Vortex electromagnetic wave modal purity estimation method and system based on main lobe ripple measurement, storage medium and electronic equipment

Abstract

The invention discloses a vortex electromagnetic wave modal purity estimation method and system based on main lobe ripple measurement, a storage medium and electronic equipment. The method comprises the following steps: measuring the electric field amplitude and phase of vortex electromagnetic waves in a free space; finding a vortex electromagnetic wave beam center through phase distribution; gradually determining the position of a vortex electromagnetic wave main lobe by taking the beam center as a circle center; calculating the average amplitude and the difference between the maximum amplitude and the minimum amplitude along the circumference where the main lobe is located, and calculating the relative main lobe ripple; and finally, calculating to obtain the modal purity of the vortex electromagnetic wave. According to the invention, the modal purity of the generated vortex electromagnetic wave can be accurately calculated, the subsequent collection and processing of the received data are facilitated, and the influence of the waste of the collected information caused by the modal aliasing can be effectively reduced.

Description

Technical Field

[0001] The present application relates to the field of signal processing technology, and in particular to a method, system, computer-readable storage medium and electronic device for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement. Background Art

[0002] Vortex electromagnetic waves carry orbital angular momentum, thus reflecting a new degree of freedom in addition to the traditional degrees of freedom such as intensity, phase, frequency, and polarization. In theory, infinite modes can be generated at any frequency. These modes are mutually orthogonal and propagate independently, forming an infinite-dimensional Hilbert space. This space, like the time domain and frequency domain, can theoretically modulate more information on it. However, in actual situations, the number of array elements that can be used is limited; according to the duality property of the Fourier transform, it can be known that l is equivalent to the "frequency" of the array element index n. If the UCA array factor is regarded as the result of the continuous Fourier transform of the spatial function, then the UCA array factor is the result of the discrete Fourier transform after uniform periodic sampling of the spatial function. According to the Fourier transform theory, uniform periodic sampling will lead to the periodic extension of the spectrum, and the period is the inverse of the sampling interval. Therefore, the uniformly distributed circular array is equivalent to uniform sampling of the spatial azimuth angle, which will lead to the periodic extension of the OAM spectrum in the OAM domain with a period of N. The periodic extension of the OAM spectrum produces OAM harmonics, which also means that pure vortex electromagnetic waves cannot be generated, so that other harmonics will be included in the generated electromagnetic waves, which will affect its application.

[0003] In summary, in order to reduce the impact of vortex electromagnetic wave modal aliasing on its application and prevent the inability to effectively receive and process the received electromagnetic waves, resulting in information waste, it is necessary to obtain the proportion of the fundamental wave and harmonics of the generated vortex electromagnetic waves in advance and calculate the modal purity of the generated vortex electromagnetic waves. Summary of the invention

[0004] The purpose of the present application is to provide a method, system, storage medium and electronic device for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement, so as to solve or alleviate the problems existing in the above-mentioned prior art.

[0005] In order to achieve the above objectives, this application provides the following technical solutions:

[0006] The present application provides a method for estimating the modal purity of a vortex electromagnetic wave based on main lobe ripple measurement, comprising: step S101, measuring the electric field amplitude and phase of the vortex electromagnetic wave in free space; step S102, finding the center of the vortex electromagnetic wave beam through phase distribution; step S103, determining the main lobe position of the vortex electromagnetic wave one by one with the beam center as the center of the circle; step S104, calculating the average amplitude and the maximum and minimum amplitude differences along the circumference of the main lobe and calculating the relative main lobe ripple; step S105, calculating the modal purity of the vortex electromagnetic wave according to the relative main lobe ripple obtained in step S104.

[0007] Preferably, in step S101, the electric field amplitude and phase of the vortex electromagnetic wave in free space are measured.

[0008] Preferably, in step S102, according to the electric field phase in free space measured in step S101, the electric field is decomposed into a spatial phase and a pure vortex phase, which is described by the following formula:

[0009]

[0010] Where r is the distance from the source point to the field point, l is the OAM modulus, is the azimuth of the field point with respect to the source point. The first term in the above equation is the spatial phase, and the second term is the pure vortex phase. Assuming that the phase section takes the beam center as the origin, a polar coordinate system is established, and the distance between the source and the phase section is R0, then any point on the section is The distance from the source can be expressed as

[0011]

[0012] It can be seen from the above formula that when ρ remains unchanged, r remains unchanged, so the spatial phase will not change. On concentric circles with the same polar diameter, the electric field phase is the same, that is, the equal phase lines are concentric circles with the beam center as the center.

[0013] Take any three adjacent equal phase lines, the radii of the three equal phase lines are recorded as ρ1, ρ2, ρ3, and the spacing between the equal phase lines is Δρ1, Δρ2, and their winding phase value is set to φ0. In the actual scene, R0>>ρ1, ρ2, ρ3, so the above formula can be simplified to

[0014]

[0015] So, for ρ2,

[0016]

[0017] From the definition of equal phase lines, we know that the change of kr caused by adjacent equal phase lines in the polar direction is 2π, so for ρ1 and ρ3 respectively

[0018]

[0019] According to the above formula, we can get

[0020]

[0021] It can be seen from the above formula that the spatial phase distribution of vortex electromagnetic waves can be used to estimate the radius of the three equal-phase lines by measuring the distance between any three equal-phase lines, thereby determining the center of the circle on the equal-phase line observation interface.

[0022] Preferably, in step S103, according to the center position measured in step S102 and the electric field amplitude of the free space vortex electromagnetic wave measured in step S101, the circumference is expanded outwards with the center of the beam as the center, and the circumference with the largest average electric field amplitude is found, which is the main lobe position of the vortex electromagnetic wave.

[0023] Preferably, in step S104, according to the main lobe position found in step S103, the average amplitude is calculated along the circumference of the main lobe and the maximum and minimum amplitudes are recorded, and then the difference between the maximum amplitude and the minimum amplitude is calculated and recorded as the main lobe ripple value. Then the relative main lobe ripple is defined as the ratio of the main lobe ripple value to the oscillation center amplitude as the relative main lobe ripple, and the symbol is used. express

[0024]

[0025] Where N is the number of array elements, J l (·) is the first kind of Bessel function, 2N|J l-N (kasinθ)| is the oscillation amplitude range, |J l (kasinθ)| is the amplitude of the oscillation center.

[0026] Preferably, in step S105, the ratio of the -1st harmonic to the fundamental wave is defined as the first harmonic ratio

[0027]

[0028] It can be seen that HFR is related to the relative main lobe ripple. Only two times the difference

[0029]

[0030] At the same time, modal purity is defined as

[0031]

[0032] Where m represents the m-th order harmonic.

[0033] According to the experiment, it can be concluded that the main harmonic component of the vortex electromagnetic wave generated by the uniform circular ring array is the -1 harmonic. Therefore, the relationship between the modal purity and the first harmonic ratio can be obtained as follows:

[0034]

[0035] pass With p l,N It can be seen that the modal purity of the generated vortex electromagnetic wave can be directly calculated by measuring the relative main lobe ripple.

[0036] An embodiment of the present application also provides a vortex electromagnetic wave modal purity estimation system based on main lobe ripple measurement, including: a vortex electromagnetic wave measurement unit, configured to receive vortex electromagnetic waves in free space and measure the amplitude and phase of the electric field; a center determination unit, configured to determine the center position of the vortex electromagnetic wave beam according to the phase of the received vortex electromagnetic wave; a main lobe calculation unit, configured to find the main lobe position of the vortex electromagnetic wave with the beam center as the center of the circle; a relative main lobe ripple calculation unit, configured to calculate the relative main lobe ripple of the collected vortex electromagnetic wave; and a modal purity calculation unit, configured to calculate the modal purity of the collected vortex electromagnetic wave.

[0037] An embodiment of the present application also provides a computer-readable storage medium on which a computer program is stored, wherein the program is any of the above-described methods for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement.

[0038] An embodiment of the present application also provides an electronic device, comprising: a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements any of the above-described methods for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement.

[0039] Beneficial effects:

[0040] In the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement provided by the present application, first, the electric field amplitude and phase of the vortex electromagnetic wave in free space are measured; the center of the vortex electromagnetic wave beam is found through phase distribution; then the main lobe position of the vortex electromagnetic wave is determined one by one with the beam center as the center of the circle; along the circumference of the main lobe, the average amplitude and the maximum and minimum amplitude differences are calculated and the relative main lobe ripple is calculated; finally, the modal purity of the vortex electromagnetic wave is calculated according to the relative main lobe ripple. Through the present invention, the modal purity of the generated vortex electromagnetic wave can be accurately calculated, which is conducive to the subsequent collection and processing of the received data, and can effectively reduce the impact of modal aliasing on the information waste caused by the collected information. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings constituting part of the present application are used to provide a further understanding of the present application. The exemplary embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. Among them:

[0042] Figure 1 A schematic diagram of a flow chart of a method for locating a single-track synthetic aperture radar interference source according to some embodiments of the present application;

[0043] Figure 2 is a phase line diagram of a spatial phase cross section according to the present application;

[0044] Figure 3 The modal purity according to the present application varies with the array element.

[0045] Figure 4 It is a unit configuration diagram according to the present application. DETAILED DESCRIPTION

[0046] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present application and does not limit the present application. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present application without departing from the scope or spirit of the present application. For example, a feature shown or described as a part of an embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desired that the present application includes such modifications and variations within the scope of the appended claims and their equivalents.

[0047] Exemplary Methods

[0048] like Figure 1 As shown, the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement includes:

[0049] Step S101, measuring the electric field amplitude and phase of the vortex electromagnetic wave in free space.

[0050] Step S102, finding the center of the vortex electromagnetic wave beam through phase distribution;

[0051] Specifically, according to the electric field phase in the free space measured in step S101, the electric field is decomposed into a spatial phase and a pure vortex phase, which is described by the following formula:

[0052]

[0053] Where r is the distance from the source point to the field point, l is the OAM modulus, is the azimuth of the field point with respect to the source point. The first term in the above equation is the spatial phase, and the second term is the pure vortex phase. Assuming that the phase section takes the beam center as the origin, a polar coordinate system is established, and the distance between the source and the phase section is R0, then any point on the section is The distance from the source can be expressed as

[0054]

[0055] It can be seen from the above formula that when ρ remains unchanged, r remains unchanged, so the spatial phase will not change. On concentric circles with the same polar diameter, the electric field phase is the same, that is, the equal phase lines are concentric circles with the beam center as the center.

[0056] like Figure 2 As shown, take any three adjacent equal phase lines, the radii of the three equal phase lines are recorded as ρ1, ρ2, ρ3, and the spacing between the equal phase lines is Δρ1, Δρ2, and their winding phase value is set to φ0. In the actual scenario, R0>>ρ1, ρ2, ρ3, so the above formula can be simplified to

[0057]

[0058] So, for ρ2,

[0059]

[0060] From the definition of equal phase lines, we know that the change of kr caused by adjacent equal phase lines in the polar direction is 2π, so for ρ1 and ρ3 respectively

[0061]

[0062] According to the above formula, we can get

[0063]

[0064] It can be seen from the above formula that the spatial phase distribution of vortex electromagnetic waves can be used to estimate the radius of the three equal-phase lines by measuring the distance between any three equal-phase lines, thereby determining the center of the circle on the equal-phase line observation interface.

[0065] Step S103, taking the beam center as the center of the circle, successively determining the main lobe position of the vortex electromagnetic wave;

[0066] Specifically, according to the circle center position measured in step S102 and the electric field amplitude of the free space vortex electromagnetic wave measured in step S101, the circumference is expanded outwards with the center of the beam as the circle center, and the circumference with the largest average electric field amplitude is found, which is the main lobe position of the vortex electromagnetic wave.

[0067] Step S104, calculating the average amplitude and the maximum and minimum amplitude differences along the circumference of the main lobe and calculating the relative main lobe ripple;

[0068] Specifically, according to the main lobe position found in step S103, the average amplitude is calculated along the circumference of the main lobe and the maximum and minimum amplitudes are recorded, and then the difference between the maximum amplitude and the minimum amplitude is calculated and recorded as the main lobe ripple value. Then the relative main lobe ripple is defined as the ratio of the main lobe ripple value to the oscillation center amplitude, and the symbol is used. express

[0069]

[0070] Where N is the number of array elements, J l (·) is the first kind of Bessel function, 2N|J l-N (kasinθ)| is the oscillation amplitude range, |J l (kasinθ)| is the amplitude of the oscillation center.

[0071] Step S105, calculating the modal purity of the vortex electromagnetic wave according to the relative main lobe ripple obtained in step S104;

[0072] Specifically, the ratio of the first harmonic to the fundamental wave is defined as the first harmonic ratio.

[0073]

[0074] It can be seen that HFR is related to the relative main lobe ripple. Only two times the difference

[0075]

[0076] At the same time, modal purity is defined as

[0077]

[0078] Where m represents the m-th order harmonic.

[0079] Depend on Figure 3 As described above, (a) is M = 10, a = λ. (b) is M = 1, a = λ; it can be seen that the main harmonic component of the vortex electromagnetic wave generated by the uniform circular ring array is the -1 harmonic. Therefore, it can be concluded that the relationship between modal purity and the first harmonic ratio is:

[0080]

[0081] pass With p l,N It can be seen that the modal purity of the generated vortex electromagnetic wave can be directly calculated by measuring the relative main lobe ripple.

[0082] Through the present invention, the modal purity of the generated vortex electromagnetic wave can be accurately calculated, which is beneficial to the subsequent collection and processing of the received data and can effectively reduce the impact of modal aliasing on the waste of collected information.

[0083] Exemplary Systems

[0084] Figure 4 The embodiment of the present application also provides a vortex electromagnetic wave modal purity estimation system based on main lobe ripple measurement, including: a vortex electromagnetic wave measurement unit, configured to receive vortex electromagnetic waves in free space and measure the amplitude and phase of the electric field; a center determination unit, configured to determine the center position of the vortex electromagnetic wave beam according to the phase of the received vortex electromagnetic wave; a main lobe calculation unit, configured to find the main lobe position of the vortex electromagnetic wave with the beam center as the center of the circle; a relative main lobe ripple calculation unit, configured to calculate the relative main lobe ripple of the collected vortex electromagnetic wave; and a modal purity calculation unit, configured to calculate the modal purity of the collected vortex electromagnetic wave.

[0085] The vortex electromagnetic wave modal purity estimation system based on main lobe ripple measurement provided in the embodiment of the present application can implement any of the above-mentioned vortex electromagnetic wave modal purity estimation method steps and processes based on main lobe ripple measurement, and achieve the same technical effect, which will not be repeated here one by one.

[0086] Exemplary Devices

[0087] The present application provides an electronic device, including a storage medium and a processor, the processor being suitable for executing various programs; and a memory being used to store multiple programs; it is characterized in that when the memory executes the program on the processor, it implements the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement as described in any one of claims 1-5.

[0088] Since the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement has been introduced in detail in the specific implementation method example, it will not be described in detail here.

[0089] The processor includes a central processing unit (CPU), a network processor (NP), etc. It can also be a digital signal processor, an application-specific integrated circuit, a readily available programmable gate array or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0090] The processor can be specifically configured as follows: the input system inputs the electric field amplitude and phase of the vortex electromagnetic wave measured in free space; according to the phase of the received vortex electromagnetic wave, the center position of the vortex electromagnetic wave beam is determined; the main lobe position of the vortex electromagnetic wave is found with the beam center as the center of the circle; the relative main lobe ripple of the collected vortex electromagnetic wave is calculated; and the modal purity of the collected vortex electromagnetic wave is calculated.

[0091] It should be pointed out that, according to the needs of implementation, the various components / steps described in the embodiments of the present application can be split into more components / steps, or two or more components / steps or partial operations of components / steps can be combined into new components / steps to achieve the purpose of the embodiments of the present application.

[0092] The above-mentioned method according to the embodiment of the present application can be implemented in hardware, firmware, or implemented as software or computer code that can be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk or magneto-optical disk), or implemented as a computer code originally stored in a remote recording medium or a non-temporary machine storage medium downloaded through a network and to be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor or programmable or dedicated hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code. When the software or computer code is accessed and executed by a computer, a processor or hardware, the single-track synthetic aperture radar interference source positioning method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0093] Those of ordinary skill in the art will appreciate that the units and method steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and constraints involved in the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the embodiments of the present application.

[0094] It should be noted that the various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device and system embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0095] The device and system embodiments described above are merely illustrative, wherein the units not shown as separate may or may not be physically separated, and the units not shown as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Those of ordinary skill in the art may understand and implement it without creative work.

[0096] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method and device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement, characterized in that: include: Step S101, measuring the electric field amplitude and phase of the vortex electromagnetic wave in free space; Step S102, finding the center of the vortex electromagnetic wave beam through the phase distribution measured in the previous step; Step S103, taking the beam center as the center of the circle, successively determining the main lobe position of the vortex electromagnetic wave; Step S104, calculating the average amplitude and the maximum and minimum amplitude differences along the circumference of the main lobe and calculating the relative main lobe ripple; Step S105, calculating the modal purity of the vortex electromagnetic wave according to the relative main lobe ripple obtained in step S104.

2. The method and device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement according to claim 1, characterized in that: The step S102 specifically includes the following steps: according to the electric field phase in the free space measured in step S101, the electric field is decomposed into a spatial phase and a pure vortex phase, which is described by the following formula: Where r is the distance from the source point to the field point, l is the OAM modulus, is the azimuth of the field point with respect to the source point, k is the wave number of the signal; exp(-jkr) is the spatial phase, is the pure vortex phase; assuming that the phase section takes the beam center as the origin, establish a polar coordinate system, and set the distance between the source and the phase section as R0, then any point on the section The distance from the source can be expressed as Where ρ is the distance from the center of the circle to any point in the field. From the above formula, we can see that when ρ is constant, r is constant, so the spatial phase will not change. On concentric circles with the same polar diameter, the electric field phase is the same, that is, the equal phase line is a concentric circle with the center of the beam as the center. Take any three adjacent equal phase lines, the radii of the three equal phase lines are recorded as ρ1, ρ2, ρ3, and the spacing between the equal phase lines is Δρ1, Δρ2, and their winding phase value is set to φ0; in the actual scene, R0>>ρ1, ρ2, ρ3, so the above formula can be simplified to So, for ρ2, From the definition of equal phase lines, we know that the change of kr caused by adjacent equal phase lines in the polar direction is 2π, so for ρ1 and ρ3 respectively Where n∈Z, λ is the wavelength, according to the above formula we can get It can be seen from the above formula that the spatial phase distribution of vortex electromagnetic waves can be used to estimate the radius of the three equal-phase lines by measuring the distance between any three equal-phase lines, thereby determining the center of the circle on the equal-phase line observation interface.

3. The method and device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement according to claim 1, characterized in that: The step S103 specifically includes the following steps: according to the center position measured in step S102 and the electric field amplitude of the free space vortex electromagnetic wave measured in step S101, the center of the beam is taken as the center of the circle; the circumference is expanded outward in sequence to find the circumference with the largest average electric field amplitude, which is the main lobe position of the vortex electromagnetic wave.

4. The method and device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement according to claim 1, characterized in that: The step S104 specifically includes the following steps: according to the main lobe position found in step S103, the average amplitude is calculated along the circumference of the main lobe and the maximum and minimum amplitudes are recorded, and then the difference between the maximum amplitude and the minimum amplitude is calculated, which is recorded as the main lobe ripple value; then the relative main lobe ripple is defined as the ratio of the main lobe ripple value to the oscillation center amplitude as the relative main lobe ripple, and the symbol is used. express Where N is the number of array elements, a is the radius of the antenna array that generates vortex electromagnetic waves, and J l (·) is the first-kind Bessel function of order l, 2N|J l-N (kasinθ)| is the oscillation amplitude range, |J l (kasinθ)| is the amplitude of the oscillation center.

5. The method and device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement according to claim 1, characterized in that: The step S105 specifically includes the following steps: defining the ratio of the -1st harmonic to the fundamental as the first harmonic ratio to measure the vortex mode purity; it can be seen that HFR is related to the relative main lobe ripple Only two times the difference At the same time, modal purity is defined as Where m represents the m-order harmonic; According to the experiment, it can be concluded that the main harmonic component of the vortex electromagnetic wave generated by the uniform circular ring array is the -1 harmonic; therefore, the relationship between the modal purity and the first harmonic ratio can be obtained as follows: pass With p l,N It can be seen that the modal purity of the generated vortex electromagnetic wave can be directly calculated by measuring the relative main lobe ripple.

6. A device for estimating modal purity of vortex electromagnetic waves based on main lobe ripple measurement, characterized in that: include: a vortex electromagnetic wave measuring unit configured to receive the vortex electromagnetic wave in free space and measure the amplitude and phase of the electric field; A center determination unit, configured to determine the center position of the vortex electromagnetic wave beam according to the phase of the received vortex electromagnetic wave; A main lobe calculation unit is configured to find the main lobe position of the vortex electromagnetic wave with the beam center as the center of the circle; A relative main lobe ripple calculation unit, configured to calculate and obtain the relative main lobe ripple of the collected vortex electromagnetic wave; The modal purity calculation unit is configured to calculate the modal purity of the collected vortex electromagnetic wave.

7. A storage medium storing a plurality of programs, characterized in that: The program application is loaded and executed by a processor to implement the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement as described in any one of claims 1-5.

8. An electronic device, comprising a storage medium and a processor; the processor is adapted to execute various programs; and the memory is adapted to store a plurality of programs; characterized in that: When the memory executes the program on the processor, the method for estimating the modal purity of vortex electromagnetic waves based on main lobe ripple measurement as described in any one of claims 1-5 is implemented.

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