Technical Articles

The following excerpt appeared as the cover story in the September, 1993 Sensors magazine.

Frequency-Modulated Laser Ranging

Neal Woodbury, Arizona State University
Michael Brubacher, Phase Laser Systems Inc.
James R. Woodbury

................. a recently developed distance ranging technique appears to offer significantly improved dependability and measuring accuracy in difficult industrial applications. Developed by Phase Laser Systems Inc., this technique makes innovative use of differential phase measurement technology.

PRINCIPLES OF OPERATION

There are three physical properties of laser light that can be exploited in the measurement of distance:

• Light travels in a straight line. This property makes feasible a variety of possible geometric methods for measuring distance, most of which depend on some form of triangulation. These methods are limited in that they require at least two spatially separate reference points.

• Laser light is coherent. The use of diffraction (destructive and constructive interference) of the light is an excellent method for measuring very short distances (inches or less) with submicron accuracy. The technique, however, is not easily usable for greater distances.

• Light propagates through space with a very well-known velocity. In principle, this offers an extremely accurate way to determine distances of any required length. It is technically difficult, though, to accurately time the departure/return of a light pulse traveling ~ 1 ft/ns. Resolution of ¹/8 in., e.g., requires a temporal accuracy of ~ 10 ps.

Two general methods might be used to accurately measure the time required for light to make a round trip between the measuring device and the object to be measured. The simplest, conceptually, is the time-of-flight approach that measures the elapsed time between when a short pulse of light leaves the instrument and when the returning reflected or scattered pulse is detected. Unfortunately, making direct measurements of time intervals with < 10 ps accuracy remains relatively expensive. Conceptually more complex, but electronically simpler, is to measure the phase of a modulated light beam when it leaves the instrument, and then compare that phase to the phase of the return light.

Performing Differential Phase Measurements. If a laser beam is modulated at a particular frequency, and reflected or scattered from an object a certain distance away, it is possible to measure the relative modulation phases of the transmitted beam and the light returning from the object. As illustrated in Figure 1, this relative phase is related to the distance between the instrument and the object by the following expression:

In terms of the electronics involved, it is much easier to measure the relative phases of two modulated light or electric signals than it is to measure the time of arrival of the leading edge of an optical or electronic pulse. The reason is that the phase difference between two modulated signals of the same frequency is time independent. One can therefore measure the phase difference over a time period much longer than the desired time resolution of, e.g., 10 ps. In principle, the more cycles of the modulation over which the measurement is taken, the more accurate the result. This suggests that the two simple ways to increase the accuracy of the relative phase determination are to increase the time of the measurement, and decrease the wavelength (increase the frequency) of the modulation.

The Modulo Problem. Since there are obvious limits on the amount of time one wants to wait before a distance measurement of the required accuracy is obtained, it would be advantageous to make the wavelength of the modulation as short as is practically possible. Laser diodes can be modulated at frequencies in the 10 GHz range (wavelengths of an inch or two), but electronic components designed to operate in this frequency range are typically rather complex. For many applications, much lower frequencies (e.g., 100 MHz) can be used to obtain sufficiently accurate distance measurements (see “Choice of a Modulation Frequency”).

It is important to note that decreasing the wavelength can create another problem. The relative phase of two sine waves is typically measured by multiplying the two signals together in an electronic mixer and then averaging the result of this multiplication over many modulation cycles. Stated mathematically, this becomes:

evaluating this expression
including the gain of the
integrating amplifier gives:

What can be seen is that it is not the phase itself that is actually measured, but rather the cosine of the phase.

If the round-trip distance to be measured is larger than the modulation wavelength, then the cosine of the phase is no longer single valued. In other words, there will be more than one distance that corresponds to a given phase measurement:

In order to remove this degeneracy, it is necessary to measure the relative phase at two or more different modulation frequencies:

and both x and n are uniquely determined, thus allowing the measurement of the true distance.

The Slope Problem. The fact that the measured value is actually the cosine of the phase raises another problem. consider the sensitivity of the measured value to small changes in the distance. There are regions of the cosine function given in Equation 4 that are much more sensitive than others to small changes in the distance. Mathematically speaking, the derivative of the measured value with respect to distance is dependent on distance:

We can see that there will be certain values of the total distance where the change of the measured value with respect to the distance is zero. In this region of the curve, the accuracy of the measurement will be very poor.

The solution is to acquire additional information on each measurement, this time by repeating the measurements at each modulation frequency with two different reference phases, separated by . This way, for each measurement performed in an insensitive region of the curve, a corresponding measurement will be performed in the sensitive region. The basic effect is of measuring both the cosine and the sine of the phase. Between those two measurements, all of the information theoretically available at a particular modulation frequency is obtained.

Choice of a Modulation Frequency. This selection depends on the distances to be measured and the accuracies desired. As previously noted, the higher the modulation frequency, the greater the accuracy. Beyond a point, however, higher modulation frequencies also imply more costly electronics components and more technical problems with shielding and stray capacitance in the circuit.

Because distance measuring is the primary application of this measurement technique, the relevant constraint is the ability to measure distances of several tens of feet with accuracies of ¹/8 in. or less. It is quite feasible to measure the cosine of the phase angle to within one part per thousand; 1000 x ¹/8 in. = ~10 ft. This corresponds to a frequency of ~100 MHz.

Working near 100 MHz has another advantage in that the circuit can incorporate a transmitter and a receiver very similar in design to those used in radio wave transmission and reception. Because 100 MHz is part of the FM band, the technology for both driving a transmitter at this frequency and detecting very small signals has been well developed. Very sophisticated, compact, low-cost ICs are available specifically to amplify weak signals in the FM band.

The Circuit. Inexpensive, readily available ICs common in the communications industry perform the bulk of the analog signal processing. As shown in Figure 2, the system consists of three basic elements: the transmitter, the receiver, and the reference frequency generator. The reference frequency generator creates three frequencies: a 93 ± 0.455 MHz transmit frequency; a 93 MHz receiver local oscillator (L.O.) frequency; and a 0.455 MHz reference frequency. Each of these frequencies has well-defined phases relative to each other, since they are all synchronized to the same crystal resonator.

When the modulated laser light hits the target, a reflected or scattered beam returns and is detected by a photodiode. This signal is amplified and mixed with the receiver frequency. This results in a 0.455 MHz signal that maintains the phase information of the signal from the photodiode. This signal is then amplified, and its phase is determined relative to the 0.455 MHz reference signal in a second mixer followed by an averaging circuit. This measured phase output is related to the distance between the instrument and the object.

The frequency of modulation of the transmitted laser beam can be changed between two values (0.455 MHz above and below the roughly 93 MHz receiver reference frequency) by an onboard processor, as can the phase of the 0.455 MHz reference signal (between 0 and 900). The processor also monitors the phase output via a 12-bit A/D converter.

ACCURACY

In its simplest configuration, the gauge is expected to achieve absolute accuracy of ~ ¹/8 in. over a distance of ~ 20 ft. This distance can almost certainly be increased several fold with minor modification and no loss of accuracy.

A key benefit of the modulated laser technique is that as long as a clear signal is received, measurement accuracy does not degrade with increasing distance. The laser could, in principle, therefore be configured to accurately measure distances to surfaces at 100 ft. Accuracies of ⁴⁰/1000 in. have been achieved under test conditions. In addition, even greater accuracies can be attained by means of longer averaging times, the values in this discussion are based on 1-2 s averaging times.

OTHER APPLICATIONS

Measurement of distance is fundamental to hundreds of vital industrial, defense, and consumer tasks. With ranges extended up to a mile or more, they could find applications in such disparate fields as collision avoidance systems, military target ranging, tanker car load-out, truck positioning, robotics, and laser measuring tapes.

ACKNOWLEDGMENT

The authors thank Evert Fruitman and Frank Davis for valuable advice and assistance. Neal Woodbury wishes to acknowledge support from National Science Foundation grant DMB911-58251.

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Neal Woodbury is a professor of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604. He is also a Development Consultant with Phase Laser Systems Inc. Michael Brubacher is President, Phase Laser Systems Inc., 14255 N 79th Street, Suite 6, Scottsdale, AZ 85260; 480-998-4828, fax 480-998-5586. James Woodbury is an electronics engineering consultant in the communications industry.

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