Jeremy M. Coupland

Surface measurement errors using commercial scanning white light interferometers

This paper examines the performance of commercial scanning white light interferometers in a range of measurement tasks. A step height artefact is used to investigate the response of the instruments at a discontinuity, while gratings with sinusoidal and rectangular profiles are used to investigate the effects of surface gradient and spatial frequency. Results are compared with measurements made with tapping mode atomic force microscopy and discrepancies are discussed with reference to error mechanisms put forward in the published literature. As expected, it is found that most instruments report errors when used in regions close to a discontinuity or those with a surface gradient that is large compared to the acceptance angle of the objective lens. Amongst other findings, however, we report systematic errors that are observed when the surface gradient is considerably smaller. Although these errors are typically less than the mean wavelength, they are significant compared to the vertical resolution of the instrument and indicate that current scanning white light interferometers should be used with some caution if sub-wavelength accuracy is required.

Particle image velocimetry: three-dimensional fluid velocity measurements using holographic recording and optical correlation

We report on an original use of optical correlation techniques and holographic recording to provide three-dimensional velocity vector information from particle image velocimetry.

Determination of the transfer function for optical surface topography measuring instruments—a review

A significant number of areal surface topography measuring instruments, largely based on optical techniques, are commercially available. However,implementation of optical instrumentation into production is currently difficult dueto the lack of understanding of the complex interaction between the light and the component surface. Studying the optical transfer function of the instrument can help address this issue. Herea review is given of techniques for the measurement of optical transfer functions. Starting from the basis of a spatially coherent, monochromatic confocal scanning imaging system, the theory of optical transfer functions in three-dimensional (3D) imaging is presented. Further generalizations are reviewed allowing the extension of the theory to the description of conventional and interferometric 3D imaging systems. Polychromatic transfer functions and surface topography measurements are also discussed. Following presentation of theoretical results, experimental methods to measure the optical transfer function of each class of system are presented, with a focus on suitable methods for the establishment of calibration standards in 3D imaging and surface topography measurements.

Particle image velocimetry: rapid transparency analysis using optical correlation

Particle image velocimetry (PIV) provides a means of measuring instantaneous 2-D velocity vector fields from a plane of interest within an unsteady flow. The technique was pioneered by Dudderar and Simpkins in 1977 and has since been used to study convection currents, flow around unexcited jets, and more recently breaking wave phenonema. In its simplest form, PIV uses double-exposure photography to record the position of seeding particles contained within a thin sheet of light illuminating a section of the flow. The resulting transparency is divided into a grid of small interrogation regions which are systematically analyzed to obtain the average displacement of the particle images recorded within each region. If the time interval between

Holography, tomography and 3D microscopy as linear filtering operations

In this paper, we characterize 3D optical imaging techniques as 3D linear shift-invariant filtering operations. From the Helmholtz equation that is the basis of scalar diffraction theory, we show that the scattered field, or indeed a holographic reconstruction of this field, can be considered to be the result of a linear filtering operation applied to a source distribution. We note that if the scattering is weak, the source distribution is independent of the scattered field and a holographic reconstruction (or in fact any far-field optical imaging system) behaves as a 3D linear shift-invariant filter applied to the refractive index contrast (which effectively defines the object). We go on to consider tomographic techniques that synthesize images from recordings of the scattered field using different illumination conditions. In our analysis, we compare the 3D response of monochromatic optical tomography with the 3D imagery offered by confocal microscopy and scanning white light interferometry (using quasi-monochromatic illumination) and explain the circumstances under which these approaches are equivalent. Finally, we consider the 3D response of polychromatic optical tomography and in particular the response of spectral optical coherence tomography and scanning white light interferometry.

Particle image velocimetry: high-speed transparency scanning and correlation-peak location in optical processing systems

In order to exploit the full potential offered by optical correlation processing in the analysis of transparencies obtained by particle image velocimetry one needs to advance the transparency and to track the position of correlation peaks at great speed. In the following, this procedure is discussed with reference to an optical analysis system based on a high-speed ferroelectric optically addressed spatial light modulator. We present a system that uses scanning optics both to scan through the input transparency and to locate the correlation peaks in the resulting optical output distributions as a practical solution to the problem. The feasibility of this approach is demonstrated at a processing speed of ~500 autocorrelations/s when a one-dimensional acousto-optic output scanning device is used.

Particle image velocimetry: Estimation of measurement confidence at low seeding densities

Abstract In order to optimise the spatial resolution of particle image velocimetry, it is often necessary to take measurements from regions of the photographic record which contain few particle images. If Youngs fringe analysis is used in these cases, the observed fringe pattern is confused by extraneous spatial frequency components or speckle noise. If spatial correlation analysis is employed, spurious correlation peaks occur. In this paper we introduce a definition of signal to noise ratio appropriate to particle image velocimetry and investigate the statistical variation of this ratio as a function of the seeding particle size and concentration.

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. A difference between the filter characteristics derived in each case is found. However this paper discusses these differences and explains the equivalence of the two approaches when applied to a weakly scattering object.

Bacteriorhodopsin as a high-resolution, high-capacity buffer for digital holographic measurements

Recent trends in optical metrology suggest that, in order for holographic measurement to become a widespread tool, it must be based on methods that do not require physical development of the hologram. While digital holography has been successfully demonstrated in recent years, unfortunately the limited information capacity of present electronic sensors, such as CCD arrays, is still many orders of magnitude away from directly competing with the high-resolution silver halide plates used in traditional holography. As a result, present digital holographic methods with current electronic sensors cannot record object sizes larger than several hundred microns at high resolution. In this paper, the authors report on the use of bacteriorhodopsin (BR) for digital holography to overcome these limitations. In particular, BR is a real-time recording medium with an information capacity (5000 line-pairs/mm) that even exceeds high resolution photographic film. As such, a centimetre-square area of BR film has the same information capacity of several hundred state-of-the-art CCD cameras. For digital holography, BR temporarily holds the hologram record so that its information content can be digitized for numeric reconstruction. In addition, this paper examines the use of BR for optical reconstruction without chemical development. When correctly managed, it is found that BR is highly effective, in terms of both quality and process time, for three-dimensional holographic measurements. Consequently, several key holographic applications, based on BR, are proposed in this paper.

Holographic particle image velocimetry: signal recovery from under-sampled CCD data

Holographic particle image velocimetry (HPIV) has now been demonstrated by several research groups as a method to make three-component velocity measurements from a three-dimensional fluid flow field. More recently digital HPIV has become a hot topic with the promise of near-real-time measurements without the often cumbersome optics and wet processing associated with traditional holographic methods. It is clear, however, that CCD cameras have a limited number of pixels and are not capable of resolving more than a small fraction of the interference pattern that is recorded by a typical particulate hologram. In this paper, we consider under-sampling of the interference pattern to reduce the information content and to allow recordings to be made on a CCD sensor. We describe the basic concept of model fitting to under-sampled data and demonstrate signal recovery through computer simulation. A three-dimensional analysis shows that in general, periodic sampling strategies can result in multiple particle images in the reconstruction. It is shown, however, that the significance of these peaks is reduced in the case of high numerical aperture (NA) reconstruction and can be virtually eliminated by dithering the position of sampling apertures.