Electromagnetic Spectrum and Remote Sensing Systems

Spectral signatures and sensor types

A spectral signature is the curve that shows how the reflectance of a material changes with wavelength across the electromagnetic spectrum. Because absorption and reflection depend on the chemical and physical makeup of a surface, each material has a characteristic curve, and this is the basis for identifying materials in multispectral and hyperspectral images. Reflectance is the quantity that forms the signature itself, so it is part of the signature rather than a separate factor that influences it. Seasonal conditions, such as the moisture content or growth stage of vegetation, change the reflectance, so the same surface can show a different signature at different times of the year.

Signatures are most useful for choosing bands. Clear water absorbs most of the incident near-infrared energy, so it returns little signal in NIR bands and appears dark there. Snow and cloud both reflect strongly in the visible range, but snow absorbs strongly in the shortwave infrared near 1.55 to 1.75 \mum while cloud stays reflective, so this range gives the greatest contrast between them. Where the reflectance curves of different materials are widely separated, a sensor band there discriminates them well; where the curves nearly converge, the band gives little discrimination. Such curves are normally measured with a spectroradiometer.

Sensor types are distinguished by the number and width of their bands. A multispectral sensor records a small number of relatively broad bands, which need not be adjacent. A hyperspectral sensor records a very large number of narrow, contiguous bands, typically only a few to ten nanometres wide, which gives a nearly continuous spectrum for each pixel. Ten separated bands about 40 nm wide therefore indicate a multispectral design, whereas hundreds of adjacent bands of 1 nm each indicate a hyperspectral design, and a single band cannot constitute a multispectral sensor.

Several sensors are associated with particular spectral domains. Thermal infrared imagery records emitted radiation in roughly the 8 to 14 \mum region, and it is provided by Landsat TM and NOAA AVHRR, whereas SPOT, CARTOSAT, IKONOS and QuickBird operate in the visible and near-infrared only. MODIS carries 36 spectral bands and Hyperion carries 242 narrow bands, which is consistent with Hyperion being a hyperspectral instrument. Landsat TM is a whisk-broom scanner that records across the track, whereas the LISS-III sensor uses a linear CCD array that records along the track. Imaging radar bands are identified by letter, and NovaSAR operates in S-band, RISAT-1 in C-band, TerraSAR-X in X-band and ALOS PALSAR in L-band.

• signature — the reflectance-versus-wavelength profile of a material. e.g. Two minerals with different absorption features have different signatures even under the same illumination.
• hyperspectral — many narrow contiguous bands. e.g. A sensor with 200 bands of 5 nm each is hyperspectral.
• multispectral — few broad bands, not necessarily contiguous. e.g. A sensor with four bands of 100 nm each is multispectral.

Sensor field of view and swath

The field of view (FOV) is the angular extent over which a sensor receives radiation, and the instantaneous field of view (IFOV) is the angle seen by one detector at a given moment. For a nadir-looking sensor at altitude H with a full across-track field of view \theta, the ground swath width is W = 2H\tan(\theta/2). For example, a sensor at 10 km with a 60 degree FOV has a swath of about 2 \times 10 \times \tan 30^\circ \approx 11.5 km.

A push-broom sensor uses a linear array of detectors that records the full swath at once, so the across-track ground resolution equals the swath width divided by the number of detectors in the row. A swath of 2 km recorded by 2000 detectors therefore gives 2000\ \text{m}/2000 = 1 m. In a push-broom sensor the dwell time of each pixel equals the time needed to record one full scan line, so if a scan line takes 5\times10^{-3} s, each pixel is observed for that duration.

In a whisk-broom scanner, a rotating mirror sweeps across the track and the detector records samples at fixed intervals. The ground distance between successive samples is the platform ground speed multiplied by the sampling interval \Delta T, so \Delta T governs the pixel spacing along the scan direction.

Across-track scanners record each line at a single instant with the nadir at its centre. Relief displacement therefore acts radially away from the nadir across the track and is absent along the flight line. Because of the forward motion of the platform combined with the across-track sweep, straight linear features in the image appear as sigmoidal (S-shaped) curves.

Geometric correction is the process of removing distortions. External geometric errors arise from variations in platform position, attitude and Earth rotation, and they are removed by fitting a mathematical model through ground control points. Rectification then uses the resulting transformation coefficients to map the image to a standard datum and map projection. Registration, by contrast, aligns an image with another image or a map, and field data are normally used for validation rather than for registration.

Spatial frequency describes how quickly image intensity varies. Low frequencies lie near the centre of the shifted Fourier spectrum, and high frequencies lie at increasing radial distance toward its outer edge. A horizontal feature in the image produces components along the vertical axis of the spectrum, and a vertical feature produces components along the horizontal axis.

For along-track stereo, CARTOSAT-1 carries forward and aft cameras that view the same ground strip at different moments of one pass, so the stereo pair is acquired on the same day.

EM spectrum regions and wave relation

The electromagnetic spectrum is ordered by wavelength from the shortest to the longest as gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves. The ordering runs in reverse with frequency, so gamma rays have the highest frequency and radio waves the lowest.

For any electromagnetic wave, the speed equals the product of its frequency and its wavelength, c = \nu\lambda. This follows because the wavelength is the distance covered in one period, and the number of periods per second is the frequency. The energy of a single photon is E = hc/\lambda, which in electronvolts with \lambda in nanometres becomes E \approx 1240/\lambda eV. For example, light at 500 nm carries about 1240/500 \approx 2.48 eV.

Whether a surface reflects specularly or diffusely depends on its roughness relative to the wavelength. A surface that is smooth compared with the wavelength reflects specularly, whereas a surface whose roughness is comparable to or larger than the wavelength reflects diffusely. A single surface may therefore reflect microwaves specularly and visible light diffusely. Optical remote sensing relies mainly on diffusely reflected radiation, which carries the spectral information of the surface material.

Satellite Earth observation uses the visible and thermal infrared regions for optical and thermal imaging, and microwave bands for radar. Gamma rays are absorbed in the atmosphere, and the broad radio range is not used directly for Earth observation imaging.

• diffuse reflection — reflection scattered in many directions, typical of rough surfaces. e.g. A dry grass field viewed at visible wavelengths gives diffuse reflection.
• specular reflection — mirror-like reflection in one direction, typical of smooth surfaces. e.g. Calm water at a wavelength much larger than its ripples reflects specularly.

Radiometric quantities and units

Spectral reflectance is the ratio of the reflected energy to the incident energy at a given wavelength, \rho(\lambda) = E_{\text{refl}}(\lambda)/E_{\text{inc}}(\lambda). It is dimensionless and lies between 0 and 1, and it characterises the surface material. Transmittance, radiance and irradiance refer to different quantities and are not this ratio.

The units of the common radiometric quantities should be memorised. Radiant flux is a power measured in watts. Radiant energy is the time integral of flux and is measured in joules. Radiant exitance is the flux per unit area and is measured in \text{W m}^{-2}. Reflectance is dimensionless. Spectral radiance is the radiance per unit wavelength interval, with units \text{W m}^{-2}\,\text{sr}^{-1}\,\mu\text{m}^{-1}, since radiance has units of \text{W m}^{-2}\,\text{sr}^{-1} and the wavelength interval adds a \mu\text{m}^{-1} term.

Statistical descriptors of radiance values have their own units. Skewness and kurtosis are standardised moments, each being a ratio of central moments to a power of the standard deviation, so their units cancel and they are dimensionless. The mean and standard deviation carry the same units as the radiance values.

Image quality is assessed with statistics of the pixel values. Univariate statistics such as the mean and standard deviation, the histogram of pixel values, and multivariate statistics such as inter-band covariance and correlation are all used for this purpose. The swath, which is the width of ground covered by one pass, describes the coverage of the sensor and is not a quality measure.

Albedo is reflectance integrated over all directions. White-sky albedo assumes diffuse illumination from the whole incident hemisphere, and its geometry is therefore bi-hemispherical.

For a Lambertian surface, the radiance leaving the surface is L_s = \rho E/\pi, where \rho is the reflectance and E is the irradiance. The radiance reaching the sensor is the surface radiance multiplied by the atmospheric transmissivity \tau, plus the path radiance L_p, so L = \tau\rho E/\pi + L_p. For example, with \rho = 0.3, E = 400\ \text{W m}^{-2}, \tau = 0.9 and L_p = 1.5\ \text{W m}^{-2}\text{sr}^{-1}, the sensor radiance is about 0.9 \times 0.3 \times 400/\pi + 1.5 \approx 35.9\ \text{W m}^{-2}\text{sr}^{-1}.

Blackbody radiation and Wien's law

A blackbody absorbs all incident radiation and emits radiation at every wavelength, with a spectrum that depends only on its absolute temperature. Wien's displacement law gives the wavelength of peak emission as \lambda_{\max} = 2898/T micrometres, with T in kelvin. Temperatures in Celsius must first be converted by T = t + 273. For example, a forest fire at 700 °C has T = 973 K, so \lambda_{\max} = 2898/973 \approx 2.98\ \mum, which rounds to 3.0 \mum.

Applied to the Sun and the Earth, Wien's law gives a peak near 0.48 \mum for a surface at 6000 K and near 9.7 \mum for a surface at 300 K. Because a blackbody emits at all wavelengths, the Sun emits a small amount of microwave radiation. The solar and terrestrial spectra overlap only partly, so the solar spectrum is not contained within the terrestrial one. A 300 K surface emits almost nothing at green wavelengths near 0.5 \mum.

The total radiant exitance of a blackbody follows the Stefan-Boltzmann law, M = \sigma T^4, so the emitted power depends on the fourth power of the absolute temperature. Doubling the absolute temperature therefore multiplies the total emission by 2^4 = 16. Consequently, the ratio of the total exitance of two blackbodies is (T_1/T_2)^4, so a 6000 K source and a 300 K source differ by a factor of 20^4 = 160000.