Lab EDM Calibration

Purpose:This lab will teach the students to understand the basic principles of Electronic Distance Measuring using an electro-optical EDM on a total station, and EDM calibration techniques.

Overview:The basic principle of an EDM is the indirect determination of time required for a beam of light to travel between two points. This principle was put to use in the early 1950’s in Sweden with the introduction of the Geodimeter.

How an EDM Works:

The instrument at one station emits a modulated beam of light, usually infrared, to a reflector at another station. The reflector sends the light back to the instrument, where a phase comparison is made between the projected and reflected pulses. The velocity of light is the basis for the computation of the distance. The infrared emitted light leaving the instrument is modulated into wavelengths that are proportional to the modulating frequency, where the wavelength is given by:

 = V / f (Eq. 1-1)

 = wave length

V = velocity of light through the atmosphere, m/sec

f = modulating frequency, Hz (hertz = cycles per second)

The velocity of light in the atmosphere will vary with temperature, humidity, and pressure. In order to obtain an accurate velocity, atmospheric interference must be accounted for.

Measurement Principle of EDM:

D = ½ (m + d) (Eq. 1-2)

D = distance

d = the amount the received beam is out of phase with the

transmitted signal.

m = integer number of wavelengths in the double path of light.

Lab #1 (Continued)

Objective:Using the Topcon Total Station GTS 4, do the following:

  1. Determine the proper ppm correction of the EDM.
  2. Determine the EDM total offset constant using a baseline of unknown length. (TOC)
  3. Determine the proper Glass Constant and Instrument Offset Constant (IOC, GC)
  4. Take proper field notes.

Field Work Procedure for TOC, GC, and IOC:

  1. Find a level area and mark three points A, B, C on a straight line.
  2. Set the instrument’s TOC (instrument constant) to zero.
  3. Measure AC and AB using three tripods with tribrach’s erected over the three points with the instrument at A.
  4. Leave tripods and tribrach’s in place and place the instrument at B and prism at A. Measure BA and BC.
  5. Place the instrument at C with prisms at A and B. Measure CB and CA.
  6. Calculate the average distances AB, AC and BC.
  7. Calculate the Instrument Offset Constant (IOC).
  8. Measure the prism and calculate the Glass Constant (GC).
  9. Calculate the IOC.

Calculation Procedure for ppm Correction:

Given:

Wavelength modulation frequency, f0 = 14985.4 kHz

Wavelength of infrared carrier beam, 1 = 0.900m

Wavelength, 0 = 20 m

Velocity of light in a vacuum, V0 = 299,792.458 km/sec

Observe the Following at Time of Observations:

p = Atmospheric pressure (Use average of 762.0 mmHg)

t = Air temperature, C

  1. Calculate the refractive index of air under standard conditions, ng:


Lab #1 (Continued)

  1. Calculate the refractive index of air under the condition at time of observation, na:

(Eq. 1-4)

  1. Calculate the reference index of refraction for the instrument, n0:

n0 = V0 / (0 f0) (Eq. 1-5)

  1. Calculate the manufacture’s EDM reference index of refraction, N0, and the refractive index for the conditions at the time of observation, Na:

N0 = (n0 – 1)106 (Eq. 1-6)

Na = (na – 1)106 (Eq. 1-7)

  1. Finally compute the Correction (ppm):

Correction (ppm) = (N0 - Na) (Eq. 1-8)

Calculation for Glass Constant (GC)

Glass Constant (GC) = 1.517 * t - a

Calculation for IOC and TOC:

A B C

Segment / Horizontal
distance (m) / Average
distance(m)
AB
BA
BC
CB
AC
CA

ABmeasure+TOC+BCmeasure=ACmeasure

TOC= ACmeasure–(ABmeasure+ BCmeasure)

TOC=IOC-GC

IOC=TOC+GC

Submit:Lab write-up containing the following:

  1. Procedures and record of measurements taken.
  2. Calculations, substitutions, with formulas used. (repetitive calcs in spread sheet OK)
  3. Analysis and conclusions

Items for your analysis:

  1. Does your prism constant match the value advertised by the manufacturer?
  2. Does your ppm correction match that from the manufacturer chart or slide rule?

3. Does your IOC match that of the manufacturer?

4. In your opinion what are the TRUE values for AC, AB, and BC?

5. Other observations and conclusions?