Coherence scanning interferometry (CSI) is a widely used optical method for surface topography measurement of industrial and biomedical surfaces. The operation of CSI can be modeled using approximate physics-based approaches with minimal computational effort. A critical aspect of CSI modeling is defining the transfer function for the imaging properties of the instrument to predict the interference fringes from which topography information is extracted. Approximate methods, for example, elementary Fourier optics, universal Fourier optics, and foil models, use scalar diffraction theory and the imaging properties of the optical system to model CSI surface topography measurement. In this work, the simulated topographies of different surfaces, including various sinusoids, two posts, and a step height, calculated using the three example methods are compared. The presented results illustrate the agreement between the three example models.
Coherence scanning interferometry (CSI) is a widely used optical method for surface topography measurement of industrial and biomedical surfaces. The operation of CSI can be modelled using approximate physics-based approaches with minimal computational effort. A critical aspect of CSI modelling is defining the transfer function for the imaging properties of the instrument in order to predict the interference fringes from which topography information is extracted. Approximate methods, for example, elementary Fourier optics, universal Fourier optics and foil models, use scalar diffraction theory and the imaging properties of the optical system to model CSI surface topography measurement. In this paper, the measured topographies of different surfaces, including various sinusoids, two posts and a step height, calculated using the three example methods are compared. The presented results illustrate the agreement between the three example models.
Approximate and rigorous methods are widely used to model light scattering from a surface. The boundary element method (BEM) is a rigorous model that accounts for polarization and multiple scattering effects. BEM is suitable to model the scattered light from surfaces with complex geometries containing overhangs and re-entrant features. The Beckmann–Kirchhoff (BK) scattering model, which is an approximate model, can be used to predict the scattering behavior of slowly varying surfaces. Although the approximate BK model cannot be applied to complex surface geometries that give rise to multiple scattering effects, it has been used to model the scattered field due to its fast and simple implementation. While many of the approximate models are restricted to surface features with relatively small height variations (typically less than half the wavelength of the incident light), the BK model can predict light scattering from surfaces with large height variations, as long as the surfaces are locally flat with small curvatures. Thus far, attempts have been made to determine the validity conditions for the BK model. The primary validity condition is that the radius of curvature of any surface irregularity should be significantly greater than the wavelength of the light. However, to have the most accurate results for the BK model, quantifying the validity conditions is critical. This work aims to quantify the validity conditions of the BK model according to different surface specifications, e.g., slope angles (SA) and curvatures. For this purpose, the scattered fields from various sinusoidal and combinations of sinusoidal profiles are simulated using the BEM and the BK models and their differences are compared. The result shows that the BK model fails when there are high SA ( ⪆ 38 deg) and small radii of curvature ( ⪅ 10 λ) within a sinusoidal profile. Moreover, it is shown that for a combination of sinusoidal profiles the BK model is valid for profiles with a high maximum slope angle value ( ⪆ 38 deg) if the average of positive SA is low ( ⪅ 5 deg).
Approximate and rigorous methods are widely used to model light scattering from a surface. The boundary element method (BEM) is a rigorous model that accounts for polarisation and multiple scattering effects. BEM is suitable to model the scattered light from surfaces with complex geometries containing overhangs and re-entrant features. The Beckmann- Kirchhoff (BK) scattering model, which is an approximate model, can be used to predict the scattering behaviour of slowlyvarying surfaces. Although the approximate BK model cannot be applied to complex surface geometries that give rise to multiple scattering effects, it has been used to model the scattered field due to its fast and simple implementation. While many of the approximate models are restricted to surface features with relatively small height variations (typically less than half the wavelength of the incident light), the BK model can predict light scattering from surfaces with large height variations, as long as the surfaces are “locally flat” with small curvatures. Thus far, attempts have been made to determine the validity conditions for the BK model. The primary validity condition is that the radius of curvature of any surface irregularity should be significantly greater than the wavelength of the light. However, to have the most accurate results for the BK model, quantifying the validity conditions is critical. This work aims to quantify the validity conditions of the BK model according to different surface specifications, e.g., slope angles and curvatures. For this purpose, the scattered fields from various sinusoidal profiles are simulated using the BEM and the BK models and their differences are compared. The result shows that the BK model fails when there are high slope angles and large curvatures, and these conditions are quantified.
A common-path spatial phase shifting digital speckle pattern shearing interferometry setup is introduced for simultaneous measurement of in-plane and out-plane strain components under dynamic loading using two laser beams with different wavelengths that symmetrically illuminate the test object and a single detector. The simplicity, stability, and efficiency of the arrangement are provided by using a glass plate as a shearing device, which is capable of tuning the sensitivity continuously. The phase is recovered from a single frame by the Fourier method. In this setup, the spatial carrier frequencies can be adjusted independent of the amount of the lateral shear. Ultimately, the desired field of view can easily be achieved by simple imaging optics. To validate the feasibility and the flexibility of our technique, the proposed setup is used to evaluate the in-plane and out-plane strain maps of an aluminum plate, which is deformed under dynamic stress in its plane. The temporal phase stability of the proposed system is also investigated.
The spatial phase shifting digital speckle pattern shearing interferometry (DSPSI) system has been widely used to determine map of deformation. In this paper a common-path DSPSI setup is introduced for in-plane strain measurement under dynamic loading, using two laser beams with different wavelengths that symmetrically illuminate the test object, and a single detector. The simplicity, stability and efficiency of the arrangement are provided using a glass plate as a shearing device which is capable of tuning the sensitivity continuously. The phase is recovered from a single frame by the Fourier method. In this setup the spatial carrier frequencies can be adjusted independent of the lateral shearing amount. Ultimately, the desired field of view can easily be achieved by simple imaging optics. To validate the feasibility and the flexibility of our technique, the proposed setup is used to evaluate the strain map of an aluminum plate which is deformed under dynamic stress in its plane. Experimental results are presented and discussed.
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