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. 2025 Sep 10;17(18):2453.
doi: 10.3390/polym17182453.

Multi-Objective Optimization of an Injection Molding Process for an Alvarez Freeform Lens Using an Integrated Optical System and Mold Flow Analyses

Po-Yu Yen  1 , Chao-Ming Lin  1 , I-Hsiu Chang Chien  1
Affiliations

Multi-Objective Optimization of an Injection Molding Process for an Alvarez Freeform Lens Using an Integrated Optical System and Mold Flow Analyses

Po-Yu Yen et al. Polymers (Basel). .

Abstract

This study optimizes the design and fabrication of an injection-molded Alvarez freeform lens using Moldex3D mold flow analysis and CODE V optical design simulations. The dual-software approach facilitates the transition between the manufacturing simulations and the optical design/verification process, thereby addressing the conversion issues between the two analysis modules. The optical quality of the designed lens is evaluated using spot diagram, distortion, and modulation transfer function (MTF) simulations. The Taguchi design methodology is first employed to identify the individual effects of the key injection molding parameters on the quality of the fabricated lens. The quality is then further improved by utilizing two multi-objective optimization methods, namely Gray Relational Analysis (GRA) and Robust Multi-Criteria Optimization (RMCO), to determine the optimal combination of the injection molding parameters. The results demonstrate that RMCO outperforms GRA, showing more substantial improvements in the optical quality of the lens. Overall, the proposed integrated method, incorporating Moldex3D, CODE V, Taguchi robust design, and RMCO analyses, provides an effective approach for optimizing the injection molding of Alvarez freeform lenses, thereby enhancing their quality. Future research could extend this methodology to other optical components and more complex optical systems.

Keywords: Alvarez lens; GRA; MTF; RMCO; Taguchi method; distortion; mold flow analysis; spot diagram.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Main steps in injection molding process: (a) heating/melting, (b) filling/packing, and (c) ejection/cooling.
Figure 2
Figure 2
Surface profile of Alvarez lens.
Figure 3
Figure 3
Optical configuration of Alvarez lens system in two operation modes (Green indicates: Lenses; Orange indicates: Light): (a) wide-angle (Zoom 1) and (b) telephoto (Zoom 2).
Figure 4
Figure 4
Multiple lens combinations used for imaging experiments in CODE V(2023.03) simulation software: (a) Zoom 1 and (b) Zoom 2.
Figure 5
Figure 5
Grid and mesh for MFA simulation of gate and runner system for the injection molding of an Alvarez lens.
Figure 6
Figure 6
Flowchart of overall analysis framework.
Figure 7
Figure 7
Spot diagrams of optical design: (a) Zoom 1 and (b) Zoom 2.
Figure 8
Figure 8
Deformation grid diagrams of optical design at FoV 0°: (a) Zoom 1 and (b) Zoom 2.
Figure 9
Figure 9
Diffraction MTF of optical design: (a) Zoom 1 and (b) Zoom 2.
Figure 10
Figure 10
GRA response diagram. (The red circle indicates the largest correlation coefficient.)
Figure 11
Figure 11
Box plots for spot diagram: (a) Zoom 1 and (b) Zoom 2.
Figure 12
Figure 12
Spot diagrams: (a) Zoom 1 and (b) Zoom 2.
Figure 13
Figure 13
Box plots for distortion: (a) Zoom 1 and (b) Zoom 2.
Figure 14
Figure 14
Distortion: (a) Zoom 1 and (b) Zoom 2.
Figure 15
Figure 15
Box plots for modulation transfer function (MTF): (a) Zoom 1 and (b) Zoom 2.
Figure 16
Figure 16
Modulation transfer function (MTF): (a) Zoom 1 and (b) Zoom 2.
See this image and copyright information in PMC

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