Fourier optics modelling of coherence scanning interferometers

Abstract

We propose an instrument model for coherence scanning interferometry using familiar Fourier optics methods, the spectrum of plane waves, and the assumption that the light source spectral bandwidth is the dominant factor in determining fringe contrast as a function of optical path length. The model is straightforward to implement, is computationally efficient, and reveals many of the common error sources related to the optical filtering properties of the imaging system. We quantify the limits of applicability of the model related to the geometrical approximations for conventional Fourier optics, particularly for high numerical apertures, and when using the fringe contrast for determining surface heights. These limitations can be overcome by using a three-dimensional imaging model.

A novel material measure for characterising two-dimensional instrument transfer functions of areal surface topography measuring instruments

“…Some examples are sharp steps, Siemens star or starshaped grooves, and chirp structures as illustrated in figure 1. De Groot et al proposed a kind of material measure based on a line object or a sharp step [13][14][15]. For small step heights, their results match those of the traditional knife-edge method for MTF [14].…”

“…In addition, due to factors such as the spatial and temporal coherence effects, an optical system is usually nonlinear [9,11,12]. However, in measurements of surfaces with very low feature heights (=l), the optical system can be approximated as a linear system [13][14][15].…”

“…Conventionally, the so-called modulation transfer function (MTF) is measured for experimentally characterising the OTF or the spatial resolving power of optical instruments. For incoherent optical imaging, the definition of MTF is clear and well-known procedures can be applied [14]. However, the MTF is less clear to define the bandwidth characteristics of areal surface topography measuring instruments.…”

“…However, the MTF is less clear to define the bandwidth characteristics of areal surface topography measuring instruments. To overcome this problem, the instrument transfer function (ITF) is applied instead [13][14][15]. The ITF, w H , ˜( ) is defined as:…”

Physically based rendering method to derive realistic simulation of chromatic confocal measurements

“…To address this problem, intensive research is being conducted in many places to develop models for such measurement processes [4], [5]. Modeling plays a crucial role in correcting the systematic errors and improving the measurement uncertainty.…”