Kirchhoff Approximation for multi-layer rough surface

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Kirchhoff Approximation for multi-layer rough
surface
By

• Noppasin Niamsuwan

ElectroScience Laboratory, Ohio State University
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Motivation
Motivation
Transmitted Wave
Receiving Wave ?
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Huygens principle
Huygens principle
Observer
known
Total field on the surface
Greens function
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Huygens principle (cont.)
Huygens principle
Func. of distance between surface and observer
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Tangent plane approximation
Tangent plane approximation
We know the reflected field from the flat
surface
At each point on the surface, we evaluate the
reflected field (E_reflected) as if it is on the
flat surface.
Tangent plane
This is our FIRST APPROXIMATION
- Surface needs to be relatively smooth.
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Single interface
Single Interface
Observer (reflected)
interface
Observer (transmitted)
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Single interface
Single Interface
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Multiple interfaces ???
Multiple interfaces ???
Observer
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Multiple interfaces (cont.)
Multiple interfaces (cont.)
MULTIPLE REFLECTION
Observer
SECOND APPROXIMATION
- How many orders of reflection we need to keep
???
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Multiple interfaces (cont.)
Multiple interfaces (cont.)
SHADOWED REGION
Not directly illuminated
- Not a problem for deterministic case
- However, for statistical case, we need some
function to approximate this effect
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Multiple interfaces (cont.)
Multiple interfaces (cont.)
Computation (Ray Tracing)
- Straight forward

• Too expensive

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Multiple interfaces (cont.)
Multiple interfaces (cont.)
Computation (Layer by Layer)
1. Compute the scattered field from the uppermost
interface
2. Those fielded produced by the upper interface
become incident field of lower interface
3. Group the incident field that has the same
incident angle
4. Solve for the scattered field
5. Repeat (4) with the other inc. angle
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Multiple interfaces (cont.)
Multiple interfaces (cont.)
Computation (Layer by Layer)
STEP 1 (result)
20 deg