Derivation of the transport of intensity equation
The Transport of Intensity equation is derived from the hydrodynamic continuity equation. Parallels between the hydrodynamic formulation of non-relativistic quantum mechanics and classical scalar wave optics are shown below.
| non-relativistic quantum mechanics (Schrödinger) | monochromatic scalar electromagnetic waves (Helmholtz) |
|
|---|---|---|
| wave function |  |
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| wave equation |  |
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| momentum density |  |
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| continuity equation |  |
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| paraxial approximation/TIE |  |
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