In this paper, we investigate and validate the elliptical deformation phenomenon observed in interference rings generated by transmission Tolansky interference measurements, which significantly influences the accuracy of precision measurements. Transmission Tolansky interference is a critical technique for measuring small angles, surface parallelism, refractive indices, and other parameters in applications such as gravitational wave detection, high-power lasers, wafer lithography, and precision computer numerical control machining. However, elliptical interference rings hinder measurement precision. Thus, we elucidate the mechanisms underlying this deformation and propose strategies to mitigate it, enhancing the reliability of transmission Tolansky interference measurements.

The elliptical deformation of interference rings is analyzed using the imaging characteristics of parallel plates. We examine three primary factors influencing eccentricity: parallel plate thickness (d₁), light incidence angle (I), and distance between CCD camera and point light source ( f ). Theoretical modeling establishes the relationship between these factors and eccentricity (e) using geometric optics and interference principles. MATLAB is employed to visualize this relationship, demonstrating trends in eccentricity variation with changes in the three parameters. Zemax simulations corroborate the theoretical predictions, revealing a positive correlation of eccentricity with light incidence angle and parallel plate thickness, and a negative correlation with CCD-to-point light source distance. To validate these findings, we conduct physical experiments using a 632.8 nm helium-neon laser, a rotatable parallel plate, a beamsplitter, and a CCD camera. By systematically varying the parameters, we observe morphological changes in the interference rings and quantify their eccentricity.

Theoretical analysis and MATLAB visualizations demonstrate that eccentricity increases with parallel plate thickness (d₁) and light incidence angle (I) while decreasing with CCD-to-point light source distance ( f ) (Figs. 6‒8). These findings are confirmed through Zemax simulations and experimental validation, which show consistent trends. For instance, increasing the parallel plate thickness from 50 to 200 mm raises eccentricity from 0.2138 to 0.4375 (Table 8), while varying the incidence angle from 15° to 75° also increases eccentricity (Table 9). Conversely, increasing the CCD-to-point light source distance reduces eccentricity (Table 10). The comprehensive analysis reveals that elliptical deformation arises from differential refraction effects in the sagittal and meridional planes, with actionable guidance provided for mitigating this issue in practical applications.

In this paper, we advance precision optical measurements by providing a detailed understanding of the elliptical deformation phenomenon in transmission Tolansky interference rings. By integrating theoretical, simulated, and experimental approaches, we demonstrate that adjusting parallel plate thickness, light incidence angle, and CCD positioning can effectively control eccentricity. These findings offer practical strategies to enhance measurement accuracy across fields such as microelectronics manufacturing and fundamental physics research.