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.

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.

A new approach to vector scattering: the 3s boundary source method.

This paper describes a novel Boundary Source Method (BSM) applied to the vector calculation of electromagnetic fields from a surface defined by the interface between homogenous, isotropic media. In this way, the reflected and transmitted fields are represented as an expansion of the electric fields generated by a basis of orthogonal electric and magnetic dipole sources that are tangential to, and evenly distributed over the surface of interest. The dipole moments required to generate these fields are then calculated according to the extinction theorem of Ewald and Oseen applied at control points situated at either side of the boundary.

Effects of defocus on the transfer function of coherence scanning interferometry.

Coherence scanning interferometry (CSI) offers three-dimensional (3D) measurement of surface topography with high precision and accuracy. Defocus within the interferometric objective lens, however, is commonly present in CSI measurements and reduces both the resolving power of the imaging system and the ability to measure tilted surfaces. This Letter extends the linear theory of CSI to consider the effects of defocus on the 3D transfer function and the point spread function in an otherwise ideal CSI instrument.

On tilt and curvature dependent errors and the calibration of coherence scanning interferometry.

Although coherence scanning interferometry (CSI) is capable of measuring surface topography with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterize the performance of surface measuring instruments and offers considerable insight into the origins of these errors. Furthermore, from the measurement of a precision sphere, a process to calibrate and partially correct instruments has been proposed.

Focus variation microscope: linear theory and surface tilt sensitivity.

In a recent publication [3rd International Conference on Surface Metrology, Annecy, France, 2012, p. 1] it was shown that surface roughness measurements made using a focus variation microscope (FVM) are influenced by surface tilt. The effect appears to be most significant when the surface has microscale roughness (Ra≈50  nm) that is sufficient to provide a diffusely scattered signal that is comparable in magnitude to the specular component.

Model-based defect detection on structured surfaces having optically unresolved features.

In this paper, we demonstrate, both numerically and experimentally, a method for the detection of defects on structured surfaces having optically unresolved features. The method makes use of synthetic reference data generated by an observational model that is able to simulate the response of the selected optical inspection system to the ideal structure, thereby providing an ideal measure of deviation from nominal geometry. The method addresses the high dynamic range challenge faced in highly parallel manufacturing by enabling the use of low resolution, wide field of view optical systems for defect detection on surfaces containing small features over large regions.

Coherence scanning interferometry: measurement and correction of three-dimensional transfer and point-spread characteristics.

When applied to the measurement of smooth surfaces, coherence scanning interferometry can be described by a three-dimensional linear filtering operation that is characterized either by the point-spread function in the space domain or equivalently by the transfer function (TF) in the spatial frequency domain. For an ideal, aberration-free instrument, these characteristics are defined uniquely by the numerical aperture of the objective lens and the bandwidth of the illumination source. In practice, however, physical imperfections such as those in lens aberrations, reference focus, and source alignment mean that the instrument performance is not ideal.

Coherence scanning interferometry: linear theory of surface measurement.

The characterization of imaging methods as three-dimensional (3D) linear filtering operations provides a useful way to compare the 3D performance of optical surface topography measuring instruments, such as coherence scanning interferometry, confocal and structured light microscopy. In this way, the imaging system is defined in terms of the point spread function in the space domain or equivalently by the transfer function in the spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable to weakly scattering objects; however, for the case of surface scattering, the system is linear if multiple scattering is assumed to be negligible and the Kirchhoff approximation is assumed.

Determination of overlap in lidar systems.

The overlap profile, also known as crossover function or geometric form factor, is often a source of uncertainty for lidar measurements. This paper describes a method for measuring the overlap by presenting the lidar with a virtual cloud through the use of an imaging system. Results show good agreement with horizontal hard target lidar measurements and with geometric overlap calculated for the ideal aberration-free case.

Synthetic aperture interferometry: error analysis.

Synthetic aperture interferometry (SAI) is a novel way of testing aspherics and has a potential for in-process measurement of aspherics [Appl. Opt. 42, 701 (2003)].

Particle image identification and correlation analysis in microscopic holographic particle image velocimetry.

This paper discusses the different analysis methods used in holographic particle image velocimetry to measure particle displacement and compares their relative performance. A digital holographic microscope is described and is used to record the light scattered by particles deposited on cover slides that are displaced between exposures. In this way, particle position and displacement are controlled and a numerical data set is generated.

Measurement of steep aspheric surfaces using an anamorphic probe.

Synthetic aperture interferometry has been previously proposed as a possible in-process method to measure aspheric form (R. Tomlinson, Appl. Opt.

Rotationally invariant pattern recognition by use of linear and nonlinear cascaded filters.

We discuss the merits of using single-layer (linear and nonlinear) and multiple-layer (nonlinear) filters for rotationally invariant and noise-tolerant pattern recognition. The capability of each approach is considered with reference to a two-class, rotation-invariant, character recognition problem. The minimum average correlation energy (MACE) filter is a linear filter that is generally accepted to be optimal for detecting signals that are free from noise.

Computer-aided lens assembly.

We propose a computer-aided method of lens manufacture that allows assembly, adjustment, and test phases to be run concurrently until an acceptable level of optical performance is reached. Misalignment of elements within a compound lens is determined by a comparison of the results of physical ray tracing by use of an array of Gaussian laser beams with numerically obtained geometric ray traces. An estimate of misalignment errors is made, and individual elements are adjusted in an iterative manner until performance criteria are achieved.

Digital shearing method for three-dimensional data extraction in holographic particle image velocimetry.

We report a new digital shearing method for extracting the three-dimensional displacement vector data from double-exposure holograms. With this method we can manipulate both the phase and the amplitude of the recorded signal, which, like optical correlation analysis, is inherently immune to imaging aberration. However, digital shearing is not a direct digital implementation of optical correlation, and a considerable saving in computation time results.

Synthetic aperture interferometry: in-process measurement of aspheric optics.

A scanning probe consisting of a source and receive fiber pair is used to measure the phase difference between wave fronts scattered from the front and rear surfaces of an aspheric optic. This system can be thought of as a classical interferometer with an aperture synthesized from the data collected along the path of the probe. If the form of either surface is known, the other can be deduced.