On the use of a multiple beam optical sensor for in situ curvature monitoring in liquids

Several methods have been developed since the early 1900 to extract thin film stresses from the curvature of the substrate to which it is attached. One robust method particularly suitable for in situ curvature monitoring is the multiple beam optical sensor, which consists in measuring the change in relative spacings between parallel laser beams reflecting off the curved substrate. Although the technique is already well established for curvature monitoring in low pressure, gaseous environments, its use in liquid media has not yet received similar attention. Moreover, in the majority of the published work so far, spot spacings have been assumed to depend linearly on curvature. In this paper, it is first shown that this assumption may induce significant errors, particularly at large curvature. A more accurate set of equations is proposed. Next, the relationship between spot spacings and curvature is established when the substrate of interest is in a liquid, and a constitutive formula is proposed in that case as well. Finally, some practical aspects of the multiple beam technique for performing curvature measurements in a liquid are discussed. Various factors disturbing the measurement resolution are identified, with a specific interest for thin film anodizing, and a cell design is proposed to minimize their effect.