451200 Geomatics Science 2

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451-200 Geomatics Science 2

• Lecture 3
• EDM Operation and Calibration

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How would you measure the distance?
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At the end of todays lecture students should

• Understand the fundamental theory underpinning
  the operation of EDMs
• Understand the measurement processes used in EDMs
• Know what error sources affect EDM measurements.
• Understand why calibration of EDMs is essential.
• Know how to carry out a field calibration for
  EDMs.
• Know how to carry out a baseline calibration for
  EDMs.

 
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So how does an EDM work?
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How does an EDM work? The Pulse Method
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What are some of the assumptions made in this
method?

• The speed of light in a vacuum is well known.
  However, the measurements surveyors take are of
  course not in a vacuum. Therefore, we must apply
  corrections for atmospheric conditions.
• Because the velocity of light is so great, it is
  not possible to directly measure the time
  interval that passes while the light beam
  travels. To get an accuracy of 0.003 m, it would
  be necessary to measure the time interval to an
  accuracy of 5 x 10-12 seconds.

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So how do we get around this?

• To get around this problem, EDM instruments
  measure the phase difference between the
  transmitted and received signals.
• By measuring the phase difference of a single
  frequency, the fractional part of the distance
  can be determined very accurately, but the total
  distance is unknown.
• By utilizing several different frequencies, the
  total distance can then be resolved.

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The method of phase measurement
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Methods of phase measurement

• optical/mechanical
• moving a set of prisms over unit length (U),
  prism is moved until null meter is reading zero
• not susceptible to cyclic error
• electric analogue phase measurement
• electric digital phase measurement

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Fundamental theory of EDM

• Velocity of light
• Frequency spectrum
• Wave theory
• Modulation
• Refractive index

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Velocity of light

• speed of light in a vacuum (c0) is a well known
  constant, having an accepted value of 299,792,458
  m/s 1.2 m/s.
• This velocity is affected by temperature,
  pressure, and humidity.
• The usual practice is to observe the temperature
  and pressure (for light waves, the humidity is
  usually ignored) at the instrument and/or
  reflector.

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Frequency spectrum
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Wave theory

• The frequency (f) of a signal is the number of
  oscillations per second.
• The wavelength (?) is the length between two
  successive crests of a sinusoidal wave.

l c/f
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Modulation

• Modulation is the process of systematically
  altering some parameter of the wave.
• Required due to short wavelengths being used -
  difficult to resolve ambiguities
• Unstable phase of the signal at the end of a long
  path
• modulation signal a much longer wavelength
• two types - frequency and amplitude
• microwaves - direct frequency modulation
• infra red - direct intensity modulation

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Modulation
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Refractive index

• c0 is the velocity of light in a vacuum.
• The ratio between the velocity of light in a
  vacuum (c0) and the actual velocity (c) is known
  as the refractive index n.
• for EDM, air
• value close to unity
• influenced by
• gaseous composition of the atmosphere, nearly
  constant
• amt of water vapour in the atmosphere
• temp and pressure of the gaseous mixture
• frequency of the radiated signal (dispersion)
• modulated waves travel at different velocities -
  group velocity

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Group refractive index

• mixing of two dissimilar frequencies producing a
  narrow band of frequencies.
• different frequencies travel at different
  velocities in a dispersive medium.
• sum of all frequencies - group velocity.
• smaller than velocities of individual
  frequencies.
• modulation information important, therefore we
  need the group velocity.
• Barrel and Sears defined for standard dry air at
  0C, 760 mm Hg, and a carbon dioxide content of
  0.03

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Group refractive index

• Reduced to ambient conditions

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Error analysis

• differentiating the equation for the group
  velocity of light can determine the effects of
  errors in the variable t, p, and e on the derived
  quantity nL
• for t 15oC, p 1007mb, e 13mb and ng
  1.0003045

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EDM Classification
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Corrections to measured data
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First velocity correction (k)
subs (2) in (1)
n is the actual value of the refractive index,
distance actually displayed by the distance meter
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Reference refractive index

• instrument specific/ fixed by manufacturer
• defines the refractive index for which the
  instrument provides directly a correct distance
• defined by

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First velocity correction

• difference between the true wave path d and the
  distance read from the instrument d

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First velocity correction

• First velocity corrections for short range
  electro optical instruments given in a form

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Second velocity correction
dn
mean refractive index
for actual wave path
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Why do we need to consider the calibration of
survey instruments?
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EDM errors

• Gross
• Systematic
• Random

http//www.geom.unimelb.edu.au/kealyal/451200.htm
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Additive constant

• All distances measured by a particular
  EDM/reflector combination are subject to a
  constant error. It is caused by three factors
• electrical delays, geometric detours, and
  eccentricities in the EDM
• differences between the electronic centre and the
  mechanical centre of the EDM
• differences between the optical and mechanical
  centres of the reflector
• The additive constant or zero/index correction is
  added to measured distances to correct for these
  differences.
• Note that this error may vary with changes of
  reflector, after jolts, with different instrument
  mountings and after service.

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Scale error

• The scale error describes errors that are
  linearly proportional to the length of line
  measured. These can arise from
• variations in the modulation frequency of the
  EDM,
• non-homogeneous emission/reception patterns from
  the emitting and receiving diodes (phase
  inhomogeneities),
• unmodelled variations in atmospheric conditions
  which affect the velocity of propagation,
• errors in the collection and use of atmospheric
  data. This includes the use of uncalibrated
  thermometers/barometers, not taking atmospheric
  measurements in the shade and the incorrect entry
  of the atmospheric correction into the EDM.

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Cyclic error

• Cyclic error is a function of the internal phase
  measurement of an EDM. Phase measurement error
  is caused by
• electrical coupling between the reference signal
  and the measurement signal
• optical crosstalk between transmitter and
  receiver optics in EDMs
• sinusoidal curve over the measurement unit length
  

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Calibration

• Field calibration
• Baseline calibration
• http//www.geom.unimelb.edu.au/kealyal/451200.htm

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At the end of todays lecture students should

• Understand the fundamental theory underpinning
  the operation of EDMs
• Understand the measurement processes used in EDMs
• Know what error sources affect EDM measurements.
• Understand why calibration of EDMs is essential.
• Know how to carry out a field calibration for
  EDMs.
• Know how to carry out a baseline calibration for
  EDMs.