Abstract
Surface topography measuring interference microscopy is a three-dimensional (3D) imaging technique that provides quantitative analysis of industrial and biomedical specimens. Many different instrument modalities and configurations exist, but they all share the same theoretical foundation. In this paper, we discuss a unified theoretical framework for 3D image (interferogram) formation in interference microscopy. We show how the scattered amplitude is linearly related to the surface topography according to the Born and the Kirchhoff approximations and highlight the main differences and similarities of each. With reference to the Ewald and McCutchen spheres, the relationship between the spatial frequencies that characterize the illuminating and scattered waves, and those that characterize the object, are defined and formulated as a 3D linear filtering process. It is shown that for the case of near planar surfaces, the 3D filtering process can be reduced to two dimensions under the small height approximation. However, the unified 3D framework provides significant additional insight into the scanning methods used in interference microscopy, effects such as interferometric defocus and ways to mitigate errors introduced by aberrations of the optical system. Furthermore, it is possible to include the nonlinear effects of multiple scattering into the generalized framework. Finally, we consider the inherent nonlinearities introduced when estimating surface topography from the recorded interferogram.
Highlights
Surface topography measuring interference microscopy [1], and closely related coherent imaging techniques, such as digital holographic microscopy [2] and optical coherence tomography (OCT) [3], are key tools for biomedical imaging and the surface measurement of engineered materials
The imaging capability of a 2D imaging system can be characterized by its 2D transfer function, by the 2D coherent transfer function (CTF), which is the scaled pupil function for coherent illumination, and by the 2D optical transfer function (OTF), which is the autocorrelation of the 2D CTF for incoherent illumination
We provide a unified theoretical framework for 3D image formation in surface topography measuring interference microscopy
Summary
Surface topography measuring interference microscopy [1] (hereafter, just referred to as interference microscopy), and closely related coherent imaging techniques, such as digital holographic microscopy [2] and optical coherence tomography (OCT) [3], are key tools for biomedical imaging and the surface measurement of engineered materials. Phase-shifting interferometry (PSI) [4] and coherence scanning interferometry (CSI, known as scanning white-light interferometry [5]) are the two most common modalities of interference microscopy (see Fig. 1) and have been used for high-accuracy three-dimensional (3D) measurements in a broad range of applications, due to their high sensitivity to small variations in object geometry and low measurement noise (subnanometer level) at all system magnifications [1]. Interference microscopy is a well-established technique, enhancement in measurement capability and general applicability have been driven by continuous advances in the freedom and complexity of new product design, enabled by precision manufacturing and additive manufacturing [8]. In the absence of noise, environmental disturbances and mechanical imperfections, the measurement accuracy of interference microscopy is limited by the imaging model and the inversion algorithm for object reconstruction.
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