Recent advancements in optical microstructure fabrication through glass molding process

Optical microstructures are increasingly applied in several fields, such as optical systems, precision measurement, and microfluid chips. Microstructures include microgrooves, microprisms, and microlenses. This paper presents an overview of optical microstructure fabrication through glass molding and highlights the applications of optical microstructures in mold fabrication and glass molding. The glass-mold interface friction and adhesion are also discussed. Moreover, the latest advancements in glass molding technologies are detailed, including new mold materials and their fabrication methods, viscoelastic constitutive modeling of glass, and microstructure molding process, as well as ultrasonic vibrationassisted molding technology.

Recently, the demand for 3D microsurface structures, such as microgrooves, micropyramids, microprisms, and microlenses, has been increasing in the optical industry. Components with microsurface structures, particularly microstructure arrays, yield new functions for light operation, thereby significantly improving the imaging quality of optical systems [1].
Microstructure arrays are configurations of several lenses or prisms in micro/nano scale. Microstructure arrays can provide various optical functions because of their special geometrical features. The basic types of microstructure arrays are displayed in Fig. 1 according to the element shape. The optical performance of microstructure arrays with element size ranging from 5 to 50 mm is mainly achieved through their refraction and reflection properties. Through multiple imaging, microstructure arrays can raise the light energy utilization ratio and realize the miniaturization of optical systems. Moreover, combining different types of microstructure arrays can enhance beam guidance control, smart scan, and other complex functions (Fig. 2). These functions have driven the wide-scale application of microstructure arrays in liquid crystal displays, mobile phones, palm pilots, televisions, and other electronic products. An example of a microstructure based on the refraction principle is the wave-front sensor, which is composed of a microlens array and a charge-coupled device array.
The optical performance of microstructure arrays with element size ranging from 0.5 to 5 mm is mainly dependent on their interference and diffraction reflection properties. Light passing through microstructure arrays can produce entirely different phenomena than those created with macro lenses. As shown in Fig. 3, microstructure arrays are equipped with both 1D and 2D diffraction. The complex design and cycle structures of microstructure arrays enable them to accomplish several functions, such as antireflection, polarization beam splitting, optical waveguide coupling, light beam transformation, and integration.
Optical component with microstructures using diffraction principle is most commonly used in diffraction grating. Diffraction grating is a component of optical devices that consist of a surface ruled with close, equidistant, and parallel lines to resolve light into the spectra.

Positioning sensor in machine tools and measurement equipment
The simplest positioning sensor is the grating ruler, which is used as the checkout gear in numerical control machine tools. In the installation of a grating ruler, the line on the indicator grating will generate a small angle with the line on the ruler grating. The lines on the two gratings cross each other and overlap, forming black fringes near the intersection and bright fringes in other places when light passes through the grating. These fringes are called Moiré fringes (Fig. 4).
Moiré fringes change between bright and dark with the movement of grating. The system will output the pulse after signal processing, circuit amplification, shaping, and differentiation. Each output of a pulse is represented by the distance of a grid. Thus, the moving distance of the working table can be obtained by counting the pulses.

Fabrication methods for optical microstructures
The demand for optical microstructures has dramatically increased in various fields. However, microstructures are difficult to machine on hard and brittle material, including glass [3,4].

Glass molding
Glass molding process (GMP) is an alternative approach that produces glass optical microstructures by replicating the shape of the mold to the heated glass preforms without further machining processes [30][31][32][33]. Figure 5 shows the GMP technology of the microstructure array.
In terms of fabrication cost and process time, GMP is certainly an excellent approach for producing precision optical elements, such as aspherical and Fresnel lenses, diffractive optical elements (DOEs), and microprism and microlens arrays. Recent works [35][36][37] have also reported glass molding for microstructures, which can be alternatively called hot embossing or thermal imprinting.
In terms of production cost and environmental compatibility, hot compression molding is a promising manufacturing method for producing precision glass lenses with microgrooves. Hot compression molding can produce lenses having form accuracy, surface finish, and optical performance that are comparable to lenses manufactured through conventional techniques of material removal. Figure 6 shows the process flow of microgroove forming. The process can be divided into four stages according to the thermal cycle: Heating, pressing, annealing, and cooling. At the heating stage, a glass preform is placed on the lower mold. Inert gas, such as nitrogen (N 2 ), is flowed to purge the air in the machine chamber. The molds and the glass preform are then heated to the molding temperature by a heat source, such as infrared lamps ( Fig. 6 (a)). At the pressing stage, the glass preform is pressed by closing the two mold halves ( Fig. 6(b)). At the annealing stage, the formed lens is slowly cooled down while a small pressing load is maintained to release the internal stress ( Fig. 6(c)). At the cooling stage, the glass lens is cooled rapidly to ambient temperature and released from the molds (Fig. 6(d)). Through these four stages, the shapes of the mold cores are precisely replicated to the glass lens.
However, several technical challenges associated with the molding process have prevented the application of the microgroove forming process for high-volume lens production. These challenges include thermal shrinkage of the lens upon cooling, optical surface finish, precise mold shape, mold life, and selection of process parameters [38].

Fabrication methods for the microstructure mold
To extend the GMP method to creating microstructures on glass surfaces, the microstructure mold should be machined with high accuracy and efficiency. Hard materials, such as silicon carbide (SiC), tungsten carbide (WC), and fused silica, are ideal mold materials for continuous surfaces because of their high hardness and toughness under molding conditions. Although creating microstructures on these hard materials have been attempted several times, the low-cost fabrication of microstructures with desirable shape and accuracy has not yet been realized [39]. Grinding and milling are conventional ways for the high-accuracy production of microstructures on hard materials. Nevertheless, the costs of these processes for medium-to highvolume production are extremely high [40]. Micro-electric discharge machining and micro-electrochemical machining have been applied in the microstructure fabrication on WC. Although these methods can machine complex 3D shapes regardless of the material's hardness [41][42][43][44][45], the surface roughness is low, which hinders the creation of the optical surface. A popular strategy for producing microstructures on molds is indentation, which is a patented process developed by Yan et al. [46]. This technique is based on the advantage of having a negligible small tool wear and a stable manufacturing process. In addition, various 3D shapes can be realized by reactive ion etching, which utilizes chemically reactive plasma to remove materials deposited on SiC molds [47][48][49]. In terms of the process rate, roughness, and shape of the machined structure, laser technique is also an effective approach for microstructure mold fabrication. Femto-second laser combined with FIB milling can realize the rapid fabrication of high-quality microstructures on wide surface areas [50]. As mentioned, microstructure molds made of hard materials are difficult to produce. However, single-point diamond cutting is a promising approach for creating microstructures, provided that a new material can be coated on the WC mold surface for the cutting process. This new material must possess excellent machinability for microstructure fabrication and high hardness to achieve a durable mold.
The electro-less deposition of nickel (Ni) in a bath containing hypophosphite was first observed by Wurtz [51] in 1844 and was then introduced to industrial application by Riddell in 1946 and1947 [52,53]. Since then, electro-less nickel phosphide (Ni-P) has emerged as an outstanding hard coating material because of its strong hardness, excellent corrosion resistance, and antiwear property. Given that the shape deformation and machinability of the Ni-P layer significantly change under different phosphorus contents, the effect of the phosphorus content on the thermal phase transformation and microstructure evolution during heating has attracted considerable research attention [54,55]. The preparation process of the Ni-P plating mold and the finished Ni-P plating mold are depicted in Fig. 7.

Microstructure generation through diamond cutting
The application of ultra-precision machining with diamond tools has rapidly grown in the manufacture of highprecision machined parts for advanced industrial applications [56]. The outstanding hardness and crystalline structure of diamond tools promote the fabrication of microstructures on Ni-P plating materials with submicron form accuracy and surface roughness in the nanometer range [57]. First, the Ni-P layer is coated on the substrate through electro-less plating method. Microstructures are then created on the Ni-P surface through single-diamond point cutting. Finally, the shape of the microstructures is replicated on the glass surface through GMP. By utilizing V-shaped diamond tools, microstructures can be generated on the Ni-P plating layer, as shown in Fig. 8(a). Similarly, with the use of R-shaped diamond milling tools, microlens arrays can be formed through high-speed milling, as shown in Fig. 8 However, the crystal transition of electro-less Ni-P would occur in amorphous materials once the temperature exceeds 400°C [58], causing mold surface deformation and diminishing the accuracy of glass molding. To avoid mold surface deformation and achieve accurate and precise fabrication of microstructures for high-quality mold, an initial heat treatment method is proposed to eliminate irregular concave deformation during the crystallization process [59]. The amorphous plating is heated to the annealing temperature (approximately 600°C) to ensure the complete transformation into the crystalline state. The improved procedure of fabricating microgroove mold on crystallized Ni-P plating is presented in Fig. 9. In this way, less deformation of the mold occurs under the condition of GMP, and microstructure machining on the mold through single-point diamond cutting can be performed on the ultra-precision cutting machine (Nanoform ® X, Precitech Corp., United States), as shown in Fig. 10.
Although diamond cutting on the Ni-P plating can be utilized to fabricate microstructures on the mold, the machining process is still hindered by many challenges [60]. Burr adversely influences the mold surface roughness and form accuracy during the mold machining process [61][62][63]. Burr easily forms at the microstructure edge when ductile material is cut, as shown in Fig. 11. The mechanism of the burr formation can be revealed by considering the edge radius of the diamond cutting tool and the cutting   depth of the workpiece material. Burr formation can be effectively eliminated by using a diamond tool with an edge radius of 57 nm instead of 100 nm. However, as the cutting depth is decreased, more burrs are generated again. Thus, an approach that optimizes the nose radius and the cutting depth to minimize burr formation is established to generate fine microgrooves.
Chipping is another defect in the mold machining process, as shown in Fig. 12. Many attempts have been made to optimize the processing parameters and consequently reduce mold defects. With the advancements in the machining process and the exploration of the removal principle for Ni-P plating material, microstructure molds with high form accuracy and low surface roughness can be obtained. Figure 13 shows fine microgroove and micropyramid molds created through single-point diamond cutting. With the recent advances in numerical simulation capabilities and computing technology, finite element method can address issues that some variables are remarkably difficult to experimentally measure by providing deeper insight into the process and performance  prediction [64]. However, a reliable simulation model requires an accurate representation of materials with temperature-dependent mechanical and thermal properties. Lens molding is typically performed at a temperature range of 150-200 ºC above the glass transition temperature (T g ), at which the glass viscosity generally lies between 10 7.6 and 10 9.0 Pa$s [65]. In this temperature range, which is also referred to as the transition temperature range, the glass can be described as a viscoelastic material exhibiting stress relaxation. A general Maxwell model is established to describe the deformation during the pressing stage, as shown in Fig. 14 [66]. The time-dependent response is characterized by the deviatoric terms: where, and ε are the stress and strain, respectively.
Equation (1) is evaluated for a current time t based on the past time τ. Gðt -τÞ is not a constant value but is represented by a Prony series, as shown in Eq. (2): where w i is the relative moduli, and t ri is the reduced time that describes the shift in time resulting from the temperature.
Figure 15 [35] shows the 2D simulation model of the GMP for microgrooves. The upper mold, which is flat and fixed at the top, and the lower mold with microgrooves will move upward to press the softened glass. Simulation results are obtained, and Fig. 16 [35] shows the equivalent stress distribution at the displacement of 15 mm at 570°C.

3D microstructure modeling
2D numerical simulation is used to illustrate the details of the GMP for microstructures, and the molding condition is optimized. However, 2D simulation cannot reveal the glass material flow among microstructure forming, such as microgrooves and micropyramids, because the crosssection of the V-groove is the same as that of the pyramid at the vertex. Therefore, 3D simulation must be incorporated in the numerical analyses of micropyramid forming, and the General Maxwell model is extended to the 3D simulation. Figure 17 [36] shows the 3D models of the GMP for microgrooves and micropyramids. Figures 18  and 19 [36] illustrate the stress and strain distributions for microgrooves and micropyramids.
3.2 Glass molding process for microstructures 3.2.1 Glass molding equipment and molding conditions Different molding machines are widely used to conduct the GMP at high temperatures. Commercially available machines include two leading machines that are discussed in this section. Both of these machines provide the capability and flexibility required for scientific research and industrial practice, i.e., precise control over the mold position, load, and temperature while incorporating an extremely flexible design that can accommodate numerous tests.
1) Glass molding machine PFLF7-60A Figure 20 shows the photograph of the glass molding machine PFLF7-60A, and Fig. 21 depicts its basic structure and functional features.
The machine is equipped with a drive system, a force adaptive control, a precision position control, and a data collector. Basic adjustments of the machine are introduced in the following.  A. Adjustment of the cylinder (i) Cylinder 1 (heating 1) Cylinder 1 increases the mold temperature with slight or without any pressure, and it adjusts the upward and downward positions depending on the weight of the cylinder. Cylinder 1 is also equipped with two regulators, a pressure adjuster, and an adjuster for mold contact. In this working position, the lens should be preliminarily heated to a high temperature in preparation for the next position.
(ii) Cylinders 2 and 3 (heating 2 and 3) Cylinders 2 and 3 are primarily intended to apply slight pressure while raising the mold temperature. Thus, a proper pressure control must be implemented. In these two working positions, the lens should be heated to the molding temperature.
(iii) Cylinder 4 (pressing) Cylinder 4 is primarily intended to facilitate actual molding. Optimum pressure control must be performed on the molds with the lens inside. Cylinder 4 is also equipped with a two-control system consisting of an electropneumatic regulator and a manual regulator.
(iv) Cylinders 5 and 6 (cooling 1 and 2) Cylinders 5 and 6 are primarily intended to apply slight pressure and decrease the mold temperature. In these two working positions, the temperature of the lens should be reduced at a low speed to complete the annealing process.    [36] (v) Cylinder 7 (cooling 3) Cylinder 7 is mainly intended to decrease the mold temperature with slight or without any pressure. In this working position, the lens should be cooled to approximately 200°C.
B. Other adjustments (i) Cooling water flow adjustment The flow rate can be confirmed at a flow rate meter of cooling water. In addition, the cooling water should flow and maintain a temperature of 20°C during the heating operation.
(ii) Nitrogen flow adjustment A flowmeter can check the nitrogen pressure and adjust the nitrogen flow rate to the appropriate value through specific methods. Moreover, nitrogen flows through the driving time of the heating should never be interrupted.   2) Glass molding machine GMP211 Figures 22 and 23 show the photograph and schematic of the ultra-precision glass molding machine GMP211 (Toshiba Corp., Shizuoka, Japan).
Having transfer performance at the nanometer level, the machine enables thermal transfer on glass, quartz, and plastic materials to produce various nanoimprinted products. In addition, this machine excels at reproducing molding conditions, and it provides stable quality among molded parts. Uniform and high-speed heating is realized via the infrared lamp. Meanwhile, nitrogen gas is used to purge the air to protect the molds from oxidation at high temperatures. The molding chamber is covered with a transparent silica glass tube, which allows infrared rays through but separates the nitrogen gas from the air outside. Once the glass preform reaches the molding temperature, the lower mold is driven upward to close the molds, whereas the upper mold is held stationary. Thus, microgrooves are formed. Annealing is then conducted to release the internal stress. Finally, the molded glass plate is cooled to room temperature naturally. Consequently, high-precision and high-quality optical elements can be produced with high productivity through heating, pressing, annealing, and cooling. Table 1 presents typical molded products created through the glass molding machine; the products are obtained from the Toshiba Machine Co., Ltd. website.
3) Comparison between machine PFLF7-60A and GMP211 During the entire molding process, particularly the heating and pressing processes, the glass and the mold must cut off oxygen to prevent oxidation, which may damage the surface quality of the glass and reduce the service life of the mold. Current glass molding machines generally offer two ways to isolate oxygen. The GMP211 by Toshiba Machine Co., Ltd. provides a vacuum environment for lens fabrication, whereas the PFLF7-60A by SYS Co., Ltd. offers a nitrogen environment. Both approaches of avoiding oxidation have advantages and disadvantages, as shown in Table 2. In addition, seven stations, namely, three heating stations, one pressing station, and three cooling stations, are placed in the PFLF7-60A machine to realize automatic production in the chamber simultaneously. By contrast, the GMP211 machine tends to be a more suitable for academic research, as it is more economic because the process occurs at one position.

4) Molding condition control
The thermal expansion of glass is also noteworthy. The volume-temperature relationship of a commonly used glass L-BAL42 (Ohara Corp., Kanagawa, Japan) is plotted in Fig. 24. The softening point (P s ) is defined as the temperature at which the glass deforms under its own weight and behaves as liquid. The yielding point (A t ), which is also called the "deformation point," is the temperature at which glass reaches its maximum expansion   and low plasticity, and therefore starts to shrink. When such a melt is gradually cooled, the volume decreases abruptly to the transition temperature (T g ), below which volume shrinkage occurs at a slower rate. The pressing of a glass lens is always performed above T g . The annealing point (P a ) is the upper end of the annealing range for the pressed glass lens, at which the internal stress is reduced to a practically acceptable value over a short period. The strain point (P st ) represents the lower end of the annealing temperature range and the upper limit of the service temperature of a glass component. During annealing, glass is slowly cooled down from P a to below P st . Molding temperature should be carefully chosen for a good replication of optical microstructures. If pressing is performed above A t and sustained to keep the shape of the lens during cooling, the volume expansion around A t will lead to a sharp increase in the pressing load. In turn, the glass will adhere to the molds. By contrast, if pressing is conducted below A t , a high pressing load will be required because the glass is not sufficiently softened at this temperature range. In this case, significant residual stresses will occur in the glass lens, and the high pressing load may also shorten the service life of the molds. This problem is critical when molding micro Fresnel lenses and DOEs, in which the molds have extremely fine grooves on the surface. Therefore, a suitable temperature must be selected for the pressing in the GMP for microstructures.   Fig. 24 Plot of volume change against temperature for a typical optical glass L-BAL42, showing strongly temperature-dependent thermal expansion characteristics [38] Another major issue in glass molding is the determination of the holding time and the holding pressure. Experiments have been conducted to explore the relationship between mold displacement and pressing load during creep and stress relaxation [1]. Figure 25 schematically shows the changes of the pressing load and the mold displacement in time sequence. Consequently, the holding time and the holding pressure for molding different types of glasses can be determined in the molding process depending on their time-pressing load value.

Test of molded microstructures
Evaluating formed microstructures is important in the study of optical microstructures along with the rapid development of measuring instruments. The microscope and the interferometer are the most extensively used measuring instruments because of their high accuracy, strong intuition, and user-friendly interface.
Microscopes have many types. The most widely used is the optical microscope, which uses light to image the sample. Other major types of microscopes are the electron microscope, including the transmission electron microscope and the scanning electron microscope, and the scanning probe microscope. The laser electron microscope LEXT OLS4100 is a new type of microscope that has gained popularity because of its quick imaging, aesthetics, and revolution of 0.12 mm. Figure 26 shows the laser scanning microscope photographs of the surface morphology of microgrooves and micropyramids molded through the PFLF7-60A. Figure 27 illustrates the microstructure profiles of the mold and the glass after the experiment.   [67].
The filling behaviors of the glass at different friction coefficients are studied using ABAQUS. As shown in Fig. 30, the filling ratios of the glass tend to become larger as the friction coefficient decreases. Therefore, decreasing the friction coefficient between the glass and the mold is a feasible way to avoid the incomplete filling.

Friction reduction through ultrasonic vibration
Ultrasonic vibration has been recently proposed to improve the forming ability of the molding process [68][69][70]. To clarify the mechanism of ultrasonic vibration during the molding pressing, filling experiments are conducted on the PFLF7-60A (SYS Co., Ltd., Japan) (Fig. 20). Figure 31 shows a self-developed ultrasonic vibration-assisted molding machine, which is installed by the Advanced Machining Technology Laboratory in Beijing Institute of Technology. In addition, simulation using ABAQUS is  As shown in Figs. 32 and 33, both the simulation and experiment results show that the glass-filled depth with ultrasonic vibration is significantly larger than the filling depth without ultrasonic vibration. Moreover, ultrasonic vibration can achieve a well-distributed internal stress and reduce the residual stress.
Interface friction between the mold and the glass can be resolved through the frictional contact model shown in Fig.  34. Given that both the Ni-P mold and the glass have a certain surface roughness, the compressive stress between the convex portion of the mold surface and the glass surface is much higher than that in other areas. Consequently, fracture has a higher probability of occurring in high-stress areas, indicating that the tangential motion at the glass-mold interface often causes portions of the glass material to separate from the glass surface and adhere to the mold surface. The ultrasonic vibration applied to the mold can significantly reduce the contact time between the mold and the glass, resulting in a decreased tangential motion and bonding probability. Thus, the stress concentration in the glass layer close to the mold is released presumably because of the reduced friction at high temperatures.

Methods to increase mold life
Additional steps can be added into the molding process to increase the mold life when no negative effects are introduced on form accuracy [71,72]. A two-step pressing method based on the conventional method is proposed. The first pressing step is performed at a high temperature near the softening point, such that the glass behaves as a viscous liquid, and most of the material deformation can be achieved at a low load. After the first step, the pressing load is reduced, and the temperature is lowered to a value between the transition point and the yielding point. Then, the second pressing is conducted at this temperature to close the molds and obtain the final shape of the lens. This two-step pressing method can achieve both high lens accuracy and long mold life.
Demolding ability is a crucial requirement of a mold for glass lenses. That is, the finished lens should be easily removable from the molds. In high-temperature glass molding, the surface of the mold tends to oxidize, and the oxidized material diffuses into the glass, causing adhesion of the glass lens to the mold. Therefore, a release agent is usually coated onto the surface of the mold to prevent oxidation. The lifetime of a mold is almost completely dependent to the release agent coating. The wearing and flaking of this coating reduces the lifetime of the mold. Moreover, the deterioration of the oxidation resistance of the release agent as a result of the in-diffusion of elements from the mold leads to an increased level of wettability by the glass, which further reduces the lifetime of the mold. Thus, the lifetime of the mold is influenced both by the interactions between the release agent and the mold and that between the release agent and the glass. Therefore, the selection of an appropriate release agent for the mold substrate is critical.

Outlook
In this paper, we presented an overview of the recent progress in optical microstructure fabrication through  GMP. To date, several aspects in this area, such as glass molding technology, aspherical lens and microstructure Ni-P plating mold fabrication, and precise measuring instruments, are still at an immature phase. Other aspects, such as freeform microstructure mold design and fabrication, uniformity of the molded microstructures, conformity of microstructure shape in large-area fabrication [73][74][75], and new material preparation, exhibit great potential for next-generation molding processes despite being at their infancy.
1) Freeform microstructure fabrication Optical systems using freeform lenses are becoming a viable solution to both imaging and nonimaging optics because of their capability to reduce the number of elements in an optical system and accurately control light irradiation. A freeform lens is loosely defined as an optical element that is not symmetric around its optical axis [76][77][78][79][80].
Refractive freeform lens consists of two refractive freeform arrays containing 15Â9 single freeform lenslets. Two glass wafers with lithographically structured apertures were bonded together to form a substrate containing three layers of apertures. Refractive freeform arrays are necessary in the constantly developing landscape for extending the image quality of artificial compound eye camera systems [81][82][83][84][85]. Given that freeform glass optics cannot be produced in a large volume through traditional processes, such as grinding, lapping, and polishing, the molding of glass microstructure optics has become a viable manufacturing process. However, replication requires a high-precision mold. Thus, the fabrication of freeform microstructures is expected to receive considerable research attention in the future.
2) Infrared material microstructures "Infrared materials" is a general term for several kinds of materials. Among which, the most commonly used is the chalcogenide glass (in Fig. 35), which contains one or more chalcogenide elements (aside from oxygen) [86][87][88]. Glass-forming abilities decrease with increasing molar weight of constituent elements, i.e., S > Se > Te. As an ordinary optical glass, chalcogenide glass is also moldable [89], which means complex shapes can be developed without using traditional expensive processes, such as single-point diamond turning or polishing. Infrared material microstructures will be widely used in various aspects of industrial and optical systems because of their semiconducting and physical properties, such as high refractive index, low phonon energy, and high nonlinearity [90,91]. A molding method significantly lowers the cost and improves the production. Thus, an increasing number of chalcogenide glass lenses will be made through the GMP in future.