Advanced manufacturing is often limited by detection accuracy, with commonly used high-precision detection methods including optical detection, electron beam detection, and thermal imaging. Among these, optical detection offers advantages such as high efficiency, high sensitivity, and non-destructive testing. However, the accuracy of optical detection remains a challenge that restricts its broader application. By leveraging the polarization characteristics of light, an additional dimension of effective information can be introduced to improve detection accuracy. The polarization characteristics of light are widely used in semiconductor detection. For example, horizontal and vertical line-space patterns on wafer surfaces exhibit different sensitivities to light polarization, leading to varying detection sensitivity for the same type of defects. Optical lenses are critical devices in optical detection, but research shows that lenses can affect the polarization characteristics of light, which in turn affects detection accuracy. While previous studies have attempted to reduce the influence of lens polarization through coatings, no quantitative method exists to control the effect of lenses on polarization characteristics during the optical design process. Therefore, developing a simple and effective design method for controlling bidirectional attenuation in lenses to improve detection accuracy holds scientific significance. In typical lens designs, bare lenses are often used, and ideally, bare lenses only affect bidirectional attenuation in polarization characteristics. In this paper, we explore a method to control bidirectional attenuation through light deflection angle.

Using Fresnel equation simulations, we verified Chipman’s conclusion that bidirectional attenuation is primarily influenced by the back surface of the lens. Since bidirectional attenuation is not a primary design criterion in optical systems, we attempted to represent it with a more intuitive index. By modeling an ideal lens and evaluating the influence of various optical incident and exiting angles on bidirectional attenuation, we discovered that the bidirectional attenuation caused by both the front and back surfaces of the lens is equivalent when the light deflection angle is the same. This led to the development of a strategy to control bidirectional attenuation in optical design using the light deflection angle. Given that different lens materials are used in optical design, we also evaluated the refractive index of the ideal lens model and found that the bidirectional attenuation values remained consistent across different refractive indexes for the same deflection angle, eliminating refractive index as a factor. We established the functional relationship between deflection angle and bidirectional attenuation through data fitting, arriving at a quadratic equation. The fitting accuracy and adjusted R-squared values confirmed the high precision of the fit. In addition, we analyzed the cumulative bidirectional attenuation in a multi-lens system using a cumulative multiplication approach.

An ultraviolet microscope detection lens (Fig. 16) is designed using the bidirectional attenuation-light deflection angle (B-L) formula. Its initial structure is determined by the B-L formula and primary aberration theory, resulting in the design of a three-element lens. The first lens is curved toward the object side, while the third lens is curved toward the image side (Fig. 9). Maintaining symmetry in the design helps correct for coma, astigmatism, and distortion. During optimization, the B-L formula is used to effectively control the light deflection angle, ensuring that the lens meets the expected bidirectional attenuation performance. However, a fully symmetrical structure cannot achieve the required magnification, leading to the application of the Stop-Shift theory to break the lens symmetry and finalize the design. The resulting design meets the required imaging performance, with the root mean square (RMS) radius of the full field of view exceeding the diffraction limit. Field curvature is controlled within ±0.8 μm, and distortion is kept below 0.25%. The actual bidirectional attenuation performance, as traced through ray simulations, closely matched the predictions from the system bidirectional attenuation-light deflection angle (S-B-L) formula, fulfilling the performance expectations.

In this study, we propose a method for controlling bidirectional attenuation based on light deflection angle. Through analysis using Fresnel equations, we identify the intrinsic relationship between light deflection angle and bidirectional attenuation. By employing statistical methods, the theoretical derivation is simplified, leading to the formulation of the B-L equation for the relationship between deflection angle and bidirectional attenuation. In addition, an S-B-L formula for evaluating the cumulative bidirectional attenuation in multi-lens systems is developed. The ultraviolet microscope designed using this approach demonstrates the expected bidirectional attenuation performance. The results indicate that light deflection angle can be used to effectively characterize bidirectional attenuation. Simplifying control metrics in this way facilitates lens designs that meet expected bidirectional attenuation performance while also reducing design time.