# Transmitter directivity model¶

Handybeam core, in general, is a performance oriented modelling tool. To energise the simulated acoustic field, it uses groups of point-like sources; where groups of points stand for surfaces. In one interpretation, the original surface needs to be “sampled” densely enough to obtain desired accuracy of representation. Representing large radiating surfaces by sampling it with pointlike radiators is a good enough approximation for a wide class of problems. Using this way, effectively any radiation pattern can be simulated.

A further performance improvement is achieved by treating point sources as not exactly pointlike monopoles, but rather, as point sources that radiate with some directivity. Again, this is a good enough approximation for a number of cases of interest; in particular, wherever the radiating surface is smaller than approximately 2 lambda, (2x wavelength).

## Default directivity model¶

A default model of directivity used in Handybeam is to model the amplitude directivity as 2nd order polynomial of form:

Todo

detailed equation here

Be notified that with such model, one can model radiator that:

- is circular-symmetric around a certain axis (specified with the normal)
- exhibits at most one phase-reversal (one lobe) over the frontal aspect (90 degrees off the normal)
- the radiation pattern in the rear aspect is not important

Such model is suitable for modelling radiation pattern of simple ultrasonic transducers of diameter less than 2 lambda.

If You need a radiation pattern more complex than this, you can set the polynomial coefficients to such values, that the point-like radiator is effectively omni-directional, and then, revert to simulating complex radiators by means of groups of point-like reflectors.

## Sinc function directivity model¶

Todo

describe the approach and data structure used

## Bessel function directivity model¶

The Bessel function is an analytical solution to a surface integral, where the surface is circular. In effect, theoretically, a perfect radiating piston can be represented by using the bessel function as a radiation directivity function. This includes multiple side lobes, which amplitudes and locations are perfectly represented. y using scaling coefficients, it is also possible to fit this model into measured data, so that real radiators and experimental data can be represented and integrated using the rest of the Handybeam system.

Be advised that accurate evaluation of bessel function is complicated in the numerical domain, nd hence, the implementations tend to be either slow or inaccurate.

Todo

describe the approach and data structure used