Science > Physics > Modelling light reflected off a non-uniform cloud of droplets
| Topic: |
Science > Physics |
| User: |
"David Wimp" |
| Date: |
22 Oct 2003 12:42:28 AM |
| Object: |
Modelling light reflected off a non-uniform cloud of droplets |
I am trying to get a handle on how to model the light that would
reach a camera from a cloud of tiny droplets. I think they could be
assumed to form an aerosol. I have looked a bit at what atmospheric
scientists have done with this regard, but they are solving a different
problem. They are measuring the density of a uniform aerosol by
directing a light (lasers) into the aerosol and measuring how much comes
back to the source. At least, that is what I have found. I am
interested in the case where the cloud is expanding as if from an
explosion and somewhat backlighted by the sun. My hunch (superstition?)
is that more light will reach the camera when the cloud is more dense
and has more density concentrated in the center and that as the cloud
expands and becomes more uniformly distributed, the total amount of
light reaching the camera will decrease. I have gotten as far as
assuming that the drops are spherical mirrors and I could probably model
the density as a function of the distance from the center as a normal
distribution. My belief is based on the idea that the light reflected
off the spheres on the same side of the cloud as the camera will be
reflected back towards the dense center and then back towards the
camera. With multiple reflections, the light will tend to move towards
the areas with less density. Of course, on the back side of the cloud,
the situation is reversed. Does this sound like a familiar problem or
something that might have been solved somewhere?
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| User: "Andrew Resnick" |
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| Title: Re: Modelling light reflected off a non-uniform cloud of droplets |
22 Oct 2003 06:58:20 AM |
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In <8Nolb.188888$0v4.14598617@bgtnsc04-news.ops.worldnet.att.net> David
Wimp wrote:
I am trying to get a handle on how to model the light that would
reach a camera from a cloud of tiny droplets. I think they could be
assumed to form an aerosol. I have looked a bit at what atmospheric
scientists have done with this regard, but they are solving a
different problem. They are measuring the density of a uniform
aerosol by directing a light (lasers) into the aerosol and measuring
how much comes back to the source. At least, that is what I have
found. I am interested in the case where the cloud is expanding as
if from an explosion and somewhat backlighted by the sun. My hunch (
superstition?) is that more light will reach the camera when the
cloud is more dense and has more density concentrated in the center
and that as the cloud expands and becomes more uniformly distributed,
the total amount of light reaching the camera will decrease. I have
gotten as far as assuming that the drops are spherical mirrors and I
could probably model the density as a function of the distance from
the center as a normal distribution. My belief is based on the idea
that the light reflected off the spheres on the same side of the
cloud as the camera will be reflected back towards the dense center
and then back towards the camera. With multiple reflections, the
light will tend to move towards the areas with less density. Of
course, on the back side of the cloud, the situation is reversed.
Does this sound like a familiar problem or something that might have
been solved somewhere?
As stated, this problem is undefined. Too many aspects of the problem
are not spelled out. Let's start with the simplest case: Incoherent
scattering, uniform particle size, "small" particles, and the light gets
"scattered once"... either the indices of refraction of the drops and
air are close, or the density is low, or something like that. Then you
just get Beer's law: the intensity drops off exponentially with the
"optical thickness"
Ok, so now let's make the light multiply scatter: If the relative
indices are very different, if the density is very high, something like
that. Then, you can think of the photons diffusing through the medium:
Diffusion correlation spectrosopy, critical opalescence, radiative
transfer, and stuff like that gets involved and the equations get much
more complex. Sometimes it's possible to speak of an "effective
refractive index" and recover Beer's law.
Since you mentioned sunlight, you are only dealing with incoherent
scattering... unless you are looking at a very narrow waveband, which I
hope you are not doing! Coherent multiple scattering really sucks. At
least it's possible to write down the equations. Sometimes.
For coherent scattering, if the light scatters once, the far-field
pattern is proportional to the Fourier transform of the scattering
geometry. Think Laue' patterns.
I have yet to see a book that really treats this stuff nicely. I have
class notes written by Jim Locke at Cleveland State that are outstanding,
and several of us have begged him to publish the notes in a real book.
I can help you more, if you want to email me directly.
--
Andrew Resnick, Ph. D.
National Center for Microgravity Research
NASA Glenn Research Center
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| User: "Timo Nieminen" |
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| Title: Re: Modelling light reflected off a non-uniform cloud of droplets |
22 Oct 2003 03:52:37 AM |
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On Wed, 22 Oct 2003, David Wimp wrote:
I am trying to get a handle on how to model the light that would
reach a camera from a cloud of tiny droplets.
[cut]
I am
interested in the case where the cloud is expanding as if from an
explosion and somewhat backlighted by the sun.
You can probably ignore the expansion. In the time it takes light to cross
from one side of the cloud to the other, it's not going to move much. The
exception will be if you really want to calculate Doppler shifts.
My hunch (superstition?)
is that more light will reach the camera when the cloud is more dense
and has more density concentrated in the center and that as the cloud
expands and becomes more uniformly distributed, the total amount of
light reaching the camera will decrease.
"Somewhat backlighted" means that the sun isn't directly behind the cloud?
So all the light reaching the camera is scattered light? I'd expect the
maximum light to reach the camera when the cloud has expanded enough to
fill the field of view. The cloud will be less bright as it expands, but
it'll be bigger.
I have gotten as far as
assuming that the drops are spherical mirrors and I could probably model
the density as a function of the distance from the center as a normal
distribution. My belief is based on the idea that the light reflected
off the spheres on the same side of the cloud as the camera will be
reflected back towards the dense center and then back towards the
camera. With multiple reflections, the light will tend to move towards
the areas with less density. Of course, on the back side of the cloud,
the situation is reversed. Does this sound like a familiar problem or
something that might have been solved somewhere?
Haven't heard of this being done before. I'll have to think about what
multiple reflections will do.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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