Surveying instruments

Geomatics engineers do not need to be expert field operators of every instrument, but they do need to know what each instrument measures, how accurate it can be, what its typical errors are and how those errors are found and controlled. That knowledge lets an engineer choose the right tool for a job, write a sensible specification, check a contractor's work and recognize when a result is too good or too bad to be true. This lesson is a tour of the main instrument families: levels, total stations, GNSS receivers, scanners and airborne sensors, and the accessories that hold them all together. Step-by-step field use of levels and total stations, including set-up, booking and checks, is taught in CIV-250 lessons 4 to 7, and GEOM-210 takes the field work further.

What every instrument has in common

Every surveying instrument does three things: it defines a reference, such as a horizontal line, a vertical axis or a satellite clock; it compares a target with that reference; and it records the result. Each of those steps can go wrong in a systematic way that repeats on every observation, or in a random way that varies from one observation to the next. Good instruments are designed so that the main systematic errors either cancel when the instrument is used correctly or can be measured and removed. Good procedures are designed so that whatever is left shows up as a misclosure, rather than hiding in the result.

Three words describe how an instrument performs. Resolution is the smallest change it can display. Precision is how closely repeated measurements agree. Accuracy is how close the result is to the truth. A display reading to 0.1 mm does not make a level accurate to 0.1 mm, and a very precise instrument that is out of adjustment can be consistently wrong. Manufacturers' specifications usually quote a standard deviation from a standard test procedure, such as the ISO 17123 series, under good conditions; field results are almost always a little worse.

Levels

A level provides a horizontal line of sight. An automatic level uses a compensator, a small pendulum of prisms or mirrors hanging in the telescope, to keep the line of sight horizontal once the instrument has been roughly leveled with a circular bubble. A digital level works the same way but reads a bar-coded rod electronically, removing reading and booking errors and storing the observations. Laser levels send out a rotating horizontal beam that a detector on a rod or on a machine can find, which is ideal for setting out grades on construction sites but less precise than optical or digital leveling.

The main error of a level is collimation error: the line of sight is not exactly horizontal but tilts by a small angle. If the backsight and foresight distances are equal, the error is the same on both readings and cancels when one is subtracted from the other. That is why careful leveling keeps sight lengths balanced. The two-peg test measures the collimation error directly.

Other level errors include the compensator not settling, rods that are not plumb or have worn bases, heat shimmer near the ground and settlement of the instrument or rod between readings. Precise leveling for vertical control uses invar rods, short balanced sights, readings well above the ground and two-way runs, and can achieve better than 1 mm per kilometer.

Theodolites and total stations

A theodolite measures horizontal and vertical angles using a telescope that rotates about a vertical axis and a horizontal (trunnion) axis, with graduated circles read electronically in modern instruments. A total station is a theodolite with a built-in EDM, a processor and data storage, so that one pointing gives a horizontal angle, a zenith angle and a slope distance, from which the instrument computes coordinates. Total stations are the workhorses of property, engineering and construction surveying.

A perfectly adjusted total station has three geometric conditions. The line of sight is perpendicular to the trunnion axis; when it is not, there is collimation (line-of-sight) error. The trunnion axis is perpendicular to the vertical axis; when it is not, there is trunnion-axis (tilting-axis) error. The vertical circle reads exactly 90° when the line of sight is horizontal; when it does not, there is vertical index error. In addition, the vertical axis itself must be truly vertical, which depends on how carefully the instrument is leveled; electronic tilt sensors measure the remaining tilt and correct the angles for it.

The first three errors share a useful property: they change sign when the telescope is transited and the instrument is pointed at the same target on the other face. Averaging face-left and face-right readings therefore removes them. Modern instruments also let the operator measure the errors with a calibration routine and apply corrections automatically, but measuring on both faces remains the standard way to obtain angles of the highest accuracy, and to catch pointing blunders.

Robotic total stations add servo motors and automatic target recognition, so the instrument can find and follow a prism carried by one person, who controls the instrument from a data collector at the target. Motorized instruments are also used as permanent monitoring stations, measuring prisms on a dam, a bridge or a slope every few minutes and sending alerts if any point moves beyond a set threshold. Reflectorless EDM allows measurement to walls, rock faces and other surfaces that are unsafe or impossible to reach, at shorter ranges and lower accuracy than to a prism.

Prisms and targets matter as much as the instrument. Each prism has a constant, an offset between its optical center and the plumb line that the EDM must apply, and mixing prisms with different constants is a classic cause of a constant distance error of 30 mm or so. Tribrachs, the bases that hold instruments and targets on tripods, have optical or laser plummets that drift out of adjustment and must be checked regularly, because a 2 mm centering error at each end of a 50 m line is worth as much as a 16″ angle error.

Calibration and checks

Instruments are checked in three ways. Field checks, such as the two-peg test, the face-left and face-right comparison and a check shot to a known point at the start and end of every set-up, are done constantly by the crew. Periodic calibration, done by the firm or a service center, measures collimation, trunnion and index errors and the EDM constant and scale. Traceable calibration compares EDM distances with a calibration baseline, a line of pillars whose separations are known very precisely.

In the US, the National Geodetic Survey has published procedures for calibration base lines, and many states maintain them, often through the state department of transportation or a university. State minimum technical standards for land surveys typically require that instruments be maintained and calibrated so that the survey meets its accuracy standard. Coulee Geomatics calibrates its EDMs on a base line each spring before the main field season and keeps the reports on file.

GNSS receivers

A GNSS receiver tracks signals from navigation satellites and measures the range to each of them. Survey-grade receivers track several constellations (GPS, GLONASS, Galileo and BeiDou) on several frequencies, measure the phase of the carrier wave as well as the code, and either work in real time with corrections from a base station or network, or log raw data for later processing. Lesson 6 explains how these measurements become coordinates. As instruments, GNSS receivers are simple to set up, need a clear view of the sky, and are affected by signal reflections (multipath) from nearby buildings, vehicles and water. Antenna heights must be measured to the correct reference point, and antenna calibration models, which describe how the electrical phase center shifts with satellite elevation, are part of every precise processing run.

Scanners, cameras and airborne sensors

A terrestrial laser scanner measures millions of distances and angles per minute by sweeping a laser beam across its surroundings, producing a point cloud. Mobile mapping systems put scanners and cameras on vehicles, and airborne lidar and aerial cameras fly on aircraft and drones (uncrewed aerial vehicles). These instruments combine a ranging or imaging sensor with GNSS and an inertial measurement unit that tracks the sensor's position and orientation many hundreds of times per second. Lessons 7 and 8 cover them in detail. For the engineer, the key point is that their accuracy depends as much on the positioning and orientation system and on calibration of the angles between the sensors as on the sensor itself.

Data collectors and software

Almost every modern instrument is operated through a field controller running survey software. The controller stores the job's coordinate system, control points and design data, prompts the operator through routines, applies corrections and checks tolerances. That brings a real risk: if the coordinate system, geoid model, prism constant or units are wrong in the controller, every measurement will be wrong in the same way, often without obvious symptoms. Coulee Geomatics uses a job set-up checklist, reviewed by a second person, for every new project, and the first observation of each day is a check on a known control point.

Reducing a level run

Because leveling is the foundation of vertical control, every geomatics engineer should be able to reduce a level run and judge whether its misclosure is acceptable. The script below reduces a closed loop on the height of instrument method, computes the misclosure, compares it with an allowable value of \(k\sqrt{L}\), where \(L\) is the loop length in kilometers, and distributes the misclosure in proportion to distance.

# Reduce a closed level loop, check the misclosure and adjust in proportion to distance
import math

start = ("BM COULEE 7", 902.417)
# (point, backsight, foresight, distance from previous set-up to this point in m)
obs = [("TP1", 1.623, None, 0),
       ("TP1", 1.402, 0.874, 140),
       ("TP2", 0.987, 2.115, 130),
       ("TP3", 2.311, 1.664, 150),
       ("TP4", 1.205, 0.562, 145),
       ("BM COULEE 7", None, 2.314, 135)]

name0, elev = start
hi = elev + obs[0][1]
points, run = [], 0.0
for pt, bs, fs, d in obs[1:]:
    run += d
    elev = hi - fs
    points.append([pt, elev, run])
    if bs is not None:
        hi = elev + bs

closing = points[-1][1]
mis = closing - start[1]
L_km = run / 1000
allow = 0.012 * math.sqrt(L_km)
print(f"Loop length {run:.0f} m, misclosure {mis * 1000:+.1f} mm, allowable {allow * 1000:.1f} mm")
print("Within tolerance" if abs(mis) <= allow else "Exceeds tolerance: re-run the loop")

for pt, e, dist in points:
    corr = -mis * dist / run
    print(f"{pt:12s} raw {e:9.4f}  correction {corr * 1000:+5.1f} mm  adjusted {e + corr:9.4f}")

Loop length 700 m, misclosure -1.0 mm, allowable 10.0 mm
Within tolerance
TP1          raw  903.1660  correction  +0.2 mm  adjusted  903.1662
TP2          raw  902.4530  correction  +0.4 mm  adjusted  902.4534
TP3          raw  901.7760  correction  +0.6 mm  adjusted  901.7766
TP4          raw  903.5250  correction  +0.8 mm  adjusted  903.5258
BM COULEE 7  raw  902.4160  correction  +1.0 mm  adjusted  902.4170

The loop is 700 m long, so the allowable misclosure at 12 mm per square root of kilometer is about 10 mm. The computed misclosure is only 1 mm, so the loop passes and the correction at each point grows in proportion to the distance from the start until it removes the whole misclosure at the closing bench mark. A large misclosure would mean a blunder, such as a misread rod, a moved turning point or a wrong bench mark elevation, and the loop would be re-run rather than adjusted.

Choosing an instrument

Instrument selection starts from the required accuracy, the size of the area and the environment. For a precise settlement monitoring program on a building, a digital level and invar rods are hard to beat. For a property boundary in a treed valley, a total station traverse from GNSS control is often the best combination. For a 40 km pipeline route, GNSS for control with airborne lidar for terrain is usual. For the inside of a pump station, a terrestrial scanner captures everything in an hour. Coulee Geomatics prices jobs by thinking first about the deliverable and its accuracy, then about which combination of instruments meets that accuracy with the least time in the field and the least risk to the crew.

Safety is part of that choice. Instruments that reduce time on the road shoulder, on a rail line or near open water, such as reflectorless total stations, scanners and drones, are often chosen as much for the reduced risk to people as for speed. Every job starts with a hazard assessment, and the instrument plan is part of it.