Effects of defocus on the transfer function of coherence scanning interferometry

Interferometric microscope with a confocal focusing for inner surface defect detection of ICF capsule

Inner surface defects of inertial confinement fusion (ICF) capsule are a key factor leading to ignition failure; however, there are still no effective and non-destructive detection methods available. To solve this problem, we propose the first interferometric microscope with confocal focusing (CFIM). CFIM first uses confocal technology to achieve accurate axial positioning of both capsule and the camera, thereby ensuring that the inner surface of the capsule is precisely and clearly imaged at the camera. Then, phase-shifting interferometry based on a short-coherence source and a spherical reference is applied to obtain inner defects result from null inner surface interferograms. In addition, in-situ focusing is realized by the axial adjustment of camera, but not by the capsule, to ensure that the outer defects and the fake inner defects caused by it have the same pixel coordinates, thereby solving the confusion of fake inner defects. The comparative experimental results of the CFIM and the scanning electron microscope (destructive detection) prove the feasibility of the proposed method. With unique precision confocal focusing and in-situ focusing ability, CFIM provides the first approach for non-destructive detection of inner surface defects of ICF capsule to the best of our knowledge.

Surface measuring coherence scanning interferometry beyond the specular reflection limit

The capability of optical surface topography measurement methods for measurement of steep and tilted surfaces is investigated through modelling of a coherence scanning interferometer. Of particular interest is the effect on the interference signal and measured topography when tilting the object at angles larger than the numerical aperture slope limit (i.e. the specular reflection limit) of the instrument. Here we use theoretical modelling to predict the results across a range of tilt angles for a blazed diffraction grating. The theoretically predicted interference patterns and surface height measurements are then verified directly with experimental measurements. Results illustrate the capabilities, limitations and modelling methods for interferometers to measure beyond the specular reflection limit.

Three-dimensional transfer function of optical microscopes in reflection mode

Three-dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection-slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three-dimensional Fourier transform of the 3D transfer function results in a complex-valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can be obtained.

Scattering and three-dimensional imaging in surface topography measuring interference microscopy

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.

3D modeling of coherence scanning interferometry on 2D surfaces using FEM

Despite the fact that optical profilers, such as coherence scanning interferometers, are frequently used for fast and contactless topography measurements in various fields of application, measured profiles still suffer from the wave characteristics of light, which leads to systematic deviations that are still not sufficiently investigated. In order to analyze these systematic deviations and their physical relations, we apply a rigorous simulation model considering both the transfer characteristics of the measurement instrument as well as the geometry and material of different measurement objects. Simulation results are compared to measurement results for different polarizations, wavelengths and interferometer types, considering surface structures including edges, slopes and different materials as the main reasons for those deviations. Compared to former publications, a full three-dimensional (3D) modeling of the image formation with regard to two-dimensional (2D) surface structures is provided. The advantages of 3D modeling in contrast to a time efficient 2D approach are discussed. Further, an extract of an atomic force microscope (AFM) measurement result is used as the basis for the FEM simulation in one example in order to achieve most realistic simulation results.

A review of selected topics in interferometric optical metrology

This review gathers together 15 special topics in modern interferometric metrology representing a sampling of historical, current and future developments. The selected topics cover a wide range of applications, including distance and displacement measurement, the testing of optical components, interference microscopy for surface structure analysis, form and dimensional measurements of industrial parts, and recent applications in semiconductor manufacturing and consumer electronics. Techniques range from laser Fizeau systems to dynamic ellipsometry using polarized heterodyne interferometry.