before the determination of the output date, or even after the determination of the output date. This processing and / or forwarding step is highly flexible. One embodiment involves capturing the resulting distribution of the at least one luminous point and forwarding it with coherent light of increased intensity from another light source, so that further data processing can be performed using the output date from the process. This is particularly advantageous if, after the calculation, the intensity of the distribution of the at least one luminous point is too low, making a reliable determination of the output date impossible or only possible with errors.

[0074] The processing module can have more than one input and multiple outputs. The information contained in the distribution of the at least one light point can be optically transmitted, split, combined, or superimposed. Furthermore, the information or the resulting distribution can be transmitted at a modified frequency. The processing module can also convert the optical signal of the distribution into an electromagnetic signal, convert an electromagnetic signal into an optical signal, and amplify a signal, particularly an optical or electro-optical signal.

[0075] In another aspect, the problem is solved by a transparent display device for generating a two-dimensional transparent pattern, wherein the display device is designed and configured to be used as an optical processing scheme and / or as a holographic filter, in particular a Fourier hologram, in a method for performing a computational operation using holography.

[0076] The use of the transparent display device advantageously achieves that, in addition to the display device, only commercially available devices are required to carry out the above-mentioned method, some of which are designed and configured to carry out the said method.

[0077] A transparent display device can be used both as an optical processing scheme and as a holographic filter. Thus, for example, it is possible to implement the first embodiment of the method, in which an arrangement comprising an optical processing scheme and a holographic filter arranged behind it is used, by means of two transparent display devices arranged one behind the other.

[0078] As described above, the display of the device can be switched. This allows different arithmetic operations to be performed. For example, a NAND gate operation can be performed first, followed by a matrix multiplication.

[0079] Cascading the elements enables more complex calculations. For example, processing schemes Dj and holographic filters Fj can be arranged in different ways, where i is a positive integer index that numbers the respective components. For instance, the processing schemes Dj and the holographic filters Fj can be arranged alternately: D1, F1, D2, F2, D3, F3... Furthermore, at least one other holographic filter can be placed behind a given holographic filter Fi. An example of this is: D1, F1, D2, F2, F3, D3, F4... Since each of these elements is implemented with a transparent display device, switching between different processes is quick and easy.

[0080] If the signal is too weak at any point in the beam path, it can be measured at a suitable location and reproduced with amplification using an appropriate device. This advantageously ensures that the luminous intensity of the reproduced signal is strong enough to prevent errors in further processing.

[0081] The transparent display device can have the same features as the holographic filter and / or the optical processing scheme, both of which have already been described above.

[0082] The invention will now be explained in more detail using exemplary embodiments. These will show...

[0083] Fig. 1 shows an experimental optical setup for a method of performing a computational operation using holography.

[0084] Figures 2 to 5 each show a schematic representation of the operation of a calculation operation of a NAND gate according to the above method; Figure 6 shows a flowchart of a method for performing a calculation operation; Figure 8 shows a schematic representation of the operation of a calculation method for determining a non-trivial part of an integer; Figure 7 shows an enlarged optical processing scheme of the calculation method from Figure 8.

[0085] Fig. 9 shows a schematic representation of the operation of a calculation method which assigns recorded measured values ​​to one of several functions,

[0086] Fig. 11 shows a schematic representation of the operation of a calculation method for finding a prime factor of a positive integer; Fig. 10 shows an optical processing scheme of the calculation method from Fig. 11 as an enlargement.

[0087] Fig. 12 shows an experimental optical setup for carrying out the above method, in which a calculation operation is performed in two steps; Fig. 13 shows an experimental optical setup for carrying out the above method, in which a calculation operation is performed in two steps; Fig. 14 shows an experimental optical setup for carrying out the above method, in which two Fourier holograms are arranged one behind the other.

[0088] In a first step 110 of a procedure 100 for performing a computational operation using holography, a Fourier hologram 302 is produced based on a graphical representation 314 of a given input data from a multitude of possible input data. This will first be explained using the example of a NAND gate. The possible input data in this case are 00, 01, 10, and 11. The graphical representation 314 is used to produce a Fourier hologram 302.

[0089] The Fourier hologram 302 transmits spatial frequencies of the graphical representation 314 of the given input data. If the given input data is 00, the Fourier hologram 302 transmits the spatial frequencies of the graphical representation 314 of the given input data 00. Graphical representations 314 of other possible input data, which are similar to the graphical representation 314 of the given input data 00, are transmitted with varying degrees of attenuation depending on the degree of similarity.

[0090] The respective graphic representation 314 is shown in figures 2 to 5 on the respective Fourier hologram 302.

[0091] In a second step 120, an optical processing scheme 320 is created for the arithmetic operation of the NAND gate. Here, the optical processing scheme 320 is a two-dimensional, transparent element that displays a multitude of graphical representations 314 of the possible input data, each arranged at a predetermined position within the transparent element. In this case, the three graphical representations 314 of the input data 00, 01, and 10 are arranged in a first row of the processing scheme 320, and the remaining input data 11 is arranged in a second row of the processing scheme 320.

[0092] In a third step 120, an arrangement 330 consisting of the processing scheme 320 and the Fourier hologram 302 is illuminated with light 342 from a coherent light source 340. Behind the Fourier hologram 302, in an evaluation plane in which a detector 360 is arranged, a distribution 350 of luminous points 352 is created, the most intense being the luminous point 352 that originates from the input data on the optical processing scheme 320 corresponding to the specified input data. For the specified input data 00, the luminous point 352 is located at an upper left end in the representation of Figure 2, since the graphical representation 314 of the specified input data 00 on the optical processing scheme 320 is also located at an upper left end.

[0093] Since the other graphical representations 314 of the possible input data, i.e., 01, 10, and 11, exhibit a certain similarity to the given input data 00, further luminous points 352 are generated when using the Fourier hologram 302, which was produced with the given input data 00. However, these additional luminous points are less bright than the luminous point 352 that originates from the given input data 00. Because the similarities between the input data 01 and 10 and the given input data 00 are equal, the brightness of the respective luminous points 352 is equal, while the intensity of the luminous point 352 that originates from input data 11 is weaker.

[0094] In a subsequent step 140, the output date of the NAND gate is determined based on the distribution 350 of the luminous points 352 in the evaluation plane. The detector 360 determines the value of the output date based on the positions and intensities of the distribution 350 of the luminous points 352 in the evaluation plane. Here, the intensity of the light 342 from the coherent light source 340 and the intensities of the resulting luminous points 352 can be uniquely determined. Furthermore, the position of this most intense luminous point 352 on the detector 360, or in the detector plane, allows the possible input date from which the luminous point 352 originates. The output date corresponds to this possible input date.

[0095] In this case, only the vertical coordinate of the respective luminous point 352 needs to be evaluated, since the arrangement on the optical processing scheme 320 is cleverly chosen. If the vertical coordinate corresponds to the first row, the result is 1, since the NAND gate of the inputs 00, 01, and 10 yields 1 as the output. If the detector 360 determines the second row as the vertical coordinate, the result is 0, since the NAND gate of the input 11 yields 0 as the output. The laser light 342 emitted by the laser source 340 is expanded by a beam expander 343, so that a first lens 345 and a first transparent display device 200, which is arranged directly behind the first lens 345, are completely illuminated. The first transparent display device 200 implements an optical processing scheme 320. The image of the first transparent display device 200 is focused using the first lens 345.In the direction of propagation, a second transparent display device 201 is arranged shortly before the focus, and a second lens 346 is arranged shortly after the focus. The second transparent display device 201 realizes a Fourier hologram 302. The detector 360 is arranged at a predetermined distance behind the second lens 346. Both the first transparent display device 200 and the second transparent display device 201 are each connected to a control computer 362, which controls the first transparent display device 200 and the second transparent display device 201 such that the optical processing scheme 320 corresponding to the computational operations is displayed on the first transparent display device 200, and the Fourier hologram 302 corresponding to the predetermined input data is displayed on the second transparent display device 201.

[0096] The method according to the invention can be applied to a number of different arithmetic operations. In a corresponding method 100, which finds a non-trivial divisor of an integer, the optical processing scheme 320 can be selected as described below. For integers greater than 1, columns containing multiples of the respective integers are arranged in a two-dimensional scheme. The number of multiples is chosen to be equal to the absolute value of the respective number, i.e., one multiple for the number 1, two multiples for the number 2, three multiples for the number 3, and so on. For example, the third multiple of two, i.e., 2 x 3, which equals 6, is not needed for the second column, since this number is present in the third column as a double multiple. This clever choice of the optical processing scheme 320 simplifies the subsequent evaluation in the detector 360.Only multiples of the numbers one to ten are considered in the optical processing scheme 320; alternatively, such a processing scheme 320 can be significantly larger. The processing scheme 320 is stored in the control computer 362 as a high-transparency image on a low-transparency background and can be displayed or shown on the first transparent display device 200.

[0097] For different data inputs, i.e., for numbers whose non-trivial divisors are to be determined, different Fourier holograms 302 are displayed on the second transparent display device 201, which serve as filters. In this case, the corresponding Fourier hologram 302 is displayed on the transparent display device 201 for the data input of the number 48. This is illustrated in Figure 7, where the number 48 is written on the Fourier hologram 302. Those skilled in the art will understand that the corresponding Fourier hologram 302 for the number 48 is a complex pattern, which is not shown here for the sake of simplicity. The experimental setup could, for example, be the optical experiment described above.

[0098] When the arrangement 330, comprising the optical processing scheme 320 and the Fourier hologram 302, is illuminated, the detector 360 detects the most intense luminous point at the position corresponding to the eighth column and the sixth row, corresponding to the position in the optical processing scheme 320 that corresponds to the multiplication of the numbers 6 and 8. The detector 360 outputs this coordinate of the luminous point 352, which is stored in the control computer 362. The output of the present method 100 is thus the coordinate values ​​(8; 6) or the numbers 8 and 6.

[0099] The detector 360 passes these coordinate values ​​to a further processing module 370, which can process this result optically, electronically and / or optoelectronically.

[0100] Another method 100 serves the purpose of assigning measured values ​​or measured values ​​to one of several functions. It is known in the prior art to fit a fitting function to measured measured values. The optical processing scheme 320 can be selected as described below.

[0101] In a first column-shaped area 324 of the processing scheme 320, graphical representations of several functions, in this case Gaussian distributions, i.e., Gaussian bell curves, with different distribution widths, are arranged one below the other. In a second column-shaped area 325 of the processing scheme 320, graphical representations of further functions, in this case downward-opening parabolas with different widths, are arranged one below the other in the same manner as in the first column-shaped area 324.

[0102] In a third column-shaped area 326 and a fourth column-shaped area 327 of the processing scheme 320, graphical representations of further functions are shown one below the other in the same way as in the first two column-shaped areas 324 and 325, firstly a negative power function -x 3 as well as a negative power function -x 4 It is easily possible to add further columns with different functions, for example trigonometric functions, sawtooth functions, etc.

[0103] In this case of the procedure, the Fourier hologram 302 is generated or calculated from a graphical representation of the measured function values ​​and displayed on the first transparent display device 200. When the arrangement 330, comprising the optical processing scheme 320 and the Fourier hologram 302, is illuminated, several luminous points 352 typically appear per analysis area. The integrated brightness of the luminous points 352 is highest in the analysis area where the measured values ​​show the greatest similarity to the respective function. The detector 360 transmits the coordinates of the brightest sector to the further processing module 370.

[0104] The processing unit 370 interprets the columns as one of the predefined functions, e.g., a Gaussian bell curve or a parabola, and the rows as the specifying parameters, e.g., different widths of the respective functions. For the Gaussian bell curve, the standard deviation is a measure of its width. If the processing module 370 is a computer, the values ​​can be stored in a two-dimensional data structure, e.g., an array.

[0105] It is also possible to evaluate the distribution of the luminous points 352 on the detector 360 based on their intensities and to calculate with the help of a computer which function best corresponds to this distribution of the luminous points 352.

[0106] Another method 100 is used to calculate a prime factor of an integer positive

[0107] Number. For this purpose, an optical processing scheme 320 is used, which has a two-dimensional table in which prime numbers greater than 2 are arranged in ascending order along the horizontal direction in the first row, and the positive integers are listed vertically downwards in the first column on the left. The table is filled by multiplying the respective numbers in the first row by the respective numbers in the first column.

[0108] This table is displayed as a high-transparency image on a low-transparency background on the first transparent display device 200.

[0109] From a data input, i.e., a graphical representation of a number whose prime factors are to be calculated, a Fourier hologram 302 is calculated and displayed on the second transparent display device 201. In this case, the number 114 was used as the input.

[0110] When the arrangement 330, comprising the optical processing scheme 320 and the Fourier hologram 302, is illuminated, the brightest luminous point 352 appears on the detector 360 at the position where the number 114 is mapped onto the processing scheme 320 using the Fourier hologram 302. The detector 360 transmits the coordinates of the luminous points 352 or luminous point 352 to the further processing module 370. In this case, there is only one luminous point 352 with the coordinate value (8; 6), i.e., the ninth column counted from the upper left corner and the seventh row counted from the top. The number 114 is located at this position. If the input in the two-dimensional table were located at another position, another luminous point 352 would be visible on the detector 360.

[0111] If the processing module 370 is a computer, then the assigned values ​​of the first row of the two-dimensional table, i.e., the prime numbers, can be stored in an array X as follows: X[1]:=2; X[2]:=3; X[3]:=5; X[4]:=7; X[5]:=11; X[6]:=13; X[7]:=17;

[0112] X[8]:=19; X[9]:=23; etc. In the present embodiment, the coordinate value (8; 6), which is interpreted as the product of the eighth prime number in the array, i.e., 19, and the number 6, is assigned the value of the array X[8], which is equal to 19, as a prime factor to the coordinate (8; 6). Thus, method 100 returns the value 19 as output, which is a prime factor of the input. Another embodiment of method 100, in which an arithmetic operation is performed in two steps, can be experimentally realized as follows. Here, each step involves processing an arrangement of a processing scheme and a Fourier hologram.

[0113] The first processing scheme 320 is illuminated with coherent, parallel light by a laser 340. This coherent, parallel light can be generated, for example, using a polarizing filter (not shown), a gray wedge, and a pinhole aperture. A laser 340 (not shown) illuminates a first processing scheme 320 of the first step of the computational operation. Using a first lens 345, which is positioned at a distance of its focal length f downstream of the first processing scheme 320, the Fourier transform of the pattern of the first processing scheme 320 is generated at a distance of focal length f downstream of the first lens 345, where a first Fourier hologram 302 is located. The first Fourier hologram 302 was generated from a graphical representation of the given input data of the first step of the computational operation and filters the spatial frequencies of the graphical representation of the given input data of the first step.Following the first Fourier hologram 302, a second lens 346 is arranged at a distance of focal length f, which images the light filtered by the Fourier hologram 302 into an imaging plane of the first step. This image in the imaging plane serves as the second optical processing scheme 321 for the second step of the computational operation, which is fundamentally structured the same way as the first step.

[0114] In this process, the optical elements of the first step, i.e. the first processing scheme 320, the first lens 345, the first Fourier hologram 302 and the second lens 346, are arranged in a so-called 4f arrangement or 4f setup, which is known in the prior art.

[0115] With the help of a third lens 347, which is arranged at a distance of focal length f after the image in the imaging plane, the Fourier transform of the image in the imaging plane or of the second optical processing scheme 321 is created at a distance of focal length f after the third lens 347, where a second Fourier hologram 303 is arranged.

[0116] The second Fourier hologram 303 was generated using a graphical representation of the given input data for the second step of the computational operation and filters the spatial frequencies of the graphical representation of the given input data for the second step. Following the second Fourier hologram 303, a fourth lens 348 is arranged at a distance of focal length f. This lens focuses the light filtered by the second Fourier hologram 303 onto an imaging plane of the second step, where a detector 360 is located. The optical elements of the second step, i.e., the second processing scheme 321, the third lens 347, the second Fourier hologram 303, and the fourth lens 346, are arranged in a so-called 4f arrangement or 4f setup. With this experimental setup, the method 100, which performs a computational operation in two steps, can be implemented.For example, a NAND gate can be used in the first step and an OR gate in the second step.

[0117] In the experimental setup described above, there is no optical element at the point where the image is positioned in the imaging plane between the first and second steps. In a further embodiment, a processing module 370 can be arranged at this point, as shown in Figure 13. On a first side facing the second lens 346, the processing module 370 has a detector 371, which detects the light filtered by the Fourier hologram 302 and imaged by the second lens 346. The detection data can then be sent to a forwarding module 372, which is arranged on a rear side of the processing module 370 and has a matrix of laser diodes 373. The laser diodes 373 of the forwarding module 372 can be controlled such that the light pattern or image generated by the laser diodes 373 is identical to the light pattern or image detected by the detector 371.Image. Alternatively, it is also possible that the light pattern or image generated by the laser diodes 373 is structurally identical but has different wavelengths. If a different wavelength is used, it goes without saying that the optical elements in the subsequent step, e.g., the Fourier hologram, must be adapted to this wavelength. The relay module 372 can also be used if the intensity after a given step is too low, so that the detection accuracy in a subsequent step would suffer. In this respect, the relay module 372 can be compared to a repeater in telecommunications.

[0118] Another embodiment of method 100, in which two Fourier holograms 302, 303 are arranged one behind the other, can be experimentally realized as follows. Here, the optical elements, i.e., the first processing scheme 320, the first lens 345, the Fourier holograms 302, 303, and the second lens 346, are again arranged in a 4f configuration, with the first Fourier hologram 302 and the second Fourier hologram 303 positioned directly adjacent to each other midway between the first lens 345 and the second lens 346. The first processing scheme 320 can be implemented by a first transparent display device 200, the Fourier hologram 302 by a second transparent display device 201, and the Fourier hologram 303 by a third transparent display device 202.

[0119] Reference symbol list

[0120] 100 procedures

[0121] 110 Production of a holographic filter 300, in particular Fourier hologram 302

[0122] 120 Creating an optical processing scheme 320 based on the arithmetic operation

[0123] 130 Illuminating an arrangement 330, which has the processing scheme 320 and the holographic filter 300, with light 342 from a coherent light source 340, such that a distribution 350 of at least one luminous point 352 is created.

[0124] 140 Determining the issue date based on the distribution

[0125] 200 transparent display devices

[0126] 201 transparent display device

[0127] 202 transparent display device

[0128] 302 Fourier hologram

[0129] 303 Fourier hologram

[0130] 314 graphic representation

[0131] 320 Processing scheme

[0132] 321 Processing scheme

[0133] 330 Arrangement

[0134] 340 laser source

[0135] 342 Laser light

[0136] 343 Beam expander

[0137] 345 lens

[0138] 346 lens

[0139] 347 lens

[0140] 348 lens

[0141] 350 distribution

[0142] 352 Illuminated dot

[0143] 360 detector

[0144] 362 control computers

[0145] 370 Further processing module

[0146] 371 Detector

[0147] 372 Forwarding module

[0148] 373 Laser diode

Claims

Claims 1. Method (100) for performing a computational operation using holography, wherein the method (100) generates an output data from a given input data of a plurality of possible input data using the computational operation.

2. Method (100) according to claim 1, further comprising: Production (110) of a holographic filter, in particular a Fourier hologram (302, 303), based on a graphical representation (314) of the given input data; Creating (120) an optical processing scheme (320, 321) based on the computational operation; Illuminating (130) an arrangement (330) comprising the processing scheme (320, 321) and the holographic filter with light (342) from a coherent light source (340) such that a distribution (350) of at least one luminous point (352) is produced; and determining (140) the output date based on the distribution (350) of the at least one luminous point (352).

3. Method (100) according to claim 1, further comprising: Creating (110) an optical processing scheme (320, 321) based on a graphical representation (314) of the given input data; Production (120) of a holographic filter, in particular a Fourier hologram (302, 303) based on the computational operation; Illuminating (130) an arrangement (330) comprising the processing scheme (320, 321) and the holographic filter with light (342) from a coherent light source (340) such that a distribution (350) of at least one luminous spot (352) is produced; and determining (140) the output date based on the distribution (350) and / or intensity of the at least one luminous spot (352).

4. Method (100) according to claim 2 or 3, characterized in that the holographic filter, in particular the Fourier hologram (302, 303), is designed and set up to filter spatial frequencies of the graphical representation of the given input data or spatial frequencies of a plurality of graphical representations (314) of the possible input data.

5. Method (100) according to one of claims 2 to 4, characterized in that the optical processing scheme (320, 321) is a two-dimensional, transparent element (322) which has a plurality of graphic representations (314) of the possible input data or a graphic representation (314) of the predetermined input data, each of which is arranged at a predetermined position of the transparent element.

6. Method (100) according to the preceding claim, characterized in that the graphical representation (314) of the possible input data is two-dimensional and includes at least one character and / or at least one symbol.

7. Method (100) according to one of claims 2 to 6, characterized in that the output date is determined using an evaluation unit (360) for evaluating the output date, which is designed and configured to decide, on the basis of a position, positions and / or intensities of the distribution (350) of the at least one luminous point (352), what the value of the output date is.

8. Method (100) according to one of claims 5 to 7, characterized in that information is encoded in an intensity, a wavelength and / or a polarization of the light (342) of a graphic representation (314) of a possible input data.

9. Method (100) according to one of claims 2 to 8, characterized in that the computational operation comprises at least two steps, each of the at least two steps comprising the processing of an arrangement (330) of a processing scheme (320, 321) and a holographic filter, in particular a Fourier hologram (302, 303).

10. Method (100) according to one of claims 2 to 9, characterized in that the arrangement (330) comprises at least two holographic filters arranged one behind the other, in particular Fourier holograms (302, 303).

11. Method (100) according to one of claims 2 to 10, characterized in that the holographic filter, in particular the Fourier hologram (302, 303), and / or the optical processing scheme (320, 321) is implemented using at least one transparent display device (200, 201, 202) which is switchable.

12. Method (100) according to one of the preceding claims, characterized in that the arithmetic operation is a linear transformation, a matrix multiplication and / or an operation of differential calculus.

13. Method (100) according to one of the preceding claims, characterized in that the method (100) serves for data processing in which the specified input date is a first string and the output date is a second string which supplements the first string.

14. Method (100) according to any one of claims 2 to 13, further comprising: electronic, optical or electro-optical processing (370) and / or forwarding (370) of information contained in the distribution (350) of the at least one luminous point (352).

15. Transparent display device (200, 201, 202) for generating a two-dimensional transparent pattern for use as an optical processing scheme (320, 321) and / or as a holographic filter, in particular a Fourier hologram (302, 303), in a method (100) according to any one of claims 2 to 14.

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