Electromagnetic Radiation

Deck scope — four big topics.

1. EM radiation principles — wave vs particle, wavelength/frequency, energy.
2. EM radiation models — the wave model and the particle/quantum model.
3. Energy interactions in the atmosphere — scattering, absorption, transmission.
4. Energy interactions with Earth-surface features — reflection, absorption, transmission at the target.

The four elements in every passive optical remote-sensing chain — memorize the letters.

• A — the energy source / illumination (usually the Sun for optical; the sensor itself for active systems like radar).
• B — the Earth’s atmosphere (traversed twice for reflected solar: down then back up).
• C — the Earth’s surface (the target — reflects/absorbs/transmits).
• D — the sensor (records the radiance that reaches it).

Two complementary models of EM energy. Neither alone is complete; both describe the same radiation.

• Wave model — best for describing propagation, wavelength, frequency, polarization.
• Particle (quantum) model — best for describing energy content and interaction with matter (absorption, emission).

Wave model. EM radiation is a transverse wave traveling through vacuum at the speed of light (c = 3 × 10⁸ m/s).

• The wave carries an electric field E and a magnetic field M.
• E and M are perpendicular to each other and both are perpendicular to the direction of propagation.

Wave equation.

λ = c / ν (equivalently c = λν)

• λ (lambda) — wavelength (peak-to-peak distance), typical units µm (1 µm = 10⁻⁶ m).
• c — speed of light, 3 × 10⁸ m/s.

• ν (nu) — frequency, Hz (cycles per second).

• Key takeaway: wavelength and frequency are inversely related. Long wavelength ↔ low frequency ↔ low energy (see slide 9).

The EM spectrum (Hess & McKnight, 2014). Bands arranged by wavelength, shortest to longest:

• Most Earth-observation sensors live in visible, near-IR, mid-IR, thermal-IR, and microwave windows.

The EM spectrum is continuous — the “bands” we name (visible, IR, etc.) are just convenient regions of a continuum of waves, ordered by frequency and wavelength.

Visible light — only the narrow band 0.4 – 0.7 µm is detectable by the human eye, out of a spectrum that spans more than twelve orders of magnitude. Nearly all of “remote sensing” lives outside what we can see.

• Violet ≈ 0.4 µm, blue ≈ 0.45, green ≈ 0.55, red ≈ 0.65–0.7 µm.

Particle (quantum) theory. EM radiation is made of discrete packets — quanta (also called photons).

Q = hν = hc / λ

• Q — energy of a quantum, Joules.
• h — Planck’s constant, 6.626 × 10⁻³⁴ J·s.

• ν — frequency (Hz); λ — wavelength.

• Longer wavelength → lower energy per photon. That’s why long-wavelength sensors (thermal, microwave) must view larger ground areas — they need a bigger footprint to collect enough energy for a detectable signal.

Stefan–Boltzmann law. Every object above absolute zero (0 K = −273 °C) emits EM radiation.

M_λ = σ · T⁴

• M_λ — total emitted radiation per unit area (W/m²).
• σ (sigma) — Stefan–Boltzmann constant, 5.6697 × 10⁻⁸ W·m⁻²·K⁻⁴.
• T — absolute temperature in Kelvin.

• The law assumes a blackbody — an ideal radiator that absorbs all incident energy and re-emits it. Real objects are described by M_λ = ε · σ · T⁴, where ε (emissivity, 0–1) is how close the object is to a true blackbody.

• Key point: emitted energy scales with the fourth power of temperature — small temperature changes produce big radiance changes (why thermal sensors are sensitive).

Wien’s displacement law. Gives the peak-emission wavelength of a blackbody:

λ_max = 2897.8 / T (λ_max in µm, T in K)

• Sun (T ≈ 6000 K): λ_max ≈ 0.483 µm (green-blue visible light).

• Earth (T ≈ 300 K): λ_max ≈ 9.66 µm (thermal infrared).

• Consequence for sensors: use visible/NIR to measure reflected solar, and thermal infrared (8–14 µm) to measure emitted Earth radiation.
• Hotter object → shorter peak wavelength (why a stove burner glows red, then orange, then white).

Three things the atmosphere does to radiation passing through it:

• Scattering — photons are redirected unpredictably by particles or molecules.
• Absorption — photons are taken up by molecules (converted to heat or re-radiated).

• Transmission — photons pass through unchanged (this is what we want for imaging).

• Path length matters: low-sun / high-latitude imagery traverses more atmosphere and suffers more scattering + absorption.

Three types of atmospheric scattering — classified by particle size relative to wavelength.

• Rayleigh scattering — particles ≪ λ (air molecules). Inverse-λ⁴ dependence — affects shorter wavelengths most. Why the sky is blue.
• Mie scattering — particles ≈ λ (dust, smoke, pollen, aerosols). Influences longer wavelengths / all visible. Creates hazy skies.
• Non-selective scattering — particles ≫ λ (cloud droplets, ice). Affects all wavelengths equally → clouds appear white because blue, green, and red are all scattered in the same proportion.

Selective atmospheric absorbers — different molecules absorb different wavelengths:

• Ozone (O₃) — absorbs harmful ultraviolet (protects the biosphere).
• Carbon dioxide (CO₂) — absorbs in the far infrared (thermal band, hence its role in the greenhouse effect).

• Water vapor (H₂O) — absorbs in the longwave infrared and shortwave microwave.

• Consequence: we can’t image at every wavelength — see slide 15 for the “windows” that do transmit well.

Atmospheric windows — bands where the atmosphere is mostly transparent to EM radiation. Remote-sensing instruments are designed to fit inside them.

• Visible (0.4 – 0.7 µm)
• Near-infrared (0.7 – 1.3 µm)
• Middle / short-wave infrared (1.3 – 3.0 µm, with gaps)
• Thermal infrared (3.0 – 5.0 µm and 8 – 14 µm — the big thermal window)

• Microwave (1 mm – 1 m) — used by radar; essentially all-weather.

• Blocked regions (opaque) are dominated by H₂O and CO₂ absorption in the IR.

Energy balance at the target — “How can plants grow in the shade?” The answer is implied by this slide: diffuse/scattered light is still energy, and even shaded canopies receive enough for photosynthesis.

• Energy incident on any body is either reflected, absorbed, or transmitted.
• The proportions depend on:
  • The feature (leaf, water, concrete — each has its own spectral signature).
  • The wavelength (a leaf reflects little red, lots of NIR; a lake does the opposite).
• Conservation: reflected + absorbed + transmitted = total incident energy (see slide 18).

Active vs. passive remote sensing (the slide’s diagram didn’t survive PDF conversion — here’s the concept in full).

• Passive — the sensor only receives natural energy. The source is the Sun (reflected solar) or the target’s own thermal emission. Most optical/thermal imagers are passive. Examples: Landsat OLI/TIRS, MODIS, SPOT, IKONOS.

• Active — the sensor emits its own energy pulse and measures what bounces back. Not Sun-dependent, works day or night, and usually penetrates clouds. Examples: RADAR, LiDAR, scatterometers, SRTM.

• Short-answer mnemonic: Passive listens; active shouts and listens.

Radiant flux budget at the target. For any wavelength λ, the incident flux Φ_I(λ) splits into three parts:

Φ_I(λ) = Φ_R(λ) + Φ_T(λ) + Φ_A(λ)

• Φ_R — reflected energy.
• Φ_T — transmitted energy.

• Φ_A — absorbed energy.

• Reflectance (ρ, rho): ρ(λ) = Φ_R(λ) / Φ_I(λ) — the fraction reflected at each wavelength. Plotted vs. λ, this gives a spectral signature (also called spectral reflectance curve) for a surface — the foundation of all optical classification.

Three reflection regimes.

• Specular (mirror-like) — angle of incidence equals angle of reflection. Energy bounces in one direction only.
  • Examples: calm water surface, polished metal, wet pavement, glass.
• Lambertian (perfectly diffuse) — energy reflects uniformly in all directions; brightness appears the same from every viewing angle.
  • Natural example: freshly fallen snow; matte dry sand; whitewashed walls. (No real surface is perfectly Lambertian — it’s an ideal.)
• Regular / real surfaces — somewhere between the two. Most natural surfaces are diffuse-dominated with a specular component; this is why sensor geometry (BRDF) matters for precise measurements.