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Abstract
This paper presents the design and fabrication of a novel double-sided aspherical Fresnel (DSAF) lens on a curved substrate to tackle the Fresnel lens problems such as long focal length and large volume. This novel lens contains a curved substrate and a bifacial aspherical Fresnel lens. The structural design and nonlinear optimization method of the lens were discussed. Then, the optical characteristics of the DSAF lens were also analyzed by Ray-tracing simulations. Furthermore, to manufacture the DSAF lens, considering the machining accuracy and cost-effectiveness, a combined method of single-point diamond turning (SPDT) and press molding was proposed for generating the DSAF lens with PMMA material. Machining accuracy was used to validate the performance of the molds before production of the DSAF lens, followed by testing of the fabricated DSAF lens. The results show that the DSAF lens has the advantages of more design degree, short focal length, small volume, and good light-gathering, etc. which is suitable for mass production. The study provides a cost-effective method for the design and preparation of ultrathin Fresnel lenses.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Energy is vital to the development of nations and the improvement of people’s lives. With global fossil energy shortages and environmental problems are becoming increasingly prominent, the issue of finding green and clean alternative energy sources is becoming increasingly urgent [1,2]. In the field of renewable energy, high concentrating photovoltaic (HCPV) technology [3–5] has attracted much attention. Fresnel lens is widely used in HCPV modules and the function is to focus sunlight from a large area onto a small area of the Photovoltaic (PV) cells. Therefore, it is necessary to design and optimize the lens from new structures and methods to achieve maximize the concentration of solar energy.
Fresnel lens is the most common optical element with functional microstructures, which is widely used in various optical applications [6–8], such as lighting, solar power generation, and surface modification of metal materials, owing to its good light concentration, light-weight, and low cost. Since the high cost of PV cells, optimizing the Fresnel lens structure is one of the preferred options to improve the performance and reduce the initial cost of HCPV systems [9–11]. However, the compact volume, thin thickness, and light-weight of the lens design are still a major challenge.
According to the substrate, typical Fresnel lens can be mainly divided into flat and curved. Flat Fresnel lens [12,13] is widely used in photovoltaic systems and solar thermal systems owing to its ease manufactured. Li et al. [14] proposed an improved flat condenser lens that can absorb different wavelengths. Ma et al. [15] designed an aspherical and concave array coupled lens, which greatly reduced the weight and thickness of the lens. Gupta et al. [16] designed a hybrid solar-photovoltaic-thermal (SPVT) system that can simultaneously generate electricity and supply hot water. Since the limitation of the lens’s structure, a precise tracking system must be used to strictly control the angle of incidence of the incident light, otherwise, it is easy to deflect the concentration point of the solar cell, resulting in a significant reduction in energy conversion efficiency. Nevertheless, the complexity and installation cost of the light collection system is significantly increased, which is not conducive to the large-scale use of Fresnel-lens concentrating systems.
Unlike flat Fresnel lenses, curved Fresnel lenses can be optically coupled or directly fixed on the solar cell surface, which has obvious advantages in terms of optical quality, miniaturization, and light-weight [17–20]. Hiramatsu et al. [21] studied the focusing efficiency of the planar and curved Fresnel lens, and indicated that the curved Fresnel lens can absorb both direct and diffuse light with a higher focus efficiency than that of the planar Fresnel lens. Araki et al. [22] found that a circular Fresnel lens helps to reduce the tooth depth of the non-working surface and light loss, and can achieve conversion efficiency in a small area. Liang et al. [23] coupled a circular Fresnel lens with a curved surface, and the first curvature as a design parameter can provide more design freedom. Donovan et al. [24] considered the lens size and shape as the main factors affecting the concentrating efficiency of the Fresnel lens. However, it is still difficult to design such a curved lens efficiently optically that can be fabricated at a low cost. The symmetrical biplanar Fresnel lens [25] brings a simplified solution of an optical system with reduced volume, thickness, and focal length. Meanwhile, the double-sided Fresnel structure design can greatly reduce the lens material unrelated to optical performance, resulting in a thinner lens and better-focusing effect.
Volume and thickness are essential to the design and fabrication of Fresnel lenses. However, there still has been a demerit of research on Fresnel lenses: (1) The conversion rate of solar cell energy is limited by the effect of the lens concentration, the closer to the lens edge, the greater the loss of optical energy reflection, which means weak the energy conversion efficiency [26]; (2) In a Fresnel lens, there is a trade-off between high focusing power and small size. Typical Fresnel lenses with long focal lengths are not conducive to light gathering and also increase in size and weight [27].
To address these issues, a novel Fresnel lens architecture composed of a curved substrate coupled to a bifacial aspherical lens to achieve minimized focal length and weight was developed in this study. The bifacial aspherical lens consists of several concentric rings. This novel lens, named Double-sided Aspherical Fresnel (DSAF) lens, provides more design freedom. The DSAF lens is lighter and more compact than the traditional lens, which is large and heavy due to the functional microstructure on only one side and the long focal length. Since a series of optically aspherical designs on the front and rear surfaces of the novel lens and the curved substrates is applied, it can be designed with a variety of focal lengths and sizes. Furthermore, we attempt fabricating the DSAF lens by combining single-point diamond turning (SPDT) and hot press molding. By which high precision DSAF lens could be obtained at a low cost and high efficiency.
This paper is organized as follows. Section 2 describes the structural design of the DSAF lens and nonlinear optimization method. Section 3 discusses the optical performances of the DSAF lens. Section 4 presents the fabrication and evaluation methods of the DSAF lens. Section 5 outlines conclusions.
2. Principle and design of the lens
In this section, the design and optimization methods of the DSAF lens are described in Section 2.1 and Section 2.2, respectively. A design example is used to verify the method in Section 2.3.
2.1 Proposed DSAF lens
The cross-sectional profiles of the conventional lens and the DSAF lens are shown in Fig. 1. The previous literature review pointed out some optical drawbacks of conventional lenses. The DSAF lens avoids these issues with its unique design - composed of a curved substrate and a bifacial aspherical lens with concentric rings coupled, as shown in Figs. 1(d) and 1(e). The curved substrate is used to improve the field of view and light gathering efficiency, while the bifacial aspherical lens is used to reduce the focal length and weight. The optical path length conservation theorem, Snell's law, and the edge ray theorem [28] are used to calculate the initial structural dimensions of the surface of the novel lens. Subsequently, the structure of the novel lens is optimized by using total internal reflection (TIR) and refraction phenomena.
Fig. 1. (a) Flat Fresnel lens; (b) Double-sided Fresnel lens; (c) Curved Fresnel lens; (d) DSAF lens; (e) Composition of the DSAF lens.
For the convenience of description, this article refers to the central ring of the novel lens as the 1st ring, and from the center to the outside are the 2, 3, …, N rings. The convex surface of the curved substrate is called the front surface, and the concave surface of the curved substrate is called the rear surface.
In the design of aspheric Fresnel lenses, eliminating chromatic aberration and stray light are a challenge. To resolve these problems, nonlinear optimization methods are proposed for front surface rings tooth tip modification and rear surface rings shifting. Therefore, the novel lens design can be subdivided into four steps, as illustrated in Fig. 2.
Fig. 2. (a) Biconvex lens; (b) Original optical surface; (c) Optical surface curvature adjustment; (d) Tooth tip modification of the front surface rings; (e) Novel lens stricture; (f) Displacement of the rear surface rings.
Step 1. Construct a biconvex lens to obtain virtual optical surfaces with different rings positions.
Step 2. The optical surface on the lens is cut into n parts, and the optical surface is translated onto the substrate by the sink-and-stretch method.
Step 3. The radius of curvature and focal length of the first ring on the front and back surfaces are used as a reference to construct an iterative relationship between adjacent rings to adjust the radius of the surface of each ring, and finally achieve a consistent design of the focal point of all rings.
Step 4. Determining the amount of tooth tip modification for each ring on the front surface by optical path analysis. Then the lens rear surface rings are shifted to suppress stray light.
As mentioned above, the novel lens has the following advantages:
· Short focal length and thin thickness. A bifacial aspherical lens design can reduce the focal length difference between the distal rings and the central rings, which means shorter focal lengths and smaller volumes. Coupled with a bi-Fresnel lens design, the amount of material that has nothing to do with optics is removed more, which means reducing thickness.
· Large acceptance angle and high optical efficiency. The novel lens combines the advantages of the curved lens [29] and the “fisheye” effect, solving the problem of light energy reflection loss at the edge of the Fresnel lens. Meanwhile, the focal point can be theoretically be stably placed on the designed focal plane when the inclination angle of the incident light changes, so that more light can be collected.
2.2 Lens design and optimization
The design method and nonlinear optimization of each ring on the front and rear surfaces of the lens are described in this section. The design degree of freedom is increased by setting the radius of curvature of the rings on the front and back surfaces to be variable.
· Front surface rings design: The optical surfaces of the lens are mainly used in the form of spherical or aspheric, free-form surfaces [30], where the aspherical surface can reduce the diffuse light spots caused by the thickness difference between the center and the edge of the spherical surface and improve the optical quality. Therefore, the aspheric surface is chosen to design the novel lens in this paper. The aspheric surface equations as follows: [31,32]
Figure 3 illustrates the design principles and the significance of each parameter of this novel lens. According to Lensmaker’s equation, when the lens material is certain, the virtual radius of curvature and focal length can be determined as follows:
The 1st ring in the center of the novel lens is obtained by direct translation of the optical surfaces. Consequently, the radius of the 1st ring is only related to the wavelength, $\lambda $, and the focal length, f, namely:
where the 1st focal length, $f_1^1$, and the system focal length, f, are equal, i.e., $f_1^1 = f$.For the subsequent analyses, the design method of each ring from the 2nd ring onwards is explained. In the paraxial approximation condition, the radius of each ring, which can be determined as follows:
where $r_n^1$ is the bottom of the nth ring teeth position relative to the optical axis. Subsequently, the optical surface is cut into n parts with $r_n^1$ as the radius. Translating optical surfaces to the curved substrate by the sink-and-stretch method. However, the focal length of each ring is not at the same point.To guarantee a consistent focal point for each ring, the radius of the optical surface of each ring is changed. As illustrated in Fig. 4, the focal deviation of the adjacent rings on the front surface is the sum of the base vector height and the depth of the groove of the lens face type, namely:
where $L_n^1$ indicates the base vector height of the nth ring, hn denotes the depth difference between the top of the nth ring and the bottom of the n-1th ring, namely the tooth depth. Taking the 1st ring radius, $r_1^1$, and focal length, $f_1^1$, as the reference, the remaining ring radius, $r_n^1$, and focal length, $f_n^1$, can be calculated by Eq. (4) and Eq. (5).The optical surface of the rear surface can be approximated as flat when designing the optical surface of each ring on the front surface. that is, R2 tends to infinity. Equation (2) can be represented as follows:
From this, the radius of each ring on the front surface can be inverse derived, i.e. $R_2^1$, $R_3^1$,….
As previously mentioned, based on Eq. (4) and Eq. (5), the focal length and radius of the 1st ring on the front surface are determined, and the design of the other rings on the front surface can be carried out. Then, the radius of the optical surface of each ring is adjusted according to Eq. (6) to ensure that the focal points are all focused on a point. Finally, the structural design of the front surface of the lens is completed.
· Rear surface rings design: To simplify the calculation, the optical surface of the rear surface is designed with the same parameters as the front surface, but it is opposite in value. Since the novel lens is designed based on the biconvex lens principle, each ring on the rear surface can be seen as a biconvex lens ring. Therefore, the radiuses of the rings on the front and rear surfaces are equal, namely:
Due to the thickness of the lens is much smaller than the radius of the ring optical surface, it can be ignored when designing the rings on the rear surface. On the nth ring of the front and rear surfaces, the relationship between the radius of the optical surface and the focal length can be rewritten as:
Solve Eq. (8) to obtain the radius of the optical surface of each ring on the rear surface. Ultimately, a consistent design of the optical surface focus on each ring on the front and rear surfaces of the lens is achieved.
· Nonlinear optimization of the lens. The optimization methods of tooth tip modification and ring displacement are presented for each ring on the front and rear surfaces, respectively.
- (1) Tooth tip modification of each ring on the front surface. According to the law of refraction, when the incident light passes through the tooth tip of each ring on the front surface, a part of the area will make the light refraction or total reflection, which eventually leads to the light can not converge to the focal spot position, resulting in light energy loss, called the tooth tip shading effect, as shown in Fig. 5(a). Therefore, to improve the focusing efficiency of the lens, the tooth tip of each ring on the front surface of the lens needs to be modified to eliminate the negative effect of the tooth tip shading effect.
Assuming that the light is incident from the point $A ({P_{n1}},{Z_{n1}})$ on the nth ring of the front surface, and its refraction ray passes through the point $C({P_{n0}},{Z_{n0}})$ on the n-1st ring, as shown in Fig. 6. From Eq. (1), the coordinates of the tooth bottom of the n−1st ring $C({P_{n0}},{Z_{n0}})$ and the equation ${Z_n} = F({P_n})$ of the optical surface of the nth ring can be derived. The equations of the tangent and normal at the point $A ({P_{n1}},{Z_{n1}})$ as follows:
According to Eq. (9) to Eq. (11), the optimized equation of tooth tip coordinates of each ring on the front surface can be obtained as follows:
Consequently, once the coordinates of the tooth bottom of the previous ring are known, the coordinates of the tooth tip of the next ring can be deduced for the modification of the tooth tip on the front surface.
Figure 7(a) illustrates the shape of the novel lens after tooth tip modification. The modified rings on the front surface change the area of the non-working area between two adjacent rings, resulting in the formation of a diffuse spot on the focal plane of the lens after the light passes through the novel lens. However, the diffuse spot is too large to reduce the focusing efficiency. Additionally, light through the tip of each tooth of the front surface will cause local changes in the optical path. After refracting through the nth ring of the front surface, the light will be emitted in the n−1th ring on the back surface, which will cause the stray light phenomenon. Therefore, to improve the optical performance of the lens, it is necessary to shift the rings on the lens rear surface.
- (2) Displacement of each ring on the rear surface. The main purpose of the rear ring shift is to ensure that the light path after refraction by the lens remains parallel to eliminate stray light. In other words, light refracted through the nth ring of the front surface will be emitted from the nth ring of the rear surface.
The displacement of each ring on the rear surface depends on the amount of tooth tip modification of each ring on the front surface. Hence, the specific method for shifting each ring on the rear surface as follows:
Step 1. The Ray-tracing method is used to analyze the optical path of the incident light after refraction, and find the intersection of the refracted light passing through the top and bottom of the teeth on the front surface and the virtual optical surface on the rear surface, respectively.
Step 2. On the virtual optical surface of the rear surface, intercept the area with refracted light passing through it and move along the refracted light path, as illustrated in Fig. 7(b).
Step 3. There exists a new intersection between the refracted light passing over the tooth bottom of the different rings on the front surface and the substrate on the rear surface, which is the new coordinate of the tooth bottom of each ring on the rear surface.
Based on the above analysis, it is clear that if we know the focal length and mounting size, the design of the DSAF lens can be realized. Additionally, the algorithms required to design the novel lens are also developed, as shown in Fig. 8.
2.3 Design example
To demonstrate and verify the validity of the design method of the novel lens, we design a DSAF lens in this section. The higher order of the Fresnel lens surface type, the higher requirement for machining accuracy. Therefore, considering the machining accuracy and light illumination, in this study, the parabolic surface was chosen as the optical sphere of the lens [33]. The structural design and optimization method were illustrated by the DSAF lens with PMMA material [34].
For simplicity, the initial optical surfaces of the front and rear surfaces of the DSAF lens were the same design parameters. R indicates the initial radius of the curved substrate, Dlens denotes the radial diameter of the lens, and other design parameters are shown in Table 1.
Table 1. Design parameters of the DSAF lens
We start by encoding the calculation procedure into MATLAB software to find the contour point data for each ring. Then, using Auto CAD software to fit the contour bus of the DSAF lens to save computing resources and increase efficiency. After that, the curves were imported into SolidWorks software to generate a 3D model. The Ray-tracing simulation will be described in the following section.
3. Performance evaluation of the DSAF lens
To verify and analyze the performance of the DSAF lens, we take the 3D model of the novel lens in Section 2.3 as an example for further study. The Ray-tracing simulations are one of the effective methods to test the optical performance of the Fresnel lens [35]. Therefore, this paper chose to Ray-tracing method as the simulation tool.
The light propagation in the DSAF lens illuminated by a parallel source was analyzed. The number of rays was 271, the luminous flux of each ray was 1 watt, the spectrum was 380∼760 nm, and the receiving screen was set up in the focal plane. The subsections hereafter reproduce the main results including stray light, energy, and illumination distribution of the focal point on the focal plane.
3.1 Straylight analysis
Stray light is a key part of the optical analysis, which directly affects the optical quality of the lens. The ray-tracing of the DSAF lens on the receptor, as shown in Fig. 9. It can be seen that the lens forms a clear focus point on the receiving screen, the refraction angle of the light from each ring is different, and the refraction lines are regularly arranged without a stray light phenomenon. This indicates that the shading effect and stray light have been largely eliminated by the tooth tip modification of the front surface rings and the shifting of the rear surface rings, which improves the light utilization.
3.2 Focus capability analysis
Luminous flux is one of the important indicators of the intensity of lens light gathering and can directly reflect the working ability of the lens in the optical system. Luminous flux is the light energy of all light waves passing through a certain cross-section per unit of time, indicating the overall brightness of the light source.
Figure 10(a) shows the energy diagram of the original light on the receiving screen. The Kanter diagram of the original light after refraction through the lens, as shown in Fig. 10(b). It can be observed that the luminous flux in the focal plane was 71764 lm. The light intensity energy distribution of the DSAF lens, as shown in Fig. 11. The maximum light intensity was 69617 cd, which indicates that the lens has a better light intensity capability.
Fig. 10. (a) Original light on the receiving screen; (b) Refracted light candela plot on the receiving screen.
Illuminance is the amount of luminous flux received per unit area. The simulation results of the focal light intensity distribution of the novel lens, as shown in Fig. 12. The blue and green lines indicate the variation of the focal energy of the optics in the vertical and horizontal directions, respectively. It can be observed that a distinct Gaussian spot was formed in the focal plane, which indicates the better light gathering ability of the lens. Additionally, the light intensity varies continuously at the focal plane, indicating that the lens is uniformly illuminated.
From the above results, the simulation results verify the correctness of the design method of the novel lens. The novel lens has a good concentrating effect and the light intensity is uniform in the focal plane, which is indicated that the novel lens can be applied to the solar concentrating system.
4. Experimental procedures of the DSAF lens
Manufacturing technology is critical to promoting the application of the novel lens. However, developing a suitable low-cost and high-efficiency machining method for Fresnel lenses is still a tough issue. Optical machining techniques such as the beam direct writing method [36], thin-film deposition method [37], and replication technique [38] have their drawbacks and limitations of use in terms of the machining process, production efficiency, and cost. Hot press molding technology [39] is considered to be a cost-effective processing method. Nevertheless, it requires high machining accuracy and durability of the mold. Fortunately, single-point diamond turning (SPDT) technology [40] can achieve surface machining accuracy from tens of micrometers to micrometers or even sub-microns, but the tool wears out easily when working with microstructures for a long time.
To achieve the machining of the DSAF lens, we propose a new method for DSAF lens fabricating by combining the advantages of hot press molding technology and SPDT. In other words, the lens molds were first fabricated with the SPDT, and then the DSAF lens was fabricated with a hot press molding. This method has advantages such as low cost and good product consistency.
In this section, the process of machining lens molds is detailed in Section 4.1. The molding device and processes are investigated in Section 4.2. In Section 4.3, the molding quality and optical properties of the molded lens are analyzed.
4.1 Mold fabrication
A machining process of the molds for hot press molding is discussed. According to the lens design parameters shown in Table 1, the upper and lower mold profiles can be obtained, as shown in Fig. 13. The machining process of the molds can be divided into rough machining and finishing machining. It is composed of four main stages:
Firstly, a cylindrical blank was machined with an aspheric substrate by using a CNC lathe (MH450, TEMA, China), where the blank material is STAVAX ESR (S-136). Then, to ensure sufficient finish and durability of the mold surface, a 200 µm thick layer of Ni-P alloy was uniformly plated on the aspheric substrate using electroplating. Subsequently, the aspheric substrate surface was finished with an ultra-precision diamond lathe (Nano form X, USA), in which the spindle speed was 1500 r/min, the Z-axis feed was 5 µm, and the feed rate was 12 mm/min. Finally, a series of rings with the same circular center were machined on the finished aspheric substrate, where the spindle speed was 2000 r/min, the Z-axis feed was 2 µm, and the feed rate is 2 mm/min.
The overview of the DSAF lens molds machining process is shown in Fig. 14. First, the toolpath was planned according to the geometry of the lens mold. Then, to avoid tool interference and verify the accuracy of the machining process, the generated CNC code was imported into MATLAB software for the morphological simulation of the machining quality. Lastly, the machining code was introduced into the ultra-precision lathe to machine the curved substrates of the upper and lower molds, respectively. The novel lens molds were machined with a slow tool servo. Dimensional and surface integrity inspections of the molds were measured by a 3D surface profiler (NewViewTM 7300, ZYGO, USA) and surface roughness profiler (PGI Optics AAU, Talysurf, UK), respectively. The detailed molds machining procedures, as we show in Dataset 1 (Ref. [41]).
For further investigation, the surface shape contours of both molds were measured, and the results are plotted in Fig. 15. It can be found that the measured and theoretical values of all ring surfaces match well, and the tooth tips of each ring are complete. Meanwhile, although these randomly distributed errors in ring contouring may reduce shape accuracy, these errors do not exceed the reserved machining margin (5 µm). The surface roughness of upper and lower molds is 5.3 nm and 2.831 nm, respectively. In addition, for both upper and lower molds, the ring profile error gradually increases from the center surface to the outer surface, which may be related to the gradual increase of Z-axis feed and line cutting speed. If the machining process parameters are optimized, it is still possible to further improve the machining precision of the molds.
4.2 Hot press molding process
To achieve the fabrication of the DSAF lens, we design a homemade press apparatus. The manufacturing process of the hot press molding is also described in this section.
· Hot press molding condition: The DSAF lens was conducted using a homemade press apparatus, as depicted in Fig. 16. The machine consists of two main parts: hardware and software. The hardware part mainly consists of frame, pressurizing device, temperature control, mold module, scale, and proximity switch. The software part mainly consists of a computer, operation control card, stepper motor driver, and Z-axis drive motor controller, etc. Mold positioning installation accuracy is 1 µm.
· Hot press molding process. The hot press molding process for the novel lens can be mainly divided into four steps, as illustrated in Fig. 17. Firstly, to avoid the formation of air pockets, a flat-shaped PMMA is used in press molding. The upper mold is dropped closer to the stationary lower mold. The mold groups and substrate will be heated to 180 °C for 5 min. Secondly, a preheated substrate will be placed into the molds group and then the molding chamber will be closed. The press head presses the substrate at a speed of 0.05 mm/s and a pressure of 1.2 kN. Meanwhile, the pressure temperature is maintained constant. Thirdly, the pressing force will be held on for 25 min, and the temperature will be lowered from 180 °C to 60 °C. Finally, until naturally cooled to room temperature, the molded DSAF lens is demolded from the mold groups.
In addition, the operation control card, stepper motor, and grating ruler are used for precise control of the entire molding process. As a motion actuator, the stepper motor converts electrical pulse signals into line displacements. The grating ruler monitors the downward linear displacement of the indenter in real-time and feeds the signal to the operation control card. Thus, the closed-loop motion control system consisting of the above-mentioned devices is formed. The detailed hot press molding parameters of the novel lens as shown in Table 2.
Table 2. Hot press molding parameters of the novel lens
4.3 Lens characterization analysis
To evaluate the dimensional accuracy and the quality of the molded DSAF lens with the PMMA substrate using the hot press molding, surface profile and shape were measured by a 3D optical profiler and a super depth-of-field microscope (RH-2000, HiROX, Japan). The focal length of the molded lens was measured by an automatic focal length measurement (F200).
· Dimensional accuracy evaluation. The microscope images and profile of the molded DSAF lens are shown in Fig. 18. It can be observed that the surface integrity of the DSAF lens fabricated by the hot press molding process is well, and there are no obvious defects on the tips and bottoms of the tooth of the rings.
Fig. 18. (a)∼(b) Microscope image of the front surface of the molded DSAF lens; (c)∼(d) Microscope image of the rear surface of the molded DSAF lens; (e) The cross-sectional profile of the DSAF lens front surface; (f) The cross-sectional profile of the DSAF lens rear surface.
The results of surface profile inspection on both sides of the lens are shown in Figs. 18(e) and 18(f). The measured values of each ring profile on the front and rear surfaces of the lens are in agreement with the theoretical values. The molded quality of the lens decreases sequentially from the center to the periphery, but within the allowable error range, which is related to the machining quality and processes of lens molds. The error of the tooth tip of each ring on the front surface is within 5 µm, and the replication ratio is 96.155%. The error of the tooth tip of each ring on the rear surface is within 2 µm, and the concave reproduction guarantee is 97.188%. Based on these observations, it can be concluded that the hot press molding can be used for the fabrication of the novel lens.
· Measurement of the focal length. The focal length of the DSAF lens is also experimentally determined. The focal length measurement set-up is depicted in Fig. 19. The measurement results of focal length for the DSAF lens are shown in Table 3. It can be seen that the average focal length of the novel lens is 20.54 mm, the mean Std Dev and the Std Dev are 0.087 mm and 0.42%, respectively. The focal length error between the measurement and the theoretical value is within 3%, which demonstrates the correctness of the design methodology and simulation results.
Table 3. Measured Focal Length (mm)
From the above results, unlike other aspheric lenses, this double-sided aspheric Fresnel lens can be fabricated using existing machining technology, which has certain advantages in terms of production cost and production efficiency. The study has significance for the promotion and application of this novel lens.
5. Conclusions
In this study, a novel double-sided aspherical Fresnel (DSAF) lens on curved substrate is proposed, when facing the challenges brought by Fresnel lenses in terms of focal length and volume. This novel lens possesses two main components, namely curved substrates to reduce the volume and a bifacial aspherical Fresnel lens to reduce the weight and the length. A nonlinear optimization method was used, which is greatly simplifies the design and solution process of the DSAF lens. The optical performances of the DSAF lens have been analyzed by the example of calculation and Ray-tracing simulation. The simulation results show that the DSAF lens can improve light utilization effectively, suppress stray light, and have high focusing efficiency, which demonstrates the feasibility and superiority of our proposed method. Subsequently, the DSAF lens with higher quality was fabricated by hot press molding. The molded accuracy and optical capabilities of the DSAF lens were evaluated.
Our research has successfully demonstrated that the optical performance of the lens can be improved using a double-sided Fresnel lens design on a curved surface. The results presented in this paper mainly demonstrate the optical performance of the novel lens from the principle and theory. To achieve the engineering application of this lens, further work will not only focus on the effect of molding process parameters on the dimensional accuracy of the molded lens but will also investigate the optical properties of the lens under different materials. In addition, coupling this novel lens to the PV cells is the matter of our future research. The hot press molding technique for fabricating lenses has limitations in terms of processing size and efficiency. Therefore, the development of new lens machining techniques, such as 3D printing, should be considered in future work. In summary, we believe that the DSAF lens design approach can inspire new potential in other optical application scenarios such as LED lighting, spotting mirrors, detectors, etc. where mounting space and weight are required.
Funding
National Natural Science Foundation of China (51875491, 51975501).
Acknowledgments
We acknowledge Huazhong University of Science and Technology for the support in this research.
Disclosures
The authors declare no conflicts of interest.
Data availability
Detailed mold machining procedures are shown in Dataset 1 (Ref. [41]). Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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