Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 335 / 2 / ii

Table of contents
- Solution ii

Solution

Let the incident plane wave be

ψ_{i} (r) = e^{i k_{0} r_{0} \cdot r},

and define the scattering vector

q = k_{0} (r - r_{0}) .

For

r

much larger than the diameter of

D

, the far-field pattern follows from

G_{0} (r - r^{'}) \sim \frac{e ^{i k_{0} r}}{4 π r} e^{- i k_{0} r \cdot r^{'}} .

V (q) = \int_{D} V (r^{'}) e^{- i q \cdot r^{'}} d^{3} r^{'},

the Born result is

ψ_{B} (r) \sim e^{i k_{0} r_{0} \cdot r} + \frac{e ^{i k_{0} r}}{4 π r} V (q) .

The corresponding Rytov logarithmic perturbation is

ϕ_{1} (r) \sim a (r) V (q), a (r) = \frac{e ^{i k_{0} (r - r_{0} \cdot r)}}{4 π r} .

Therefore

ψ_{R} (r) \sim e^{i k_{0} r_{0} \cdot r} exp [a (r) V (q)] .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version