Design of High-Smoothness Freeform Lens for Laser Beam Shaping

Fig. 3. Mesh distribution and error function distribution of target surface. (a) Results after 1st iteration; (b) results after 2nd iteration; (c) results after 3rd iteration; (d) results after 4th iteration

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Fig. 4. RMSE of normalized error distribution function at different iterations

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Fig. 5. Distribution of vector field of $r$ . (a) Result after 1st iteration; (b) result after 2nd iteration; (c) result after 3rd iteration; (d) result after 4th iteration

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Fig. 6. Distribution of irradiance of incident beam

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Fig. 7. Design examples of two freeform lens. (a)(b) Lens 1 and its irradiance distribution at target surface; (c)(d) lens 2 and its irradiance distribution at target surface

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Fig. 8. Results of surface fitting. (a) Distribution of raw and fitting data points; (b) difference between raw and fitting data points

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Fig. 9. Irradiance distribution of a freeform lens reshaped by a sixth-order polynomial fitting

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Fig. 10. Analysis results of tolerances. (a) Irradiation uniformity of different combined tolerances; (b) sample number at different uniformity ranges

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Fig. 11. Influence of target plane position on irradiation uniformity. (a) Irradiance distribution on target planes with the distance of 80-120 mm; (b) irradiation uniformity of target surface at different positions

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Table 1. Design parameters of free-form surface shaping lens
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Table 1. Design parameters of free-form surface shaping lens
Design parameter Freeform lens 1 Freeform lens 2
Radius of incident beam /mm 10 10
Lens material PMMA PMMA
Distance between lens and target surface /mm 100 200
Target area /（mm×mm） 30×30 60×40

Table 2. Coefficients of the fitted polynomial
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Table 2. Coefficients of the fitted polynomial
$i$ a_i x²^py²^q
0 -0.62 $1$
1 0.01252 $x^{2}$
2 0.01233 $y^{2}$
3 -5.21×10^-5 $x^{4}$
4 -5.339×10^-5 $x^{2} y^{2}$
5 -5.06×10^-5 $y^{4}$
6 1.986×10^-7 $x^{2} y^{4}$
7 2.019×10^-7 $x^{4} y^{2}$
8 1.053×10^-7 $x^{6}$
9 1.027×10^-7 $y^{6}$

Table 3. Tolerance range
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Table 3. Tolerance range
Tolerance type Range Number of samples
x direction displacement error -0.5-0.5 mm 200
y direction displacement error -0.5-0.5 mm 200
x direction tilt error -1°-1° 200
y direction tilt error -1°-1° 200

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Zemao Zang, Zhouping Su, Wenyu Zhang, Jiaqiang Shao. Design of High-Smoothness Freeform Lens for Laser Beam Shaping[J]. Acta Optica Sinica, 2023, 43(8): 0822023

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