A method for calculating a discrete multi-step phase hologram

Abstract

The application discloses a kind of discrete multi-step phase hologram calculation methods, comprising: the amplitude of target pattern is obtained and is used as constraint condition;Based on the constraint condition, in the inversion process of iterative angular spectrum algorithm, the numerical continuous phase of holographic plane is discretized into equal-interval step phase distribution, and the corresponding discrete multi-step phase hologram is generated in holographic plane;Discrete multi-step phase hologram is obtained by 3D printing technology.The application forms the phase difference of equal-interval step by discretizing the numerical continuous phase of holographic plane into equal-interval step phase distribution in the inversion process of iterative angular spectrum algorithm, to provide a new method for ultrasonic sound field regulation, expand the application of 3D printing precision in acoustic manufacturing, particle manipulation and other aspects, and promote the development of ultrasonic application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sound field regulation, and particularly relates to a calculation method of a discrete multi-step phase hologram. BACKGROUND

[0002] Sound field regulation plays an important role in many applications such as acoustic tweezers, particle manipulation, ultrasonic imaging and the like. Traditional sound field regulation can be divided into two kinds, one of which is an ultrasonic phased array, which realizes the regulation of an arbitrary sound field by realizing different amplitude and phase distributions through active driving of array units, but it is expensive and has low spatial information content.

[0003] The other method is to combine a phase hologram, which contains higher spatial information and is simple to make, but for finer sizes, it is more severely challenged in terms of 3D printing precision, and traditional continuous phase holograms are difficult to achieve. SUMMARY

[0004] In order to solve the above problems existing in the prior art, the application provides a calculation method of a discrete multi-step phase hologram. The technical problem to be solved by the application is solved by the following technical scheme:

[0005] The application provides a calculation method of a discrete multi-step phase hologram, comprising:

[0006] obtaining the amplitude of a target pattern and taking it as a constraint condition;

[0007] Based on the constraint condition, the numerical continuous phase of the holographic plane is discretized into an equal-interval step phase distribution in the inversion process of the iterative angular spectrum algorithm, and a corresponding discrete multi-step phase hologram is generated on the holographic plane.

[0008] The discrete multi-step phase hologram is obtained by 3D printing technology.

[0009] In an embodiment of the application, based on the constraint condition, the numerical continuous phase of the holographic plane is discretized into an equal-interval step phase distribution in the inversion process of the iterative angular spectrum algorithm, and a corresponding discrete multi-step phase hologram is generated on the holographic plane, comprising:

[0010] Based on the constraint condition, the iterative angular spectrum algorithm is used to perform a preset number of iterations between the holographic plane and the imaging plane, and the holographic plane contains a continuous phase of 0-2pi.

[0011] After discretizing the continuous phase of 0-2pi into an equal-interval step phase distribution according to a preset step number, a corresponding step phase hologram is formed on the holographic plane.

[0012] In an embodiment of the present application, the continuous phase of 0-2π is discretized into an equidistant stepped phase distribution according to the following formula:

[0013]

[0014] wherein N represents the preset number of steps, n represents the nth step in the preset number of steps, and n∈[1, N].

[0015] In an embodiment of the present application, the preset number of steps N = 2, 4 and 8.

[0016] After the continuous phase of 0-2π is discretized into an equidistant stepped phase distribution according to the preset number of steps, the step of forming a corresponding stepped phase hologram on the holographic plane comprises:

[0017] After the continuous phase of 0-2π is discretized into a two-step distribution, a four-step distribution and an eight-step distribution according to the preset number of steps N, the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram are formed on the holographic plane.

[0018] In an embodiment of the present application, before the step of obtaining a discrete multi-step phase hologram by 3D printing technology, further comprising:

[0019] The thickness of the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram is calculated respectively:

[0020]

[0021] wherein T0 represents the initial thickness of the phase hologram, k m represents the wave number in water, k h represents the wave number of the hologram material, and T(x, y) represents the corresponding thickness of the pixel at coordinate (x, y) in the two-step phase hologram, the four-step phase hologram or the eight-step phase hologram in the holographic plane.

[0022] In an embodiment of the present application, the step of obtaining a discrete multi-step phase hologram by 3D printing technology comprises:

[0023] Each pixel in the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram is equivalent to a one-dimensional transmission line to obtain the STL file corresponding to the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram.

[0024] Based on the stereolithography STL file and the thickness corresponding to the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram, the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram are printed by using 3D printing technology.

[0025] In one embodiment of the present invention, the hologram material is a photosensitive resin or a transparent resin.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] This invention provides a method for calculating discrete multi-step phase holograms. Based on the iterative angular spectrum algorithm, the numerically continuous phase of the holographic plane is discretized into equally spaced step phase distributions, thereby forming equally spaced step phase differences in the holographic plane. This provides a new method for ultrasonic sound field manipulation, expands the application of 3D printing precision in acoustic manufacturing, particle manipulation, and other fields, and promotes the development of ultrasonic applications.

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0029] Figure 1 This is a flowchart of a method for calculating discrete multi-step phase holograms provided in an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of an embodiment of the present invention, which discretizes the numerically continuous phase of a holographic plane into a multi-step phase hologram with equal intervals.

[0031] Figure 3 This is the target pattern provided in the embodiments of the present invention;

[0032] Figure 4 This is a method for generating, provided by the embodiments of the present invention. Figure 3 Discrete multi-step phase hologram of the sound field of the target pattern shown;

[0033] Figure 5 This is a method for generating, provided by the embodiments of the present invention. Figure 3 The thickness distribution map corresponding to the discrete multi-step phase hologram of the sound field of the target pattern shown;

[0034] Figure 6 This is provided by the embodiments of the present invention. Figure 3 The simulated sound pressure amplitude distribution of the target pattern is shown in the XY plane.

[0035] Figure 7 This is provided by the embodiments of the present invention. Figure 3 The XY plane sound pressure amplitude distribution diagram of the target pattern experimental test is shown.

[0036] Figure 8 This is provided by the embodiments of the present invention. Figure 4 The figure shows the step thickness distribution curve at the midpoint of the discrete multi-step phase hologram along the Y-axis. Detailed Implementation

[0037] The application will be further described in detail below with reference to specific embodiments, but the embodiments of the application are not limited thereto.

[0038] Embodiment one

[0039] Figure 1 is a flow chart of the calculation method of the discrete multi-step phase hologram provided by the embodiment of the application. As shown in Figure 1 the embodiment of the application provides a calculation method of a discrete multi-step phase hologram, comprising:

[0040] S1, obtaining the amplitude of the target pattern and taking it as a constraint condition;

[0041] S2, based on the constraint condition, discretizing the numerical continuous phase of the holographic plane into an equal-interval step phase distribution in the inversion process of the iterative angular spectrum algorithm, and generating a corresponding discrete multi-step phase hologram on the holographic plane;

[0042] S3, obtaining the discrete multi-step phase hologram through 3D printing technology.

[0043] Specifically, first, the target pattern is set, then the amplitude of the target pattern is taken as a constraint condition, and the iterative angular spectrum algorithm is used to iterate back and forth between the holographic plane and the imaging plane, and the phase information of the forward (reverse) propagation is retained, so that the numerical continuous phase distribution is obtained on the holographic plane through the inversion process, and the required acoustic field information is obtained on the imaging plane, wherein the acoustic field information contains amplitude information and phase information. Then, the continuous phase of the reverse propagation obtained by the first iteration is discretized into an equal-interval step phase distribution, and after 50 iterations, the final discrete multi-step phase hologram is generated on the holographic plane, and the discrete multi-step phase hologram can be further obtained by 3D printing technology.

[0044] It can be seen that the multi-step phase hologram optimized based on the iterative angular spectrum algorithm of the application can recover the information stored by the ultrasonic wave front, so as to reconstruct the acoustic pressure field diffracted by any target pattern, and the purpose of reconstructing a high-efficiency acoustic field image is achieved through the multi-step phase hologram, wherein the acoustic field image refers to the image of the imaging plane. This method expands the application of 3D printing precision in acoustic manufacturing, particle manipulation and the like under the premise of maintaining the image reconstruction quality, and is conducive to promoting the development of ultrasonic applications.

[0045] Optionally, in the step S2, based on the constraint condition, the numerical continuous phase of the holographic plane is discretized into an equal-interval step phase distribution in the inversion process of the iterative angular spectrum algorithm, and a corresponding discrete multi-step phase hologram is generated on the holographic plane, comprising:

[0046] S201, based on the constraint condition, using an iterative angular spectrum algorithm to perform a preset number of iterations between a holographic plane and an imaging plane, the holographic plane containing a continuous phase of 0-2π;

[0047] S202, according to a preset step number, the continuous phase of 0-2π is discretized into an equal-interval step phase distribution, and a corresponding step phase hologram is formed on the holographic plane.

[0048] Specifically, the multi-step phase hologram generated in the embodiment depends on the selected preset step number, wherein the preset step number N=2, 4 and 8, and according to the preset step number N, the continuous phase of 0-2π is discretized into a two-step distribution, a four-step distribution and an eight-step distribution, and a two-step phase hologram, a four-step phase hologram and an eight-step phase hologram can be formed on the holographic plane.

[0049] Exemplarily, the continuous phase of 0-2π can be discretized into an equal-interval step phase distribution according to the following formula:

[0050]

[0051] In the formula, N represents the preset step number, n represents the nth step in the preset step number, n∈[1,N], and the value of φ is

[0052] Optionally, before the step of obtaining the discrete multi-step phase hologram by the 3D printing technology, the method further comprises:

[0053] The thicknesses of the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram are calculated respectively:

[0054]

[0055] In the formula, T0 represents the initial thickness of the phase hologram, k m represents the wave number in water, k h represents the wave number of the hologram material, and T(x,y) represents the corresponding thickness of the pixel at the coordinate (x,y) in the two-step phase hologram, the four-step phase hologram or the eight-step phase hologram in the holographic plane.

[0056] Optionally, in step S3, the step of obtaining the discrete multi-step phase hologram by the 3D printing technology comprises:

[0057] S301, each pixel in the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram is equivalent to a one-dimensional transmission line, and the STL files corresponding to the two-step phase hologram, the four-step phase hologram and the eight-step phase hologram are obtained;

[0058] S302, based on the STL files and thicknesses corresponding to the second-order phase hologram, the fourth-order phase hologram and the eighth-order phase hologram, printing the second-order phase hologram, the fourth-order phase hologram and the eighth-order phase hologram by using the 3D printing technology.

[0059] It should be noted that the hologram material can be selectively used photosensitive resin, transparent resin or other transparent materials.

[0060] Example two

[0061] Figure 2 is a schematic diagram provided by the embodiment of the present application for discretizing the continuous phase of the holographic plane into multi-step phase holograms with equal intervals. Exemplarily, in the process of generating the discrete multi-step phase hologram, first, the amplitude of the target pattern is given as a constraint condition, in order to facilitate calculation, the transducer plane amplitude is set to an ideal value of 1, and it is assumed that the transducer output phase is flat, so the initial phase of the phase hologram before iteration calculation can be set to 0; then, the amplitude of the image plane is replaced with the target value, and the forward propagation phase information is retained; the continuous phase of 0-2π obtained by the first iteration is divided into an equal-interval step phase distribution; finally, 50 iterations are performed back and forth between the holographic plane and the imaging plane, and the discrete phase of the second-order distribution, the fourth-order distribution and the eighth-order distribution are finally obtained in the holographic plane, as shown in Figure 2 .

[0062] Figure 3 is a target pattern provided by the embodiment of the present application, Figure 4 is a discrete multi-step phase hologram provided by the embodiment of the present application for generating the target pattern sound field shown in Figure 3 . Further, referring to Figure 3 , the target pattern "XDU" is taken as a constraint condition, and the discretization of the continuous phase is performed according to the above steps based on the iterative angular spectrum algorithm, and the preset step number N = 2, 4 and 8, then the second-order, fourth-order and eighth-order phase holograms as shown in Figure 4 can be obtained.

[0063] Figure 5 is a thickness distribution diagram corresponding to the discrete multi-step phase hologram for generating the target pattern sound field shown in Figure 3 . As shown in Figure 5 , the relationship between the discrete multi-step phase and the thickness is calculated by the embodiment, and thereby obtaining the thickness distribution of the discrete second-order, fourth-order and eighth-order phase holograms. In order to simply calculate and manufacture the second-order, fourth-order and eighth-order phase holograms, each pixel of these discrete multi-step phase holograms can be equivalent to one-dimensional transmission, thereby generating the STL files corresponding to the second-order, fourth-order and eighth-order phase holograms, and obtaining by using the 3D printing technology.

[0064] Of course, the step distribution can also be derived using other phase distribution formulas, and this embodiment does not limit this.

[0065] Figure 6 This is provided by the embodiments of the present invention. Figure 3 The image shows the XY plane sound pressure amplitude distribution from the simulation calculation of the target pattern. Please refer to [link / reference]. Figure 6 In the process of calculating discrete multi-step phase holograms based on the iterative angular spectrum method, after 50 iterations, the information stored in the wavefront can be recovered when the wavefront propagates forward from the holographic plane to the imaging plane, thereby obtaining the complex sound field of the target pattern "XDU" with different reconstructed image quality on the imaging plane, including the sound field information generated by second-order holograms, fourth-order holograms and eighth-order holograms.

[0066] As can be seen, after discretizing the continuous phase into equally spaced multi-step phase holograms, different steps correspond to different phase difference distributions, thus producing high-fidelity complex sound fields for target patterns with different effects. Based on the relationship between the sound pressure corresponding to the "XDU" region of the target image and the sound pressure distribution of the entire target image region, the image reconstruction quality generated by second-order, fourth-order, and eighth-order phases can be calculated, thereby measuring the sound field quality generated by different steps.

[0067] Furthermore, by combining an ultrasonic piezoelectric transducer, the excitation is a 3MHz 10-cycle sine wave, and the sound propagation medium is water. Figure 7 This is provided by the embodiments of the present invention. Figure 3 The XY plane sound pressure amplitude distribution diagram of the target pattern experimental test is shown in the figure. Figure 7 As shown, the sound field generated on the imaging plane by a second-order phase hologram lacks detail and has a messy distribution, while the sound field generated on the imaging plane by fourth-order and higher-order holograms has high fidelity. Figure 8 This is provided by the embodiments of the present invention. Figure 4 The diagram shows the step thickness distribution curve at the midpoint along the Y-axis of the discrete multi-step phase hologram, thus revealing the step thickness variations and values ​​of the second-, fourth-, and eighth-order phase holograms.

[0068] It should be noted that transparent materials can be used to 3D print the discrete multi-step phase hologram generated in this embodiment, which is low-cost and contains a lot of spatial information. In the above embodiments of the invention, an ultrasonic transducer is used to generate a corresponding XDU complex sound field. The thickness of the ultrasonic transducer is determined by its designed operating frequency. For example, the piezoelectric material can be PZT-4, with a thickness of 750 μm and a diameter of 50 mm, and the designed operating frequency is 3 MHz.

[0069] In addition, the size of the discrete multi-step phase hologram depends on Figure 5 To determine, Figure 5 Depend on The thickness parameters of the discrete second-order phase hologram are approximately 0.933 mm and 1.600 mm, the thickness parameters of the discrete fourth-order phase hologram are approximately 0.600 mm, 0.933 mm, 1.267 mm and 1.600 mm, and the thickness parameters of the discrete eighth-order phase hologram are approximately 0.433 mm, 0.6 mm, 0.767 mm, 0.933 mm, 1.100 mm, 1.266 mm, 1.433 mm and 1.600 mm.

[0070] In the calculation method of the discrete multi-step phase hologram provided by the application, the discrete multi-step phase hologram can generate a high-fidelity complex sound field underwater, and under the premise that the 3D printing precision is limited, a flexible holographic imaging of a complex sound field can be realized, which is different from the traditional continuous phase hologram, and has important applications in acoustic manufacturing, particle manipulation, and high-frequency complex sound field, etc.

[0071] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the application. In the specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the specification.

[0072] Although the application is described herein in conjunction with various embodiments, other variations of the disclosed embodiments can be understood and implemented by those skilled in the art with reference to the drawings, disclosure, and appended claims in implementing the claimed application.

[0073] The above is a further detailed description of the application in conjunction with specific preferred embodiments, and the specific implementation of the application cannot be limited to these descriptions. For those skilled in the art, without departing from the concept of the application, a number of simple deductions or substitutions can be made, which should be considered as falling within the scope of protection of the application.

Claims

1. A method for calculating discrete multi-step phase holograms, characterized in that, include: Obtain the amplitude of the target pattern and use it as a constraint. Based on the aforementioned constraints, during the inversion process of the iterative angular spectrum algorithm, the numerically continuous phase of the holographic plane is discretized into an equally spaced stepped phase distribution, and a corresponding discrete multi-step phase hologram is generated on the holographic plane. The discrete multi-step phase hologram was obtained using 3D printing technology. Based on the aforementioned constraints, the steps of discretizing the numerically continuous phase of the holographic plane into equally spaced stepped phase distributions and generating corresponding discrete multi-step phase holograms on the holographic plane during the inversion process of the iterative angular spectrum algorithm include: based on the aforementioned constraints, performing a preset number of iterations between the holographic plane and the imaging plane using the iterative angular spectrum algorithm, wherein the holographic plane contains continuous phases from 0 to 2π; and discretizing the continuous phases from 0 to 2π into equally spaced stepped phase distributions according to the preset number of steps, thereby forming a phase hologram with corresponding steps on the holographic plane. Preset number of steps N =2, 4, and 8; prior to the step of obtaining discrete multi-step phase holograms using 3D printing technology, the following steps are also included: Calculate the thickness of the second-order, fourth-order, and eighth-order phase holograms respectively: ； In the formula, This indicates the initial thickness of the phase hologram. Represents the wave number in water. The wavenumber of the hologram material is represented. Represents coordinates in the holographic plane The thickness of the pixel at that location in a second-order phase hologram, a fourth-order phase hologram, or an eighth-order phase hologram; The steps for obtaining discrete multi-step phase holograms using 3D printing technology include: equating each pixel in the second-order, fourth-order, and eighth-order phase holograms to a one-dimensional transmission line, respectively, to obtain the STL files corresponding to the second-order, fourth-order, and eighth-order phase holograms; and based on the stereolithography STL files and thicknesses corresponding to the second-order, fourth-order, and eighth-order phase holograms, printing the second-order, fourth-order, and eighth-order phase holograms using 3D printing technology.

2. The method for calculating discrete multi-step phase holograms according to claim 1, characterized in that, The continuous phase from 0 to 2π is discretized into an equally spaced stepped phase distribution according to the following formula: ； In the formula, Indicates the preset number of steps. Indicates the number of steps in the preset ladder. Step, .

3. The method for calculating discrete multi-step phase holograms according to claim 2, characterized in that, The step of discretizing the continuous phase from 0 to 2π into an equally spaced stepped phase distribution according to a preset step number, and then forming a phase hologram of the corresponding step on the holographic plane, includes: According to the preset number of steps N After discretizing the continuous phase from 0 to 2π into second-order, fourth-order, and eighth-order distributions, second-order phase holograms, fourth-order phase holograms, and eighth-order phase holograms are formed on the holographic plane.

4. The method for calculating discrete multi-step phase holograms according to claim 1, characterized in that, The hologram material is photosensitive resin or transparent resin.

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