# Difficulty implementing equation describing angular response of fibre-optic hydrophone

I am attempting to implement an equation in a paper which provides an approximation of the angular response of a simple fibre optic hydrophone. The equation in question (number 19) is repeated here for convenience:

The issue is that several of the variables are undefined and not obvious. In particular:

• F' and how it relates to the fibre end area F. Is it just 2*pi*fibre_end_radius?
• x' is the x co-ordinate of r' . Is this just r'cos(phi)?
• r and r' . These variables are given earlier for the Rayleigh surface integral (image below). The variables are somewhat poorly defined as: r = some position, r' = the point of integration.

in the equation:

In these equations some variables (r for example) are bolded and others are not, yet in the text no distinction seems to be made.

Can anyone make heads or tails of this? If so I'd very much appreciate any insight.

## Edit 1:

I've tried just converting second integral using polar co-ordinates from

$$\int_A \int_F dF' dA$$

to

$$\int^{2\pi}_0 \int^{a_2}_0 \int^{2\pi}_0 \int^{a_1}_0 r' r dr' d\phi' dr d\phi$$

Where $a_1$ and $a_2$ are the radii of the disk and inner-disk respectively. However the output of this does not match what the author has published.

• Bolded variables are usually vectors. – ACuriousMind Sep 25 '14 at 21:50