Helios++
Helios software for LiDAR simulations
EnergyMaths Class Referenceabstract

Some common mathematical operations concerning energy. More...

#include <EnergyMaths.h>

Static Public Member Functions

static double calcEmittedPower (double const I0, double const lambda, double const R, double const R0, double const r, double const w0)
 Compute the space distribution equation to calculate the beam energy decreasing the further away from the center. More...
 
static double calcEmittedPowerLegacy (double const I0, double const lambda, double const R, double const R0, double const r, double const w0)
 Legacy version of EnergyMaths::calcEmittedPower. More...
 
static double calcReceivedPower (double const I0, double const lambda, double const R, double const R0, double const r, double const w0, double const Dr2, double const Bt2, double const etaSys, double const ae, double const sigma)
 Solve the laser radar equation. More...
 
static double calcReceivedPowerLegacy (double const Pe, double const Dr2, double const R, double const Bt2, double const etaSys, double const etaAtm, double const sigma)
 Legacy version of EnergyMaths::calcReceivedPower. More...
 
static double calcAtmosphericFactor (double const R, double const ae)
 Compute the atmospheric factor \(\eta_a\), understood as the energy left after attenuation by air partciles in range \([0, 1]\). More...
 
static double calcCrossSection (double const f, double const Alf, double const theta)
 Compute cross section. More...
 
static double phongBDRF (double const incidenceAngle, double const targetSpecularity, double const targetSpecularExponent)
 Compute the Phong model. More...
 

Detailed Description

Some common mathematical operations concerning energy.

Author
Alberto M. Esmoris Pena
Version
1.0

Member Function Documentation

◆ calcAtmosphericFactor()

double EnergyMaths::calcAtmosphericFactor ( double const  R,
double const  ae 
)
static

Compute the atmospheric factor \(\eta_a\), understood as the energy left after attenuation by air partciles in range \([0, 1]\).

\[ \eta_a = \exp\left( -2 R a_e \right) \]

Parameters
RThe target range \(R\)
aeThe atmospheric extinction \(a_e\)
Returns
The atmospheric factor \(\eta_a\)

◆ calcCrossSection()

double EnergyMaths::calcCrossSection ( double const  f,
double const  Alf,
double const  theta 
)
static

Compute cross section.

\[ C_{S} = 4{\pi} \cdot f \cdot A_{lf} \cdot \cos(\theta) \]


Paper DOI: 10.1016/j.isprsjprs.2010.06.007

Returns
Cross section

◆ calcEmittedPower()

double EnergyMaths::calcEmittedPower ( double const  I0,
double const  lambda,
double const  R,
double const  R0,
double const  r,
double const  w0 
)
static

Compute the space distribution equation to calculate the beam energy decreasing the further away from the center.

\[ P_e = I_0 \exp\left[- \frac{ 2 \pi^2 r^2 w_0^2 }{ \lambda^2 \left(R_0^2 + R^2\right) }\right] \]

Parameters
I0The average power
lambdaThe wavelength
RThe target range (in meters)
R0The minimum range of the device (in meters)
rThe radius
w0The beam waist radius
Returns
Calculated emitted power

◆ calcEmittedPowerLegacy()

double EnergyMaths::calcEmittedPowerLegacy ( double const  I0,
double const  lambda,
double const  R,
double const  R0,
double const  r,
double const  w0 
)
static

◆ calcReceivedPower()

double EnergyMaths::calcReceivedPower ( double const  I0,
double const  lambda,
double const  R,
double const  R0,
double const  r,
double const  w0,
double const  Dr2,
double const  Bt2,
double const  etaSys,
double const  ae,
double const  sigma 
)
static

Solve the laser radar equation.


Report title: Signature simulation and signal analysis for 3-D laser radar
Report authors: Tomas Carlsson, Ove Steinvall and Dietmar Letalick

\[ P_r = \frac{ I_0 D_r^2 \eta_s \sigma }{ 4 \pi R^4 B_t^2 } \exp\left[-\left( \frac{2\pi^2r^2w_0^2}{\lambda^2\left(R_0^2 + R^2\right)} + 2Ra_e \right)\right] \]

Parameters
I0Average power
lambdaWavelength
RTarget range
R0Minimum range
rRadius
w0beam waist radius
Dr2Squared receiver diameter
Bt2Squared beam divergence
etaSysEfficiency of scanning device
aeAtmospheric extinction coefficient
sigmaCross section between target area and incidence angle
Returns
Calculated received power

◆ calcReceivedPowerLegacy()

double EnergyMaths::calcReceivedPowerLegacy ( double const  Pe,
double const  Dr2,
double const  R,
double const  Bt2,
double const  etaSys,
double const  etaAtm,
double const  sigma 
)
static

Legacy version of EnergyMaths::calcReceivedPower.

Parameters
PeThe emitted power
etaAtmThe atmospheric factor
See also
EnergyMaths::calcReceivedPower
EnergyMaths::calcAtmosphericFactor

◆ phongBDRF()

double EnergyMaths::phongBDRF ( double const  incidenceAngle,
double const  targetSpecularity,
double const  targetSpecularExponent 
)
static

Compute the Phong model.


Paper title: NORMALIZATION OF LIDAR INTENSITY DATA BASED ON RANGE AND SURFACE INCIDENCE ANGLE
Paper authors: B. Jutzi, H. Gross


The documentation for this class was generated from the following files: