Deterministic form-position deflectometric measurement of monolithic multi-freeform optical structures via Bayesian multisensor fusion

With the continuous advancement of photoelectric performance in major equipment and advanced instruments, traditional optical elements are increasingly inadequate to meet the demands of modern systems in terms of high precision, integration, and stability. The geometry of optical elements has evolved from ordinary planes, spheres, and cylinders to aspheric and freeform surfaces, and further toward monolithic multi-surface optics. Monolithic multi-surface elements offer enhanced design flexibility, relaxed tolerance requirements, reduced assembly complexity, and improved compactness and stability in optical systems. However, measurement presents significant challenges, which require the simultaneous specification of form quality and relative positions of multiple functional surfaces. Currently, there are few mature systems capable of measuring and characterizing multiple surfaces of a monolithic element at one stop.

 

In a new paper published in Light: Advanced Manufacturing, a team of scientists, led by Professor Xiangchao Zhang from Shanghai Engineering Research Center of Ultra-Precision Optical Manufacturing, School of Information Science and Technology, Fudan University, China, and co-workers have proposed an integrated form-position deflectometric system for measuring monolithic multi-freeform optical elements. Based on Bayesian multi-sensor fusion, they developed a new full-probability deflectometric measurement method, which has reformulated the traditional measurement process as a Bayesian estimation problem based on multi-source observations. More notably, this approach constructed a complete uncertainty propagation model to evaluate the uncertainty of the deflectometric system. By propagating uncertainties and integrating calibration priors into the measurement model, it achieves a tightly coupled fusion of multi-sensor observational data, fully exploiting the available multi-sensor information. The reported method and technique enhance accuracy and determinacy of deflectometric measurements, enabling high-precision form-position measurement of monolithic optical elements. It will provide new selection for ultra-precision and in-situ optical measurement.

 

A deflectometric measurement framework with probabilistic description capability is proposed based on physical uncertainty modelling. This framework tightly coupled multi-sensor observations by propagating and updating uncertainties, while embedding calibration priors into the measurement model. These priors impose stringent constraints on the deflectometric optical path, thereby significantly enhancing measurement accuracy and determinacy. These scientists summarize the principle of their method:

 

“We design a multi-sensor deflectometric measurement system that exploits the complementary precision and sensitivity characteristics of the sensors to address the limitations of traditional deflectometry in positioning. This system effectively elevates deflectometry from relative measurement to absolute measurement.”

 

“We construct an uncertainty evaluation method for based on virtual equipment, establishing a physical model-driven virtual system to simulate the real measurement process. The system parameters and noise models, which align with actual system characteristics, are generated through empirical testing and calibration. Subsequently, the system parameters noise is imported into the measurement process using the Monte Carlo method, allowing for rapid and thorough evaluation of measurement uncertainty for specific tasks.”

 

“The presented technique can be used to integrated form-position measurement of monolithic optical elements. And a geometric-constraint-based registration method was developed to evaluate the form-position quality, achieving accuracy levels of hundreds of nanometers for surface forms and tens of microns for surface positions. This approach provides a new selection for measuring monolithic optics, aligns with the development trends and application needs of performance-driven next-generation manufacturing.”

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