The thickness measurement method based on dual-channel light directly radiating on the two end faces of the thickness sample has gradually become an international hotspot. This is because the measurement results are only related to the end face characteristics of the thickness sample, the measurement optical path and environmental parameters, and the influence of the auxiliary agent, radiation, with the internal optical path of the thickness sample in the traditional method excluded. Among these, Tolansky interferometry features both angle and thickness measurements, which provides a new possibility for research into high-precision thickness measurement methods for double-end faces. Additionally, this means that the series radius of the interference concentric ring is adopted to calculate the measured thickness. In the thickness measurement using the common-path Tolansky interference scheme, the image of the interference concentric ring has an obvious ring nesting phenomenon, and even misaligned nesting occurs. This phenomenon will affect the image recognition accuracy of the radius and interfere with the subsequent thickness measurement results. Therefore, it is important to investigate technical schemes to eliminate or suppress this phenomenon in thickness measurements using the common-path Tolansky interference scheme.

Based on the dual-beam interference principle of the point light source, the Tolansky interference image is displayed by MATLAB virtual simulations. Then the experimental pictures of whether the interference concentric rings are different or not are displayed via the common-path Tolansky interferometer and the dual-arm optical path structure experimental system similar to the Michelson interferometer. That means there is an interference loop nesting in the former, and no interference loop nesting in the latter. After a detailed study, it is found that the biggest difference between the two systems is the existence of a multi-faceted structure of the common-path Tolansky. Additionally, the laser will reflect multiple times between these faces, while the dual-arm optical path structure similar to the Michelson interferometer does not have this multiple reflection phenomenon.

Given this, based on the geometrical optics principle, we employ the multiple reflection method to carry out theoretical analysis and formula derivation and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation relationship between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, the transmittance K_t, the reflectivity K_r, and the reflectivity K of the mirror is acquired. Thus, a new simulation model of interference concentric rings is obtained. On this basis, the interference concentric ring is simulated by MATLAB. The simulation results show that the interference concentric rings obtained based on the multiple reflection theory are in good agreement with the experimental images in terms of the structure and intensity profile, which also confirms the correctness of the theory. Given the strong correlation between the beam intensity after multiple reflections and the parameters of incident light intensity, transmittance K_t, reflectivity K_r, and reflectivity K, the interference concentric ring images with different collocations of these parameters are further virtually studied. The results show that by adjusting the transmittance and reflectivity of the interferometric spectroscope and the reflectivity of the interferometric mirror, the nesting phenomenon can be suppressed.

Based on the theoretical analysis and virtual simulation, interference spectrometers with different spectral ratios and interference mirrors with different reflectivities are replaced in the common-path Tolansky interference experimental system to realize different collocations among these parameters. The experimental results are in good agreement with the virtual simulation results, which verify the proposed method for suppressing the nesting phenomenon.

We propose an analysis method of multiple reflections among multiple planes, and obtain the expression of optical path difference and interference intensity different from double beam interference. Meanwhile, the correlation between the beam intensity after multiple reflections and the incident light intensity of the interference spectrometer, transmittance K_t, reflectivity K_r, and reflectivity K of the reflector is obtained. Thus, a new simulation model of an interference concentric ring is obtained, with the theory of common-path Tolansky interference analysis perfected.

Based on a new theoretical basis, a method to suppress the nesting phenomenon of the interference ring is proposed to suppress the phenomenon by reasonably adjusting the transmittance, reflectance of the interference spectrometer, and reflectivity of the interference mirror. Finally, a guarantee is provided for accurate extraction of the series ring radius by the common-path Tolansky interference thickness measurement technology.

The nesting or misplaced nesting of the common-path Tolansky interference ring causes bifurcation and ambiguity in each interference ring, which not only changes the interference level at the center of the circle, but also affects the recognition accuracy of each ring radius. As a result, there will be errors in the measured thickness inversion via the ring radius, which is unfavorable for accurate thickness measurement using the common-path Tolansky interference. The MATLAB virtual simulation and experimental results show that the nesting phenomenon comes from multiple reflections among multiple surfaces, and the intensity of the reflected light beam can be quickly weakened by adjusting the transmittance and reflectance of the interference spectroscope and the reflectivity of the interference mirror reasonably. Finally, the interference result is approximately double beam interference, and the nesting phenomenon is effectively restrained. This provides a guarantee for accurate radius extraction of the common-path Tolansky interference concentric ring series and accurate thickness measurements.