Geomatics / surveying III course: Module 3 Theodolite measurement and errors, Module 4 EDM measurement and errors

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30 Lectures , 5 AssignmentsRecommended Texts:Surveying :H Kahmen & W Faig

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APG3017DSURVEYING IIITheodolite errors and mitigationCentringElectronic circle reading systemsVertical circle indexing compensation Vertical axis tilt sensorsGeneral observing principles with electronic angle measurements

Module 3: Theodolite Measurement and Errors2Theodolite errors Axis errors:Collimation axis errorTrunnion axis errorvertical axis errorCollimation axis error

ecec=ec+cCollimation axis error

ec=ec+c

Collimation axis error minimum of "c" at horizon, maximum (undefined) at zenithec=ec+c

Collimation axis error Eliminate by taking mean of CL & CR (reduce for 180 degree difference)Reduce by laboratory calibration, with mechanical adjustment (or application of stored correction)Trunnion axis error

Trunnion axis error Eliminate by taking mean of CL & CRReduce by laboratory calibration, with mechanical adjustment (or determine correction using striding level)t90-z90-z'zz'eeetz

Trunnion axis error

minimum of zero at horizon, maximum (undefined) at zenithVertical axis error

Vertical axis error

minimum of zero at horizon, maximum (undefined) at zenithVertical axis error Reduce by careful leveling (use vertical circle indexing device)Reduce using vertical axis tilt sensorPlate level error Detect by rotating through 180Mechanical adjustment on opto-mechanical instrumentsNot applicable if tilt sensor present (no plate level)Vertical axis (standing axis) is no longer verticalTrue verticalHorizontal axis not horizontalTrue HorizontalMisalignment between plate level and horizontal axisVertical circle index error Detect by observing angle on both CL (z) and CR (360-z)Eliminate by taking mean of CL and CR readingsOnce measured, can also be stored and used to correct CL-only readings

Circle eccentricity error For single index, eliminate by taking mean of CL and CRFor double index, error is eliminated by using mean of two index readings

single index double indexCircle graduation errors Random errors are small and insignificantPeriodic errors are generated in circle manufacture periodicity depends upon the manufacturing technique. Effect can be reduced by observing on different parts of the circle only possible for opto-mechanical instruments where the circle can be rotated. In some electronic theodolites the entire circle is sampled for a single measurement and the effect is averaged out.Interpolation errors occur in electronic theodolites due to a mismatch between coarse and fine reading systems. Can be calibrated and applied as a correction (generally only by the manufacturer)Projection error Error is: e = a' a

Eliminate by bodily rotating theodolite by 90 halfway through observations vertical axis tilted horizontal circle i a a '

Centreing Plumbbob: low accuracy, affected by windOptical plummet: requires iteration with levelling; if eyepiece is in tribrach it is difficult to calibrate and adjust.

right-angle prism lasersurvey marktribrach Laser plummet: optics above the tribrach, so can be checked easilyCentreing Plumbing rod: good accuracy, but bulkyPillar mounting: forced centreing (not beacon plate)tripod bull'seye bubblesurvey mark plumbing rod Electronic circle reading Absolute: unambiguous coding systemCoded disc:photodiode/LED arrays sinusoidal slit track

from: Kahmen & FaigElectronic circle reading Dynamic absolute reading system:

DTTo

Electronic circle reading +=Incremental reading system:Up to 20000 fine lines photolithographed onto a a discLine count can be converted to an angleFractional part determined by projecting one image through a slit, creating a Moir fringe:

Can be combine with elements of the absolute encoded disc systemMoir fringe Tilt compensators Liquid:180verticalsilicon oil 180verticalsilicon oil Tilt compensators Pendulum:180verticalglass plate180verticalglass plateTilt sensors Reflection:

Tilt sensors Transmission:

General observing tips for high accuracy Level and centre accurately; shade the instrument; allow the tilt sensor time to stabilise.Always observe on CL and CRObserve horizontal directions separately from zenith angles and distancesObserve multiple arcs, changing circle settings where possibleComplete all zenith angles measurements to one target, before observing the nextObserve RO, but only as a check (do not adjust)Module 4: EDM and Errors30PrinciplesBasic ComponentsErrors in EDMCalibration of EDMObservation Procedures and Reductions

EDM principles Dt can be determined using either:Pulse timing (requires high accuracy in time measurement)Phase comparison of low frequency modulation signal

EDM principles Only the fractional part can be measured. The cycle ambiguity must be resolved using different modulation frequencies, superimposed upon a high frequency carrier.

BASIC COMPONENTS Oscillator:Carrier signal generated by an infra-red Ga-As diodeAmplitude modulated by a range of modulation (pattern frequencies)

BASIC COMPONENTS - 2 Transmitter: modulated beam collimated and transmitted via total station optics (coaxial with telescope)Receiver: beam splitter used to take off infra-red beam to photodetector

from: Leica Newsletter, July 2000PHASE COMPARATOR Received signal is demodulated and the phase of the received modulation signal is compared to that of the generated signalProblem of resolution of integer number of cycles is resolved by using a number of modulation frequencies, ranging from coarse to fineMultiple readings taken, and the displayed result is the average of several hundred measurementsFor pulsed (time-of-flight) systems the measurement is much simpler, and just requires the accurate measurement of the return time for the pulseMultiple measurements also made, and averagedAMBIGUITY RESOLUTION Modulation patterns of different wavelength (scale):

10000m scale83651000 m scale 363.0100m scale 62.8510 m scale 2.845

PHASE vs PULSE MEASUREMENTS Pulse (ToF) units use low power laser infra-red, phase units do not necessarily use lasersPhase comparison is more accuratePulsed systems have greater rangeHand-held laser ranging and reflectorless ranging use pulsed laserMost high-end models use both pulsed and phase comparison in the same unit (pulsed for reflectorless, phase with reflectors, and for greater accuracy)Errors and biases in EDMZero ConstantsPropagation of errorsMultipathScale factor and determination with zero constantCyclic errorATR errors

Corner cube reflectors

Total internal reflectionPath of light through the reflector is the samePrism constant takes into account change of medium to glassOptical centre should be over the pole regardless of prism tiltHigh precision ball reflectors

Red ring,