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The amplitude describes the received signal strength (peak power) of one echo (commonly referred to as intensity), which is affected by the wavelength and energy of the transmit pulse, the distance to the target, the target reflectance, the transmission in the atmosphere, and the receiver and detector characteristics. 
Backscatter Coefficient / Gamma
The backscatter coefficient (γ) [m2*m-2] is defined as backscatter cross-section normalized to the cross-section of the incoming beam (i.e. footprint area) and enables the comparison of measurements with different resolution easily. ,
Backscatter Cross-section / Sigma
The backscattering or backscatter cross-section (σ), also referred to as radar cross section, is the effective area of collision of the laser beam and the target, considering the directionality and strength of reflection . It is a product of the target area, the target reflectivity and the factor 4π/Ω describing the scattering angle of the target in relation to an isotropic scatterer .
(Whole) Angle of the widening of the laser beam. Due to the typically varying energy distribution within the laser beam the angle is limited to the region where the energy decrease from the maximum follows the ratio of 1/e2.
The diffuse reflection is an uniform reflection of light with no directional dependence. Diffuse reflection originates from a combination of internal scattering of light, i.e. the light is absorbed and then re-emitted, and external scattering from the rough surface of the object. (For calculation, cf.  Eq. 38)
Temporally connected part of the whole backscattered laser power that was detected by the receiver and that can be allocated to a certain reflecting surface element. 
Temporal length of a detected echo. Due to the fact that the echo will not have an exact rectangular form, the duration is - if not stated differently - the temporal length where the power of the echo is above the half maximum (full width at half maximum (FWHM) or the full duration at half maximum (FDHM).
A feature (or attribute) describes a specific LiDAR information (geometric or radiometric) of an object such as height, diameter, amplitude, echo widths, etc.
Illuminated area(s) within the divergence of the laser beam.
Geometric information comprises the detailed geometric presentation of a scanned object. The object geometry is derived from the xyz coordinates of the object's point cloud and describes for example the height, wide, shape etc. of the object.
The term half width of a non-negative function with one single maximum is the difference between two values that have a function value that descents to the half of the maximum value. Typically for this half width value the term FWHM (full width at half maximum) is used. If the function value depends on time the abbreviation FDHM (full duration at half maximum) is often used.
Remark: In the case of a normal distribution with a standard deviation (sigma) and an expectation value of zero the FWHM can be calculated by
FWHM=2* √(2*ln(2))* σ=2.35* σ. 
Characterization of the backscattered signal strength of an echo. Often this specification is not accurately defined. The term intensity can e.g. express the maximum as well as the total energy of one echo., , 
Continuously emitted connected light resp. energy packet with a very small wavelength range.
A laser scanner is a measurement device recording by active illumination of object surfaces. Range and angular observations of reflecting objects in the sensor coordinate system are made, while the observation direction varies continuously within the field of view with the help of a deflection unit. In general, for the range measurement two different methods are in use:
In both methods time differences are determined that have to be converted to metric range values. Next to the observation of distances and ranges further observations (e.g. maximal echo amplitude) can be recorded by the laser scanner system.
- the time-of-flight of a laser pulse, where the travelling time between an emitted pulse and received echo is determined,
- and the continuous wave ranging, where the phase difference between the amplitude modulated continuously emitted laser beam and its received echo is estimated.
Light Detection And Ranging (LiDAR)
LIDAR is an optical remote sensing technology that measures properties of scattered light to find range and/or other information of a distant target.
The normalized amplitude describes the backscattered signal strength normalized to the average altitude (Anorm = A * 1/Range2 * Altitude2). 
Number of Returns
The number of returns are the recorded returns per laser pulse. The number of returns detected for a pulse depends on the distribution of surfaces and their reflectance in the laser wavelength encountered along the path of the laser beam.  p.182
Points within one specific coordinate system. Next to geometric information further point attributes like the intensity information, time stamp, classification results, etc. can be added to the singular points. The main difference to raw data is that the sequence of points may not follow the measurement process (may be arbitrary) and furthermore the point cloud must not provide all observations or attributes.
Temporal length of a pulse. Due to the fact that the pulse will not have an exact rectangular form, the duration is - if not stated differently - the temporal length where the power of the echo is above the half maximum (full width at half maximum (FWHM) or the full duration at half maximum (FDHM)).
Radiometric information describes the full profile of laser energy that was scattered back to the sensor. Radiometric information can be features like amplitude, echo width, backscatter cross-section etc.
The reference signature is defined as the significant collection of features connected with known and measured vegetation parameters (= reference data).
The signature of an object ist defined as the collection (or matrix) of features.
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