Theoretical simulation and experimental confirmation of duty cycle effect on stroboscopic white light interferometry for M(O)EMS dynamic characterization

Abstract

Stroboscopic white light interferometry (SWLI) has been known as a useful measurement technique for vibrating samples such as micro-electro-mechanical systems (MEMS) or micro-opto-electro-mechanical systems (M(O)EMS) because it enables dynamic mode reconstruction and characterization of the tested system. An approximate model simulation without any experimental confirmation previously indicated that the duty cycle of the light could reduce the accuracy of the measurement. To provide a comprehensive insight into this important phenomenon, the study investigated theoretically and experimentally the effect of duty cycle of the light. An atomic force microscopy cantilever beam vibrating at its second resonant frequency was measured and the experimental measurements were analyzed and compared with the simulated results. In general, a reasonable correspondence between the mathematical model and the experimental measurements has been observed when the duty cycle is less than 15% and the average deviation is kept within 15.4% of the vibration amplitude. However, it is verified that the SWLI using white light LED has its physical detection limits when the cycle time of the strobed light or the light exposure time of the imaging device is more than 20%, in which the maximum measured error can significantly exceed 38.4% of the vibration amplitude.

An insight on optical metrology in manufacturing

“…As shown in appendix A, various Mirau-related systems and methods have been further developed and patented to meet diverse demands for better interferometric optical design, vibration-resistant optical design and algorithms, thickness measuring methods, and dynamic measuring methods and strategies. WLI microscopes [140][141][142][143][144][145] have been widely used for measuring film thickness and monitoring surfaces with discontinuities of more than several wavelengths. In contrast to laser phaseshifting interferometry (PSI) employing a light source with a long coherence length, WLI uses a broadband light source with a short coherence length of approximately 1 µm [146].…”

“…laser light) or a quasi-monochromatic light source (e.g. a single-color LED), WLI employs a light source with a broad visible spectrum ranging from 400 nm to 700 nm [144]. A broadband light source has a shorter coherence length than a monochromatic light source and produces an interferogram with OPD-modulated contrast.…”