Compensation method for obtaining accurate, sub-micrometer displacement measurements of immersed specimens using electronic speckle interferometry

Abstract

We proposed and validated a compensation method that accounts for the optical distortion inherent in measuring displacements on specimens immersed in aqueous solution. A spherically-shaped rubber specimen was mounted and pressurized on a custom apparatus, with the resulting surface displacements recorded using electronic speckle pattern interferometry (ESPI). Point-to-point light direction computation is achieved by a ray-tracing strategy coupled with customized B-spline-based analytical representation of the specimen shape. The compensation method reduced the mean magnitude of the displacement error induced by the optical distortion from 35% to 3%, and ESPI displacement measurement repeatability showed a mean variance of 16 nm at the 95% confidence level for immersed specimens. The ESPI interferometer and numerical data analysis procedure presented herein provide reliable, accurate, and repeatable measurement of sub-micrometer deformations obtained from pressurization tests of spherically-shaped specimens immersed in aqueous salt solution. This method can be used to quantify small deformations in biological tissue samples under load, while maintaining the hydration necessary to ensure accurate material property assessment.

Age-related changes in human peripapillary scleral strain

“…Mean displacement measurement uncertainty was ±16 nm at the 95% confidence level (Fazio et al 2012a), which demonstrates that ESPI possesses extremely high spatial resolution and low measurement uncertainty (measurement error) when used for measuring deformations in immersed spheroid pressure vessels.…”

“…This work should be viewed with several limitations in mind, which have been described in detail in our previous reports (Fazio et al 2012a; Fazio et al 2012b). Briefly, there is error in the displacement measurement at the outer edge of the specimen due to ESPI phase map reconstruction difficulties.…”

“…We positioned the ONH and peripapillary sclera at the center (apex) of the posterior scleral specimen and analyzed strains in a relatively narrow band around the ONH to avoid these edge effects. Under these conditions, our ESPI system has a measurement uncertainty of ±16 nm (Fazio et al 2012a) and possesses sufficient measurement precision and spatial resolution to capture the local scleral deformation changes between sectors within the peripapillary and mid-peripheral sclera, as well as the small but significant changes in the sector deformations with age.…”

“…Testing hypotheses concerning age-, race-, or disease-related changes in scleral biomechanics greatly benefits from this approach, and the optimized ESPI technique we developed, coupled with inflation testing of the intact posterior scleral shell, allows scleral strain analyses that are not possible with other measurement methods. We demonstrated and extensively discussed (Fazio et al 2012a) the necessity of using displacement measurement techniques with extremely high spatial and measurement resolution to capture the small, localized strain variations around the ONH, as well as the small but significant deformation changes with age (Fazio et al 2012b). …”

“…Correlation-based displacement measurement techniques such as DIC (Schreier et al 2000; Bornert et al 2009) are constrained by a compromise between spatial resolution and displacement measurement uncertainty, because increasing the spatial resolution (lowering pixel subset size) increases the measurement uncertainty (Robert 2007). Speckle-based interferometry techniques such as the ESPI method used in this work are more suitable for assessing small, localized strain variations since displacement measurement resolution is decoupled from spatial resolution because each pixel performs as a stand-alone interferometer and can measure displacements with a ±16 nm accuracy (Fazio et al 2012a). The shear components of the scleral strain tensor represent the difference in local displacement components along orthogonal directions.…”