Fourier profilometry

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Fourier profilometry is a method for measuring profiles using distortions in periodic patterns. The method uses Fourier analysis (a 2-dimensional Fast Fourier transform) to determine localized slopes on a curving surface.

Periodic function function that repeats its values in regular intervals or periods

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of 2π radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic.

Fourier analysis Branch of mathematics regarding periodic and continuous signals

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.

Dimension minimum number of independent coordinates needed to specify any point within a mathematical space

In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.

This allows a x, y, z coordinate system of the surface to be generated from a single image which has been overlaid with the distortion pattern.

Curvilinear coordinates Coordinate system whose directions vary in space

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. Commonly used curvilinear coordinate systems include: rectangular, spherical, and cylindrical coordinate systems. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.

It is used specifically in measuring the shape of the human cornea for use in contact lens design.

Cornea part of the eye

The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. The cornea, with the anterior chamber and lens, refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is approximately 43 dioptres. The cornea can be reshaped by surgical procedures such as LASIK.

Contact lens lens worn directly on the eyeball that can come in many ronbowl coulwers

A contact lens, or simply contact, is a thin lens placed directly on the surface of the eye. Contact lenses are considered medical devices and can be worn to correct vision, or for cosmetic or therapeutic reasons. In 2004, it was estimated that 125 million people worldwide use contact lenses, including 28 to 38 million in the United States. In 2010, the worldwide market for contact lenses was estimated at $6.1 billion, while the US soft lens market was estimated at $2.1 billion. Multiple analysts estimated that the global market for contact lenses would reach $11.7 billion by 2015. As of 2010, the average age of contact lens wearers globally was 31 years old, and two-thirds of wearers were female.

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A signal generator is an electronic device that generates repeating or non-repeating electronic signals in either the analog or the digital domain. It is generally used in designing, testing, troubleshooting, and repairing electronic or electroacoustic devices, though it often has artistic uses as well.

Image registration mapping of images into a coherent coordinate system

Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.

Schlieren photography

Schlieren photography is a visual process that is used to photograph the flow of fluids of varying density. Invented by the German physicist August Toepler in 1864 to study supersonic motion, it is widely used in aeronautical engineering to photograph the flow of air around objects.

Spectrogram Visual representation of the spectrum of frequencies of a signal as it varies with time

A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data is represented in a 3D plot they may be called waterfalls.

Spectrum analyzer

A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that a spectrum analyzer measures is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Optical spectrum analyzers also exist, which use direct optical techniques such as a monochromator to make measurements.

Holonomic brain theory is a branch of neuroscience investigating the idea that human consciousness is formed by quantum effects in or between brain cells. This is opposed by traditional neuroscience, which investigates the brain's behavior by looking at patterns of neurons and the surrounding chemistry, and which assumes that any quantum effects will not be significant at this scale. The entire field of quantum consciousness is often criticized as pseudoscience, as detailed on the main article thereof.

3D scanning device that analyses real-world objects or environments to collect data on their shape and possibly their appearance

3D scanning is the process of analyzing a real-world object or environment to collect data on its shape and possibly its appearance. The collected data can then be used to construct digital 3D models.

Profilometer instrument used to measure the roughness of a surfaces profile

A profilometer is a measuring instrument used to measure a surface's profile, in order to quantify its roughness. Critical dimensions as step, curvature, flatness are computed from the surface topography.

Flow visualization flow visualization

Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them.

Geophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the Earth's interior hold essential information concerning seismic activities and the internal structure. Hence, detection and analysis of the electric and Magnetic fields is very crucial. As the Electromagnetic and gravitational waves are multi-dimensional signals, all the 1-D transformation techniques can be extended for the analysis of these signals as well. Hence this article also discusses multi-dimensional signal processing techniques.

Synthetic schlieren

Synthetic schlieren is a process that is used to visualize the flow of a fluid of variable refractive index. Named after the schlieren method of visualization, it consists of a digital camera or video camera pointing at the flow in question, with an illuminated target pattern behind. The method was first proposed in 1999.

Heat flux

Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a flow of energy per unit of area per unit of time. In SI its units are watts per square metre (W⋅m−2). It has both a direction and a magnitude, and so it is a vector quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.

Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images. This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering, with new applications being found all the time. Compared to strain gages and extensometers, the amount of information gathered about the fine details of deformation during mechanical tests is increased due to the ability to provide both local and average data using digital image correlation.

A structured-light 3D scanner is a 3D scanning device for measuring the three-dimensional shape of an object using projected light patterns and a camera system.

Ptychography

Ptychography is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means the interference patterns are generated by one constant function moving laterally by a known amount with respect to another constant function. The interference patterns occur some distance away from these two components, so that the scattered waves spread out and ‘fold into’ one another, as shown in the figure.

In time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series.

White light scanner

A white light scanner (WLS) is a device for performing surface height measurements of an object using coherence scanning interferometry (CSI) with spectrally-broadband, "white light" illumination. Different configurations of scanning interferometer may be used to measure macroscopic objects with surface profiles measuring in the centimeter range, to microscopic objects with surface profiles measuring in the micrometer range. For large-scale non-interferometric measurement systems, see structured-light 3D scanner.

Specular holography is a technique for making three dimensional imagery by controlling the motion of specular glints on a two-dimensional surface. The image is made of many specularities and has the appearance of a 3D surface-stippling made of dots of light. Unlike conventional wavefront holograms, specular holograms do not depend on wave optics, photographic media, or lasers.

Neopolarogram

The term neopolarogram refers to mathematical derivatives of polarograms or cyclic voltammograms that in effect deconvolute diffusion and electrochemical kinetics. This is achieved by analog or digital implementations of fractional calculus. The implementation of fractional derivative calculations by means of numerical methods is straight forward. The G1- and the RL0-algorithms are recursive methods to implement a numerical calculation of fractional differintegrals. Yet differintegrals are faster to compute in discrete fourier space using FFT.

An MRI artifact is a visual artifact in magnetic resonance imaging (MRI). It is a feature appearing in an image that is not present in the original object. Many different artifacts can occur during MRI, some affecting the diagnostic quality, while others may be confused with pathology. Artifacts can be classified as patient-related, signal processing-dependent and hardware (machine)-related.

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