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How to Calculate Fan Angle & Distance

Laser systems embrace many levels of complexity. High-tech lasers can track and remove space debris, while everyday laser pointers use the same underlying technology. Industrial laser-measurement systems are common, as the properties of a laser allow engineers to calculate accurate dimensions from the projected image of a beam. The working distance can be easily calculated by using the beam̵7;s fan angle -- a parameter dependent on its divergence -- and measuring the size of the image. Conversely, using known working distances provides a means of determining the fan angle.

Things You'll Need

Laser measurements
Scientific calculator
Laser data sheet

Instructions

Fan Angle Calculation
- 1
  Check the laser measurements you will use to calculate the fan angle. You need two measurements: a working distance in inches or millimeters and a projected beam width expressed in the same units.
- 2
  Divide the beam width by 2 and note your answer. For example, if the beam width is 1.58 inches, the answer is 0.79 inch.
- 3
  Divide your answer by the working distance. Write down this value. For example, if the answer is 0.79 inch and the working distance is 6 inches, the value is 0.13167.
- 4
  Calculate the arctangent, in degrees, of the value you wrote down. Multiply the answer by 2 and note the result. For example, if the value is 0.13167, the arctangent is 7.5 degrees and the result is 15 degrees.
- 5
  Check your work. Record the result, which is the fan angle in degrees.
Working Distance Calculation
- 6
  Check the laser measurements you will use to calculate the working distance. You need the fan angle of the laser in degrees, together with a projected beam width in inches or millimeters.
- 7
  Divide the fan angle by 2 and note the answer. Calculate the tangent of the answer and write it down. For example, if the fan angle is 10 degrees, the answer is 5 degrees and the tangent is 0.08749.
- 8
  Divide the beam width by 2 and note the answer. For example, if the beam width is 2.4 inches, the answer is 1.2 inches.
- 9
  Divide your answer by the tangent. Write down the result. For example, if the answer is 1.2 inches and the tangent is 0.08749, the result is 13.72 inches.
- 10
  Check your work. Record the result, which is the working distance.

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