Module 7/8 Flashcards
LASER
is the acronym for Light Amplification by Simulated Emission of Radiation. Laser light is made of waves with the same wavelength, moving in
the same direction and in phase. These properties
of laser light are referred
as monochroma-city, collima-on
and coherence.
3D laser scanners employ
Nd:YAG-‐Neodymium-‐doped
YttriumAluminum Garnet, Nd:Y3Al5O12.
LIDAR
Light Detection and Ranging
TLS
Terrestrial Laser Scanning
ALS
Airborne Laser Scanning
Terrestrial Laser
Reigl z420i (1000m range)
Nd:YAG 1064 nm lasers
• Laser rangefinder error = 4 mm at 1000m
• Laser backscatter off ground. Mirror and rotational stepper motors direct laser beam
• Distance = (c x Tflight)/2
Bare Ground Error Budget: • Laser rangefinder error = 0.4 cm at 1000m • GPS error ~1-4 cm+ • Registration Error = 2-5 cm • Estimated RMSE • 2.6-6.5 cm vertical
TLS (LIDAR) for Civil Engineer Geotechnical
• Topographic design • Landslides, Liquefaction,Lat. Spread • Accretion & Erosion • Settlement measurement • River Scour • Excavation displacements • Quay & sea walls • Geomorphic change detection
TLS (LIDAR) for Civil Engineer Structural
- Structural displacements\ deflections \rotations
- Failure patterns
- Design vs. built differences
- Concrete deformations
- Modeling interior space/utilities.
Typical Terrestrial LIDAR Setup
RTK-DGPS Base Photogrammetric Camera RTK-DGPS Rover Benchmark Laser
3D Terrestrial Laser Scanner
- Range finder electronics
- Laser beam
- Polygon mirror
- Body
- TCP/IP Ethernet interface
- Laptop computer
- Camera
- USB interface
- Software
A diagram for the RIEGL Z-SeriesTerrestrial 3D laser scanners.
Solar Spectrum:
Non-‐MonochromaAc
Non-‐Collimated
Non-‐Coherent
Laser Light
Monochromatic (single wavelength)
Collimated (in the same direction)
Coherent (in phase)
The electromagnetic spectrum
V=ƒ λ
The propagating velocity of electromagnetic waves (V), commonly known as the speed of light, is 299,792,458 m/sec in a vacuum. The relationship of V, λ, and f is the same for all wave types.
The wavelength of peak power is predicted for a given target temperature by
Wien’s law:
λmax = 2,898,000 nm-‐K/T
Human body 310°K (98.6°F, 37°C)
λmax ~ 9700 nm-‐K/T
The energy of a single photon an electromagnetic wave
carries is a function of frequency be calculated as:
E=hf = h V/λ
where h is Plank’s constant, 4.135 x 10-15 electron volts-sec or 6.626069 x 10-34 J-sec.
Electronic waves have wave length (λ), and frequency (f) and carry energy (E).
Electromagnetic Radiation from Our LIDAR laser.
Our scanner has a Nd:YAG laser has a wavelength of 1064 nm. Calculate the frequency of the laser wave and the energy that the wave
carries (1 photon) in a vacuum.
ƒ =V/λ=299792458/1064•10^‐9 m/cycle = 2.8•10^14 cycles/sec
E=hƒ=hV/λ
=6.626069•10-‐34J-‐s 2.8 •10^14 cycles/sec=1.867•10^‐19J
=Energy that the wave carries (of one photon in a vacuum at 1064 nm and 2.8 10^14cycles/sec.
Our Riegl z420i
is a low power 1064 nm
(infrared) Nd:YAG laser and eye safe.
Reflector Registration
Registered from best
fit to common
reflectors.
500m
Topnext RTN-DGPS Control for Positioning
Digital Photo Overlay LIDAR 80° scanning window GPS Controller w/ Cellular Modem CORS Network Differential
TLS Processing Proc
A: Scan B: Registration C: Surface Modeling TIN Quantify +/or Change Detection
Registration
Registering (Merging) multiple scans eliminates shadow zones Picture--(2 false-colored scans in white and red)
Sometimes Tripods Do Not Work: Overcoming Obstacles and Shadows
Elevated (20 m) Terrestrial LIDAR
1) Downward view of terrain/vegetation
2) Improved grazing angle
3) Flat terrain max range = H / tan 3°-5°
Registration by the Translation matrix
SOCS>PROCS>GLOCS
SOCS – Scanners
Own Coordinate System
PROCS –Project Coordinate System
GLOCS-‐Global (Georeferenced) Coordinate System
Scanner’s Own Coordinate System (SOCS)
the coordinate of the scanner’s raw data.
Project Coordinate System (PRCS)
The coordinate system
defined by the user. We fix one of the scans as ‘Registered’, and adjust
all other scans to it’s coordinate system (SOCS–>PRCS).
Global Coordinate System (GLCS)
is the Georeferenced coordinate system into which the entire project is embedded (e.g. UTM, State Plane northings, eastings, elevation; (PRCS-->GLCS)
2D Coordinate Transformation using Direction Cosines
- x’A=xΑcosα+yAsinα+c
* y’A=-xΑsinα+yAcosα+d
3D Coordinate Transforma1on – Euler Angles
The transformation matrix we seek is the product of the three sequential transformations (in the correct order) or T(2,1)=T(2,F’‘,F’)T(F’,1)
Direction Cosines-‐3D Coordinate Transformation
3D coordinate transformation is similar to 2D with an added dimension, the objective
is to find the coordinates of Point A in the X’Y’Z’ system if the coordinates of that
point in the XYZ system are known. Again from analytical geometry:
• x’ = x cos(x’, x) + y cos(x’, y) + z cos(x’, z) + c
• y’ = x cos(y’, x) + y cos(y’, y) + z cos(y’, z) + d
• z’ = x cos(z’, x) + y cos(z’, y) + z cos(z’, z) + e
This transformation has nine independent parameters
Point cloud vs. Reflector Registration
RMSE=Root Mean Square Error= sqrt((z1,i-z2,i)^2/n)
For a large sample population of n, RSME^2=M^2+o(omega)^2
For large unbiased population, RMSE=o(omega)
Comparison between Terrestrial and Airborne LIDAR
-‐ Laser Rangefinder: Optech ALTM 3100 -‐ 1064nm w/integrated IMU&GPS. -‐ Pre-‐Trench Flight 1: Fixed wing at 900m (Airborne1,El Segundo, California) -‐ Post Trench Flight 2: Helicopter at 210m (Terrapoint, The Woodlands, Texas)
• Laser rangefinder error
= 2-‐3 cm
• GPS error=5-‐10cm
• IMU error=~9cm@900m
Vendors quoted RMSE
– 18cm vertical (95%CI)
– 0.3-‐0.45m horizontal (1σ)
Airborne systems
Airborne systems collect
overlapping swaths of data
Waveform based lidar is typical in airborne systems
Residual, Mean of the residuals, sample dispersion
Ri=Residual=(zi-zknown,i)
M=mean of residual=sample bias= sum of Ri/n
o(omega)=sample dispersion=sqrt(sumof(Ri-M)^2/(n-1))
Blind Comparison of Airborne and Terrestrial
LIDAR
• Terrestrial LIDAR had almost no bias with pre- and post-trench
Airborne LIDAR had negative bias in both pre- and post-trench
μ = -23.6 - -8.7 cm, and σ = 5.6 - 20.0 cm
(errors exceeded both vendors specifications)
• Terrestrial data had 1/4-1/10 mean error and 1/1.4-1/5 dispersion of airborne
data.
• Multi-epoch elevation change terrestrial residuals were 1/3 of airborne residuals.
Index of Refraction
• The ratio between the propagation rates in a
vacuum and in atmosphere is the index of
refraction which can be expressed as follows:
• n=c/V
• where c is the speed of light in a vacuum and n
is the index of refraction. The value of n is
around 1.0003.
Refraction
The LASER wavelength of an electromagnetic wave decreases as the propagation velocity drops. Since the wave energy does not change and the frequency remains fixed. This effects the estimation of range distance.
Index of refraction
λo/λ = (c/ƒ)/(v/ƒ)=c/v=n
n=index of refraction ƒ=frequency c=speed of light in a vacuum v=speed of light in air λo = wavelength in a vacuum λ=wavelength in air
Temperature
- The effect of temperature on the index of refraction is the most profound.
For example, for a temperature change of 5 Cº from 10Cº to 15Cº, the corresponding change in
the index is more than 5ppm.
Minor effects on refraction: Atmospheric Pressure Humidity
The humidity has the least effect on the index of refraction.
For a 10 percent increase in humidity from 30 to 40 percent,
the change in the index is about 0.087 ppm when λ=0.915 μm
Actual V, λ, and Error
n=c/V
λ =V/ƒ
t=Distance/V
DistanceError=Vt-Distance(vacuum)
•Significant problem if the target distance is large.
•Understand how the
distance is being calculated.
•Be mindful of temperature.
