A spatial frequency filtering based diffractive optical element beam shaping method

Abstract

The application relates to a kind of diffractive optical element beam shaping methods based on spatial frequency filtering, obtain incident light beam, based on the homogenization light beam of preset, obtain corresponding geometric analytical phase distribution;Adjust the homogenization light beam to rectangular flat-top light beam, the phase correction processing of obtained geometric analytical phase;Based on spatial frequency filtering method processing the geometric analytical phase after phase correction, get the light field regulation and control distribution requirement after processing, the light field regulation and control distribution requirement after processing has phase and amplitude regulation and control requirement simultaneously;Design diffractive optical element, make it realize the light field regulation and control distribution requirement required, and utilize the diffractive optical element to realize the incident light beam shaping as the rectangular flat-top light beam.The application can realize the light beam homogenization effect of high uniformity, edge sharp and high diffraction efficiency, and obtain wide application prospect in laser welding, photoetching and biomedical and other aspects.

Description

Technical Field

[0001] This invention relates to the technical field of optical elements, systems or instruments, and in particular to a beam shaping method for diffractive optical elements based on spatial frequency filtering. Background Technology

[0002] Laser beams typically exist as Gaussian beams, meaning their energy is distributed in a Gaussian pattern. This characteristic means that when lasers are used in fields such as laser processing, welding, engraving, drilling, nuclear physics, and biomedical engineering, the non-uniformity of energy can cause a sharp increase in localized temperature, interfering with the interaction between the laser and matter and affecting the application's effectiveness, thus limiting the widespread use of lasers. Therefore, in practical applications, to eliminate the adverse effects of this energy non-uniformity and meet specific needs, it is necessary to adjust the Gaussian beam into a flat-top beam with a more uniform energy distribution. A flat-top beam has a more uniform energy distribution, enabling more efficient energy utilization and reducing damage to the surrounding area.

[0003] Diffractive optical elements (DOEs) use two-dimensionally distributed diffraction units to precisely control the phase distribution of the laser wavefront, thereby changing the phase of the input beam to obtain the desired intensity distribution. Furthermore, they offer high energy efficiency, making DOEs an ideal choice for beam shaping.

[0004] Traditional methods primarily utilize optimization algorithms, such as the Gerchberg-Saxton (GS) algorithm, simulated annealing algorithm, and artificial intelligence algorithms, to iteratively optimize and obtain the phase distribution of the DOE based on the desired beam shaping results. However, the phase obtained through algorithmic iteration is usually discrete, and the phase distribution exhibits randomness and instability, leading to constructive or destructive interference at the output surface, which in turn introduces severe speckle noise.

[0005] To address the speckle noise problem, existing technologies primarily optimize the phase of the DOE (Design for Electron Emissions) from two aspects: firstly, by optimizing the algorithm, such as employing dual constraints (simultaneously constraining amplitude and phase) or modifying the iteration method of the optimization algorithm; while these methods can suppress some speckle, the phase distribution still exhibits a chaotic and disordered arrangement, and the homogenization effect of the homogenized beam is as follows: Figure 1 As shown in (a), the problem is not fundamentally solved. Another approach used in the prior art is to calculate an analytical solution for a specific shape. The phase of the obtained analytical solution is periodically arranged, which theoretically can produce a speckle-free output beam. However, this method only uses geometric assumptions and ignores diffraction effects. This will cause adjacent mapping points to overlap and interfere, ultimately resulting in an intensity lower than initially assumed. Furthermore, there are fewer overlapping mapping points near the edges compared to the middle, thus the intensity at the edges becomes greater, as shown in (a). Figure 1 As shown in (b); in some scenarios, the phase map is corrected by a constant less than 1, and the optimization result is as follows. Figure 1 As shown in (c), another problem this brings is that the transition area increases, which reduces the edge sharpness of the reshaped image and affects its practical application. Summary of the Invention

[0006] This invention solves the problems existing in the prior art and provides a beam shaping method for diffractive optical elements based on spatial frequency filtering.

[0007] The technical concept of this invention is to perform frequency domain filtering on the corrected analytical solution phase, perform Fourier transform on the phase and then filter it using a spatial filter, and then obtain a new phase distribution of the diffractive optical element through inverse Fourier transform; by adjusting the size and shape of the spatial filter, a beam homogenization effect with sharp edges and good uniformity can be obtained; since the light field obtained by this method is a complex amplitude distribution, which has both phase and amplitude information, the complex amplitude control can be further achieved by using a dual-phase method through a purely phase-encoded diffractive optical element.

[0008] The technical solution adopted in this invention is a beam shaping method for diffractive optical elements based on spatial frequency filtering, the method comprising the following steps:

[0009] S1 acquires the incident beam and obtains the corresponding geometric analytical phase distribution based on the preset homogenized beam;

[0010] S2 adjusts the homogenized beam into a rectangular flat-top beam and performs phase correction processing on the obtained geometric analytical phase;

[0011] S3 processes the geometric analytical phase after phase correction based on the spatial frequency filtering method to obtain the processed optical field modulation distribution requirements, which simultaneously have phase and amplitude modulation requirements.

[0012] S4 designs a diffractive optical element to achieve the required light field modulation distribution and uses this diffractive optical element to shape the incident beam into the rectangular flat-top beam.

[0013] Preferably, in S1, for any point (x, y) on the input plane of the incident beam, after passing through the original diffractive optical element, it corresponds to a point (x', y') on the output plane; the transmittance t(x, y) of the original diffractive optical element satisfies Where i is an imaginary number, λ is the wavelength, and f is the focal length.

[0014] Preferably, in S2, based on the incident beam and the beam waist of the preset rectangular flat-top beam, the homogenized beam is adjusted, and the transmittance of the corrected diffractive optical element is t(x,y)', satisfying...

[0015]

[0016] Among them, a 1x and a 1y For the beam waist radius corresponding to the incident beam, a 2x and a 2y The waist radius of the pre-defined rectangular flat-top beam is |k|<1; here, the waist radius refers to half of the beam's lateral width, that is, the position of the point where the light intensity drops to 1 / e2 of the central light intensity, away from the center.

[0017] Adjust k to obtain a homogenized beam with phase correction.

[0018] The adjustments here include, but are not limited to, using algorithm optimization, substituting different k values ​​to confirm the optimization results, and setting different k values ​​for different optimization objectives.

[0019] Preferably, in S3, the spatial frequency filtering method performs a Fourier transform on the phase-corrected geometric analytical phase, filters it through a spatial filter, and then obtains the processed transmittance function by inverse Fourier transform, which serves as a representation of the optical field control distribution requirements.

[0020] Preferably, in S4, a diffractive optical element is designed using a dual-phase encoding method, and the complex amplitude of the incident light field is controlled.

[0021] Preferably, for any two-dimensional complex amplitude light field U(x,y), any vector is decomposed into two vectors with equal modulus, resulting in U(x,y)=Bexp(iθ1(x,y))+Bexp(iθ2(x,y)), where B=A max / 2 is a constant, A max Let exp(iθ1(x,y)) be the maximum value of the amplitude A(x,y), and exp(iθ2(x,y)) be the phase terms.

[0022] By splicing θ1(x,y) and θ2(x,y) onto the same diffractive optical element using a specific method (such as the checkerboard method), the complex amplitude of the incident beam can be controlled.

[0023] Preferably, θ1(x,y) and θ2(x,y) are phase screen structure functions that satisfy the following conditions:

[0024]

[0025] in, For phase.

[0026] Preferably, the edge sharpness of the homogenized beam after being processed by the designed diffractive optical element is greater than that of the homogenized beam after phase correction.

[0027] Preferably, the root mean square error R MSE The method evaluates the degree to which the actual output intensity approximates the ideal output intensity, evaluates the energy conversion efficiency of the diffractive optical element by energy concentration η, and evaluates the smoothness of the beam in the signal region by non-uniformity σ.

[0028] Preferably, the diffractive optical element is optimized based on the evaluation of the shaped beam.

[0029] This invention relates to a beam shaping method using a diffractive optical element based on spatial frequency filtering. The method involves acquiring an incident beam, obtaining a corresponding geometrically resolute phase distribution based on a preset homogenized beam, adjusting the homogenized beam to a rectangular flat-top beam, and performing phase correction processing on the obtained geometrically resolute phase. The method further involves processing the phase-corrected geometrically resolute phase using a spatial frequency filtering method to obtain the processed optical field control distribution requirements, which simultaneously have phase and amplitude control requirements. Finally, a diffractive optical element is designed to achieve the required optical field control distribution requirements, and this element is used to shape the incident beam into the rectangular flat-top beam.

[0030] The beneficial effects of this invention are that it can achieve a beam homogenization effect with high uniformity, sharp edges and high diffraction efficiency, and has broad application prospects in laser welding, photolithography and biomedicine. Attached Figure Description

[0031] Figure 1 The diagram shows the effect of processing speckle noise in the prior art. (a) is the beam homogenization effect after homogenization by the algorithm optimization method, (b) is the beam homogenization effect obtained by the analytical solution method, and (c) is the beam homogenization effect after phase correction.

[0032] Figure 2 This is a flowchart of the method of the present invention;

[0033] Figure 3 This is a schematic diagram illustrating the effect of the method of combining the present invention;

[0034] Figure 4 The diagrams show the phase diagrams, output intensity distribution diagrams, and corresponding output intensity profiles of diffractive optical elements obtained based on different optimization methods. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to embodiments, but the scope of protection of the present invention is not limited thereto.

[0036] like Figure 2 As shown, this invention relates to a beam shaping method for diffractive optical elements based on spatial frequency filtering, the method comprising the following steps:

[0037] S1 acquires the incident beam and obtains the corresponding geometric analytical phase distribution based on the preset homogenized beam;

[0038] S2 adjusts the homogenized beam into a rectangular flat-top beam and performs phase correction processing on the obtained geometric analytical phase;

[0039] S3 processes the geometric analytical phase after phase correction based on the spatial frequency filtering method to obtain the processed optical field modulation distribution requirements, which simultaneously have phase and amplitude modulation requirements.

[0040] S4 designs diffractive optical elements, such as using the checkerboard method to achieve the required complex amplitude control, and finally obtains the phase distribution of the diffractive optical element. The diffractive optical element is then used to shape the incident beam into a preset rectangular flat-top beam.

[0041] like Figure 3 As shown, for the input laser beam, the present invention uses analytical methods to obtain the phase distribution in S1 and S2. Specifically, in order to obtain a homogenized beam and correct it into a rectangular flat-top beam, the output at this time is a beam with low edge sharpness. Then, in S3, the phase of the corrected analytical solution is processed by a spatial frequency filtering method to obtain the transmittance function of the complex amplitude distribution. In order to adapt to the pure phase modulation mode of DOE, a dual-phase encoding method is further used in S4 to realize the complex amplitude control of the incident light wave, so as to obtain a homogenized beam with high edge sharpness at the bottom of the target output.

[0042] The method will be further explained below with reference to the steps.

[0043] (1) Obtain the incident beam and, based on the preset homogenized beam, obtain the corresponding geometric analytical phase distribution;

[0044] For any point (x,y) on the input plane of the incident beam, it corresponds to a point (x',y') on the output plane after passing through the original diffractive optical element;

[0045] For a linear invariant system, the output function g(x',y') is the convolution of the input function o(x,y) and the system impulse response. The relationship between the output function and the input function is expressed by equation (1).

[0046] g(x',y')=∫∫ο(x,y)h(x'-x,y'-y)dxdy (1)

[0047] Where h(x'-x,y'-y) is the impulse response of the system on the output plane (x',y') to the point (x,y) on the input plane. In the 2f system, the output function is the Fourier transform of the input function, so the impulse response function of the system is given by equation (2).

[0048] h(x'-x,y'-y)=fft(δ(x'-x,y'-y)) (2)

[0049] Substituting equation (2) into equation (1) yields equation (3).

[0050]

[0051] Therefore, the system's transmittance function satisfies equation (4).

[0052]

[0053] Where i is an imaginary number, λ is the wavelength, and f is the focal length.

[0054] (2) Adjust the homogenized beam to a rectangular flat-top beam and perform phase correction processing on the obtained geometric analytical phase;

[0055] Based on the incident beam and the beam waist of the preset rectangular flat-top beam, the beam is homogenized.

[0056] In this invention, when the output surface is a rectangular flat-top beam, the transmittance distribution of the DOE satisfies equation (5).

[0057]

[0058] Where erf(t) is the error function, satisfying w is the waist radius of the incident Gaussian beam, a is the size of the output plane target beam, and L is the size of the DOE. Equation (5) is further approximated as equation (6).

[0059]

[0060] Where a1 and a2 are the beam waist radii of the input and output beams, respectively, and k is a constant; by optimizing the value of k, the transmittance function of the diffractive optical element with better uniformity (after phase correction) can be obtained.

[0061] (3) Based on the spatial frequency filtering method, the geometric analytical phase after phase correction is processed to obtain the processed optical field modulation distribution requirement, which has both phase and amplitude modulation requirements.

[0062] The spatial frequency filtering method performs a Fourier transform on the phase-corrected geometric analytical phase, filters it through a spatial filter, and then obtains the processed transmittance function through an inverse Fourier transform, which serves as a representation of the optical field control distribution requirements.

[0063] In this invention, considering the low edge sharpness of the homogenized beam after processing (2), a frequency domain filtering method is proposed, expressed as equation (7).

[0064] t'(x,y)=ifft(fft(t(x,y)')*T(x,y)) (7)

[0065] Where T(x,y) is the spatial filtering function.

[0066] The edge sharpness of the homogenized beam processed by the designed diffractive optical element will be greater than that of the homogenized beam after phase correction.

[0067] (4) Design diffractive optical elements to achieve the required light field control distribution, and use the diffractive optical elements to shape the incident beam into the rectangular flat-top beam.

[0068] In this invention, the transmittance function t'(x,y) after filtering has both amplitude and phase distribution, so it is necessary to achieve complex amplitude control. Here, a diffractive optical element is designed using a dual-phase encoding method to enable complex amplitude control of the homogenized beam after processing.

[0069] For any two-dimensional complex amplitude optical field U(x,y), Based on the principle of vector decomposition, any vector can be decomposed into two vectors with equal magnitudes, resulting in equation (8).

[0070] U(x,y)=Bexp(iθ1(x,y))+Bexp(iθ2(x,y)) (8)

[0071] Where B = A max / 2 is a constant, A max Let exp(iθ1(x,y)) be the maximum value of the amplitude A(x,y), and exp(iθ2(x,y)) be the phase terms.

[0072] By splicing θ1(x,y) and θ2(x,y) onto the same diffractive optical element, the complex amplitude of the incident beam can be controlled. θ1(x,y) and θ2(x,y) are phase screen structure functions that satisfy equations (9) and (10).

[0073]

[0074] in, For phase.

[0075] By using methods including but not limited to the checkerboard method, θ1(x,y) and θ2(x,y) can be spliced ​​onto the same DOE to achieve the control of the complex amplitude of the incident light field.

[0076] The method of the present invention uses the root mean square error R MSE The evaluation measures how closely the actual output intensity approximates the ideal output intensity, use energy concentration η to evaluate the energy conversion efficiency of the diffractive optical element, and use non-uniformity σ to evaluate the smoothness of the beam in the signal region.

[0077] Optimize diffractive optical elements based on the evaluation of the shaped beam.

[0078] Specifically, the root mean square error R MSE The energy concentration η and the non-uniformity σ satisfy equations (11), (12), and (13), respectively.

[0079]

[0080] Where S and N′ represent the signal region and non-signal region of the output beam, respectively, distinguished by the presence or absence of a light intensity signal; I is the average light intensity within the signal region; and I' is the output surface light intensity. t The target light intensity on the output surface.

[0081] To verify the advantages of this method, simulations were performed on the algorithm optimization method, the analytical solution method, and the DOE phase calculation method of this invention. The incident beam had a beam waist of 3mm, the outgoing beam was a square flat-top beam (beam waist 1.5mm*1.5mm), and the lens focal length was 300mm. The results are as follows: Figure 4 As shown in Table 1, the evaluation indicators for different DOE phase calculation methods are as follows.

[0082] Table 1 Evaluation Indicators for Different DOE Phase Calculation Methods

[0083] <![CDATA[R MSE ]]> η σ Algorithm optimization methods 79.14％ 89.15％ 23.45％ Analytical solution method 13.5％ 95.13％ 17.6％ Method of the present invention 3.79％ 97.18％ 3.56％

[0084] Obviously, the root mean square error R of this invention MSE The actual output intensity is significantly lower than the other two, meaning it approximates the ideal output intensity much better. The energy concentration η reaches over 97%, resulting in the highest energy conversion efficiency of the diffractive optical element, the lowest non-uniformity σ, and a high degree of smoothness and minimal fluctuation in the beam across the signal region. The method of this invention is significantly superior to existing technologies.

[0085] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0086] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0087] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0088] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0089] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0090] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A beam shaping method for diffractive optical elements based on spatial frequency filtering, characterized in that: The method includes the following steps: S1 acquires the incident beam and obtains the corresponding geometric analytical phase distribution based on the preset homogenized beam; S2 Adjust the homogenized beam into a rectangular flat-top beam and perform phase correction processing on the obtained geometric analytical phase; S3 processes the phase-corrected geometric analytical phase using a spatial frequency filtering method to obtain the processed optical field modulation distribution requirements, which simultaneously have phase and amplitude modulation requirements. The spatial frequency filtering method performs a Fourier transform on the phase-corrected geometric analytical phase, filters it through a spatial filter, and then uses an inverse Fourier transform to obtain the processed transmittance function, which serves as a representation of the optical field modulation distribution requirements. S4 uses a dual-phase coding method to design a diffractive optical element to achieve the required optical field control distribution. It also uses this diffractive optical element to shape the incident beam into the rectangular flat-top beam, thereby achieving complex amplitude control of the incident optical field. For any two-dimensional complex amplitude light field Decomposing any vector into two vectors with equal magnitude yields... ,in, It is a constant. Amplitude The maximum value, and For phase terms; and By splicing them onto the same diffractive optical element, the complex amplitude of the incident beam can be controlled. and For the phase screen structure function, satisfying, ， ， in, For phase.

2. The beam shaping method for diffractive optical elements based on spatial frequency filtering according to claim 1, characterized in that: In S1, for any point on the input plane of the incident beam The point that corresponds to the output plane after passing through the original diffraction optical element. The transmittance of the original diffractive optical element satisfy ,in, It is an imaginary number. For wavelength, It is the focal length.

3. The beam shaping method for diffractive optical elements based on spatial frequency filtering according to claim 2, characterized in that: In S2, based on the incident beam and the beam waist of the preset rectangular flat-top beam, the homogenized beam is adjusted, and the transmittance of the corrected diffractive optical element is [value missing]. ,satisfy ， in, and The beam waist radius corresponding to the incident beam. and The beam waist radius corresponding to the preset rectangular flat-top beam is |k| < 1; Adjust k to obtain a homogenized beam with phase correction.

4. The beam shaping method for diffractive optical elements based on spatial frequency filtering according to claim 1, characterized in that: The edge sharpness of the homogenized beam processed by the designed diffractive optical element is greater than that of the homogenized beam after phase correction.

5. The beam shaping method for diffractive optical elements based on spatial frequency filtering according to claim 1, characterized in that: With root mean square error The evaluation measures the degree of approximation between the actual output intensity and the ideal output intensity, using energy concentration. To evaluate the energy conversion efficiency of diffractive optical elements, in terms of inhomogeneity Evaluate the smoothness of the beam in the signal region.

6. The beam shaping method for diffractive optical elements based on spatial frequency filtering according to claim 5, characterized in that: Optimize diffractive optical elements based on the evaluation of the shaped beam.

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