Rahul Mandal

Bio: Rahul Mandal is an academic researcher from Loughborough University. The author has contributed to research in topics: Coherence scanning interferometry & Interferometry. The author has an hindex of 4, co-authored 4 publications receiving 114 citations.

Coherence scanning interferometry: linear theory of surface measurement

Abstract: 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.

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

Abstract: 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. Currently, these imperfections often go unnoticed as the instrument performance is typically only verified using rectilinear artifacts such as step heights and lateral grids. If an object of varying slope is measured, however, significant errors are often observed as the surface gradient increases. In this paper, a new method of calibration and adjustment using a silica micro-sphere as a calibration artifact is introduced. The silica microsphere was used to compute the point-spread and TF characteristics of the instrument, and the effect of these characteristics on instrument performance is discussed. Finally, a straightforward method to correct for phase and amplitude imperfections in the TF is described using a modified inverse filter.

Application of linear systems theory to characterize coherence scanning interferometry

Abstract: This paper considers coherence scanning interferometry as a linear filtering operation that is characterised by a point spread function in the space domain or equivalently a transfer function in the frequency domain. The applicability of the theory is discussed and the effects of these functions on the measured interferograms, and their influence on the resulting surface measurements, are described. The practical characterisation of coherence scanning interferometers using a spherical reference artefact is then considered and a new method to compensate measurement errors, based on a modified inverse filter, is demonstrated.

Tourism Potentials of Fossil Parks as Geoheritage Sites: A Study in Western and South Western Region of West Bengal, India

Abstract: Fossils are paleontological treasures manifesting preserved remains, impression, or traces of organisms that existed in past geological ages. Fossil parks are one of the major geotourism attractions especially when they attain the status like world heritage sites. From geotourism promotion perspective, the fossil parks have exceptional heritage and scientific values as admired by UNESCO. Geosite and geomorphosite tourism is still at its juvenile stage in India despite of the positive efforts of Geological Survey of India who recognized 26 geological sites as National Geological Monuments including the seven fossil parks. With increasing interest on fossils as geoheritage, geopark network of the country has been strengthened with inclusion of new sites. In the year 2006, angiosperm wood fossils have been discovered from Illambazar forest of Birbhum District in and around a tribal village named Amkhoi. A fossil park is inaugurated in the year 2018, and its success encourages its extension and further planning for geotourism. This paper is an attempt to apply SWOT-AHP analysis on Amkhoi Fossil Park, the first fossil park of West Bengal which is youngest among the fossil parks of the country in order to evaluate its sustainability aspects.

Characterisation of Areal Surface Texture

Abstract: Introduction to surface topography.- The areal field parameters.- The areal feature parameters.- Areal filtering methods.- Areal form removal.- Areal fractal methods.- Choosing the appropriate parameter.- Characterization of individual areal features.- Multi-scale signature of surface topography.- Correlation of areal surface texture parameters to solar cell efficiency.- Characterisation of cylinder liner honing textures for production control.- Characterization of the mechanical bond strength for copper on glass plating applications.- Inspection of laser structured cams and conrods.- Road surfaces.

Principles of interference microscopy for the measurement of surface topography

Abstract: Interference microscopy plays a central role in noncontact strategies for process development and quality control, providing full 3D measurement of surface characteristics that influence the functional behavior of manufactured parts. Here I briefly review the history and principles of this important technique, then concentrate on the details of hardware, software, and applications of interference microscopy using phase-shifting and coherence scanning measurement principles. Recent advances considered here include performance improvements, vibration robustness, full color imaging, accommodation of highly sloped surfaces, correlation to contact methods, transparent film analysis, and international standardization of calibration and specification.

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

Abstract: 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.

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

Abstract: 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. This paper presents, for the first time, a critical look at the calibration and correction process. Computational techniques are used to investigate the effects of radius error and measurement noise introduced during the calibration process for the measurement of spherical and sinusoidal profiles. Care is taken to illustrate the residual tilt and curvature dependent errors in a manner that will allow users to estimate measurement uncertainty. It is shown that by calibrating the instrument correctly and using appropriate methods to extract phase from the resulting fringes (such as frequency domain analysis), CSI is capable of measuring the topography of surfaces with varying tilt with sub-nanometre accuracy.