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- TL;DR Summary
- I am developing a simple mathematical model for a Particle Image Velocimetry (PIV) system. My goal is to calculate the resulting radiance L_r emitted by a particle illuminated by a 532 nm laser.
Hello togehter,
I am new to this forum and hope this post followed all the guidelines here (I tried to summarized my issue as clean as possible, two pictures are attached). I would appreciate every help:
I am doing research on a Particle Image Velocimetry (PIV) system. For this I want to set a simple math model for the system. I hope you can help me out. Regarding this I have 2 main Questions.
1. I am trying to find a math model which is describing what is happening in a simple Particle Image Velocimetry System. So I have a laser with a wavelength of 532nm (the laser has a power of P_L and the beam radius is r_b), which is for example hitting a particle in air with a radius of r_P = 50um (the whole sphere is completely in the beam). What is the resulting radiance L_r [in W·sr⁻¹·m⁻²] emitted by the illuminated particle (the radiance L_r I want to use later to calculate the amount of light that hits my camera system)?
The camera is in a distance d_c to the particle and is in a position where the laser light can not reach the camera directly (only the light which comes from the illuminated particle).
So my thoughts on the steps are (the equations are in attachement 1, and description of all variables are in attachement 2):
A. [Equation 1.1] Calculate irradiance I_L of my laser -> used simple top hat model for the laser
B. [Equation 1.2] Calculate power P_P which hits the particle (modeling as a sphere) -> using cross section of the sphere as the area
C. [Equation 1.3] Calculate the power P_r which leaves the particle -> Alpha is the Albedo of the particle
D. [Equation 1.4 - 1.6] Calculate radiance coming from the particle (assuming that the light is going in all direction equally [isotrop]) -> using the sphere surface as the area (A_r). W is the solid angle (using the distance d_c to the camera as r and the "big" sphere surface area in the distance d_c as A)
E. [Equation 1.7] Result is in equation 1.7
My biggest uncertainty is in step C and D -> Did I have the correct thought here?
2. So the effect on the sphere: is it scattering or body reflection? Or are both the same (I am a little confused about that)? Can I use the Albedo alpha here?
Thanks in advance for the help! I would appreciate every help.
P.S. if the calculation steps A-E are not correct or are confusing you can also ignore it and suggest a new mathematical way for the 1st question. Thank you so much!
I am new to this forum and hope this post followed all the guidelines here (I tried to summarized my issue as clean as possible, two pictures are attached). I would appreciate every help:
I am doing research on a Particle Image Velocimetry (PIV) system. For this I want to set a simple math model for the system. I hope you can help me out. Regarding this I have 2 main Questions.
1. I am trying to find a math model which is describing what is happening in a simple Particle Image Velocimetry System. So I have a laser with a wavelength of 532nm (the laser has a power of P_L and the beam radius is r_b), which is for example hitting a particle in air with a radius of r_P = 50um (the whole sphere is completely in the beam). What is the resulting radiance L_r [in W·sr⁻¹·m⁻²] emitted by the illuminated particle (the radiance L_r I want to use later to calculate the amount of light that hits my camera system)?
The camera is in a distance d_c to the particle and is in a position where the laser light can not reach the camera directly (only the light which comes from the illuminated particle).
So my thoughts on the steps are (the equations are in attachement 1, and description of all variables are in attachement 2):
A. [Equation 1.1] Calculate irradiance I_L of my laser -> used simple top hat model for the laser
B. [Equation 1.2] Calculate power P_P which hits the particle (modeling as a sphere) -> using cross section of the sphere as the area
C. [Equation 1.3] Calculate the power P_r which leaves the particle -> Alpha is the Albedo of the particle
D. [Equation 1.4 - 1.6] Calculate radiance coming from the particle (assuming that the light is going in all direction equally [isotrop]) -> using the sphere surface as the area (A_r). W is the solid angle (using the distance d_c to the camera as r and the "big" sphere surface area in the distance d_c as A)
E. [Equation 1.7] Result is in equation 1.7
My biggest uncertainty is in step C and D -> Did I have the correct thought here?
2. So the effect on the sphere: is it scattering or body reflection? Or are both the same (I am a little confused about that)? Can I use the Albedo alpha here?
Thanks in advance for the help! I would appreciate every help.
P.S. if the calculation steps A-E are not correct or are confusing you can also ignore it and suggest a new mathematical way for the 1st question. Thank you so much!
