High-quality laser patterning method based on weighted feedback complex amplitude constraint
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-01-10
- Publication Date
- 2026-08-14
AI Technical Summary
[0004]本发明针对上述相位全息空间整形光场中斑点噪声破坏加工结构完整性的问题，提出了一种基于加权反馈复振幅约束的高质量激光图案化加工方法
[0036]1.本发明通过对加工图案进行复振幅约束(包括振幅和相位信息)，保证了全息光场内相位匹配关系，避免了斑点噪声的产生，使得相位全息飞秒激光图案化加工结构的质量和均匀度获得了明显提高。
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Abstract
Description
Technical Field
[0001] This invention relates to a high-quality laser patterning method based on weighted feedback complex amplitude constraints, belonging to the field of laser application technology. Background Technology
[0002] Phase holographic spatial shaping technology has been widely applied in femtosecond laser patterning due to its advantages such as high energy efficiency and good processing flexibility. To obtain a high-quality patterned processing optical field, error reduction algorithms such as the GS algorithm, ORA algorithm, and Yang-Gu algorithm are often used to calculate the phase hologram corresponding to the processed pattern. However, during iterative calculations, these algorithms only constrain the amplitude intensity of the optical field, ignoring the phase changes within the field. When there is a phase mismatch between adjacent light spots within the optical field, such as when 0 phase and π phase are adjacent, interference cancellation often occurs due to spatial phase abrupt changes, resulting in zero-intensity speckle noise in the shaped optical field. This leads to hole defects within the laser patterned structure, severely damaging the shape and functional integrity of the processed structure.
[0003] Currently, the main processing methods for reducing speckle noise are based on the time multiplexing principle (Zhang C, Zhang J, Chen R, et al. Rapid fabrication of high-resolution multi-scale microfluidic devices based on the scanning of patterned femtosecond laser[J]. Optics Letters, 2020, 45(14): 3929-3932.). This involves using spatially shaped femtosecond lasers with different phases to perform multiple processing operations at the same location, utilizing the patterned light fields of different phases to compensate for each other's speckle noise defects, which is relatively inefficient; or optimizing the initial phase conditions (Zhang C, Hu Y, Du W, et al. Optimized holographic femtosecond laser patterning method towards rapid integration of high-quality functional devices in microchannels[J]. Scientific Reports, 2016, 6(1): 33281.) This method reduces the introduction of speckle noise, but it fails when the intensity fluctuation of the light field is too large during the iteration process. It is only suitable for patterned light fields with low energy efficiency, which severely limits the large-area high-efficiency processing capability of phase holographic spatial shaping femtosecond lasers. Summary of the Invention
[0004] This invention addresses the problem of speckle noise disrupting the integrity of the processed structure in the aforementioned phase holographic spatial shaping optical field by proposing a high-quality laser patterning processing method based on weighted feedback complex amplitude constraints. This method eliminates speckle noise caused by phase mismatch through additional phase constraints, improves the algorithm's convergence capability through amplitude-weighted feedback factors, and precisely controls the energy efficiency used in processing through energy-weighted feedback factors. Ultimately, it achieves large-area, high-efficiency patterning processing with highly uniform, high-uniformity, and speckle-free intense pulse femtosecond lasers, characterized by flexible and adjustable energy efficiency.
[0005] The objective of this invention is achieved through the following technical solution:
[0006] A high-quality laser patterning method based on weighted feedback complex amplitude constraints, the specific steps of which are as follows:
[0007] Step 1: Create the target amplitude matrix and target phase matrix corresponding to the pattern to be processed; based on the physical parameters such as the size of the liquid crystal unit of the spatial light modulator, the resolution of the focusing objective lens, and the aperture of the objective lens in the processing optical path, obtain the SLM plane discrete spatial coordinate system uov and the holographic surface discrete spatial coordinate system xoy; substitute the pattern to be processed into the holographic surface coordinate system xoy to obtain the holographic surface target amplitude matrix A. aim (x, y), where the area to be processed is marked as 1, and other background areas are marked as 0; based on the pixel size of the pattern area to be processed in the target amplitude matrix, a quadratic phase function containing a phase adjustment factor k is constructed, and substituted into the SLM plane coordinate system xoy to obtain the target phase matrix.
[0008]
[0009] Where M and N are the pixel lengths of the region to be processed in the x and y directions, respectively, in the target amplitude matrix; i is an imaginary number.
[0010] Step 2: Create and initialize the holographic surface light field matrix; the light field matrix contains two pieces of information: amplitude matrix and phase matrix. The target amplitude matrix A... aim The element values of the pattern region to be processed in (x, y) are assigned to the holographic surface amplitude matrix A. out The corresponding elements in (x, y) are used; the background region amplitude is introduced and set to 0.2; the target phase matrix element values are assigned to the holographic surface phase matrix. Then the holographic surface light field matrix E out The expression for (x, y) is:
[0011]
[0012] Here, exp() represents an exponential function with base e.
[0013] Step 3: Create the initial amplitude feedback matrix M and energy feedback factor η:
[0014] M1(x,y)=1,η1=η0
[0015] In this context, the subscript number 1 indicates that the amplitude feedback matrix M and the energy feedback matrix η are updated 1 time, and η0 is the target energy efficiency of the processing area.
[0016] Step 4: Use the amplitude feedback matrix M and the energy feedback factor η to adjust the holographic surface light field matrix E. out The amplitude term A in (x, y) out Weighted feedback amplitude constraints are applied to (x, y) to obtain the corrected holographic surface amplitude matrix A′. out (x, y):
[0017]
[0018] Where the subscript j represents the number of times the amplitude feedback matrix M and the energy feedback matrix η are updated, i.e., the j-th update. and These are operators that sum the regions to be processed and the background regions, respectively.
[0019] Step 5: Apply phase constraint to the holographic surface light field; replace the holographic surface light field matrix E with the element values of the target phase matrix. out Phase term in (x, y) By matching the element values within the pattern area to be processed, the corrected holographic surface light field matrix E′ is finally obtained. out (x, y):
[0020]
[0021] Step 6: Calculate the holographic surface light field matrix E′ out (x, y) is the SLM plane optical field matrix corresponding to the back diffraction onto the SLM plane; for E′ out Performing an inverse Fourier transform on (x, y) yields the SLM plane optical field matrix E. in (u, v); Replace E with the amplitude matrix A0 of the actual incident laser. in The amplitude term in (u, v) is used to obtain the corrected SLM planar optical field matrix E′. in (u, v):
[0022]
[0023] Among them, F -1 (x) is the inverse Fourier transform operator, and || is the modulus operator for the corresponding amplitude term.
[0024] Step 7: Calculate the holographic light field matrix at the holographic surface where the SLM plane light field diffracts; for the SLM plane light field E′ in Perform a Fourier transform on (u, v) to obtain the updated holographic light field matrix E. out (x, y):
[0025] E out (x, y) = F[E'] in (u, v)]
[0026] Where F(x) is the Fourier transform operator.
[0027] Step 8: Update the amplitude feedback matrix M; based on the holographic light field matrix E out The amplitude term A within (x, y) out The fluctuation of (x, y) is used to update the element values of the amplitude feedback matrix within the processing region. The updated amplitude feedback matrix M is then:
[0028]
[0029] In this context, <> represents taking the average value of the elements within the symbolic matrix.
[0030] Step 9: Update the energy feedback factor η; Based on the ratio of the light intensity energy of the holographic light field matrix within the pattern area to the light intensity energy of the surrounding background area, update the energy feedback factor η:
[0031]
[0032] Here, ∑() is the summation operator.
[0033] Step 10: Repeat steps 4 to 9 until the uniformity of the holographic surface light field meets the processing requirements; after calculation, based on the SLM planar phase matrix... A hologram is generated and loaded into a spatial light modulator to obtain a highly uniform processing light field, ultimately resulting in a high-quality laser processing pattern.
[0034] In the above scheme, the selection of the phase modulation factor k and the desired energy efficiency η0 is related to the uniformity of the processed optical field and the material processing capability. If the phase modulation factor k is too small, it will cause spectral leakage during the holographic optical field calculation, resulting in a loss of amplitude energy in the central region of the pattern; if the phase modulation factor k is too large, it will lead to the loss of high-frequency information and blurring of the pattern edges. Similarly, if the energy efficiency η is too high, the amplitude and phase in the holographic optical field tend to be completely restricted, making it difficult for the algorithm to flexibly control the optical field information; if the energy efficiency is too low, the laser energy density will be below the material processing threshold, making processing impossible. Therefore, in practical operation, it is necessary to select appropriate phase modulation factors and desired energy efficiencies based on the actual focusing conditions and material threshold requirements.
[0035] Beneficial effects
[0036] 1. This invention ensures the phase matching relationship within the holographic light field by constraining the processing pattern with complex amplitude (including amplitude and phase information), avoiding the generation of speckle noise, and thus significantly improving the quality and uniformity of the phase holographic femtosecond laser patterned processing structure.
[0037] 2. This invention introduces an amplitude-weighted feedback factor for the processed pattern region, which improves the convergence ability of the algorithm and avoids the problem that traditional algorithms get stuck in local optima and cannot continue to optimize.
[0038] 3. This invention introduces an energy weighted feedback factor for non-processed areas, which adaptively adjusts the energy efficiency of the processed area according to the desired energy efficiency during the iteration process. This achieves flexible control of the energy efficiency of the holographic light field and solves the processing quality problems such as excessive ablation or insufficient energy caused by energy fluctuations in the processed pattern during large-area splicing processing. Attached Figure Description
[0039] Figure 1 This is a schematic diagram of the phase hologram calculation process of the algorithm used in this invention.
[0040] Figure 2 Figures show simulated light field diagrams and actual processing results obtained under different complex amplitude constraints within the same algorithm framework. (a) Using initial phase constraints and iterative phase constraints, (b) Using only initial phase constraints, (d) Using only iterative phase constraints, and (e) Without phase constraints. All four constraint algorithms additionally use adaptive weighted feedback amplitude constraints for the processed pattern region and energy-weighted feedback constraints for the non-processed region. Figures (c) and (f) show the convergence curves of uniformity U and noise contrast C under the four algorithm constraints, respectively.
[0041] Figure 3 This paper illustrates the influence of the phase modulation factor k and the desired energy efficiency η0 on the actual energy efficiency in this invention. (a) is a pseudo-color image of energy efficiency under different phase and energy parameters. (b) shows the curves of optical field uniformity and noise contrast at different desired energy efficiencies η0 corresponding to the dashed line in Figure (a). (c)-(e) are simulated optical field diagrams and actual processing results at energy efficiencies η0 of 10%, 50%, and 60%, respectively.
[0042] Figure 4 This invention illustrates the influence of the phase modulation factor k and the desired energy efficiency η0 on the optical field uniformity. (a) is a pseudo-color image of the optical field uniformity under different phase and energy parameters. (b) shows the variation curves of optical field uniformity and noise contrast under different phase modulation factors k at the positions corresponding to the dashed lines in Figure (a). (c)-(e) are simulated optical field diagrams and actual processing results under phase modulation factors k of 0.6, 1.0, and 1.4, respectively. Detailed Implementation
[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0044] Example 1
[0045] The processing light source being shaped can be a coherent laser of any wavelength and pulse width, including continuous lasers, nanosecond lasers, picosecond / femtosecond ultrafast lasers, etc. The focusing objective / lens can be any objective / lens that meets the processing energy density requirements. The processing material can be any non-transparent planar material or transparent film material. In this example, a femtosecond laser is used to process a photoresist film, and a 20x focusing objective is selected. The spatial light modulator parameters are 1920*1080 pixels, with a pixel size of 8 micrometers. The specific steps of this example are as follows: Figure 1 As shown:
[0046] Step 1: Based on the pixel size of the spatial light modulator in the processing optical path, the maximum number of pixels corresponding to the objective lens's light-passing diameter is 714. To satisfy the Nyquist sampling theorem, the spatial size of the SLM plane discrete coordinate system uov and the holographic surface discrete coordinate system xoy is set to 1428×1428 pixels. Substitute the pattern to be processed into the holographic surface discrete coordinate system to obtain the target amplitude matrix A. aim (x, y), where the pattern to be processed is a rabbit pattern, the pattern area size is 80*80 pixels, located at the center of the target amplitude matrix, and the target amplitude matrix A. aim The amplitude of the region to be processed in (x, y) is 1, and the amplitude of other regions is 0. The phase distribution is set as a specific quadratic phase containing a phase adjustment factor k. Substituting these values into the SLM plane coordinate system xoy, the target phase matrix is obtained.
[0047]
[0048] Where M and N are the pixel lengths of the processed pattern in the x and y directions, respectively; i is an imaginary number.
[0049] Step 2: Create and initialize the holographic surface light field matrix; the light field matrix contains two pieces of information: amplitude matrix and phase matrix. The target amplitude matrix A... aim The element values of the pattern region to be processed in (x, y) are assigned to the holographic surface amplitude matrix A. out The corresponding elements in (x, y) are used; the background region amplitude is introduced and set to 0.2; the target phase matrix element values are assigned to the holographic surface phase matrix. Then the holographic surface light field matrix E out The expression for (x, y) is:
[0050]
[0051] Here, exp() represents an exponential function with base e.
[0052] Step 3: Create the initial amplitude feedback matrix M and energy feedback factor η:
[0053] M1(x,y)=1,η1=η0
[0054] In this context, the subscript number 1 indicates that the amplitude feedback matrix M and the energy feedback matrix η are updated 1 time, and η0 is the target energy efficiency of the processing area.
[0055] Step 4: Use the amplitude feedback matrix M and the energy feedback factor η to adjust the holographic surface light field matrix E. out The amplitude term A in (x, y) out Weighted feedback amplitude constraints are applied to (x, y) to obtain the corrected holographic surface amplitude matrix A′. out (x, y):
[0056]
[0057] Where the subscript j represents the number of times the amplitude feedback matrix M and the energy feedback matrix η are updated, i.e., the j-th update. and These are operators that sum the regions to be processed and the background regions, respectively.
[0058] Step 5: Apply phase constraint to the holographic surface light field; replace the holographic surface light field matrix E with the element values of the target phase matrix. out Phase term in (x, y) By matching the element values within the pattern area to be processed, the corrected holographic surface light field matrix E′ is finally obtained. out (x, y):
[0059]
[0060] Step 6: Calculate the holographic surface light field matrix E′ out (x, y) is the SLM plane optical field matrix corresponding to the back diffraction onto the SLM plane; for E′ out Performing an inverse Fourier transform on (x, y) yields the SLM plane optical field matrix E. in (u, v); Replace E with the amplitude matrix A0 of the actual incident laser. in The amplitude term in (u, v) is used to obtain the corrected SLM planar optical field matrix E′. in (u, v):
[0061]
[0062] Among them, F -1 (x) is the inverse Fourier transform operator, and || is the modulus operator for the corresponding amplitude term.
[0063] Step 7: Calculate the holographic light field matrix at the holographic surface where the SLM plane light field diffracts; for the SLM plane light field E′ in Perform a Fourier transform on (u, v) to obtain the updated holographic light field matrix E. out (x, y):
[0064] E out (x, y) = F[E'] in (u, v)]
[0065] Where F(x) is the Fourier transform operator.
[0066] Step 8: Update the amplitude feedback matrix M; based on the holographic light field matrix E out The amplitude term A within (x, y) out The fluctuation of (x, y) is used to update the element values of the amplitude feedback matrix within the processing region. The updated amplitude feedback matrix M is then:
[0067]
[0068] In this context, <> represents taking the average value of the elements within the symbolic matrix.
[0069] Step 9: Update the energy feedback factor η; Based on the ratio of the light intensity energy of the holographic light field matrix within the pattern area to the light intensity energy of the surrounding background area, update the energy feedback factor η:
[0070]
[0071] Here, ∑() is the summation operator.
[0072] Step 10: Repeat steps 4 to 9 until the uniformity of the holographic surface light field meets the processing requirements; in this example, the light field quality evaluation standard for the holographic surface light field uses the uniformity U and noise contrast C of the holographic surface light field as evaluation functions:
[0073]
[0074]
[0075] in, The maximum value of the holographic amplitude matrix in the processing area. This represents the maximum value of the holographic amplitude matrix within the processing region. std() is the standard deviation operator.
[0076] After the calculation is completed, based on the SLM plane phase matrix A hologram is generated and loaded into a spatial light modulator to obtain a highly uniform processing light field, ultimately resulting in a high-quality laser processing pattern.
[0077] 2. In the above scheme, the complex amplitude constraint condition ensures the phase matching relationship of the light field between neighboring pixels during the iteration process, such as... Figure 2 As shown, Figure 2 a and Figure 2 d represents the processing result of this method. Figure 2 b and Figure 2 e represents the machining result without using phase constraints. Figure 2 a and Figure 2 d The processing quality is significantly higher than Figure 2 b and 2e. Figure 2 c and 2f show the convergence curves of optical field uniformity and noise contrast under different constraint conditions. Compared with the initial phase constraint or no phase constraint, the introduction of iterative phase constraint increases the optical field uniformity from <0.1 to more than 0.8 and reduces the noise contrast to 0.05.
[0078] In the above scheme, the selection of the phase modulation factor k and the desired energy efficiency η0 is related to the uniformity of the processed optical field and the material processing capability. In this example, as... Figure 3 Figure a shows the variation of actual energy efficiency with phase modulation factor k and energy efficiency parameter η0. Figure 3 b represents the curves showing the changes in optical field uniformity and noise contrast under different energy efficiencies with a fixed phase factor k. Figure 3 c, 3d, and 3e are... Figure 3 Figure b shows the simulated light field distribution and actual processing effect when the energy efficiency η is 0.1, 0.5, and 0.6. It can be seen that the algorithm can achieve flexible and accurate control of the holographic light field energy efficiency within the desired energy efficiency range of 0-50%, while ensuring a light field uniformity of over 80% and a noise contrast ratio of less than 0.5%. Figure 4 'a' represents the variation of optical field uniformity under the combined effects of phase modulation factor 'k' and energy efficiency. Figure 4 b is Figure 4 The curve showing the variation of optical field uniformity with phase modulation factor k at a fixed energy efficiency in equation a shows that a highly uniform holographic optical field can be obtained when k = 1 to 1.2. However, when k is too small, spectral leakage can cause the algorithm to fail to converge. Figure 4 As shown in Figure c, internal defects appeared in the optical field and the actual fabricated structure when k = 0.6. When k is too large, the edges of the optical field pattern will be blurred due to the loss of high-frequency information, such as... Figure 4 As shown in e, when k=1.4, structural defects appear around the optical field and the actual processing structure. Therefore, in actual operation, it is necessary to select an appropriate phase control factor and desired energy efficiency according to the actual focusing conditions and material threshold requirements.
[0079] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A high-quality laser patterning method based on weighted feedback complex amplitude constraint, characterized in that: Step 1: Create the target amplitude matrix and target phase matrix corresponding to the pattern to be processed; based on the physical parameters of the spatial light modulator liquid crystal cell size, focusing objective resolution, and objective aperture in the processing optical path, obtain the SLM plane discrete spatial coordinate system uov and the holographic surface discrete spatial coordinate system xoy; substitute the pattern to be processed into the holographic surface coordinate system xoy to obtain the holographic surface target amplitude matrix A. aim (x, y), where the area to be processed is marked as 1, and other background areas are marked as 0; based on the pixel size of the pattern area to be processed in the target amplitude matrix, a quadratic phase function containing a phase adjustment factor k is constructed, and substituted into the SLM plane coordinate system xoy to obtain the target phase matrix. Where M and N are the pixel lengths of the region to be processed in the target amplitude matrix in the x and y directions, respectively; i is an imaginary number; Step 2: Create and initialize the holographic surface light field matrix; the light field matrix contains two pieces of information: amplitude matrix and phase matrix. The target amplitude matrix A... aim The element values of the pattern region to be processed in (x,y) are assigned to the holographic surface amplitude matrix A. out The corresponding elements in (x,y); introduce the background region amplitude, set to 0.2; assign the target phase matrix element values to the holographic surface phase matrix. Then the holographic surface light field matrix E out The expression for (x,y) is: Where exp() represents an exponential function with base e; Step 3: Create the initial amplitude feedback matrix M and energy feedback factor η: M1(x,y)=1,η1=η0 Where the subscript number 1 indicates that the amplitude feedback matrix M and the energy feedback matrix η are updated 1 time, and η0 is the target energy efficiency of the processing area; Step 4: Use the amplitude feedback matrix M and the energy feedback factor η to adjust the holographic surface light field matrix E. out The amplitude term A in (x,y) out Weighted feedback amplitude constraints are applied to (x,y) to obtain the corrected holographic surface amplitude matrix A′. out (x,y): Where the subscript j represents the number of times the amplitude feedback matrix M and the energy feedback matrix η are updated, i.e., the j-th update. and Operators that sum the regions to be processed and the background regions, respectively; Step 5: Apply phase constraint to the holographic surface light field; replace the holographic surface light field matrix E with the element values of the target phase matrix. out Phase term in (x,y) By matching the element values within the pattern area to be processed, the corrected holographic surface light field matrix E′ is finally obtained. out (x,y): Step 6: Calculate the holographic surface light field matrix E′ out (x,y) represents the SLM plane optical field matrix corresponding to the back diffraction onto the SLM plane; for E′ out Performing an inverse Fourier transform on (x,y) yields the SLM plane optical field matrix E. in (u,v); Replace E with the amplitude matrix A0 of the actual incident laser. in The amplitude term in (u,v) is used to obtain the corrected SLM planar optical field matrix E′. in (u,v): Among them, F -1 (x) is the inverse Fourier transform operator, and || is the modulus operator for the corresponding amplitude term; Step 7: Calculate the holographic light field matrix at the holographic surface where the SLM plane light field diffracts; for the SLM plane light field E′ in Perform a Fourier transform on (u,v) to obtain the updated holographic light field matrix E. out (x,y): E out (x,y)=F[E′ in (u,v)] Where F(x) is the Fourier transform operator; Step 8: Update the amplitude feedback matrix M; based on the holographic light field matrix E out The amplitude term A within (x,y) out The fluctuation of (x,y) is used to update the element values of the amplitude feedback matrix within the processing region. The updated amplitude feedback matrix M is then: In this case, <> represents taking the average value of the matrix elements within the symbol; Step 9: Update the energy feedback factor η; Based on the ratio of the light intensity energy of the holographic light field matrix within the pattern area to the light intensity energy of the surrounding background area, update the energy feedback factor η: Where ∑() is the summation operator; Step 10: Repeat steps 4 to 9 until the uniformity of the holographic surface light field meets the processing requirements; after calculation, based on the SLM planar phase matrix... A hologram is generated and loaded into a spatial light modulator to obtain a highly uniform processing light field, ultimately resulting in a high-quality laser processing pattern.