| Title: | Monte Carlo Simulation for Surface Backscattering |
|---|---|
| Description: | Monte Carlo simulation is a stochastic method computing trajectories of photons in media. Surface backscattering is performing calculations in semi-infinite media and summarizing photon flux leaving the surface. This simulation is modeling the optical measurement of diffuse reflectance using an incident light beam. The semi-infinite media is considered to have flat surface. Media, typically biological tissue, is described by four optical parameters: absorption coefficient, scattering coefficient, anisotropy factor, refractive index. The media is assumed to be homogeneous. Computational parameters of the simulation include: number of photons, radius of incident light beam, lowest photon energy threshold, intensity profile (halo) radius, spatial resolution of intensity profile. You can find more information and validation in the Open Access paper. Laszlo Baranyai (2020) <doi:10.1016/j.mex.2020.100958>. |
| Authors: | Laszlo Baranyai <[email protected]> |
| Maintainer: | Laszlo Baranyai <[email protected]> |
| License: | LGPL-2.1 |
| Version: | 0.1.1 |
| Built: | 2024-12-19 06:43:04 UTC |
| Source: | CRAN |
This function calculates how photon energy decreases during interaction with media.
Absorb(myObject)Absorb(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Absorb function, alias Absorb.MCBS, calculates the new energy level after interaction event in the media. If photon energy falls below 0.001, a roulette algorithm makes decision when photon has 10% chance to survive with higher energy and 90% chance to loose all energy. Please keep in mind, that photons start with weight = 1 but the first interaction happens at boundary, where photons enter the media.
The Absorb function returns an MCBS object as class. Typically the same object is used in argument and result.
One parameter of a single photon is updated in this procedure:
weight |
photon energy. Its initial value is 1 and decrease according to the albedo. |
Please note that this function is designed to be used in Simulation function. You may use it separately in case you design your own procedure. In such a case, please note that function Randomize prepares trajectory data for each photon and iterations are done using move index myObject$midx. Function Absorb uses random data in roulette algorithm to make decision about photon survival at low energy level.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Launch for start position of single photon and initial direction in media.
Bounce for interaction with surface and computation of photon flux leaving media.
Move for moving single photon forward.
Scatter for single photon scattering interaction with media.
Randomize for adjustment of random trajectory vectors.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple,10) # initial weight in media cat("Photon energy level",apple$weight,"\n") # first interaction event apple$midx <- 1 apple <- Absorb(apple) cat("Photon energy level",apple$weight,"\n")## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple,10) # initial weight in media cat("Photon energy level",apple$weight,"\n") # first interaction event apple$midx <- 1 apple <- Absorb(apple) cat("Photon energy level",apple$weight,"\n")
This function is applied when photon trajectory goes out of the media or reaches the surface (z <= 0). The photon flux is summarized upon leaving semi-infinite media through the surface.
Bounce(myObject)Bounce(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Bounce function, alias Bounce.MCBS, calculates internal reflection if incident angle to surface boundary was higher than critical angle. In all other cases, Fresnel reflection is calculated according to the direction and refractive index of media. Remaining photon weight that leaves the media is collected and summarized by the position. Position is calculated as distance from incident point. This way, radial averaging is performed with rigns of width of the spatial resolution. The internally reflected part of photon energy still follows trajectory until reaches limiting energy or expected trajectory length.
The Bounce function returns an MCBS object as class. Typically the same object is used in argument and result.
The function collects photon flux in an array:
heat |
vector of photon flux scattered back from media. One element represent a ring of width of the spatial resolution. The center of the ring is the incident point. |
Please note thet this is an internal function of Simulation. Do not use it separately, unless you build your own simulation procedure. The function uses the coordinates c(x,y,z) of the current photon and the c(u,v,w) direction of its last move.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Launch for start position of single photon and initial direction in media.
Move for moving single photon forward.
Absorb for absorption of single photon energy in interaction with media.
Scatter for single photon scattering interaction with media.
Randomize for adjustment of random trajectory vectors.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch and move first photon apple$idx <- 1 apple <- Launch(apple) # first move apple$midx <- 1 apple <- Move(apple) if (apple$z <= 0) { apple <- Bounce(apple) }## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch and move first photon apple$idx <- 1 apple <- Launch(apple) # first move apple$midx <- 1 apple <- Move(apple) if (apple$z <= 0) { apple <- Bounce(apple) }
This function creates a plot of diffuse reflectance (backscattering) intensity measured on the surface. The photon flux is shown by radius (distance from incident point).
Chart(myObject,isLog=FALSE)Chart(myObject,isLog=FALSE)
myObject |
The mandatory parameter of this function is the MCBS class created by |
isLog |
Logical variable. Default value is FALSE. If set to TRUE, photon flux will be shown in logarithmic scale. |
The Chart function, alias Chart.MCBS, plots simulation results. Photon flux is computed by Simulation function. The chart shows flux according to the spatial resolution of the simulation. In case you wish to make your customized chart, please use the Export function to receive data.
This function does not have any result value.
In case you wish to customize your chart, please use Export function to receive data.
MCBS for construction of object with initial input parameters.
Setup for initial computation of specular reflection and transport albedo.
Simulation for running the simulation with adjusted parameters.
print show adjusted parameters and total backscattered reflection.
Export for export of photon flux with corresponding radii.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show simulation result Chart(apple) # show simulation result with logarithmic scale Chart(apple,TRUE)## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show simulation result Chart(apple) # show simulation result with logarithmic scale Chart(apple,TRUE)
This function exports simulation results in table format. It can be used to save results into file or make customized charts.
Export(myObject)Export(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Export function, alias Export.MCBS, provides a table with column names. Results of Monte Carlo simulation computed by the Simulation function are given as data.frame. The radii are automatically calculated according to the spatial resolution.
Results are provided as data.frame in table format. Two columns represent radii and photon flux.
Radius |
radius of concentric rings, where photon flux is calculated. Starts with incident point at radius of zero (r=0). The unit is cm. |
Flux |
calculated photon flux, 1/cm^2 |
MCBS for construction of object with initial input parameters.
Setup for initial computation of specular reflection and transport albedo.
Simulation for running the simulation with adjusted parameters.
print show adjusted parameters and total backscattered reflection.
Chart for plot of calculated photon flux profile.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show photon flux near incident point tbl <- Export(apple) tbl[1:3,] # save results into file write.table(Export(apple),tempfile("apple",fileext=".dat"))## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show photon flux near incident point tbl <- Export(apple) tbl[1:3,] # save results into file write.table(Export(apple),tempfile("apple",fileext=".dat"))
This function starts single photon into the semi-infinite media from surface (z = 0). The 3D launch direction c(u,v,w) points into the media, according to the incident angle (relative to normal) and refractive index. If incident angle was zero, the incidence is normal (perpendicular to surface). If incidence angle was not zero, elliptical distortion of circular light beam is also considered.
Launch(myObject,iAngle=0)Launch(myObject,iAngle=0)
myObject |
The mandatory parameter of this function is the MCBS class created by |
iAngle |
This optional parameter means the incident angle relative to normal. The default value is 0 (the incidence is perpendicular to surface). |
The Launch function, alias Launch.MCBS, calculates the start position of the single photon on the surface. The coordinates c(x,y,z) are computed as z = 0 and c(x,y) represent random position in circular light beam. The values z > 0 are inside the media. Beam intensity distribution is considered to be flat, what means that positions have equal probability to occur. Starting polar coordinates are adjusted randomly using uniform distribution by function Setup. If incident angle was not zero, elliptical distortion is corrected along the y-axis.
The Launch function returns an MCBS object as class. Typically the same object is used in argument and result.
Position and starting 3D vector are calculated:
x |
position along x-axis, calculated from random polar coordinates. |
y |
position along y-axis, calculated from random polar coordinates. If incident angle was not zero, this value is distorted. |
z |
initial depth, z=0 on the surface. |
u |
launch vector coordinate along x-axis. |
v |
launch vector coordinate along y-axis. If incident angle was not zero, this value is calculated according to the incident angle and refractive index. |
w |
launch vector coordinate along z-axis. If incident angle was not zero, this value is calculated according to the incident angle and refractive index. |
Theoretical models assume the incident angle is zero. During measurement, camera and lightsource cannot occupy the same direction. According to the Fresnel reflection equations, incident angle below 20° is recommended. The non-zero incident angle requires correction in computation by means of refraction of the initial direction inside media and elliptical distortion of circular light beam on the surface.
Please note that this function is not intended to use independently. It calculates start values for photon of index myObject$idx. If you want to use it to build your custom simulation, do not forget to assign index, such as myObject$idx <- 1. Index number must be between 1 and myObject$MAXLEN.
Jacques, S.L. (1998) Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues. Photochemistry and Photobiology, 67(1): 23–-32. doi:10.1111/j.1751-1097.1998.tb05161.x.
Wang, L., Jacques, S.L., Zheng, L. (1997) CONV-convolution for responses to a finite diameter photon beam incident on multi-layered tissues. Computer Methods and Programs in Biomedicine, 54: 141–-150. doi:10.1016/S0169-2607(97)00021-7.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Bounce for interaction with surface and computation of photon flux leaving media.
Move for moving single photon forward.
Absorb for absorption of single photon energy in interaction with media.
Scatter for single photon scattering interaction with media.
Randomize for adjustment of random trajectory vectors.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # calculate first photon apple$idx <- 1 apple <- Launch(apple) # see vector coordinates cat("Start position",apple$x,":",apple$y,"\n") cat("Direction",apple$u,":",apple$v,":",apple$w,"\n") # calculate first photon with 10° incident angle apple$idx <- 1 apple <- Launch(apple,10) # see vector coordinates cat("Start position",apple$x,":",apple$y,"\n") cat("Direction",apple$u,":",apple$v,":",apple$w,"\n")## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # calculate first photon apple$idx <- 1 apple <- Launch(apple) # see vector coordinates cat("Start position",apple$x,":",apple$y,"\n") cat("Direction",apple$u,":",apple$v,":",apple$w,"\n") # calculate first photon with 10° incident angle apple$idx <- 1 apple <- Launch(apple,10) # see vector coordinates cat("Start position",apple$x,":",apple$y,"\n") cat("Direction",apple$u,":",apple$v,":",apple$w,"\n")
This function is the constructor of Monte Carlo Backscattering (MCBS) class. Diffuse reflection, also called as backscattering, is the phenomena when light enters into the media, such as biological tissue, and after traveling some distance it leaves the media or tissue through the surface.
MCBS(myTissue,myLight)MCBS(myTissue,myLight)
myTissue |
collection of optical parameters of the semi-infinite medium. It is a list of numbers: |
myLight |
collection of computational parameters. It is a list of numbers: |
The MCBS function creates and initializes a class using the given parameters. The two arguments are separated according to their role. The first one describes media in which photons travel. The second defines simulation parameters. See arguments for details.
The optical parameters describing observed media typically has the relationship of mua << mus, which means absorption coefficient is much smaller that scattering coefficient. Many research papers publish the reduced scattering coefficient rmus = mus*(1-g). The general problem of comparison and validation is that list(mus=2,g=0) results the same reduced scattering coefficient like list(mus=20,g=0.9). The value of g shows the most likely direction of light after interaction event in media: g = 1 means continue forward, g = 0 means there is no expected direction and media is isotropic, g = -1 means reflected backward. In biological tissues, anisotropy factor (g) is reported to be in the range of 0.8 - 0.99.
Since argument myLight is reflecting measurement conditions and hardware setup, it can be considered constant for one system. Please note that quality of results depends on the number of photons. The more is used the better quality you get. The minimum suggested number is 100,000 photons. If you calculate the amount of photons with sensor or camera integration time, this number will increase above billion.
The argument myTissue includes optical parameters of the sample, this is expected to change during experiment such as storage, grading, etc.
The MCBS function returns an object of class. Package functions are used to access their parameters for reporting, adjustment and computation. Direct manipulation of object parameters is highly not recommended. Please use the provided functions to reach what is necessary or use them read-only.
An object of class "MCBS" is a list containing at least the following components:
mu_a |
absorption coeffieint, 1/cm |
mu_s |
scattering coefficient, 1/cm |
g |
anisotropy factor |
n |
relative refractive index of media (the other media is assumed to be air) |
albedo |
transport albedo, the descrease of photon energy after one absorption event in media. The value is initialized by |
cangle |
cosine of critical angle. The value is initialized by |
rs |
specular reflection. The value is calculated on the basis of refractive index by |
Other parameters include containers for calculation. Please do not use them directly. See examples how to extract data.
The object design was inspired by the C code "Small Monte Carlo" written by Scott Prahl (http://omlc.org).
Jacques, S.L. (1998) Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues. Photochemistry and Photobiology, 67(1): 23-–32. doi:10.1111/j.1751-1097.1998.tb05161.x.
Wang, L., Jacques, S.L., Zheng, L. (1995) MCML – Monte Carlo modeling of light transport in multi-layered tissues. Computer Methods and Programs in Biomedicine, 47: 131-–146. doi:10.1016/0169-2607(95)01640-F.
Wang, L., Jacques, S.L., Zheng, L. (1997) CONV-convolution for responses to a finite diameter photon beam incident on multi-layered tissues. Computer Methods and Programs in Biomedicine, 54: 141–-150. doi:10.1016/S0169-2607(97)00021-7.
Zołek, N.S., Liebert, A., Maniewski, R. (2006) Optimization of the Monte Carlo code for modeling of photon migration in tissue. Computer Methods and Programs in Biomedicine, 84: 50–-57. doi:10.1016/j.cmpb.2006.07.007.
Baranyai, L., Zude, M. (2009) Analysis of laser light propagation in kiwifruit using backscattering imaging and Monte Carlo simulation. Computers and Electronics in Agriculture, 69: 33-–39. doi:10.1016/j.compag.2009.06.011.
Baranyai, L. (2020) Laser induced diffuse reflectance imaging – Monte Carlo simulation of backscattering measured on the surface. MethodsX, 7: 100958. doi:10.1016/j.mex.2020.100958.
Setup for initial computation of specular reflection and transport albedo.
Randomize for adjustment of random trajectory vectors.
Simulation for running the simulation with adjusted parameters.
print show adjusted parameters and total backscattered reflection.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 cfgMedia <- c( 0.63, # absorption, 670 nm 30, # reduced scattering, 670 nm 0, # isotropic tissue assumed 1.4) # refractive index cfgSimulation <- c( 1e6, # 1 million photons 0.05, # 1 mm diameter (0.05 cm radius) laser light beam 1e-9, # limiting energy level 3, # 3 cm radius is computed 0.012) # 0.012 cm/pixel resolution is assumed apple <- MCBS(cfgMedia,cfgSimulation) cfgMedia <- c( 0.63, # absorption, 670 nm 300, # scattering, 670 nm 0.9, # anisotropic tissue with forward scattering is assumed 1.4) # refractive index apple <- MCBS(cfgMedia,cfgSimulation)## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 cfgMedia <- c( 0.63, # absorption, 670 nm 30, # reduced scattering, 670 nm 0, # isotropic tissue assumed 1.4) # refractive index cfgSimulation <- c( 1e6, # 1 million photons 0.05, # 1 mm diameter (0.05 cm radius) laser light beam 1e-9, # limiting energy level 3, # 3 cm radius is computed 0.012) # 0.012 cm/pixel resolution is assumed apple <- MCBS(cfgMedia,cfgSimulation) cfgMedia <- c( 0.63, # absorption, 670 nm 300, # scattering, 670 nm 0.9, # anisotropic tissue with forward scattering is assumed 1.4) # refractive index apple <- MCBS(cfgMedia,cfgSimulation)
This function calculates the move of single photon in media.
Move(myObject)Move(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Move function, alias Move.MCBS, calculates updated position coordinates c(x,y,z) according to the motion vector c(u,v,w) and the travel length until next interaction event.
The movement of single photon is calculated in 3 dimensional space. The length of the straight section a photon can travel until the next interaction event is estimated as -log( rnd ) where rnd is a uniformly distributed random variable from range 0-1.
The Move function returns an MCBS object as class. Typically the same object is used in argument and result.
As a result, the 3D position of the photon is updated:
x |
position along x-axis |
y |
position along y-axis |
z |
position along z-axis, the depth |
Please note that this function is designed to be used in Simulation function. You may use it separately in case you design your own procedure. In such a case, please note that function Randomize prepares trajectory data for each photon and steps are done using move index myObject$midx.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Launch for start position of single photon and initial direction in media.
Bounce for interaction with surface and computation of photon flux leaving media.
Absorb for absorption of single photon energy in interaction with media.
Scatter for single photon scattering interaction with media.
Randomize for adjustment of random trajectory vectors.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple,10) # first move apple$midx <- 1 cat("Position",apple$x,":",apple$y,":",apple$z,"\n") apple <- Move(apple) cat("Position",apple$x,":",apple$y,":",apple$z,"\n") # second move apple$midx <- 2 apple <- Move(apple) cat("Position",apple$x,":",apple$y,":",apple$z,"\n")## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple,10) # first move apple$midx <- 1 cat("Position",apple$x,":",apple$y,":",apple$z,"\n") apple <- Move(apple) cat("Position",apple$x,":",apple$y,":",apple$z,"\n") # second move apple$midx <- 2 apple <- Move(apple) cat("Position",apple$x,":",apple$y,":",apple$z,"\n")
This function prints text report about simulation parameters and calculated coeeficients (albedo, critical angle) and total backscattered reflection.
print(myObject)print(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The print function, alias print.MCBS, provides text description of simulation. Results of Monte Carlo simulation computed by the Simulation function are given as data.frame. Text report includes: absorption coefficient, scattering coefficient, anisotropy factor, refractive index, transport albedo, specular reflection, critical angle, backscattered total reflection.
Results of simulation are provided as data.frame in table format. Print function lists adjusted parameters on console, does not return any value.
MCBS for construction of object with initial input parameters.
Setup for initial computation of specular reflection and transport albedo.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show simulation report print(apple)## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Simulation(apple) # show simulation report print(apple)
This function prepares vectors of random numbers to accelerate trajectory computation. Random numbers are selected from uniform distribution.
Randomize(myObject)Randomize(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Randomize function, alias Randomize.MCBS, puts random numbers into the container vectors created with the object. During trajectory computation, each interaction event occurs randomly. Prepared container vectors accelerate computation, since values for each event are accessible with myObject$midx move index. Vector length myObject$MAXLEN is adjusted by Setup function based on transport albedo and limiting energy.
The Randomize function returns an MCBS object as class. Typically the same object is used in argument and result.
There are five containers of random numbers. Values are in the range of 0 to +1 unless indicated in description.
rmv |
length of linear section between interaction events. Used by |
rabs |
decision values for roulette algorithm. Used by |
rx1 |
new scattering direction in the range of -1 to +1. Used by |
rx1 |
new scattering direction in the range of -1 to +1. Used by |
rmu |
variable for Heyney-Greenstein phase function. Used by |
Please note that this function is designed to be used in Simulation function. You may use it separately in case you design your own procedure. In such a case, please note that function Randomize prepares random values for one photon and has to be run always before calculating single photon trajectory.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Move for moving single photon forward.
Absorb for absorption of single photon energy in interaction with media.
Scatter for single photon scattering interaction with media.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # first five random values of move length apple <- Randomize(apple) apple$rmv[1:5]## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # first five random values of move length apple <- Randomize(apple) apple$rmv[1:5]
Scattering is the interaction event in the media when photon hits structural elements and changes direction as a result of collision.
Scatter(myObject)Scatter(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The Scatter function, alias Scatter.MCBS, calculates the new direction of photon travel. In isotropic media, any new 3D direction can occur with equal probability. In anisotropic media, the new direction is decided according to the Heyney-Greenstein phase function. The isotropic and anisotropic behavior of media is shown by anisotropy factor (g). The anisotropy factor is zero (g = 0) for isotropic media, g = -1 means backward reflection (backscattering) is the most likely, while g = +1 means the most likely result is that photon continues forward (forward scattering). Biological tissues were reported to have high positive anisotropy factor g > 0.8.
The Scatter function returns an MCBS object as class. Typically the same object is used in argument and result.
As a result of Scatter function, new direction is given by c(u,v,w). These values are used in function Move to calculate next position.
u |
3D vector coordinate along x-axis |
v |
3D vector coordinate along y-axis |
w |
3D vector coordinate along z-axis |
Please note that this function is designed to be used in Simulation function. You may use it separately in case you design your own procedure. In such a case, please note that function Randomize prepares trajectory data for each photon and iterations are done using move index myObject$midx. Results of Scatter function are used in Move function.
Henyey, L.G., Greenstein, J.L. (1941) Diffuse Radiation in the Galaxy. Astrophysical Journal, 93, 70–83. doi:10.1086/144246.
Jacques, S.L. (1998) Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues. Photochemistry and Photobiology, 67(1): 23-–32. doi:10.1111/j.1751-1097.1998.tb05161.x.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Setup for initial computation of specular reflection and transport albedo.
Randomize for adjustment of random trajectory vectors.
Launch for start position of single photon and initial direction in media.
Bounce for interaction with surface and computation of photon flux leaving media.
Move for moving single photon forward.
Absorb for absorption of single photon energy in interaction with media.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple) # first interaction event cat("Direction",apple$u,":",apple$v,":",apple$w,"\n") apple$midx <- 1 apple <- Scatter(apple) cat("Direction",apple$u,":",apple$v,":",apple$w,"\n")## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) apple <- Randomize(apple) # launch with 10° incident angle and move first photon apple$idx <- 1 apple <- Launch(apple) # first interaction event cat("Direction",apple$u,":",apple$v,":",apple$w,"\n") apple$midx <- 1 apple <- Scatter(apple) cat("Direction",apple$u,":",apple$v,":",apple$w,"\n")
This function performs the basic configuration of Monte Carlo Backscattering (MCBS) class. It calculates specular reflection, transport albedo, critical angle and similar parameters.
Setup(myObject)Setup(myObject)
myObject |
The mandatory parameter of this function is the MCBS class created by |
The function Setup, alias Setup.MCBS, performs the initial calculation of essential parameters for computation. Additionally, computes the maximum expected trajectory length and prepares the launch position of all photons with random polar coordinates within circular beam.
The Setup function returns an MCBS object as class. Typically the same object is used in argument and result.
The new parameters calculated in Setup are:
albedo |
transport albedo |
rs |
specular reflection |
cangle |
cosine value of critical angle |
MAXLEN |
maximum expected length of photon trajectory. This length depends on the albedo and limiting energy. |
There are additional containers for random launch position of photons. Launch position is given with polar coordinates (radius, angle).
Please note that this function is designed to be used in Simulation function. You may use it separately in case you design your own procedure.
MCBS for construction of object with initial input parameters.
Simulation for running the simulation with adjusted parameters.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
Launch for start position of single photon and initial direction in media.
Randomize for adjustment of random trajectory vectors.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # transport albedo apple$albedo # specular reflection apple$rs## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) cfgSimulation <- c(1e6,0.05,1e-9,3,0.012) apple <- MCBS(cfgMedia,cfgSimulation) apple <- Setup(apple) # transport albedo apple$albedo # specular reflection apple$rs
This function performs all actions to run the simulation. It calls other functions that prepare computation and calculate photon trajectory. Please keep in mind, that this technique can be slow depending on the number of photons and computational power of your hardware.
Simulation(myObject,iAngle=0)Simulation(myObject,iAngle=0)
myObject |
The mandatory parameter of this function is the MCBS class created by |
iAngle |
The optional parameter |
The function Simulation, alias Simulation.MCBS, was designed to take every steps such as Setup initial conditions and compute each photon trajectory individually. It was written keeping clarity in mind. In case you want to make your own procedure, this function can be used as a template.
The result of simulation is photon flux, which is expressed as relative fluence rate (F/P, 1/cm^2) where F is the fluence rate and P is the power of light source. The fluence rate (F) is computed in concentric rings around the incident point.
The Simulation function returns an MCBS object as class. Typically the same object is used in argument and result.
The main objective of the simulation is to calculate spatial photon flux. The flux is computed with radial averaging relative to the incident point. Each value represent the average flux of the ring with the width of resolution (1 pixel).
heat |
calculated photon flux, 1/cm^2 |
Please note that quality of results depends on the number of photons. The more is used the better quality you get. The minimum suggested number is 100,000 photons. If you calculate the amount of photons with sensor or camera integration time, this number will increase above billion.
Validation of computations is difficult, because other Monte Carlo programs or the diffusion theory model can be used as reference. The diffusion theory model does not consider many parameters included in Monte Carlo simulation, such as beam radius, incident angle, anisotropy. Please note that models and reports usually use the reduced scattering coefficient rms = (1-g)*ms what means that different scattering and anisotropy parameters, like list(ms=20,g=0) and list(ms=200,g=0.9), result the same reduced scattering coefficient.
Do not access and manipulate the result data vector myObject$heat directly. You can receive results by using the Export function.
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MCBS for construction of object with initial input parameters.
Setup for initial computation of specular reflection and transport albedo.
Randomize for adjustment of random trajectory vectors.
print show adjusted parameters and total backscattered reflection.
Chart for plot of calculated photon flux profile.
Export for export of photon flux with corresponding radii.
## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) # run simulation with default incident angle apple <- Simulation(apple) print(apple) # run simulation with 10 deg incident angle apple <- Simulation(apple,10) Chart(apple)## Apple simulation data according to Qin and Lu (2006). ## DOI: 10.13031/2013.20862 # create object cfgMedia <- c(0.63,30,0,1.4) # the 100 low number of photons is only for demonstration cfgSimulation <- c(100,0.05,1e-9,3,0.1) apple <- MCBS(cfgMedia,cfgSimulation) # run simulation with default incident angle apple <- Simulation(apple) print(apple) # run simulation with 10 deg incident angle apple <- Simulation(apple,10) Chart(apple)