Coherence scanning interferometry (CSI) is a non-contacting optical technique which is widely used for the measurement of surface topography. CSI combines the lateral resolution of a high power microscope with the axial resolution of an interferometer. As with any other metrology instrument, CSI is calibrated to define measurement uncertainty. The traditional calibration procedure, as recommended by instrument manufacturers, consists of calibration of the axial and lateral scales of the instrument. Although calibration in this way provides uncertainties for the measurement of rectilinear artefacts, it does not give information about tilt-related uncertainty. If an object with varying slope is measured, significant errors are observed as the surface gradient increases. In this thesis a novel approach of calibration and adjustment for CSI using a spherical object is introduced. This new technique is based on three dimensional linear filtering theory. According to linear theory, smooth surface measurement in CSI can be represented as a linear filtering operation, where the filter is characterised either by point spread function (PSF) in space domain or by transfer function (TF) in spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable for weakly scattering objects. However, for the case of surface scattering and making use of the Kirchhoff approximation, the system can be considered linear if multiple scattering is assumed to be negligible. In this case, the object is replaced by an infinitely thin foil-like object, which follows the surface topography and, therefore, is called the foil model of the surface. For an ideal aberration free instrument, the linear characteristics are determined by the numerical aperture of the objective lens and the bandwidth of the source. However, it is found that the PSF and TF of a commercial instrument can depart significantly from theory and result in a significant measurement error. A new method, based on modified inverse filter to compensate the phase and amplitude-related errors in the system PSF/TF, is demonstrated. Finally, a method based on de-warping to compensate distortion is discussed. The application of the linear theory as well as modified inverse filter is dependent on the assumption of the shift invariance. As distortion introduces a field dependent magnification, the presence of distortion for CSI with relatively large field of view, restricts the applicability of the linear theory. Along with this restriction, distortion also introduces erroneous height measurement for objects with gradients. This new approach, based on de-warping, resolves the problems associated with distortion.

Traditionally, surface topography measurement was in the domain of quality control of engineering parts. With the advancement of manufacturing technology and affordable computational costs, different types of surfaces are produced with varied shapes and surface textures. These pose significant measurement problems, therefore, surface topography research is gaining momentum to achieve a better control of the surface. Coherence scanning interferometry (CSI) is one of the most common techniques used for measurement of surface topography. It is preferred over tactile and other non-contact techniques since it provides fast and accurate measurement with high vertical (~ 1 nm) and lateral (~1 μm) resolutions over larger areas without any damage to the surface. Essentially, CSI is treated as one dimensional (1D) superposition of the light waves from an object and a reference that generates a three dimensional (3D) interferogram. Secondly, despite the advantages, there is no standard configuration of CSI that can provide absolute surface topography measurement of an engineering part with multiple materials. An effective solution to this problem will be particularly useful in the field of semiconductor and bio-related industries where chips and instruments are made of many materials. In this Thesis, first, the CSI technique is analysed in terms of a wider theoretical framework of 3D linear filtering technique which shows the similarities among other seemingly disparate techniques such as confocal and optical coherence tomography. Due consideration to the spectral characteristic of the source and the effect of numerical aperture are given and important parameters such as vertical and lateral resolutions are computed to compare this theory with standard analysis methods. Additionally, it is shown that the 3D fringe pattern can be considered to be a superposition of a reference field and the scattered field from the top foil-like layer on the top the object. The scattered field from this foil object is dependent on the normal Fresnel reflection coefficients. Therefore, it explains the phase offset and the proportional height offset introduced by different materials, especially, metals. In an object, where multiple materials are present, each material introduces different phase to the fringe pattern and therefore, the surface topography of the entire object is altered. To overcome this problem, the optical polarising properties of the material are exploited. A novel configuration of polarisation sensitive CSI is presented where interferograms with orthogonal circular polarisations are recorded and analysed. The configuration, initially, needs to be calibrated with a material and after that at each point on the object, the refractive index and height offset can be calculated. Therefore, it can be dually used to identify unknown materials present on the object and also to compensate for the height offset introduced by each material to produce absolute surface topography of the entire object. The configuration provides good agreement with ellipsometric results for metals. Additionally, it retains the advantages of high vertical and lateral resolution same as other standard coherence scanning interferometers.

Inspection of optical components is essential to assure the quality and performance of optical systems. Evaluation of optical components includes metrology measurements of surface topography. It also requires optical measurements including refractive index, thin film thickness, reflectivity and transmission. The dispersion characteristics of optical constants including refractive index are also required. Hence, various instruments are used to make these measurements in research laboratories and for quality assurance. Clearly, it would be a significant advantage and cost saving if a technique was developed that could combine surface metrology with optical measurements. {Coherence Scanning Interferometry} (CSI) (also referred to as {Scanning White Light Interferometry} (SWLI)) has been used widely to measure surface topography with sub-nanometre vertical resolution. One of the benefits of the CSI is that the technique is non-contacting and hence non-destructive. Thus the test surfaces are not affected by the measurement using a CSI instrument whereas damage to the surfaces can occur when using traditional contact methods such as stylus profilometry. However use of CSI is geometrically limited to small areas ($\lesssim 10 \times 10$ mm) with gentle slopes ($\lesssim \ang{40}$) because of the numerical aperture of objective lens whereas stylus profilometry works well with larger areas and higher slopes due to the range of motion of the gauge and the traverse unit. Since the CSI technique is optical and involves light reflection and interference it is possible to extend the technique for the measurement of the thickness of transparent films, the roughness of surfaces buried beneath thin films or interfacial surfaces. It may also be used to determine spectral complex refractive index. This thesis provides an analytical framework of new methods to obtain complex refractive index in a visible light domain and interfacial surface roughness (ISR). It also provides experimental verification of these new capabilities using actual thin film model systems. The original Helical Complex Field (HCF) function theory is presented followed by its existing extensions that enable determination of complex refractive index and interfacial surface roughness. Further theoretical extensions of the HCF theory are also provided: A novel theory to determine the refractive index of a (semi-)transparent film is developed to address the constraint of the current HCF theory that restricted its use to opaque materials; Another novel theory is provided to measure ISR with noise compensation, which avoids erroneous surface roughness caused by the numerical optimisation affected by the existence of noise. The effectiveness of the ISR measurement with noise compensation has been verified using a number of computer simulations. Stylus profilometry is a well established method to provide a profile and has been used extensively as a 'reference' for other techniques. It normally provides a profile on which the roughness and the waviness are computed. Extension of the stylus profilometry technique to areal measurement of asymmetrical surfaces, namely raster scan measurement, requires a system to include error compensation between each traverse. The system errors and the random errors need to be separately understood particular when the measurement of a surface with nanometre-order accuracy is required. In this thesis a mathematical model to locate a stylus tip considering five mechanical errors occurring in a common raster scan profilometer is provided. Based on the model, the simulator which provides an areal measurement of a sphere was developed. The simulator clarified the relationship between the Zernike coefficients obtained from the form residual and the size of the errors in the form of partial derivatives of Zernike coefficients with respect to the errors. This provides theoretical support to the empirical knowledge of the relationship between the coefficients and the errors. Furthermore, a method to determine the size of errors directly from Zernike coefficients is proposed supported by simulations. Some of the error parameters were accurately determined avoiding iterative computation with this method whereas the errors are currently being determined by iterative computation.

This master’s thesis includes an overview of profile method of surface texture evaluation according to ISO standards and VDA automotive standards, as well as an overview of areal method according to ISO 25178 standard series, which includes a proposal for improvement of czech terminology. Suitability of application of selected measurement methods for measurement of a portfolio of automotive parts was evaluated based on measurements carried out using a contact profiler, a coherence scanning interferometer and a confocal microscope. Further recommendations for practice in surface texture metrology were also formulated. A regression analysis of the relationship between values of selected profile surface texture parameters and their areal equivalents was also performed. Its results may aid the spread of areal surface texture evaluation in the industry.

L'utilisation de franges d'interférence en lumière blanche comme une sonde optique en microscopie interférométrique est d'une importance croissante dans la caractérisation des matériaux, la métrologie de surface et de l'imagerie médicale. L'Interférométrie en lumière blanche est une technique basée sur la détection de l'enveloppe de franges d'interférence. Il a été démontré antérieurement, la capacité des approches 2D à rivaliser avec certaines méthodes classiques utilisées dans le domaine de l'interférométrie, en termes de robustesse et de temps de calcul. En outre, alors que la plupart des méthodes tiennent compte seulement des données 1 D, il semblerait avantageux de prendre en compte le voisinage spatial utilisant des approches multidimensionnelles (2D/3D), y compris le paramètre de temps afin d'améliorer les mesures. Le but de ce projet de thèse est de développer de nouvelles approches n-D qui sont appropriées pour une meilleure caractérisation des surfaces plus complexes et des couches transparentes. / The use of white light interference fringes as an optical probe in microscopy is of growing importance in materials characterization, surface metrology and medical imaging. Coherence Scanning Interferometry (CSI, also known as White Light Scanning Interferometry, WSLI) is well known for surface roughness and topology measurement [1]. Full-Field Optical Coherence Tomography (FF-OCT) is the version used for the tomographic analysis of complex transparent layers. Both techniques generally make use of some sort of fringe scanning along the optical axis and the acquisition of a stack of xyz images. Image processing is then used to identify the fringe envelopes along z at each pixel in order to measure the positions of either a single surface or of multiple scattering objects within a layer.In CSI, the measurement of surface shape generally requires peak or phase extraction of the mono dimensional fringe signal. Most of the methods are based on an AM-FM signal model, which represents the variation in light intensity measured along the optical axis of an interference microscope [2]. We have demonstrated earlier [3, 4] the ability of 2D approaches to compete with some classical methods used in the field of interferometry, in terms of robustness and computing time. In addition, whereas most methods only take into account the 1D data, it would seem advantageous to take into account the spatial neighborhood using multidimensional approaches (2D, 3D, 4D), including the time parameter in order to improve the measurements.The purpose of this PhD project is to develop new n-D approaches that are suitable for improved characterization of more complex surfaces and transparent layers. In addition, we will enrich the field of study by means of heterogeneous image processing from multiple sensor sources (heterogeneous data fusion). Applications considered will be in the fields of materials metrology, biomaterials and medical imaging.