Stationary-wave integrated Fourier transform spectrometry
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Stationary-wave integrated Fourier-transform spectrometry (SWIFTS), or standing-wave integrated Fourier-transform spectrometry, is an analytical technique used for measuring the distribution of light across an optical spectrum. SWIFTS technology is based on a
near-field Near field may refer to: * Near-field (mathematics), an algebraic structure * Near-field region, part of an electromagnetic field * Near field (electromagnetism) ** Magnetoquasistatic field, the magnetic component of the electromagnetic near f ...
Lippmann architecture. An optical signal is injected into a waveguide and ended by a mirror (true Lippman configuration). The input signal interferes with the reflected signal, creating a standing, or stationary, wave. In a counter-propagative architecture, the two optical signals are injected at the opposite ends of the waveguide. The
evanescent wave In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source (oscillati ...
s propagating within the waveguide are then sampled by optical probes. This results in an interferogram. A mathematical function known as a Lippmann transform, similar to a
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
, is later used to give the spectrum of the light.


History

In 1891, at the Académie des Sciences in Paris, Gabriel Lippmann presented a colour photograph of the Sun's spectrum obtained with his new
photographic plate Photographic plates preceded photographic film as a capture medium in photography, and were still used in some communities up until the late 20th century. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinn ...
. Later, in 1894, he published an article on how his plate was able to record colour information in the depth of photographic grainless gelatin and how the same plate after processing could restore the original colour image merely through light reflection. He was thus the inventor of true interferential colour photography. He received the Nobel Prize in Physics in 1908 for this breakthrough. Unfortunately, this principle was too complex to use. The method was abandoned a few years after its discovery. One aspect of the Lippmann concept that was ignored at that time relates to spectroscopic applications. Early in 1933, Herbert E. Ives proposed to use a photoelectric device to probe stationary waves to make spectrometric measurements. In 1995, P. Connes proposed to use the emerging new technology of detectors for three-dimensional Lippmann-based spectrometry. Following this, a first realization of a very compact
spectrometer A spectrometer () is a scientific instrument used to separate and measure spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomenon where the ...
based on a microoptoelectromechanical system (MOEMS) was reported by Knipp et al. in 2005, but it had a very limited spectral resolution. In 2004, two French researchers, Etienne Le Coarer from Joseph Fourier University and Pierre Benech from INP Grenoble, coupled sensing elements to the evanescent part of standing waves within a single-mode waveguide. In 2007, those two researchers reported a near-field method to probe the interferogram within a waveguide.E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J.-M. Fedeli, P. Royer
''Wavelength-scale stationary-wave integrated Fourier-transform spectrometry''
Nature Photonics (2007), 1, 8, 473–478
The first SWIFTS-based spectrometers appeared in 2011 based on a SWIFTS linear configuration.


Technology principle

The technology works by probing an optical standing wave, or the sum of the standing waves in the case of polychromatic light, created by a light to be analyzed. In a SWIFTS linear configuration (true Lippman configuration), the stationary wave is created by a single-mode waveguide ended by a fixed mirror. The stationary wave is regularly sampled on one side of a waveguide using nano-scattering dots. These dots are located in the evanescent field. These nanodots are characterized by an optical index difference with the medium in which the evanescent field is located. The light is then scattered around an axis perpendicular to the waveguide. For each dot, this scattered light is detected by a pixel aligned with this axis. The intensity detected is therefore proportional to the intensity inside the waveguide at the exact location of the dot. This results in a linear image of the interferogram. No moving parts are used. A mathematical function known as a Lippmann transform, similar to a Fourier transform, is then applied to this linear image and gives the spectrum of the light. The interferogram is truncated. Only the frequencies corresponding to the zero
optical path difference In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium through ...
at the mirror, up to the farthest dots are sampled. Higher frequencies are rejected. This interferogram’s truncation determines the
spectral resolution The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by \Delta\lambda, and is closely related to the resolvi ...
. The interferogram is undersampled. A consequence of this under-sampling is a limitation of the wavelength bandwidth to which the mathematical function is applied. SWIFTS technology displays the
Fellgett's advantage Fellgett's advantage or the multiplex advantage is an improvement in signal-to-noise ratio (SNR) that is gained when taking multiplexed measurements rather than direct measurements. The name is derived from P. B. Fellgett, who first made the observ ...
, which is derived from the fact that an
interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber op ...
measures wavelengths simultaneously with the same elements of the detector, whereas a dispersive spectrometer measures them successively. Fellgett's advantage also states that when collecting a spectrum whose measurement noise is dominated by detector noise, a multiplex spectrometer such as a Fourier-transform spectrometer will produce a relative improvement in the
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...
, with respect to an equivalent scanning monochromator, that is approximately equal to the square root of the number of sample points comprising the spectrum. The
Connes advantage Connes is a surname. Notable people with the surname include: *Alain Connes (born 1947), French mathematician *Janine Connes (born 1934), French astronomer See also *Conner (surname) * Albert Clinton Conner, American painter * Alexander H. Conner, ...
states that the wavenumber scale of an interferometer, derived from a helium–neon laser, is more accurate and boasts better long-term stability than the calibration of dispersive instruments.


References

{{reflist Spectroscopy Fourier analysis