Introductory Course

Fundaments of Optical Remote Sensing

Module 1

Matter Radiation Interaction

Remote sensing or what ?

Telerilevamento (from the Vocabulary of Italian Language, Treccani, 2000)
Télédétection in French language

"...long-distance detection of the appearance and the situation of a territory, particularly its weather and environmental conditions ... its natural resources (forests, water, etc..) usually by air or, now, almost exclusively from artificial satellites... "equipped with sensors sensitive to different types of electromagnetic waves.

SONAR (Sound Navigation And Ranging)	LIDAR (LIght Detection And Ranging)	RADAR (RAdio Detection And Ranging)

THEORETICAL TOOLS:
Basic Definitions and Physical Laws

Solid angle Ω

The solid angle \(\Omega\) is the ratio of the area \(\sigma\) intercepted on the surface of a sphere of radius R by a cone with the vertex in the center of the sphere and the square of the sphere radius (\(R^2\)). The measuring unit is the steradian [sr]

\(\Omega=\frac{\sigma}{R^2}=\frac{\sigma '}{R^{ '2}}\)

Monochromatic Radiance

The monochromatic radiance represents the energy collected in a unit of time and solid angle when the unit of surface of a detector is crossed by e.m. radiation of wavelength in between \(\lambda\) and \(\lambda + d\lambda\) and directed orthogonally to the surface A.

From sensors to radiation sources

To the sensor	From the source	EXEMPLE:THE SUN
RADIANT POWER \(f = dE / dt\) [W]	LUMINOSITY \(f = dE / dt\) [W]	Ex.: Sun Luminosity \(f = 3.90 \times 10^{26} W\)
IRRADIANCE \(F = dE / dt / dA\) \([W m^{-2}]\)	(RADIANT) EXISTANCE \(F = dE / dt /dA\) \([W m^{-2}]\)	Ex: Sun Exitance for a Sun radius \(R = 7 \times 10^8m\) \(F(Sun) = \frac{3.90 \times 10^{26}}{4\pi (7 \times 10^8)^2} = 6.34 \times 10^7 W m^{-2}\)
RADIANCE \(I = dE / dt / d\Omega\) \([W m^{-2}st^{-1}]\)	RADIANCE (BRILLANCE) \(I = dE / dt / dA / d\Omega\) \([W m^{-2}st^{-1}]\)	Ex.: Radiance leaving from Sun surface (assumed Lambertian i.e. isotropic) \(I = F/\pi = 2.02 \times 10^7 W m^{-2} st^{-1}\)

Inverse square law

\(f_\lambda=\frac{dE_\lambda}{dt \cdot d\lambda \cdot}=\int F_\lambda dA = \int dA \int I_\lambda(\Theta, \phi) cos\Theta d\Omega\)

\(f_\lambda =\) cost \(\leftarrow\) cons. of the Energy

\(f_\lambda = F_\lambda \int dA = F_\lambda \cdot 4\pi d^2 = F_\lambda^{'} \cdot 4\pi d^{'2} = f_\lambda^{'}\)

for a punctual Lambertian source

\(F_\lambda (d) = \frac{f_\lambda}{4\pi d^2}\)

\(F_\lambda(d) \propto \frac{f_\lambda}{d^2}\)

\(\frac{F_\lambda (d_2)}{F_\lambda (d_1)} = \frac{d_1^2}{d_2^2}\)

Blackbody Radiation

\(B_\lambda(T)=\) monochromatic radiance emitted at the
wavelength \(\lambda\) by a blackbody at the absolute
temperature \(T [W/m^3]\)
\(c=2.998 \cdot 10^8 m/s\) speed of light in the vacuum
\(h=6.626 \cdot 10^{-34} Js\) Planck’s constant
\(k=1.380 \cdot 10^{-23} J/K\) Boltzman constant

Reyleigh-Jeans approximation

\(x=\frac{h~~c}{\lambda~~k~~T}\rightarrow 0\)

\(e^x = 1 + x + ....\) Taylor

\(e^{\frac{h~~c}{\lambda~~k~~T}}\approx 1 + \frac{h~~c}{\lambda~~k~~T}\)

Emissivity

Brightness Temperature

Planck's function
\(\bbox[5px, border: 2px solid #003366]{B_\lambda(T) = \frac{2~~h~~c^2}{\lambda^5(e^{\frac{h~~c}{\lambda~~k~~T}}-1)}}\)

Brightness Temperature

Exercise: Moon surface temperature

\( T_s = \frac{hc}{\lambda~k} \frac{1}{\ln[1~+~\frac{2~hc^2}{\lambda^5~I_\lambda(T)}]} \)

\( \bbox[5px, border: 2px solid #003366]{I_{\lambda=10\mu} = 3 \cdot 10^4 erg \cdot s^{-1} \cdot cm^{-2} \mu m^{-1} sr^{-1}}\)

monochromatic radiance emitted at the
wavelength \( \lambda = 10\mu \) by he Moon surface
\( c\sim 3 \cdot 10^{10} cm/s\) speed of light in the vacuum
\( h\sim 6,6 \cdot 10^{-27} erg \cdot s\) Planck's constant
\( k\sim 1,4 \cdot 10^{-16} erg/K\) Boltzman constant

Brightness Temperature

Exercise: Earth's surface temperature

\( \bbox[5px, border: 2px solid #003366]{I_{\lambda=10\mu} = 10^4 erg \cdot s^{-1} \cdot cm^{-2} \mu m^{-1} sr^{-1}}\)

monochromatic radiance emitted at the
wavelength \( \lambda = 10\mu \) by he Moon surface
\( c\sim 3 \cdot 10^{10} cm/s\) speed of light in the vacuum
\( h\sim 6,6 \cdot 10^{-27} erg \cdot s\) Planck's constant
\( k\sim 1,4 \cdot 10^{-16} erg/K\) Boltzman constant

Brightness Temperature

(Reyleigh-Jeans approximation)

Planck's function
\(\bbox[5px, border: 2px solid #003366]{B_\lambda(T) \approx \frac{2~kcT}{\lambda^4} ~\propto~T}\)

Wien's Displacement Law

Wien's Displacement Law

Wien's Displacement Law

Exercise: choosing the best spectral range

Earth surface \(T=300K\)

\(\lambda_{MAX}=10\mu m=\)TIR


fires, lava flows \(T=800~~-1000~K\)

\(\lambda_{MAX}=3-4\mu m = \)MIR


Sun photosphere \(T=6000~K\)

\(\lambda_{MAX} = 0,5\mu m =\) VIS

Matter/Radiation Interaction

Matter/Radiation Interaction

Conservation of the energy
\(\bbox[5px, border: 1px solid black]{E_{rif} + E_{ads} + E_{trans} = E_i}\)

\(\bbox[5px, border: 1px solid black]{I_\lambda^R + I_\lambda^A + I_\lambda^T = I_\lambda^I}\)

\(\bbox[5px, border: 1px solid black]{\frac{I_\lambda^R}{I_\lambda^I}+\frac{I_\lambda^A}{I_\lambda^I}+\frac{I_\lambda^T}{I_\lambda^I}=\frac{I_\lambda^I}{I_\lambda^I}=1}\)

monochromatic

Spectral Signatures in the laboratory

\(\bbox[5px, border: 1px solid black]{\rho_\lambda=\frac{I_\lambda^D}{I_\lambda^S}}\)



\(\bbox[5px, border: 1px solid black]{\epsilon_\lambda=\frac{I_\lambda^D}{B_\lambda(T)}}\)



\(\bbox[5px, border: 1px solid black]{\Im_\lambda=\frac{I_\lambda^D}{I_\lambda^S}}\)

Kirchoff law

     at the thermodynamic equilibrium:

\(\bbox[15px, border: 1px solid black]{\rho_\lambda+\alpha_\lambda + \Im_\lambda = 1}\) \(\bbox[15px, border: 1px solid black]{\rho_\lambda+\epsilon_\lambda + \Im_\lambda = 1}\)

for not transparent materials: \(\Im_\lambda \approx 0\) \(\bbox[5px, border: 1px solid black]{\rho_\lambda + \alpha_\lambda = 1}\)

Our daily remote sensing experience
in the visible (VIS) spectral range

Our daily remote sensing experience

What?

How?

What? better?

How?

Measuring reflectances in the laboratory

Measuring reflectances in the laboratory

Measuring reflectances in the laboratory

Beyond visible.

visible and....

Aerial color picture

Measuring reflectances in the laboratory

Which "colors"
beyond visible?

Measuring reflectances in the lab & in the field

(Field Spec ASD Spectrometer)

Spectral signatures of soil, water,
vegetation (in reflectance)

Spectral signature of water

Hight transmittance

Very low transmittance

Spectral signatures of (clean/turbid) water
(in reflectance)

Spectral signatures of snow
(in reflectance)

Spectral signatures of soil, water,
vegetation (in reflectance)

Spectral signatures of vegetation
(in reflectance)

Spectral signatures of vegetation

Monitoring vegetation disease

Spectral signatures of vegetation

Spectral signatures of vegetation
(reflectance) and water (absorption)

Spectral signatures of vegetation in
different condition of water stress
water content %

Measuring reflectances in the lab & in the field

(Field Spec ASD Spectrometer)

Spectral signatures of vegetation

high transmittance

Dependence of reflected radiation on
vegetation density (Leaf Area Index)

Reflectance increases with vegetation
density where transmittance is higher

Spectral signatures of vegetation
(in reflectance)

Spectral signatures of soil, water,
vegetation (in reflectance)

Spectral signatures of different soils
(in reflectance)
Mixing

Atoms and molecule adsorb and emits at specific wavelength

\(\frac{Ze^2}{r^2} = \frac{mv^2}{r} ~~~\Rightarrow~~~ r=\frac{Ze^2}{mv^2}\)

\(l_n = mvr_n = n\hbar ~~~\Rightarrow~~~ r_n = \frac{n^{2}\hbar^{2}}{me^2Z}\)

\(E=-\frac{Ze^2}{r}+\frac{1}{2}mv^2=-\frac{1}{2}\frac{Ze^2}{r}\)

\(E_n = -\frac{m_e e^4}{2\hbar^2} \cdot \left(\frac{1}{n^2}\right)Z^2\)

\(E_n = -\frac{m_e e^4}{2\hbar^2} \cdot \left(\frac{1}{n^2}\right)Z^2~~~\)energy of Bohr orbit

\(v_{jk} = R \cdot \left(\frac{1}{n_j^2}-\frac{1}{n_k^2}\right)Z^2\)

with      \(R=\)      Rydberg constant \(~~~=\frac{2 \cdot \pi^2 \cdot m_e \cdot e^4}{h^3}\)

\(E_{mol}=E_{trasl}+E_{ele}+E_{vib}+E_{rot}\)

\(E_{trasl}~\propto~KT\)

\(E_{vib}^v = \hbar\sqrt{\frac{K}{\mu}}\left(V+\frac{1}{2}\right)~~~\Delta V = \pm 1\)     with overtones

\(E_{rot}^J = \frac{\hbar^2}{2I}J(J+1)~~~\Delta J=\pm 1\)

\(v_{jk} = \frac{E_k-E_j}{h}\)

Basic principle of multi-spectral
remote sensing

• Every material emits, absorbs, transmits or reflects differently at different wavelengths, the em radiation, according to their chemical and physical characteristics


• The spectral response curve represents, in this sense, its spectral signature


• The availability of multi-spectral observations allows, in theory, to trace back to the chemical and physical characteristics of the material that has emitted, absorbed, transmitted or reflected measured em radiation.

From the lab
to the space.

From ground to space

beyond visible

Multispectral digital image

Solar and Terrestrial radiation

Natural sources of radiation
actually available for EO

Passive Earth Observing Techniques

Natural source of
radiation (Sun) different
from the target

Diagnostic parameter:
\(\rho_\lambda\)

Natural source of
radiation (Earth)
coincident with the target

Diagnostic parameters:
\(\epsilon_\lambda, T\)

Active Earth Observing Techniques

The signal is generated
by the observation
system itself

Diagnostic Parameter

\(I_\lambda^{back} \propto\) roughness
\(\frac{c\Delta t}{2}=d=\) distance

e.g. SAR (Synthetic
Aperture Radar)

Different spectral region different capabilities

This pair of images demonstrates some of the differences between passive and active sensors. The top image is an aerial photograph (which records reflected light) of Amundsen-Scott Station, a research facility built on the South Pole. The bottom image is the same area, at approximately the same scale and orientation, from RADARSAT. RADARSAT is an active remote sensing instrument. Microwaves are generated by the sensor, reflected from the Earth's surface and back to the sensor. The radar image reveals an abandoned cluster of buildings (to the lower left of the bright dome) that are now buried under Antarctic ice. (RADARSAT image courtesy Canadian Space Agency)

Atoms and molecule in atmosphere interact
selectively with (modifying) the radiation leaving
Earth surface and directed toward the sensor.

Chemical-physical properties of
atmosphere: temperature profile

Chemical composition

Chemical composition of
atmosphere

Scattering in the atmosphere

In general we can have scattering for whatever
wavelength \(0 < \lambda < \infty \)
in the atmosphere we have scattering from particle
having dimension like:

\(10^{-8} < d < 1 \quad cm\)
\( [X~rays]~~~~~[microwaves]\)

What about clouds?

Attenuation to radiation of
different wavelengths by
common atmospheric constituents
and other particles (Source:
Tomlinson 1972)

Extinction of solar radiation
in the atmosphere

LANDSAT-TM all bands in atmospheric windows !

AVHRR:
all bands in atmospheric windows !

Reference list