Objective The space-based gravitational wave detection system utilizes laser transmission among three satellites for interferometric measurements to detect gravitational waves. This necessitates the space-borne telescope to have transmitting and receiving functions. However, when the space- borne telescope emits laser beams, inevitable backward scattering occurs due to the surface roughness of its ultra-smooth optical components (surface roughness less than 1 nm), which cannot be perfectly smooth. This backward scattering unavoidably decreases the detection accuracy of the signal light. Consequently, the level of backward stray light from the space- borne telescope needs to be below 10⁻¹⁰ to meet the requirements of gravitational wave detection. This presents significant challenges in measuring and suppressing the scattering characteristics of ultra-smooth optical components.In traditional non-contact surface roughness measurements of optical components, methods such as white light scattering and laser reflection interference are used to determine the surface profile of optical elements, followed by surface roughness calculations. However, these methods involve complex setups and high costs. For relatively smooth optical component surfaces, existing techniques such as Total Integrated Scattering (TIS) method and Angle-Resolved Scattering (ARS) Method based on optical scattering principles, exhibit low measurement accuracy. Therefore, existing methods for measuring surface characteristics parameters of optical components are inadequate to meet the measurement requirements of ultra-smooth optical components. There is a pressing need to develop prediction methods suitable for the surface characteristics parameters of ultra-smooth optical components to meet the high-precision requirements of gravitational wave detection systems.

Method In response to the measurement requirements of ultra-smooth optical components, the method for measuring the surface scatter rate of highly reflective optical elements based on dual-channel optical cavity decay technology was proposed by LI B C. This method utilizes the optical cavity decay signals obtained from two channels to determine the surface scatter rate of the optical element being tested, offering distinct advantages such as absolute measurement, immunity to fluctuations in light source amplitude, and high measurement accuracy. Leveraging this method, we further combine the GBK scalar scattering model and the optical cavity decay method to propose a prediction method for surface characteristics parameters of ultra-smooth optical components. Specifically, this method involves using dual-channel optical cavity decay technology to ascertain the surface scatter rate of the optical element, followed by establishing a series of equations linking the surface scatter rate with surface roughness and autocorrelation length using the GBK scalar scattering model. By employing this approach, the surface roughness and autocorrelation length of ultra-smooth optical components can be obtained through numerical solution of the equations. This methodology aligns with the requirements for swift and precise measurement of surface roughness in ultra-smooth optical components.

Results and Discussions To validate the applicability of the prediction method, a series of optical components with different surface characteristic parameters were predicted (Fig.5), and relative error curves of predicted surface roughness and autocorrelation lengths of the components under different surface characteristic parameters were obtained (Fig.6). From the curves, it can be seen that within the range of 0.1064 nm to 1.064 nm for surface roughness, the relative error of the predicted values consistently remains within 1%. Similarly, for autocorrelation lengths falling within the range of 1064 nm to 3192 nm, the relative error of the predicted values consistently stays within 1%. This indicates that the proposed prediction method exhibits good adaptability and effectiveness within the specified range of surface characteristic parameters.

Conclusions A prediction method for surface characteristics parameters of ultra-smooth optical components based on the GBK scalar scattering model has been developed. The results indicate that this method predicts the surface roughness and autocorrelation length of ultra-smooth optical components with high accuracy. This work enhances and diversifies the swift and high-precision measurement of surface roughness in ultra-smooth optical components, offering valuable insights for measuring surface characteristic parameters in telescope systems designed for space gravitational wave detection.