# Gaussian beam and disk overlap with shift

### Description

Calculate the overlap integral of a 2-D Gaussian beam and a uniform disk, including a shift between the centers of the beam and disk.

### Usage

1 | ```
beamDiskOverlap(s = 0, r = 1, theta.fwhm = 1)
``` |

### Arguments

`s` |
Shift between centers |

`r` |
Disk radius |

`theta.fwhm` |
Gaussian beam FWHM |

### Details

Converts the 2-D integral to 1-D for speed. Use consistent units.

### Value

Value of the overlap integral, normalized to unity for a beam much smaller than the disk.

### Author(s)

Andrew Harris

### References

"Telescope illumination and beam measurements for submillimeter astrononomy," A.I. Harris, Internat. J. IR and mm Waves, 9, 231 (1988)

### Examples

1 2 | ```
s <- seq(0, 10, 0.1)
plot(s, beamDiskOverlap(s, 4, 1), t='l', col=4)
``` |

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