Diffractive optical element beam shaping method based on spatial frequency filtering

Abstract

The invention relates to a diffractive optical element beam shaping method based on spatial frequency filtering, and the method comprises the steps: obtaining an incident beam, and obtaining corresponding geometric analysis phase distribution based on a preset homogenized beam; the homogenized light beam is adjusted to be a rectangular flat-topped light beam, and phase correction processing is carried out on the obtained geometric analysis phase; the geometric analysis phase after phase correction is processed based on a spatial frequency filtering method, a processed light field regulation and control distribution requirement is obtained, and the processed light field regulation and control distribution requirement has phase and amplitude regulation and control requirements at the same time; and designing a diffractive optical element, so that the diffractive optical element meets the required light field regulation and distribution requirements, and shaping an incident light beam into the rectangular flat-topped light beam by using the diffractive optical element. According to the invention, the light beam homogenization effect with high uniformity, sharp edge and high diffraction efficiency can be realized, and wide application prospects are obtained in the aspects of laser welding, photoetching, biomedicine and the like.

Description

Technical Field

[0001] The invention relates to the technical field of optical elements, systems or instruments, and in particular to a diffraction optical element beam shaping method based on spatial frequency filtering. Background Art

[0002] Laser beams usually exist in the form of Gaussian beams, that is, they show Gaussian energy distribution. This characteristic causes the local temperature to rise sharply due to the non-uniformity of energy when they are used in laser processing, welding, engraving, drilling, nuclear physics applications, and biomedical engineering, thereby interfering with the interaction between laser and matter, affecting the application effect, and limiting the widespread application of lasers. Therefore, in practical applications, in order to eliminate the adverse effects caused by uneven energy according to specific needs, it is necessary to adjust the Gaussian beam to a flat-top beam with uniform energy distribution. The energy distribution of a flat-top beam is more uniform, which can use energy more effectively and reduce damage to the surrounding area.

[0003] Diffractive Optical Element (DOE) can finely control the phase distribution of laser wavefront through two-dimensionally distributed diffraction units, change the phase of the input light beam, obtain the required light intensity distribution, and have high energy utilization rate. Therefore, using DOE to shape the light beam is an ideal choice.

[0004] Traditional methods mainly use optimization algorithms, such as the Gerchberg Saxton (GS) algorithm, simulated annealing algorithm, and artificial intelligence algorithm, to optimize and iterate the phase distribution of the DOE according to the required beam shaping results. However, the phase obtained by algorithm iteration is usually discrete, and the phase distribution is random and unstable, resulting in constructive or destructive interference on the output surface, which in turn brings serious speckle noise.

[0005] In order to solve the problem of speckle noise, the existing technology mainly optimizes the phase of DOE from two aspects. One is to optimize the algorithm, such as using dual constraints, that is, constraining the amplitude and phase at the same time, or modifying the iteration method of the optimization algorithm. Although these methods can suppress some speckles, the phase distribution still presents a 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 method used in the prior art is to obtain an analytical solution of a specific shape by calculation. The phase of the analytical solution obtained is arranged periodically, and theoretically a speckle-free output beam can be obtained. However, this method only uses geometric assumptions and ignores the diffraction effect, which will cause adjacent mapping points to overlap and interfere, ultimately resulting in an intensity lower than the initially assumed intensity. The number of overlapping mapping points near the edge is less than that in the middle, and the intensity at the edge becomes greater, as shown in FIG. 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 caused by this 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] The invention solves the problems existing in the prior art and provides a diffraction optical element beam shaping method based on spatial frequency filtering.

[0007] The technical concept of the present invention is to perform frequency domain filtering on the phase of the corrected analytical solution, 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 light beam homogenization effect with sharp edges and good uniformity can be obtained; since the light field obtained after optimization by this method is a complex amplitude distribution and has both phase and amplitude information, the dual-phase method is further used to realize complex amplitude control through a purely phase-encoded diffractive optical element.

[0008] The technical solution adopted by the present invention is a diffractive optical element beam shaping method based on spatial frequency filtering, the method comprising the following steps:

[0009] S1 obtains the incident light beam and obtains the corresponding geometric analytical phase distribution based on the preset homogenized light 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 a spatial frequency filtering method to obtain a processed light field control distribution requirement, wherein the processed light field control distribution requirement has both phase and amplitude control requirements;

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

[0013] Preferably, in S1, for any point (x, y) of the incident light beam on the input plane, it corresponds to a point (x', y') on the output plane after passing through the original diffractive optical element; 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, the homogenized beam is adjusted based on the incident beam and the beam waist of the preset rectangular flat-top beam, and the transmittance of the modified diffractive optical element is t(x, y)', satisfying

[0015]

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

[0017] Adjust k to obtain a phase-corrected homogenized beam.

[0018] The adjustment here includes but is not limited to utilizing algorithm optimization, substituting different k values ​​into confirming the optimization results, and setting different k values ​​for different optimization goals.

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

[0020] Preferably, in S4, a dual-phase encoding method is used to design a diffractive optical element, and complex amplitude control of the incident light field is achieved.

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

[0022] θ1(x, y) and θ2(x, y) are spliced ​​on the same diffractive optical element according to a specific method (such as the checkerboard method) to achieve complex amplitude control of the incident light beam.

[0023] Preferably, θ1(x, y) and θ2(x, y) are phase screen structure functions, satisfying,

[0024]

[0025] in, For phase.

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

[0027] Preferably, the root mean square error R MSE The degree of closeness between the actual output intensity and the ideal output intensity is evaluated, the energy conversion efficiency of the diffractive optical element is evaluated by the energy concentration η, and the smoothness of the light beam in the signal area is evaluated by the non-uniformity σ.

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

[0029] The present invention relates to a diffractive optical element beam shaping method based on spatial frequency filtering, which comprises the following steps: obtaining an incident light beam, and obtaining a corresponding geometric analytical phase distribution based on a preset homogenized light beam; adjusting the homogenized light beam to be a rectangular flat-top light beam, and performing phase correction processing on the obtained geometric analytical phase; processing the phase-corrected geometric analytical phase based on a spatial frequency filtering method to obtain a processed light field control distribution requirement, wherein the processed light field control distribution requirement has both phase and amplitude control requirements; designing a diffractive optical element to realize the required light field control distribution requirement, and utilizing the diffractive optical element to realize shaping of the incident light beam into the rectangular flat-top light beam.

[0030] The beneficial effect of the present invention is 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, biomedicine and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Schematic diagram of the effect after processing speckle noise in the prior art, wherein (a) is a diagram of the light beam homogenization effect after homogenization using the algorithm optimization method, (b) is a diagram of the light beam homogenization effect obtained using the analytical solution method, and (c) is a diagram of the light beam homogenization effect after phase correction;

[0032] Figure 2 is a flow chart of the method of the present invention;

[0033] Figure 3 It is a schematic diagram of the effect of the combination method of the present invention;

[0034] Figure 4 Phase diagrams, output light intensity distribution diagrams, and corresponding output light intensity profiles of diffractive optical elements obtained based on different optimization methods. DETAILED DESCRIPTION

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

[0036] like Figure 2 The present invention relates to a diffractive optical element beam shaping method based on spatial frequency filtering, the method comprising the following steps:

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

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

[0039] S3 processes the geometric analytical phase after phase correction based on a spatial frequency filtering method to obtain a processed light field control distribution requirement, wherein the processed light field control distribution requirement has both phase and amplitude control requirements;

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

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

[0042] The following is a further explanation of the method in combination with the steps.

[0043] (1) obtaining an incident light beam and obtaining a corresponding geometrically resolved phase distribution based on a preset homogenized light beam;

[0044] For any point (x, y) of the incident light beam on the input plane, 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 ο(x,y) and the system impulse response. The relationship between the output function and the input function is expressed as formula (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 point (x', y') on the output plane of the system to the point (x, y) on the input plane. In a 2f system, the output function is the Fourier transform of the input function. Therefore, 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 formula (2) into formula (1) yields formula (3),

[0050]

[0051] Therefore, the transmittance function of the system satisfies equation (4):

[0052]

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

[0054] (2) adjusting the homogenized beam into a rectangular flat-top beam, and performing phase correction processing on the obtained geometric analytical phase;

[0055] Adjusting the homogenized beam based on the incident beam and the beam waist of a preset rectangular flat-top beam;

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

[0057]

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

[0059]

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

[0061] (3) processing the phase-corrected geometric analytical phase based on a spatial frequency filtering method to obtain a processed light field control distribution requirement, wherein the processed light field control distribution requirement has both phase and amplitude control requirements;

[0062] The spatial frequency filtering method performs Fourier transformation on the geometric analytical phase after phase correction, filters it through a spatial filter, and then obtains a processed transmittance function by inverse Fourier transformation as a representation of the light field control distribution demand.

[0063] In the present invention, considering that the edge sharpness of the homogenized light beam after processing (2) is low, a frequency domain filtering method is proposed, which is expressed as formula (7):

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

[0065] Among them, T(x,y) is the spatial filter function.

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

[0067] (4) designing a diffractive optical element to achieve the required light field control distribution requirements, and using the diffractive optical element to shape the incident light beam into the rectangular flat-top beam;

[0068] In the present invention, the transmittance function t'(x, y) after filtering has both amplitude and phase distribution, so it is necessary to realize complex amplitude control. Here, a diffractive optical element is designed by a dual-phase encoding method to perform complex amplitude control on the processed homogenized light beam.

[0069] For any two-dimensional complex amplitude light field U(x,y), According to the principle of vector decomposition, any vector can be decomposed into two vectors with equal magnitudes, and equation (8) is obtained:

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

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

[0072] Splice θ1(x, y) and θ2(x, y) on the same diffractive optical element to achieve complex amplitude control of the incident light beam. 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 ​​on the same DOE to achieve the control of the complex amplitude of the incident light field.

[0076] The method of the present invention is based on the root mean square error R MSE The degree of closeness between the actual output intensity and the ideal output intensity is evaluated, the energy conversion efficiency of the diffractive optical element is evaluated by the energy concentration η, and the smoothness of the light beam in the signal area is evaluated by the non-uniformity σ.

[0077] The diffractive optical element is optimized based on the evaluation of the shaped beam.

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

[0079]

[0080] Among them, S and N' respectively represent the output beam signal area and non-signal area, which are distinguished by whether there is a light intensity signal, I is the average light intensity in the signal area, I' is the output surface light, I t is the target light intensity on the output surface.

[0081] In order to verify the advantages of this method, the algorithm optimization method, the analytical solution method, and the DOE phase calculation method of the method of the present invention are simulated, where the waist of the incident light beam is 3 mm, the output light is a square flat-top beam (waist is 1.5 mm*1.5 mm), and the focal length of the lens is 300 mm. The results are as follows: Figure 4 As shown in Table 1, the evaluation indicators of different DOE phase calculation methods are shown.

[0082] Table 1 Evaluation indicators of 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 MSE It is much smaller than the other two, that is, the actual output intensity is closer to the ideal output intensity, the energy concentration η reaches more than 97%, the energy conversion efficiency of the diffractive optical element is the highest, the inhomogeneity σ is the lowest, the signal area light beam is smoother and has less fluctuation. The method of the present invention is significantly superior to the prior art.

[0085] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented 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] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0087] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0088] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0089] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0090] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A diffractive optical element beam shaping method based on spatial frequency filtering, characterized in that: The method comprises the following steps: S1 obtains the incident light beam and obtains the corresponding geometric analytical phase distribution based on the preset homogenized light beam; S2 adjusts the homogenized beam into a rectangular flat-top beam, and performs phase correction processing on the obtained geometric analytical phase; S3 processes the geometric analytical phase after phase correction based on a spatial frequency filtering method to obtain a processed light field control distribution requirement, wherein the processed light field control distribution requirement has both phase and amplitude control requirements; S4 designs a diffractive optical element to achieve the required light field control distribution requirements, and uses the diffractive optical element to shape the incident light beam into the rectangular flat-top beam.

2. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 1, characterized in that: In S1, for any point (x, y) of the incident light beam on the input plane, it corresponds to a point (x', y') on the output plane after passing through the original diffractive optical element; 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.

3. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 2, characterized in that: In S2, the homogenized beam is adjusted based on the incident beam and the beam waist of the preset rectangular flat-top beam. The transmittance of the modified diffractive optical element is t(x,y)', which satisfies Among them, a 1x and a 1y Corresponding to the incident beam waist radius, a 2x and a 2y Corresponding to the waist radius of the preset rectangular flat-top beam, |k|<1; Adjust k to obtain a phase-corrected homogenized beam.

4. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 1, characterized in that: In S3, the spatial frequency filtering method performs Fourier transformation on the geometric analytical phase after phase correction, filters it through a spatial filter, and then obtains the processed transmittance function by inverse Fourier transformation as a representation of the light field control distribution requirements.

5. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 1, characterized in that: In S4, a dual-phase encoding method is used to design a diffractive optical element, and complex amplitude control of the incident light field is achieved.

6. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 5, characterized in that: For any two-dimensional complex amplitude light field U(x,y), decompose any vector into two vectors with equal modulus, and obtain U(x,y)=Bexp(iθ1(x,y))+Bexp(iθ2(x,y)), where B=A max / 2 is a constant, A max is the maximum value of the amplitude A(x,y), exp(iθ1(x,y)) and exp(iθ2(x,y)) are phase terms; θ1(x, y) and θ2(x, y) are spliced ​​on the same diffractive optical element to achieve complex amplitude control of the incident light beam.

7. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 6, characterized in that: θ1(x,y) and θ2(x,y) are phase screen structure functions, satisfying, in, For phase.

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

9. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 1, characterized in that: The root mean square error R MSE The degree of closeness between the actual output intensity and the ideal output intensity is evaluated, the energy conversion efficiency of the diffractive optical element is evaluated by the energy concentration η, and the smoothness of the light beam in the signal area is evaluated by the non-uniformity σ.

10. The method for beam shaping of a diffractive optical element based on spatial frequency filtering according to claim 9, characterized in that: The diffractive optical element is optimized based on the evaluation of the shaped beam.

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