This version reflects the comments of the core participants as reviewed and incorporated in accordance with CORD's FIPSE-supported Curriculum Morphing Project.


MODULE 6
LASER DISTANCE
MEASUREMENT


(1)Lasers can be applied to a variety of important distance-measurement tasks. This chapter describes three such methods.

· Pulse time of flight-ranging systems

· Beam-modulation telemetry

· Interferometric methods

(2)A pulsed laser ranging system is a distance-measuring device that operates by transmitting a short high-power pulse toward the target. A photodetector in the ranging system receives a reflection of the pulse. By knowing the time interval required for the signal to travel from the transmitter to the target and back to the receiver, it is possible to calculate the distance from the ranging system to the target.

(3)Laser distance-measuring systems are used for surveying, ground profile measurements, gun fire ranging measurements (military), altimeters, space radars, satellite and missile tracking, and industrial machine tool control.

(4)This chapter will acquaint you with

· Different types of distance-measuring systems

· Distance-measurement techniques in CW and pulsed systems

· Components and critical elements in laser measurement systems

(5)Before starting this chapter, you must know and use basic laser eye safety. You should have studied algebra, trigonometry, geometry, pulse circuits and digital systems. And you will need a knowledge of physical optics, especially interferometry.

Objectiv.jpg (6047 bytes)

(6)Upon completion of this chapter, you should be able to do the following:

1. Describe, in terms similar to the text, the operation of pulsed time-of-flight ranging systems, beam-modulation telemetry systems and interferometric systems.

2. Define the following terms:

Noncooperative target

Cooperative target

Unambiguous range

Round-trip transit time

Leading-edge detection

3. Draw a sketch of the waveforms for a pulsed time-of-flight ranging system. Identify the transmitter pulse, receiver pulse, round-trip transit time, and the threshold voltage for leading-edge detection.

4. Calculate a maximum pulse rate and the received power for a pulsed, noncooperative ranging system.

5. Calculate the maximum frequency and the range for a beam-modulation telemetry system.

6. Calculate an amount of displacement and a maximum measurable distance for an interferometric system.

7. Set up and operate a pulsed ranging system using a GaAs laser diode transmitter. Estimate the range accuracy and measure round-trip transit time between two points outdoors. Calculate the range from the measured round-trip transit time.

 

DISCUSSION

(7)Lasers are useful for several types of distance-measurement applications. These include military rangefinding, surveying and machine tool control. The diverse requirements of these applications mean that a variety of different methods and types of lasers are used. In this chapter we describe three of the most important types of laser-based distance measurement:

· Pulsed time-of-flight measurements

· Beam-modulation telemetry

· Interferometric methods

 

Pulsed Time-of-flight Method

(8)This method uses lasers with short pulse duration and high peak power, such as Q-switched ruby and Nd:YAG. It commonly is used for applications such as satellite and missile tracking and military rangefinding.

(9)These laser ranging systems are used to measure the distance (or range) between the source (where the ranging system is located) and some object, which we will call the target. This is accomplished by:

1. Irradiating the target with a laser pulse from the source transmitter.

2. Detecting a reflection of the beam off of the target.

3. Measuring the time required for the laser signal to travel from the source to the target and back to the detector.

(10)Because we know the velocity of light, we can convert this time measurement into a distance from source to target.

(11)A block diagram of this type of laser ranging system is shown in Figure 1.

Fig. 1
Block diagram of ranging system

 

(12)The electronic circuitry measures the interval from the time the signal leaves the laser transmitter until it is received back at the detector, and converts the result to a range.

(13)The transmitter and receiver are both optical systems, that is, telescopes. The transmitting optical system acts as an antenna to reduce the divergence angle of the transmitted beam and to aim the beam at the target. The receiver optical system acts as an antenna to collect part of the reflected beam and to "condense" or focus it onto the detector. The design of these optical systems will be discussed in more detail later.

(14)To establish the required transmitter power, detector sensitivity, and antenna size (optical aperture), we will discuss the geometrical factors that affect the relation between transmitted power and received power. In radar terminology, this relationship is called the "range equation." In the following discussion, we will study this equation in different forms as it applies to different types of targets. In each case, we will assume that the transmitted beam completely covers the entire area of the target that reflects or redirects the beam back to the source. The transmitter-to-target geometry of the radiation pattern is shown in Figure 2.

Fig. 2
Transmitter-target geometry

 

(15)In this figure, the beam is shown leaving the transmitter antenna with an aperture diameter, dta, and divergence angle, q t (radians). At the target plane, a distance R from the transmitter, the illuminated area from the transmitter is:

AR =

Equation 1

(16)The power density f tar within this area (assumed for simplicity to be uniform) is equal to the transmitter power divided by this illuminated area, and reduced by the atmosphere transmission T:

f tar =

Equation 2

(17)The value of T varies from 0 to 1, depending on the amount of absorption and scattering of light by the atmospheric condition. For a beam propagating in space, T will have a value of 1. Equation 2 will be used to describe the power density at the target in two target cases—noncooperative and cooperative targets.

 

Noncooperative Target

(18)A noncooperative target generally is regarded as a diffusely reflecting object (such as a rock, tree, building, or tank). The term "noncooperative" is used because the target has not been prepared in advance to enhance the reflected return of the transmitted beam. This means that the reflectivity, Y, at the laser wavelength of different targets can vary from less than 1% to almost 100%. When the reflectivity is not known and cannot be estimated, a value of 20% or 0.2 (absolute number) is generally used.

(19)Since the target is assumed to be diffusely reflective instead of specular (like a mirror), the reflected beam will be scattered into a hemispherical pattern, with the maximum intensity reflected normal to the target plane and the intensity dropping to zero for rays reflected parallel to the target plane. (See Figure 3.) However, since the target usually will have many surfaces that lie in different planes, we will assume that the reflected power radiates uniformly into a hemisphere.

Fig. 3
Noncooperative target

 

(20)By knowing the power density, f tar , on the target (Equation 2), the material reflectivity at the laser wavelength, U , and the projected area* of the target, we can calculate the transmitter power reflected by the target.

Ptarrefl = U f tar Atar = U f tar

Equation 3

 

where:

dtar = diameter of the target (assumed to be circular)

(21)This reflected power is radiated uniformly into a hemisphere and a fraction of it is received back at the receiver antenna. The power collected by the receiver antenna is equal to Ptarrefl multiplied by the atmospheric transmission factor, T, and the ratio of the receiver antenna area, Ara, to the area of a hemisphere with a radius equal to the range R.

Pr = Ptarrefl = TPtarrefl


Equation 4

 

where:

dra = diameter of the receiving antenna

Combining Equations 2, 3, and 4 gives

Pr =


Equation 5

For long ranges (large R), dta can be neglected in comparison with the term Rq t , and Equation 5 reduces to:

Pr =


Equation 6

We note that the power received, Pr , depends strongly on the range R, decreasing as the fourth of the range.

Example A: Received Power—Noncooperative Target

Given:

A noncooperative target with diameter dtar = 0.2 meter and reflectivity 0.5 and the following parameters:

Pt = 10 kW
q t = 10–2 radians
R = 103 meters
dta = 10 cm
dra = 10 cm
l = 1.06 ´ 10–4cm (Nd:YAG laser)
T = 0.8

Find:

The received power Pr .
Solution: We can use Equation 6 because q tR > > dta

Equation 6 is

Pr = PtY T2/8R4q t2

Pr = watts

where all distances are in meters.

This gives Pr = 1.6 ´ 10–9 W as the power received back near the transmitter.

Cooperative Target

(22)A cooperative target is one for which the reflectivity to the laser beam has been enhanced to give a higher return signal to the receiver. This usually is accomplished by placing a retroreflective device or material on the target. (See Figure 4.)

Fig. 4
Cooperative target geometry

 

(23)A common retroreflector is the "cube corner reflector." This device is usually an optical prism in the shape of a pyramid with three plane faces orthogonal to each other. The characteristics of this prism are such that a light ray entering the nonorthogonal face will undergo total internal (specular) reflection at each of the other three faces. (See Figure 5.) After reflection from each of the three faces, the light ray will emerge from the same face that it entered. The exit beam will be parallel to the entrance beam. This means that the beam appears to have been reflected by a plane mirror whose surface is perpendicular to the beam axis. This type of reflector gives a return beam independent of the exact orientation of the prism, so that alignment is not critical.

Fig. 5
Total internal reflection of a ray from
a retroreflective cube corner reflector

 

(24)The emerging beam will have a divergence angle equal to the divergence of the intercepted rays from the transmitter plus diffraction effects due to the limited size of its aperture.

(25)Assuming 100% reflectivity for the corner reflector, the returned power will be:

Ptarrefl = f tar Acc = f tar


Equation 7

 

where:

dcc = diameter (or effective diameter) of the corner cube reflector.

The divergence angle (q cc) of the return beam from the retroreflector is given by

q cc = +

Equation 8

 

where:

q cc is in radians.

l = wavelength of the laser transmitter

dcc, R, and l all are expressed in the same length units.

From the divergence angle, the area of the return beam at the receiver can be calculated as follows, with the help of Equation 8:

Artn = dr2 = =

Equation 9

The power density of the return beam at the receiver is

f r =


Equation 10

and the power received by the optical antenna (Pr) is

Pr = f r Ara

Equation 11

Combining Equations 2, 7, 8, 9, 10 and 11 gives:

Pr = Pt


Equation 12

For very long-range measurements, that is

q tR > > dta and

> > 2dcc

Equation 12 reduces to

Pr = Pt


Equation 13

For short-range measurements, that is,

2dcc > >

Equation 12 reduces to

Pr = Pt


Equation 14

(26)Comparing Equations 13 and 14, we see that the range equation is significantly different. At close range, the received power Pr is dependent on the inverse value of the square of the range (R2) and independent of corner reflector area. In contrast, at long range, the received power is dependent on the inverse fourth power of the range and on the fourth power of the corner reflector diameter (dcc4). At long ranges it is quite possible for the atmospheric transmission to be the dominant factor.

Example B: Received Power—Cooperative Target

Given:

A cooperative target with a cube corner reflector with diameter 3 cm and the following measurement conditions:

Pt = 10 kW
q t = 10–2 radians
R = 103 meters
dta = 10 cm
dra = 10 cm
l = 1.06 ´ 10–4 meters (Nd:YAG laser)
T = 0.8

Note that these measurement conditions are the same as for Example A.

Find:

The received power, Pr.

Solution:

Since 2.44 l R/dcc = 0.086 and 2dcc = 0.06 meter, we can’t use either simplifying Equation 13 or 14.

Using Equation 12

Pr = Pt

Pr = 104

Pr = 0.076 watt.

Note that this value is many orders of magnitude larger than the value calculated in Example A. This shows the effect of the cooperative target.

(27)Most range (or distance) measurements are made by counting the time for the optical signal to travel from the transmitter to the target and back to the receiver. This is called the round trip transit time (tr). Since the velocity of light is known, we can convert the time measurement into a two-way distance measurement according to the equation,

2R = c tr

Equation 15

(28)The laser most often used for laser ranging is a Q-switched laser with a short pulse. The shorter the pulse, the more accurate the range measurement can be. The laser should have a high value of peak power, to increase the received power. Most rangefinders use a Q-switched ruby or Nd:YAG laser.

(29)Usually a digital circuit, such as a time interval counter is used to measure tr . Precision ranging requires that this time be measured relative to a specific point on the pulse, e.g., the "leading edge." The leading edge of a pulse is the rising or buildup side of the pulse. This is called "leading-edge detection" and is shown in Figure 6.

Fig. 6
Pulse range measurement by leading-edge detection

 

(30)In reality, pulses with instantaneous rise times as shown in Figure 6 do not occur. Consequently, the "leading edge" for detection has to be defined more precisely. This is done by measuring time from a point on the leading edge where the signal voltage has reached a predetermined value. This is accomplished in the time interval counter with a threshold trigger circuit to start and stop the time counting. For example: The circuit might be designed to trigger the start and stop circuits in the counter when a positive increasing voltage reaches a value of 3.0 volts. A time sequence plot of leading-edge detection range measurement using a threshold detector is shown in Figure 7.

Fig. 7
Leading-edge detection, range measurement
using a threshold detector and a time interval counter

 

(31)One common source of error in leading-edge detection range circuits occurs if the voltage magnitudes of the transmitter and receiver pulses are not adjusted to the same value before they are sent to the time interval counter. The range error that this can cause is shown in Figure 8. From inspection of Figure 8 you can see that, if the receiver pulse amplitude is too high, the time interval measurement, t h, will be too short. In contrast, if the receiver pulse is too low, the time interval measurement, tl , will be too long.

Fig. 8
Range error caused by magnitude of receiver pulse
being higher or lower than the transmitter pulse

 

(32)The maximum pulse repetition frequency (prf) of a pulsed ranging system transmitter is dictated by the requirement that the transmitter not send out another pulse until the echo from the previous one has been received. The purpose of this restriction is to avoid confusion in the pulses arriving at the time interval counter. A plot of maximum unambiguous range as a function of pulse duration frequency is shown in Figure 9.

Fig. 9
Maximum unambiguous range versus pulse repetition frequency

 

(33)The accuracy of a pulsed ranging system is determined by three major factors:

1. Ability to select the same relative position on the transmitted and received pulse to measure the time interval. This is limited by noise, time jitter, signal strength and sensitivity of the threshold detector, and shortness and reproducibility of the transmitter pulse.

2. The accuracy with which fixed time delays in the system are known.

3. The accuracy of the time interval measurement instrumentation.

(34)A very accurate pulsed laser ranging system may have a range accuracy of thirty centimeters for distances of the order of kilometers.

(35)Now let us consider some of the components used in rangefinding systems. This discussion will be limited to a survey of transmitters, receivers and antennas for laser/electro-optical ranging systems. Electronic ranging circuits, range tracking loops, phase detectors, local oscillators, and digital clock circuits are beyond the scope of this chapter.

(36)Most pulsed ranging systems use ruby, Nd:YAG, or semiconductor laser diodes. Since ruby laser systems operate in the visible wavelengths, they can use higher-efficiency detectors. Nd:YAG systems normally operate at a much higher repetition rate and even have been considered in the continuous pumped, Q-switched mode where the prf can be as high as 10 kHz. Laser diodes are of lighter weight and easy to lase. But they are limited (because of low power) to relatively short ranges and cooperative targets.

(37)The receiver for a laser ranging system is a photosensitive detector that can accurately and reliably convert the incoming optical signal into an electrical signal for processing by the receiver electronics. In general, you can expect that a system with a transmitter operating at a wavelength in the UV or visible will use a vacuum photodiode or photomultiplier because of their high sensitivity and low noise figure. In the near IR, silicon photosensors and special vacuum photoemissive devices are used.

(38)The primary purpose of the transmitter antenna is to reduce angular divergence. Figure 10 shows two arrangements for reflective optics. Figure 11 shows two arrangements for refractive optics. When the laser output is diffraction-limited, beam divergence is inversely proportional to the antenna aperture diameter as shown by Equation 16.

Fig. 10
Transmitter antennas—reflective optics

 

Fig. 11
Transmitter antennas—refractive optics

q d =

Equation 16

 

where: q d = full diffraction-limited divergence angle of a laser beam from an optical antenna

l = wavelength of the laser

dt = diameter of the transmitter antenna

From this equation, we can see that the larger the antenna diameter, dt , the smaller is the transmitter beam divergence q d.

(39)Figure 12 shows three configurations for receiver antennas. The function of the receiver antenna is to gather as much of the return energy as possible and focus it onto the photodetector. To reduce the noise in the receiver, narrow-band optical filters usually are placed over the photodetector to eliminate sunlight and other sources of optical noise.

Fig. 12
Optical receiver antennas

 

(40)Pulsed laser rangefinders are used for military rangefinding applications. They are mounted on the tanks of the armies of many countries. They have been used to track satellites in orbit and rockets during their launch phase. Pulsed laser range finders are used in military applications–for example, in tracking rockets during launch phase as well as satellite movements in obit. Range finding is a complex procedure as illustrated by the following description taken in one instance of the steps to track a satellite accurately. In this example, position of a satellite laser ranging (SLR) telescope is fixed exactly. This is done with the help of a corner cube reflector whose exact position on earth is known. The corner cube is used as a fixed test target for the SLR station/telescope to help "calibrate" and ensure the overall system stability of the telescope system. Once this is accomplished, the telescope must obtain a "receive path" bearing from multiple stars. This last "telescope fix" then enables the system to smoothly and accurately track a satellite which is threading its way through the sky from one horizon to the other. If lunar range finding is the goal, retro-reflectors (placed on the moon by the astronauts) serve the purpose of the corner-cube reflector used on Earth. (Pete Latham)

(41)In one notable application, the distance to the moon was measured using a Q-switched ruby laser pulse transmitted through the telescope of an astronomical observatory. The targets were panels of retroreflectors left on the moon by Apollo astronauts. The results have led to a determination of the distance of the moon from the earth with a higher precision than had been possible previously.

 

Beam-Modulation Telemetry

(42)Continuous wave lasers also are used in optical ranging systems. Since the transmitter output has a sine wave modulation, the method is called beam-modulation telemetry. Because of the single frequency component in the modulation, this technique sometimes is called tone ranging. A typical arrangement is shown in Figure 13.

Fig. 13
Diagram of distance measurement by beam-modulation telemetry

 

(43)Range is determined by measuring the phase angle (f r) between the transmitted sine wave signal and the received sine wave signal. (See Figure 14.) This phase angle can be related to a time delay tr similar to that measured in the pulse-measurement technique. The relationship between phase angle delay f r , modulation frequency fmod , and time delay tr , is:

tr =

Equation 17

 

where: tr is the round-trip transmit time (time delay) in seconds.

f r is measured in radians.

fmod is in Hz or cycles/second.

Fig. 14
Phase comparison measurement in CW, tone ranging

 

Then, according to Equation 15, the range R will be:

R = =

Equation 18

(44)Just as in the case of pulsed time-of-flight systems, continuous beam-modulation telemetry systems have a maximum unambiguous range. This range is limited to that which causes a phase delay in the sine wave of one complete cycle. The equation for maximum unambiguous range Runamb in a CW system is:

Runamb =

Equation 19

(45)Highly accurate tone ranging systems often have several modulation frequencies or tones. The lower-frequency tones are used to prevent an ambiguous range measurement. The higher-frequency tones are used for more accuracy.

(46)The accuracy of CW tone ranging systems is limited by

1. Frequency of the tone or modulation.

2. Accuracy of the phase-measurement loop. This depends on signal strength, noise, and so on.

3. Stability of the modulation oscillator.

4. Number of cycles (or measurements) that can be averaged together for a range measurement.

5. Turbulence in the air through which the measurement is made.

6. Variations in the index of refraction of the air.

(47)There are CW tone-ranging systesms that use HeNe, argon, CO2, and other gas lasers as well as semiconductor laser diodes. The visible lasers offer the advantage of easy alignment and availability of high-efficiency detectors, whereas the CO2 laser can operate better in smog or haze. This type of distance-measurement system, which can have an accuracy better than 1 cm over distances of the order of kilometers, has been used for applications such as surveying and land profiling.

Example C: Measurement with Beam-Modulation Telemetry System

Given:

A beam-modulation telemetry system operating at a frequency of 100 kHz and measuring the length of a football field (100 yards).

Find:

The phase angle delay and the maximum unambiguous range that could be measured by the system.

Solution

Rearranging Equation 18 gives the phase angle as:

f r =

R is equal to 100 yards = 91.4 meters = 9140 cm.

f r = = 0.383 radian.

The maximum unambiguous range is:

Runamb = = = 1.5 ´ 105 cm = 1.5 km

This is much greater than the distance being measured.

Interferometric Methods

(48)Laser-based distance measurements can be done using interferometric principles. Measurements of length using optical interferometry have been performed since the 19th century. But the limited intensity and coherence of conventional light sources restricted the measurements, which were difficult and suitable for used only over distances of a few centimeters. The development of lasers removed these restrictions. Lasers have allowed interferometry to develop into a fast, highly accurate and versatile technique for measuring longer distance.

(49)Interferometric measurement of distance can be highly accurate. It offers a higher degree of precision than the pulsed time-of-flight or beam-modulation telemetry methods. However, it is best suited to measurements made in a controlled atmosphere (for example, indoors) over distances no greater than a few tens of meters.

(50)Most laser-based interferometric systems for measurement of distance use a frequency-stabilized helium-neon laser. An unstabilized laser, operating in a number of longitudinal modes, will have a total linewidth around 109 Hz. This spread in the frequency (or wavelength) will cause the interference fringes to become blurred and to lose visibility as the distance increases. An unstabilized laser is suitable for measurement only over distances of a few centimeters. Stabilized lasers, usually in a temperature-controlled environment and operating in a single longitudinal mode, are used for longer distances.

(51)We describe first the operation of a system based on the Michelson interferometer, because it is easy to understand the basic principles of interferometer distance measurement with reference to the Michelson interferometer. Later we will describe variations that provide better stability under conditions of atmospheric turbulence.

(52)Figure 15 shows the basic configuration for a Michelson interferometer. Review Course 5 on interference if necessary to understand the formation of an interference pattern. The beam from the laser falls on a beam splitter that reflects half the beam in one direction (the reference arm) and transmits the other half (the measurement arm). The two beams are each reflected by mirrors, a stationary mirror in the reference arm and a movable mirror in the measurement arm. In practice the mirrors are often cube corner reflectors (retroreflectors) which offer better stability against vibrations than conventional flat mirrors.

Fig. 15
Schematic diagram of the application of a
Michelson interferometer to measurement of distance

 

(53)The two reflected beams are recombined at the beam splitter to form an interference pattern that is viewed by an observer or measured by a recorder such as a photodetector. The character of the fringes is related to the different optical path lengths traveled by the two beams before they are recombined.

(54)Suppose, for example, that the detector is viewing a bright fringe in the interference pattern when the movable mirror is at a certain position. If the movable mirror moves a distance equal to 1/4 of the wavelength of light, the round-trip distance traversed by the light in the measurement arm will change by 1/2 wavelength, and the fringe pattern will change so that the detector now views a dark fringe. The distance mesurement thus consists of counting the number of fringe variations as the mirror moves. Each complete fringe corresponds to a phase variation equal to 2p . The variation in phase d is determined by using the equation

d = 4p D x/l

Equation 20

where l is the wavelength of the light, and D x is the distance that the movable mirror has moved. It is apparent that this method offers high precision, allowing measurements of D x to be made with an accuracy of the order of a fraction of the wavelength of light.

(55)The maximum distance D x that can be measured in this way is given by:

D x max = c/D v

Equation 21

 

where:

c = velocity of light.

D v = linewidth (i.e., spread in frequency) of the laser.

(56)This equation shows the importance of using a frequency-stabilized laser with a small line width.

(57)Note also that this measurement is a relative measurement which gives the distance that the mirror has moved from its initial position, rather than an absolute positional measurement.

Example D: Distance Measurement in a Michelson Interferometer

Given:

A HeNe laser 50 cm long with two longitudinal modes is used to measure distance in a Michelson interferometer. 2200 fringe changes are observed (bright to dark to bright) as the movable mirror is moved.

Find:

The distance the mirror moved. The maximum distance that could have been measured.

Solution:

Each fringe corresponds to a change in phase of 2p . So the total change in phase d is 2200 ´ 2p . Using Equation 20:

2200 ´ 2p = 4p D x/l

or D x = 2200 l /2 = 2200 ´ 0.6328 ´ 10–4/2

= 0.0696 cm

In a laser, the longitudinal mode spacing is c/2L where L is the length of the laser. So, a two-mode laser will have a linewidth D v equal to c/2L. Using Equation 21, we have:

D xmax = = = 2L = 2 ´ 50 = 100 cm.

 

(58)The distance measured in an optical measurement is the optical path, which is the physical path multiplied by the index of refraction of the air through which the measurement is made. Since the index of refraction is close to unity, in some cases (for example, military ranging) it is not necessary to correct for variations in the index of refraction. But in interferometric measurements requiring a high degree of precision, one must correct for changes in the index of refraction that occur as a result of changes in air pressure, temperature, and so on. The index of refraction of dry air at a pressure of 760 Torr and a temperature of 15° C is 1.0002765 at the helium-neon laser wavelength. As conditions in the air change, the index of refraction changes. It increases by:

· 0.36 part per million for an increase of 1 Torr in atmospheric pressure.

· 0.96 part per million for an increase of 1C° in temperature.

· 0.06 part per million for an increase of 1 Torr in the partial pressure of water vapor.

(59)So, a measurement system that requires high precision must include sensors for measurement of air temperature and pressure (an perhaps relative humidity) and a means (often an automated computer-based means) for correcting for the variable atmospheric parameters.

(60)A schematic diagram of a system to measure the motion of a machine tool carriage is shown in Figure 16. The system uses two photodetectors to determine the direction of the motion. The two detectors collect light from different portions of the fringe pattern. The relative phase of the modulation of the fringes will be different, depending on whether the carriage is moving toward the laser or away from the laser.

Fig. 16
Diagram of system for measurement
of motion of a machine tool carriage

 

(61)The interferometric technique described above was developed early in the laser era and was the basis of measurement systems used in the 1960s. It suffers the drawback of being very sensitive to turbulence in the air, which can wipe out the fringe pattern. This problem has been reduced by use of a two-frequency laser system that mixes two beams of different frequencies and measures the Doppler shift of the beam reflected from the moving mirror. This system, developed in the early 1970s, forms the basis for many modern interferometric distance-measuring systems.

(62)The operation of such a system is shown in Figure 17. In this figure, f1 and f2 are the two laser frequencies, and D f1 is the Doppler shift produced by the motion of the retroreflector.

Fig. 17
Diagram of two-frequency distance-measuring system

 

(63)The helium-neon laser emits light at two slightly different frequencies, f1 and f2 , with different polarization properties. The laser has an axial magnetic field that splits the fluorescent line of neon into two differently polarized frequency components separated by about 2 MHz.

(64)A polarization-sensitive beam splitter separates the two frequencies so that they travel different paths. Light with frequency f2 is sent to a fixed reflector. Frequkency f1 goes to the movable reflector attached to the part whose distance is to be measured. If the part moves with velocity v, the frequency f1 upon reflection changes by an amount f1 given by:

=

Equation 22

(65)This shift is due to the Doppler effect and is analogous to the familiar Doppler effect in acoustics. The two beams with frequencies f1 + D f1 and f2 are recombined by the beam splitter and sent to a detector. The output of the detector will contain an oscillating component at frequency f1 + D f1f2, which can be compared to the original difference frequency f1f2, generated at a second detector. This gives a measurement of D f1 and hence of v, according to Equation 22. The value of v then can be integrated over time to yield the total displacement.

(66)This type of system is not highly sensitive to degradation produced by air turbulence, air motion, and so on. It can provide measurements of motion in the one-millionth-inch regime in an industrial environment.

(67)Accurate laser-based interferometric measurements have been applied in a wide variety of practical cases in industry, such as:

· Checking accuracy of the runout of machine tools, and automatic compensation of the errors.

· Measurement of the amplitude of building vibrations.

· Dimensional control of step-and-repeat cameras in photolithographic mask-making processes in the semiconductor industry.

· Geodetic measurements of strains in the crust of the earth and tectonic plate motion.

Exercise.jpg (6215 bytes)

1. Describe, in terms similar to the text, the operation of the following distance-measurement systems:

· Pulsed time-of-flight

· Beam-modulation telemetry

· Interferometric

2. Define the following terms:

· Noncooperative target

· Cooperative target

· Unambiguous range

· Round-trip transit time

· Leading-edge detection

3. Draw a sketch of the waveforms for a pulsed time-of-flight ranging system. Identify the transmitter pulse, receiver pulse, round-trip transit time and the threshold voltage for leading-edge detection.

4. A Nd:YAG laser that emits pulses with peak power 105 watts is aimed at a noncooperative target with diffuse reflectivity of 0.3 and diameter of 3 meters at a distance of 1.5 km. The beam divergence angle is 100 milliradians, and the receiving telescope has a diameter of 12 cm. Assume that the atmospheric transmission is 90% over the range. What is the peak value of the received power? What is the maximum pulse repetition rate you could use?

5. A beam-modulation telemetry system measures the distance to a surveying pole. The operating frequency is 5 ´ 105 Hz, and the phase angle delay is 1.2 radians. What is the distance to the pole? What is the maximum value of the modulation frequency that could be used?

6. A HeNe laser operating in a single longitudinal mode, and with a line width of 1.2 ´  107 Hz, is used to measure distance in a Michelson interferometer arrangement. The detector observes a shift of one-half fringe (i.e., a change from minimum intensity to maximum intensity) as the movable mirror is displaced slightly. How far did the mirror move? What is the maximum distance that you could measure with this apparatus?

Material.jpg (5811 bytes)

Gallium arsenide laser diode

Pulse generator

Transmitter optics

Pulser for GaAs diode

Two alignment telescopes

Two corner reflectors, 1" diameter and 3" diameter

Receiver photodetector

Receiver optics

Oscilloscope, Tektronix 545 or equivalent

Polaroid camera for oscilloscope

Tripod

Alignment telescope

Timer interval meter

Sheet of white paper, four feet square

CW power meter

Optical attenuator filter, 3 db @ 900 nm

Narrow-band transmission filter, l = 900 nm

Procedur.jpg (6345 bytes)

1. Set the pulse generator for __* __ volt pulses, __*__ m sec wide, and at a pulse repetiton frequency of 100 kHz. Check for proper operation using the oscilloscope.

2. Connect the pulse generator to the pulser and the laser diode. Set up the photodetector to record the output waveforms from the laser diode.

3. Measure the average output power from the laser diode. Record data.

4. Connect the laser diode to the output optics and a sighting telescope. Mount the transmitter assembly on a tripod.

5. Connect the receiver to the input optics and the sighting telescope. Insert the transmission filter. Connect the receiver to a power supply and oscilloscope. Block the input optics and measure dark current noise. Mount the receiver assembly on a tripod.

6. Position the equipment approximately 30 meters from a 0.1-square-meter white paper target inside the building.

7. Align the system on target and measure the return signal level from the photodetector. Record. Attempt to measure range using a time interval counter.

8. Position the equipment outside, approximately 300 meters from a one-square-meter, white paper target. Repeat Step 7. Record data.

9. Replace the paper target with a corner cube reflector. Repeat Step 8. Record data.

10. Extend the range to 1000 yards, repeat Steps 7 and 9.

11. Convert the average power measurement in Step 3 and the output waveform recorded in Step 2 to peak pulse power.

12. Using the peak transmitted power calculated in Step 11, calculate the received power in Step 10 using the white paper (U = 1.0) and the corner reflector. Calculate the maximum unambiguous range.

Referenc.jpg (6229 bytes)

Bachman, C.G. Laser Radar Systems and Techniques. Dedham, MA: Artech House, 1979.

Beheim, G., and K. Fritsch. "Range Finding Using a Frequency-Modulated Laser Diodes," Applied Optics 25, 1439, May 1, 1986.

Edwards, B.E. "Design Aspects of an Infrared Laser Radar," Lasers and Applications, 47, October 1982.

Gillard, C.W.; N.E. Buholz; and D.W. Ridder. "Absolute Distance Interferometry,"Optical Engineering 20, 129, January/February 1981.

Gillard, C.W., and N.E. Buholz. "Progress in Absolute Distance Interferometry," Optical Engineering 22, 348, May/February 1983.

Greve, A., and W. Harth. "Laser-diode Distance Meter in a KERN DKM 3A Theodolite," Applied Optics 23, 2982, September 1, 1984.

Luxmoore, A.R. Optical Transducer and Techniques in Engineering Management, Chapter 5. London and New York: Applied Science Publishers, 1983.

Luxon, J.T., and D.E. Parker. Industrial Lasers and Their Applications, Chapter 10. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1985.

Ready, J.F. Industrial Applications of Lasers, Chapter 10. New York: Academic Press, 1978.

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