### 2. Theory

Because collimation error cancels if BS and FS distances are balanced, the Level Collimation process purposely uses unbalanced sight distances. The elevation difference between two points is determined using a short BS / long FS condition followed by a long BS / short FS condition. If there is a collimation error, the two elevation differences will not be the same.

Because collimation error is a function of distance, the sight length for each reading is needed. The error is then stated as ratio (e.g. ft/ft) or angle above (+) or below (-) horizontal.

A baseline which consists of four evenly spaced points is established. The points should be on an approximately straight line and placed at a uniform interval of 75 to 100 ft, Figure G-2. Points 1 and 2 are instrument locations and are marked with wooden stakes; Points A and B are elevation points and are marked with stable pins.

Figure G-2 Base Line |

The instrument is set up at point 1 (it does not have to be exactly over the point) and readings are taken to points A and B.

Figure G-3 First Setup |

The instrument is moved to point 2 (again, it does not have to be exactly over the point) and readings are taken to points A and B.

Figure G-4 Second Setup |

The elevation difference point A to point B is:

from Point 1: BS_{1 }– FS_{1}

from Point 2: BS_{2 }– FS_{2}

Because of the error, e:

from Point 1: (BS_{1 }– e) – (FS_{1 }– 2e)

from Point 2: (BS_{2 }– 2e) – (FS_{2 }– e)

If we set the two differences equal and solve for e we get Equation G-1:

Equation G-1 |

e is the total vertical error in a horizontal sight distance of d. Collimation error can be expressed as a ratio, Equation G-2, or angle, Equation G-3.

ratio | Equation G-2 | |

angle | Equation G-3 |