Imaging spectroscopy - AbsoluteAstronomy.com

Imaging spectroscopy
is similar to color photography

Color photography

Color photography is photography that uses media capable of representing colors, which are traditionally produced chemically during the photographic processing phase...

, but each pixel acquires many bands of light intensity data from the spectrum, instead of just the three bands of the RGB color model

RGB color model

The RGB color model is an additive color model in which red, green, and blue light is added together in various ways to reproduce a broad array of colors...

. More precisely, it is the simultaneous acquisition of spatially coregistered images in many spectrally

Electromagnetic spectrum

The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

contiguous bands.

Some spectral images contain only a few image planes of spectral data, while others are better thought of as full spectra at every location in the image. For example, solar physicist

Solar physics

For the physics journal, see Solar Physics Solar physics is the study of our Sun. It is a branch of astrophysics that specializes in exploiting and explaining the detailed measurements that are possible only for our closest star...

s use the spectroheliograph

Spectroheliograph

The spectroheliograph is an instrument used in astronomy. It captures a photographic image of the Sun at a single wavelength of light, a monochromatic image...

, to make images of the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

built up by scanning the slit of a spectrograph, to study the behavior of surface features on the Sun; such a spectroheliogram may have a spectral resolution of over 100,000 (

) and be used to measure local motion (via the Doppler shift) and even the magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

(via the Zeeman splitting or Hanle effect

Hanle effect

The Hanle effect is a reduction in the polarisaton of light when the atoms emitting the light are subject to a magnetic field in a particular direction, and when they have themselves been excited by polarised light....

) at each location in the image plane. The multispectral images collected by the Opportunity rover

Opportunity rover

Opportunity, MER-B , is a robotic rover on the planet Mars, active since 2004. It is the remaining rover in NASA's ongoing Mars Exploration Rover Mission...

, in contrast, have only four wavelength bands and hence are only a little more than 3-color image

Color photography

Color photography is photography that uses media capable of representing colors, which are traditionally produced chemically during the photographic processing phase...

s.

To be scientifically useful, such measurement should be done using an internationally recognized system of units.

One example application is spectral geophysical imaging

Geophysical imaging

Geophysical imaging is geophysical technique that investigates the subsurface. There are many different kinds of imaging techniques, all which are based on applied physics.Types of geophysical imaging include:...

, which allows quantitative and qualitative characterization of the surface and of the atmosphere

Earth's atmosphere

The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

, using geometrically coherent

Coherence (physics)

In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

spectrodirectional radiometric measurements. These measurements can then be used for the unambiguous direct and indirect identification of surface materials and atmospheric trace gases, the measurement of their relative concentrations, subsequently the assignment of the proportional contribution of mixed pixel signals (e.g., the spectral unmixing problem), the derivation of their spatial distribution (mapping problem), and finally their study over time (multi-temporal analysis). The Moon Mineralogy Mapper

Moon Mineralogy Mapper

The Moon Mineralogy Mapper is one of two instruments that NASA contributed to India's first mission to the Moon, Chandrayaan-1, launched October 22, 2008...

on Chandrayaan-1 was an imaging spectrometer

Imaging spectrometer

An imaging spectrometer is an instrument used in hyperspectral imaging and imaging spectroscopy to acquire a spectrally-resolved image of an object or scene, often referred to as a datacube due to the three-dimensional representation of the data. Namely, two axes of the image corresponds to...

Background

About 300 years ago, in 1704, Sir Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

published in his ‘Treatise of Light

Opticks

Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history...

’ (Newton, 1704) the concept of dispersion of light

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

. He demonstrated that white light could be split up into component colours by means of a prism

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

, and found that each pure colour is characterized by a specific refrangibility. The corpuscular theory

Corpuscular theory

In optics, corpuscular theory of light, set forward by Sir Isaac Newton, states that light is made up of small discrete particles called "corpuscles" which travel in a straight line with a finite velocity and possess kinetic energy....

by Newton was gradually succeeded over time by the wave theory

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

. Consequently, the substantial summary of past experiences performed by Maxwell

James Clerk Maxwell

James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

(1873), resulted in his equations of electromagnetic waves

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

. But it was not until the 19th century that the quantitative measurement of dispersed light was recognized and standardized.

A major contribution was Fraunhofer's

Joseph von Fraunhofer

Joseph von Fraunhofer was a German optician. He is known for the discovery of the dark absorption lines known as Fraunhofer lines in the Sun's spectrum, and for making excellent optical glass and achromatic telescope objectives.-Biography:Fraunhofer was born in Straubing, Bavaria...

discovery of the dark lines in the solar spectrum

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

(Fraunhofer, 1817); and their interpretation as absorption line

Spectral line

A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s on the basis of experiments by Bunsen

Robert Bunsen

Robert Wilhelm Eberhard Bunsen was a German chemist. He investigated emission spectra of heated elements, and discovered caesium and rubidium with Gustav Kirchhoff. Bunsen developed several gas-analytical methods, was a pioneer in photochemistry, and did early work in the field of organoarsenic...

and Kirchhoff

Gustav Kirchhoff

Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...

(1863). The term "spectroscopy

Spectroscopy

Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

" was first used in the late 19th century and provides the empirical foundations for atomic and molecular physics (Born & Wolf, 1999). Significant achievements in imaging spectroscopy are attributed to airborne instruments, particularly arising in the early 1980s and 1990s (Goetz et al., 1985; Vane et al., 1984). However, it was not until 1999 that the first imaging spectrometer was launched in space (the NASA Moderate-resolution Imaging Spectroradiometer

MODIS

The Moderate-resolution Imaging Spectroradiometer is a payload scientific instrument launched into Earth orbit by NASA in 1999 on board the Terra Satellite, and in 2002 on board the Aqua satellite...

, or MODIS).

Terminology and definitions evolve over time. At one time, >10 spectral bands sufficed to justify the term "imaging spectrometer

Imaging spectrometer

" but presently the term is seldom defined by a total minimum number of spectral bands, rather by a contiguous (or redundant) statement of spectral bands.

The term hyperspectral imaging is sometimes used interchangeably with imaging spectroscopy. Due to its heavy use in military related applications, the civil world has established a slight preference for using the term imaging spectroscopy.

Unmixing

Hyperspectral data is often used to determine what materials are present in a scene. Materials of interest could include roadways, vegetation, and specific targets (i.e. pollutants, hazardous materials, etc.). Trivially, each pixel of a hyperpsectral image could be compared to a material database to determine the type of material making up the pixel. However, many hyperspectral imaging platforms have low resolution (>5m per pixel) causing each pixel to be a mixture of several materials. The process of unmixing one of these 'mixed' pixels is called hyperspectral image unmixing or simply hyperspectral unmixing.

Models

A solution to hyperspectral unmixing is to reverse the mixing process. Generally, two models of mixing are assumed: linear and nonlinear.
Linear mixing models the ground as being flat and incident sunlight on the ground causes the materials to radiate some amount of the incident energy back to the sensor. Each pixel then, is modeled as a linear sum of all the radiated energy curves of materials making up the pixel. Therefore, each material contributes to the sensor's observation in a positive linear fashion. Additionally, a conservation of energy constraint is often observed thereby forcing the weights of the linear mixture to sum to one in addition to being positive. The model can be described mathematically as follows:

where

represents a pixel observed by the sensor,

is a matrix of material reflectance signatures (each signature is a column of the matrix), and

is the proportion of material present in the observed pixel. This type of model is also referred to as a simplex

Simplex

In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...

.

With

satisfying the two constraints:
1. Abundance Nonnegativty Constraint (ANC) - each element of x is positive.
2. Abundance Sum-to-one Constraint (ASC) - the elements of x must sum to one.

Non-linear mixing results from multiple scattering often due to non-flat surface such as buildings and vegetation.

Unmixing (Endmember Detection) Algorithms

There are many algorithms to unmix hyperspectral data each with their own strengths and weaknesses. Many algorithms assume that pure pixels (pixels which contain only one materials) are present in a scene.
Some algorithms to perform unmixing are listed below:

Pixel Purity Index (PPI) - Works by projecting each pixel onto one vector from a set of random vectors spanning the reflectance space. A pixel receives a score when it represent an extremum of all the projections. Pixels with the highest scores are deemed to be spectrally pure.
NFINDR
Gift Wrapping Algorithm
Independent Component Analysis Endmember Extraction Algorithm (ICA-EEA) - Works by assuming that pure pixels occur independently than mixed pixels. Assumes pure pixels are present.
Vertex Component Analysis (VCA) - Works on the fact that the affine transformation of a simplex is another simplex which helps to find hidden (folded) verticies of the simplex. Assumes pure pixels are present.
Principal component analysis -(PCA) could also be used to determine endmembers, projection on principal axes could permit endmember selection [ Smith,Johnson et Adams (1985), Bateson et Curtiss (1996) ]
Multi Endmembers Spatial Mixture Analysis (MESMA) based on the SMA algorithm

Non-linear unmixing algortithm also exist (support vector machine

Support vector machine

A support vector machine is a concept in statistics and computer science for a set of related supervised learning methods that analyze data and recognize patterns, used for classification and regression analysis...

s (SVM)) or Analytical Neural Network (ANN).

Probabilistics methods have also been attempted to unmix pixel through Monte Carlo Unmixing (MCU) algorithm.

Abundance Maps

Once the fundamental materials of a scene are determined, it is often useful to construct an abundance map of each material which displays the fractional amount of material present at each pixel. Often linear programming is done to observed ANC and ASC.

Sensors

MODIS
MODIS
The Moderate-resolution Imaging Spectroradiometer is a payload scientific instrument launched into Earth orbit by NASA in 1999 on board the Terra Satellite, and in 2002 on board the Aqua satellite...

— on board EOS
Earth Observing System
The Earth Observing System is a program of NASA comprising a series of artificial satellite missions and scientific instruments in Earth orbit designed for long-term global observations of the land surface, biosphere, atmosphere, and oceans of the Earth. The satellite component of the program was...

Terra
Terra (satellite)
Terra is a multi-national NASA scientific research satellite in a sun-synchronous orbit around the Earth. It is the flagship of the Earth Observing System...

and Aqua
Aqua (satellite)
Aqua is a multi-national NASA scientific research satellite in orbit around the Earth, studying the precipitation, evaporation, and cycling of water. It is the second major component of the Earth Observing System preceded by Terra and followed by Aura .The name "Aqua" comes from the Latin word...

platforms
MERIS
MERIS
MEdium Resolution Imaging Spectrometer is one of the main instruments on board the European Space Agency 's Envisat platform.This instrument is composed of five cameras disposed side by side, each equipped with a pushbroom spectrometer. These spectrometers use two-dimensional CCDs...

— on board Envisat
Envisat
Envisat is an Earth-observing satellite. It was launched on 1 March 2002 aboard an Ariane 5 from the Guyana Space Centre in Kourou, French Guyana into a Sun synchronous polar orbit at an altitude of...
Several commercial manufacturers for laboratory, ground based, aerial, or industrial imaging spectrographs

External links

About imaging spectroscopy (USGS): http://speclab.cr.usgs.gov/aboutimsp.html
Link to resources (OKSI): http://www.techexpo.com/WWW/opto-knowledge/IS_resources.html
Special Interest Group Imaging Spectroscopy (EARSeL): http://www.op.dlr.de/dais/SIG-IS/SIG-IS.html
Applications of Spectroscopic and Chemical Imaging in Research: http://www3.imperial.ac.uk/vibrationalspectroscopyandchemicalimaging/research

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