Modeling of interference microscopy beyond the linear regime

Abstract

Coherence scanning interferometry (CSI), a type of interference microscopy, has found broad applications in the advanced manufacturing industry, providing high-accuracy surface topography measurement. Enhancement of the metrological capability of CSI for complex surfaces, such as those featuring high slopes and spatial frequencies and high aspect-ratio structures, requires advances in modeling of CSI. However, current linear CSI models relying on approximate surface scattering models cannot accurately predict the instrument response for surfaces with complex geometries that cause multiple scattering. A boundary elements method is used as a rigorous scattering model to calculate the scattered field at a distant boundary. Then, the CSI signal is calculated by considering the holographic recording and reconstruction of the scattered field. Through this approach, the optical response of a CSI system can be predicted for almost any arbitrary surface geometry. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Modeling of coherence scanning interferometry using classical Fourier optics

“…[35][36][37] The problem is significantly simplified, with a penalty to the accuracy of the model at high NA, if we average these effects using the obliquity factor Ω defined in Eq. (3).…”

“…Both the shape of the interference fringes and their variation in contrast are suggestive of the surface profile, shown as a solid red line in this figure . The success of CSI has motivated research into physics-based models to predict the interference signals and measurement results for these instruments. [2][3][4][5][6][7][8][9] These models address surface topographies and materials that vary from simple to complicated, for a wide range of applications for CSI. Modeling predicts performance characteristics such as measurement noise, 10,11 topographic spatial resolution, 12 and measurement errors related to surface structure.…”

Cascaded machine learning model for reconstruction of surface topography from light scattering

“…3, the core element being a neural network. In training, computer-generated surface instances (2D cross-sectional grating profiles) are inserted into the light scattering simulation model based on a boundary element method (BEM) [11,12]. The far-field spectrum resulting from the simulation, binned into 0.1° arc intervals, is normalised (intensities converted to the 0 to 1 interval) and fed into the input layer of the neural network (number of neurons equal to the number of bins).…”

Fourier optics modelling of coherence scanning interferometers

“…The success of CSI has motivated research into physics-based models to predict the interference signals and measurement results for these instruments [1][2][3][4][5][6][7][8]. These models address surface topographies and material characteristics that vary from simple to complicated, consistent with the wide range of applications for CSI.…”