Electro-optical distance measurement

A laser gun uses optical distance measurement.

The electro-optical distance measurement (even spacing , distance measurement ) or laser distance measurement is an electronic distance measurement (EDM) using propagation time measurement of the phase position measurement or laser triangulation of light, usually laser .

Other active and passive optical distance measurement methods include: a. the light section method and triangulation in the field of geodesy and surveying .

The laser triangulation and the laser interferometer are preferably suitable for short distances (a few micrometers to 100 meters), whereas the transit time methods are more suitable for long distances (one meter to 10 ¹¹ meters).

Runtime measurement

When measuring the transit time , a brief light pulse is emitted. The pulse transit time is the time it takes for the light beam to travel from the source to a reflector, mostly retroreflector, and back to the source. By measuring this transit time , the distance between the source and the object can be determined using the speed of light . The factor 0.5 takes into account the fact that the light has to travel the distance to the object and back. The speed of light is reduced by the surrounding medium with the refractive index . ${\ displaystyle \ Delta t}$ ${\ displaystyle l}$ ${\ displaystyle n}$

${\ displaystyle l \; = \; {\ frac {c \, \ Delta t} {2 \ cdot n}}}$

The advantage of this process is the short response time. The method has measuring ranges from one meter to several tens of kilometers. The disadvantage is the required measurement of very short times (nano- to picoseconds), so it is difficult to achieve a resolution higher than a few centimeters.

In order to reduce the accuracy requirements for time measurement , methods are used in which the laser beam itself is frequency-modulated or modulated with a high-frequency signal.

This method is used by Lidar , Satellite Laser Ranging , TOF cameras and PMD sensors .

Measurement via the phase position

Laser rangefinder that measures using the phase position. The openings for the red light of the laser and next to them for the photodiode are located on the front side

The phase shift of the reflected laser beam or its modulation with respect to the emitted beam is distance-dependent. This phase shift can be measured and used to determine the distance traveled.

Laser interferometer

If the laser frequency itself is used for superimposition, the device works like a laser interferometer . Laser interferometers do not measure absolute path lengths, but only the relative change when the target or a reference mirror is moved. When moving the mirror, the sum of the emitted and reflected beam is periodically modulated ( interference ). When shifted by half a light wavelength, it runs through exactly one period. If you count the passages and multiply them by the light wavelength , you get the distance you are looking for. With a more precise evaluation of the signal, accuracies of around wavelength can be achieved, which is a few nanometers for visible light . However, the wavelength of light depends on the refractive index of the air and changes with temperature, pressure and humidity. For precise measurements, the count of the light wavelengths must be corrected with these properties of the air ( air density correction ). ${\ displaystyle 1/100}$

At greater distances, high-frequency modulation of the laser amplitude is used and it is not the laser wavelength that is evaluated, but the phase position of these modulated high-frequency signals. If you assume that the emitted beam was modulated with a frequency , you get the following graphic: ${\ displaystyle f = 1 / T}$

The phase difference is obtained from the equation:

{\ displaystyle \ phi = {\ frac {\ Delta t} {T}} \ cdot 2 \ pi}

The distance can with

{\ displaystyle s_ {n} = {\ frac {c \ cdot T} {4 \ pi}} \ cdot (\ phi +2 \ pi \ cdot n) = {\ frac {c} {2}} \ cdot ( n \ cdot T + \ Delta t)}

can be calculated.

The advantage of these methods is the higher resolution compared to runtime methods , which can be achieved with less technical effort. However, the measuring distance is shorter - because the laser necessarily works continuously at low power.

Another problem is the lack of uniqueness of the signals at distances of a multiple of half the laser or modulation wavelength.

Achieving an absolute measurement

The ambiguity of interferometric methods can be circumvented with the help of frequency modulation of the laser or its high-frequency modulation signal. A transit time component is thereby introduced into the phase measurement. A lower frequency (= longer period) gives a greater distance to a clear result, but a lower resolution. For the principle, see also FMCW radar . Methods with HF-modulated laser achieve maximum measuring distances of approximately 200 meters.

Two methods to achieve an absolute distance measurement by measuring the phase position:

Method 1

Continuous frequency modulation (functions like an FM radar); If you compare the original with the reflected signal, there is a frequency difference between the two. This difference is proportional to the distance.

Taking into account the phase difference:

{\ displaystyle L = \ Delta \ phi \ cdot {\ frac {1} {2}} \ cdot {\ frac {\ lambda _ {1} \ cdot \ lambda _ {2}} {\ mid \ lambda _ {1 } - \ lambda _ {2} \ mid}}}

However, it is not possible to precisely control the wavelength of the laser. Therefore, its wavelength must be used as a reference.

{\ displaystyle L = L _ {\ mathrm {ref}} \ cdot {\ frac {\ Delta \ phi} {\ Delta \ phi _ {\ mathrm {ref}}}}}

With direct frequency modulation of the laser, resolutions of around 1 micrometer are achieved. However, with conventional lasers you get a maximum measuring distance of 1 meter.

Method 2

In order to eliminate the uncertainty of a relative interferometric measurement, the phase position is measured at two or more discrete frequencies. The frequencies can in turn be the laser frequency itself (different lasers, for the smallest distances) or modulation frequencies of one and the same laser (frequencies must match the distances and the measuring range).

Laser triangulation

Principle of laser triangulation

With laser triangulation, a laser beam (with low requirements also the radiation of a light-emitting diode ) is focused on the measurement object and observed with a camera located next to it in the sensor , a spatially resolving photodiode or a CCD line. If the distance between the measuring object and the sensor changes, the angle at which the point of light is observed also changes and thus the position of its image on the photo receiver. The distance between the object and the laser projector is calculated from the change in position with the help of the angle functions .

The photo receiver is a light-sensitive element that determines the position of the light point in the image. The distance between the sensor and the object is calculated from this image position.

An advantage of triangulation is the fact that it is purely trigonometric relationships. The measurement can therefore take place continuously and is therefore well suited for measuring distances on moving objects. In order to reduce the external light sensitivity and the influence of inhomogeneously reflective surfaces, the measuring point must be as small and bright as possible. Such sensors often also work in pulse mode.

The method is only suitable for short distances, since its sensitivity drops to the fourth power (two-way attenuation) with the distance between transmitter and receiver. Laser and photo receiver are usually housed together in one housing.

The above scheme illustrates the relationships between the various distances. With the help of trigonometry it is possible to determine the distance from the measured distance : ${\ displaystyle x-x_ {0}}$ ${\ displaystyle x'-x_ {0} '}$

{\ displaystyle \ tan \ delta = {\ frac {x'-x_ {0} '} {f}} \ to \ tan \ alpha = {\ frac {x_ {0}} {D}}}

{\ displaystyle x = D \ cdot \ tan (\ alpha + \ delta) = D \ cdot {\ frac {\ tan \ alpha + \ tan \ delta} {1- \ tan \ alpha \ cdot \ tan \ delta}} }

{\ displaystyle x = D \ cdot {\ frac {{\ frac {x_ {0}} {D}} + {\ frac {x'-x_ {0} '} {f}}} {1 - {\ frac {x_ {0}} {D}} \ cdot {\ frac {x'-x_ {0} '} {f}}}}}

Summary

	Measuring range	comment
Runtime measurement	1 m - several km	short response time, no aperture angle
Phase modulation	frequency dependent max. 200 m	low manufacturing costs
Interferometry	10 nm - 20 m	higher cost, high resolution
Triangulation	some mm - 100 m	depending on the surface, inexpensive, robust

Measuring device

In geodesy, the distance measuring devices that work on the principle of transit time measurement or phase modulation are called tachymeters or spacers .

There are numerous devices for the DIY sector with ranges from a few cm to over 200 m and accuracies in the millimeter range. The better equipped devices can save values, calculate areas and volumes and indirectly measure lengths e.g. B. determine on the basis of a built-in inclinometer.

Web links

Individual evidence

↑ Laser rangefinder: what's inside and how does it work? Accessed January 30, 2020 (German).

↑ Joeckel / Stober / Huep: Electronic distance and direction measurement and their integration into current positioning processes . 5th edition. Wichmann, 2007, ISBN 978-3-87907-443-3 .

↑ Willy Matthews: Laser rangefinder - use optimally and measure accurately . ISBN 978-1-69814-700-0 .

[1] Laser rangefinder: what's inside and how does it work? Accessed January 30, 2020 (German).