FC - LaserAltimetryRanging

Forty question-and-answer flashcards covering principles, instrumentation, missions, equations, and key results from the planetary laser altimetry lecture.

What is the fundamental measurement principle behind a planetary laser altimeter?

Transmit a laser pulse to the surface, receive the return pulse, and determine surface distance from the round-trip travel time.

Which laser energy and wavelength were used by the Mars Orbiting Laser Altimeter (MOLA)?

48 mJ pulses at 1,064 nm (Nd:YAG, near-infrared).

How is laser spot size conventionally defined for altimeters?

By the beam’s Full Width at Half Maximum (FWHM) on the surface.

In a Gaussian beam, what fraction of total energy lies within the FWHM?

Approximately 76 % of the energy.

Which formula gives the physical length of a travelling laser pulse (“laser trail”)?

Pulse length = pulse duration × speed of light (c).

How long is the laser trail for a 20 ns pulse?

≈ 6 m (20 ns × 3 × 10⁸ m s⁻¹).

With a 20 ns pulse, what is the theoretical range precision?

About ±3 m (half of the 6 m round-trip path).

What altitude range is typical for orbital laser altimetry?

Roughly 100 km to 1,000 km above the surface.

What Earth–Moon distance is normally spanned by Lunar Laser Ranging (LLR)?

Around 400,000 km.

Which two Nd:YAG laser wavelengths dominate geodetic use and what colours do they correspond to?

1,064 nm (near-infrared) and 532 nm (green, frequency-doubled).

Write the equation for the energy of a photon.

E = h c / λ, where h is Planck’s constant and λ is wavelength.

What is the energy of a single 1,064 nm photon?

≈ 1.87 × 10⁻¹⁹ joule.

Roughly how many photons are emitted in a 40 mJ laser shot at 1,064 nm?

≈ 2 × 10¹⁷ photons.

Give the photon-budget (laser link) equation used for altimeter design.

Nᵣ = ( Eₜ / hν ) ( Aᵣ / Z² ) η tsys ( ρtar / Ω_tar ), representing received photon count.

Name four instrument parameters that maximise received photon count, per the link equation.

Higher pulse energy, larger receiver aperture, high detector quantum efficiency, and high system transmission.

For typical altimetry, how many photons leave the transmitter and how many return to the detector?

≈ 10¹⁷ photons transmitted; about 10³ photons received.

Which spacecraft carried MOLA and in what years did it operate?

Mars Global Surveyor, operating 1997–2002.

Approximately how many successful range measurements did MOLA collect?

Over 600 million measurements.

What is the highest point on Mars and its elevation above datum?

Olympus Mons, about 21,183 m.

What is the lowest measured point on Mars and its depth?

Hellas Basin floor, about −7,825 m.

State Mars’s mean planetary radius and mean equatorial radius from MOLA results.

Mean radius ≈ 3,389,508 m; mean equatorial radius ≈ 3,396,200 m.

What shot rate and single-shot precision characterize the MESSENGER Laser Altimeter (MLA)?

8 shots s⁻¹ with ≈ 30 cm single-shot precision.

What is the maximum ranging distance of MLA at Mercury?

Up to about 1,500 km.

List Clementine altimeter’s pulse energy and repetition rate.

≈ 180 mJ at 1 Hz.

What were the pulse rate and height resolution of Kaguya’s LALT instrument?

1 Hz pulse rate, ~1 m vertical resolution.

What special optical design allows LOLA to measure slopes and roughness?

A beam splitter producing five parallel laser beams per shot.

How many surface measurements per second does LOLA achieve at 28 Hz?

About 140 measurements per second (5 beams × 28 Hz).

When was ESA’s BepiColombo launched and when is arrival at Mercury expected?

Launched 20 Oct 2018; arrival anticipated in Dec 2026.

What vertical resolution and altitude range will BELA provide?

~30 cm resolution from 400–1,200 km altitude.

State BELA’s nominal pulse energy and firing frequency.

≈ 50 mJ pulses at 10 Hz.

What are the key features of emerging micro-laser altimeters?

µJ pulse energies, kHz shot rates, single-photon detection, and mass < 5 kg.

In laser ranging, what distinguishes diffuse reflection (Lambertian) from retroreflection?

Diffuse surfaces scatter light in all directions; retroreflectors return light toward the source, enabling long-range ranging.

Why are pulsed lasers preferred over continuous-wave lasers for planetary mapping?

Pulsed systems provide precise timing of individual shots, enabling accurate range determination and high peak power.

Give the small-angle approximation linking beam divergence (θ), range (Z), and spot diameter (D).

D ≈ θ × Z for small divergence angles expressed in radians.

Which five components dominate laser pulse spread (σ_r) recorded by an altimeter?

Initial pulse width, receiver response, surface roughness, wavefront curvature, and surface slope.

How does observed pulse spread correlate with terrain slope in MOLA data?

Greater slopes produce wider returned pulses; flat areas yield narrow pulses.

What is the role of the ‘range gate’ in an altimeter receiver?

It defines the time window during which the detector is sensitive, filtering out background noise and unwanted returns.

Write the simple equation relating range (z) to measured travel time (ΔT).

z = (c × ΔT) / 2, where c is the speed of light.

For a Gaussian pulse, how is FWHM related to the standard deviation σ?

FWHM ≈ 2.355 σ.

What does the Lambertian law describe in the context of laser altimetry?

It describes ideal diffuse reflection where radiance is proportional to the cosine of the emission angle.