Application of the NSGA-II Algorithm and Kriging Model to Optimise the Process Parameters for the Improvement of the Quality of Fresnel Lenses

At a Glance

Metadata	Details
Publication Date	2023-08-14
Journal	Polymers
Authors	Hanjui Chang, Yue Sun, Rui Wang, Shuzhou Lu
Institutions	Shantou University
Citations	5
Analysis	Full AI Review Included

Technical Documentation & Analysis: MPCVD Diamond for Advanced Micro-Optics

Executive Summary

This research focuses on optimizing the manufacturing quality of polymer Fresnel lenses using advanced computational methods. While the study utilizes Polymethyl Methacrylate (PMMA) and In-Mould Decoration (IMD), the core challenges—achieving high geometric precision (low nodal displacement) and minimizing residual stress in micro-optical structures—are directly relevant to the high-precision tooling and next-generation diamond optics offered by 6CCVD.

Core Achievement: Successful multi-objective optimization of injection moulding parameters (Holding Pressure and Melt Temperature) using a Kriging model combined with the NSGA-II genetic algorithm.
Performance Gain: Achieved a 59.64% optimization efficiency, reducing average nodal displacement from 0.659 mm to an optimized 0.393 mm.
Optical Quality: The optimized PMMA Fresnel lens demonstrated an average transmittance of 95.43% in the near-infrared (NIR) spectrum.
Material Limitation: The use of PMMA limits the lens application due to low thermal stability (T_g approx. 105-110 °C) and low hardness, making it unsuitable for high-power or harsh environments.
6CCVD Value Proposition: 6CCVD provides ultra-hard MPCVD diamond (PCD/SCD) materials, ideal for manufacturing highly durable, high-precision mold inserts (tooling) or for fabricating superior, high-power diamond optics that overcome the thermal and mechanical limitations of polymers.

Technical Specifications

The following hard data points were extracted from the optimization study:

Parameter	Value	Unit	Context
Optimal Holding Pressure (P)	320.35	MPa	IMD Process Optimization
Optimal Melt Temperature (T)	251.40	°C	IMD Process Optimization
Optimized Average Nodal Displacement	0.393	mm	Fresnel lens surface geometry
Original Average Nodal Displacement	0.659	mm	IMD Process (unoptimized)
Optimization Efficiency	59.64	%	Reduction in nodal displacement
Optimized Average Residual Stress (Simulation)	0.075	MPa	Result of optimal parameters
Average Transmittance	95.43	%	Measured in Near-Infrared (NIR)
PMMA Glass Transition Temperature (T_g)	105-110	°C	Polymer thermal limit
PMMA Linear Coefficient of Thermal Expansion	70-90 x 10^-6	/°C	Material property

Key Methodologies

The study employed a three-step approach focused on process selection, modeling, and optimization:

Moulding Method Comparison: Three injection moulding techniques were compared for Fresnel lens production:
- In-Mould Decoration (IMD): Selected as optimal due to superior scratch/solvent resistance and ability to protect microstructures, despite higher nodal displacement than ICM.
- Injection Compression Moulding (ICM): Produced the smallest nodal displacement (0.251 mm average) but risked damage to the serrated microstructure.
- Two-Stage Injection Moulding: Produced the largest nodal displacement (0.861 mm average).
Kriging Surrogate Model Establishment: A Kriging proxy model, a generalized regression model based on a stochastic process, was used to map the non-linear functional relationship between the two key process parameters (Holding Pressure, Melt Temperature) and the two optimization objectives (Nodal Displacement, Residual Stress).
Multi-Objective Optimization (NSGA-II): The Non-Dominated Sorting Genetic Algorithm (NSGA-II) was integrated with the Kriging model to efficiently find the Pareto optimal solution set, ensuring both convergence and diversity in the solutions.
Validation: The optimal parameters were verified via simulation and experimental testing, including transmittance measurement using a Lambda 950 UV/Vis spectrophotometer.

6CCVD Solutions & Capabilities

This research demonstrates the critical need for high-precision tooling and materials capable of withstanding the extreme pressures and temperatures required to replicate complex micro-optical structures like Fresnel V-grooves. 6CCVD’s MPCVD diamond materials offer two distinct pathways to replicate or significantly advance this technology:

1. Ultra-Hard Tooling for Mass Production (PCD)

The IMD process relies on durable molds to maintain the integrity of the V-groove microstructure over thousands of cycles. Polymer molds suffer from wear, leading to quality degradation. 6CCVD Polycrystalline Diamond (PCD) provides the ultimate solution for mold inserts.

Requirement (from Paper)	6CCVD PCD Solution	Technical Specification
High Wear Resistance (for V-grooves)	PCD Plates/Wafers	Extreme hardness (Vickers > 80 GPa) ensures minimal tool wear and consistent replication accuracy.
Large Format Tooling	Custom Dimensions	Plates/wafers available up to 125 mm in diameter, suitable for inch-size optical components.
Microstructure Fidelity	Ultra-Precision Polishing	PCD surfaces polished to Ra < 5 nm (inch-size), guaranteeing smooth, high-fidelity replication of the Fresnel microstructures.
Custom Integration	Substrate Thickness	Substrates available up to 10 mm thick for robust mold insert integration.

2. Next-Generation High-Power Optics (SCD)

The PMMA lens is limited to low-power, low-temperature applications (T_g < 110 °C). For demanding applications identified in the paper (e.g., high-power infrared communication, thermal imaging, or UV systems), Single Crystal Diamond (SCD) is the only viable material, offering unparalleled thermal, mechanical, and optical performance.

Limitation of PMMA	6CCVD SCD Solution	Performance Advantage
Low Thermal Stability (105-110 °C)	Optical Grade SCD	Highest thermal conductivity (2200 W/mK) and stability (> 1000 °C), eliminating thermal deformation and residual stress issues seen in polymers.
Limited Spectral Range	Optical Grade SCD	Excellent transmission from deep UV (< 220 nm) through visible and into the far-infrared, ideal for broadband or high-power NIR/IR applications.
Need for Custom Micro-Optics	Custom SCD Fabrication	SCD plates available up to 500 µm thickness, suitable for direct fabrication of diamond Fresnel lenses via advanced etching or laser processing.
Custom Interfacing	Metalization Services	Internal capability for custom metalization (Au, Pt, Pd, Ti, W, Cu) for bonding, electrical contacts, or anti-reflection coatings on SCD optics.

Engineering Support & Call to Action

6CCVD’s in-house PhD engineering team specializes in material selection and design consultation for projects requiring extreme performance, such as:

Designing diamond mold inserts for high-volume, high-fidelity replication of micro-optical elements.
Developing high-power optical components (lenses, windows, prisms) where thermal management and geometric stability are paramount.
Integrating custom metalization schemes for advanced sensor or communication systems based on diamond optics.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

The Fresnel lens is an optical system consisting of a series of concentric diamond grooves. One surface of the lens is smooth, while the other is engraved with concentric circles of increasing size. Optical interference, diffraction, and sensitivity to the angle of incidence are used to design the microstructure on the lens surface. The imaging of the optical surface depends on its curvature. By reducing the thickness of the lens, light can still be focused at the same focal point as with a thicker lens. Previously, lenses, including Fresnel lenses, were made of glass due to material limitations. However, the traditional grinding and polishing methods for making Fresnel lenses were not only time-consuming, but also labour-intensive. As a result, costs were high. Later, a thermal pressing process using metal moulds was invented. However, the high surface tension of glass caused some detailed parts to be deformed during the pressing process, resulting in unsatisfactory Fresnel lens performance. In addition, the complex manufacturing process and unstable processing accuracy hindered mass production. This resulted in high prices and limited applications for Fresnel lenses. These factors prevented the widespread use of early Fresnel lenses. In contrast, polymer materials offer advantages, such as low density, light weight, high strength-to-weight ratios, and corrosion resistance. They are also cost effective and available in a wide range of grades. Polymer materials have gradually replaced optical glass and other materials in the manufacture of micro-optical lenses and other miniaturised devices. Therefore, this study focuses on investigating the manufacturing parameters of Fresnel lenses in the injection moulding process. We compare the quality of products obtained by two-stage injection moulding, injection compression moulding, and IMD (in-mould decoration) techniques. The results show that the optimal method is IMD, which reduces the nodal displacement on the Fresnel lens surface and improves the transmission performance. To achieve this, we first establish a Kriging model to correlate the process parameters with optimisation objectives, mapping the design parameters and optimisation objectives. Based on the Kriging model, we integrate the NSGA-II algorithm with the predictive model to obtain the Pareto optimal solutions. By analysing the Pareto frontier, we identify the best process parameters. Finally, it is determined that the average nodal displacement on the Fresnel surface is 0.393 mm, at a holding pressure of 320.35 MPa and a melt temperature of 251.40 °C. Combined with IMD technology, product testing shows a transmittance of 95.43% and an optimisation rate of 59.64%.

Tech Support

Original Source

DOI: https://doi.org/10.3390/polym15163403

References

2012 - Surface wear of TiN coated nickel tool during the injection moulding of polymer micro Fresnel lenses [Crossref]
2012 - Analysis of processing parameters in fabrication of Fresnel lens solar collector [Crossref]
2014 - Comparison of Injection Molding Technologies for the Production of Micro-optical Devices [Crossref]
2014 - Optimization design of hybrid Fresnel-based concentrator for generating uniformity irradiance with the broad solar spectrum [Crossref]
2016 - Optimize the shape of curved-Fresnel lens to maximize its transmittance [Crossref]
2018 - Assessment and optimization of a novel solar driven natural gas liquefaction based on cascade ORC integrated with linear Fresnel collectors [Crossref]
2018 - Injection molding process optimization of a bi-aspheric lens using hybrid artificial neural networks (ANNs) and particle swarm optimization (PSO) [Crossref]
2019 - Fabrication of curved diffractive optical elements by means of laser direct writing, electroplating, and injection compression molding [Crossref]