1.

Introduction

Due to the tremendous growth in media technology in recent times, the demand for ultraprecision optical components^1,2 has increased rapidly. In addition, there has been a corresponding increase in the demand for improvement in optical performance, e.g., higher resolution and brightness. Thus, there is a growing need for precise aspheric glass lenses and ultraprecision grinding of the mold core^3,4,5 and molding techniques⁶ that are able to mass-produce the aspheric glass lenses are needed. Nowadays, the glass molding press (GMP) method⁶ is favored as the molding technique for aspheric glass lenses because fabrication through conventional glass grinding techniques is not only difficult but also gives a low mass production.

Aspheric glass lenses, produced using the GMP method, are molded by treating them by a process in which they are subjected sequentially to heating, pressing, and cooling. This leads to thermal deformation of the lenses, especially in the cooling process. The thermal deformation changes the radii of curvature of the lenses and lowers the performance of the optical system.

In this study, the thermal deformation of aspheric glass lenses during the cooling process in the GMP technique was analyzed and the results were applied to the ultraprecision grinding of the mold core in order to improve the performance of lenses used in closed-circuit televisions (CCTVs).

2.

Aspheric Glass Lens

2.1.

Design of an Aspheric Glass Lens

Aspheric surfaces can be represented by a specific equation, Eq. (1), obtained by adding the conic section and the aspheric shape factor

Eq. (1)

$$z=\frac{C·x^2}{1+\sqrt{1-(1+K)·C^2·x^2}}+\sum _{i=1}^n{A}_i·x,$$

where $C$ is the inverse of the radius of curvature, $K$ is the conic constant, and $A$ is the aspheric coefficient. In this case, the surface has a hyperbola, a parabola, an ellipse, and a sphere—various forms of a conic section—rotated about the optic axis, whose form is determined by the conic constant.

Figure 1 shows a schematic diagram of an aspheric glass lens for a CCTV optical system.

Fig. 1

Schematic optical design of aspheric glass lens.

2.2.

Thermal Deformation in the Molding of Aspheric Glass Lenses

In general, the GMP process is used for the mass production of aspheric glass lenses. In this study, progressive-type molding was applied to the GMP method. Progressive-type molding is carried out sequentially in the following three stages: heating, pressing, and cooling. This molding technique is suitable for the mass production of uniform aspheric glass lenses. Figure 2 shows a schematic of the progressive-type molding⁶ used in this study.

Fig. 2

Schematic of the progressive type molding.

In the GMP process, glass lenses are molded by heating them above the yield point (at 559°C), followed by pressing and cooling of the glass lenses, after a preform of the glass is loaded in the mold core. During the transition from the pressing stage at high temperature to the cooling stage at room temperature, molded lenses are thermally deformed due to the creation of thermal stress inside the lenses. Thermal stress is caused by the difference in the cooling rate due to the difference in the thickness of a lens. The thermal deformation varies according to the shape and the size of the lenses, leading to errors in the value of the designed lenses’ form accuracy. This further leads to lower optical performance of aspheric glass lenses. Figure 3 schematically describes the thermal deformation during the GMP process.

Fig. 3

Schematic description of thermal deformation during glass molding press processing.

3.

Experimental Equipment and Condition

4.

Molding Analysis and Compensation Process

The form accuracy of the mold core made using ultra precision grinding was found to be 0.213 μm peak to vally roughness height (P-V). Ten aspheric glass lenses molded using the grinded mold core were made to have a form accuracy in the range of 3.6 to 3.8 μm (P-V), affected by thermal deformation that occurred during the molding process. It was observed that the values had deviated sharply from the standard specification [below 0.8 μm (P-V)] of the designed lens. Figures 4(a) and 4(b) respectively show the form accuracy of the mold core before the compensation process and an aspheric glass lens after molding.

Fig. 4

Form accuracy of (a) mold core and (b) molded lens before compensation.

To compensate for the form accuracy errors that occurred during the thermal deformation of the molded lenses, the compensation algorithm, which is given by Eqs. (2) and (3), was used.

During the compensation process, the aspheric equation, Eq. (1), was divided into a spherical term $Z_{\mathrm{sp}}$ and an aspheric term/coefficient $Z_{\mathrm{a}}$ to reduce the parameters. The spherical term was made constant to determine the aspheric coefficient using the nonlinear curve-fitting method.⁷ A sag value $Z_{\mathrm{n}}$ of compensation in the aspheric equation was obtained by adding the spherical term $Z_{\mathrm{sp}}$ of the designed lens and the aspheric coefficient $Z_{\mathrm{a}}$, which is the sum of the aspheric term of the designed aspheric surface and the compensation aspheric term $Z_{\mathrm{com}}$ that represents the thermal deformation. In this process, the compensation factor $\alpha$ is set at 0.85, and it reduces reshrinkage of the compensated mold core and influences the measurement of errors in lenses. Figure 5 shows the nonlinear curve-fitting results of the shrinkage-compensated aspheric coefficient $Z_{\mathrm{a}}$.

Fig. 5

Result of nonlinear curve-fitting.

The form accuracy of the mold core reprocessed as the compensation shape by ultraprecision grinding was 0.157 μm. The form accuracy of the 10 aspheric glass lenses remolded using the mold core made during the compensation process was found to be in the range 0.3 to 0.45 μm. After the compensation process, the form accuracy of the aspheric glass lenses improved from 3.7 to 0.35 μm. These results agreed with the standard specifications. Thus, it was proven that the compensation algorithm of thermal deformation is suited for molding aspheric glass lenses. Figure 6 shows the form accuracy of a mold core and a molded lens after the compensation process. Figure 7 shows pictures of the mold core and molded lenses.

Fig. 6

Form accuracy of (a) mold core and (b) molded lens after compensation.

Fig. 7

Photograph of mold core and molded lens.

5.

Conclusion

In this study, the thermal deformation phenomenon that occurs during the molding of aspheric glass lenses was analyzed for aspheric glass lenses used in CCTVs. The mold core was reprocessed by using the compensation aspheric coefficient determined by using the nonlinear curve-fitting method for the compensation of thermal deformation during the molding of aspheric glass lenses. The GMP technique was implemented using the reprocessed mold core and the progressive-type molding method, and the following results were obtained: