Advances in Analog Distance Sensing

September 1, 2004 By: Brian Duval

This introduction to noncontact displacement sensors will be helpful to anyone who's thinking about adding one or more inductive, ultrasonic, or optical devices to an automated manufacturing operation.

In the beginning, noncontact displacement sensors either saw something or they didn't, and they passed this information along as an ON/OFF, discrete signal. These simple sensing systems are still at work in many applications today. For more advanced automated applications, however, design engineers may need additional information. In response, some manufacturers developed sensors capable of measuring distance and displacement by providing a distance-proportional analog output. These sensors can be used for a variety of purposes, including absolute distance measurement, thickness calculation, slope and deformation control, linear distance measurement, position control, profile logging, centering control, and diameter/eccentricity measurement.

Displacement sensors come in a variety of designs and operating principles. The inductive devices at upper left are 12 mm tubular, 12 mm square-bodied, and 18 mm flatpack. The OADM 12 mm self-contained laser sensor (lower left) measures 12 × 37 × 34 mm thick and weighs only 37 g. Above right are 20 mm square and 12 mm tubular ultrasonic sensors.

Known collectively as displacement sensors, analog output sensors, linear sensors, or distance sensors, these devices allow a user to determine more than simple presence or absence while enjoying the simplicity of sensor integration. Based on inductive, ultrasonic, or optical technologies, the sensors provide an analog output signal proportional to the distance between the sensor and the object of interest. Their typical operating parameters, by type, are given in Figure 1, and the terminology is illustrated in Figures 2, 3, 4, and 5.

Figure 1.
Displacement Sensor Parameters by Type
  Inductive Ultrasonic Optical
Measuring Distance 0 to >10 mm 20 to >2500 mm 15 to >1000 mm
Resolution 0.1 µm ±0.3 µm ±2 µm
Repeat Accuracy 1 µm ±0.5 µm ±2 µm
Linearity 0.4%-5% 0.5% 0.06%-1.2%
Reaction Time 0.35 ms 30 ms 0.9 ms
Teach-In Programming Yes Yes Yes


Figure 2. Resolution corresponds to the smallest possible change in distance that causes a detectable change in the output signal.


Figure 4. Linearity is the deviation from a proportional linear function or a straight line, given as a percentage of the upper limit of the measuring range (full scale).


Figure 3. Repeat accuracy is the difference between measured values in successive measurements within a period of 8 hours at an ambient temperature of 23ºC ±5ºC.


Figure 5. Reaction time is the time required by the sensor?s signal output to rise from 10% to 90% of the maximum signal level. For sensors with digital signal processing, it is the time required for calculation of a stable measured value.

Inductive Sensors

Inductive distance sensors work best on electrically conductive metal targets such as steel, aluminium, or metallic alloys. Because their measuring principle is based on the evaluation of inductive eddy currents, they are very resistant to all kinds of nonmetallic environmental contaminants including dust, cutting fluids, and oil. Both current and voltage analog outputs are available. Innovative new technologies have led some manufacturers to build tubular inductive distance sensors as small as 6.5 mm dia. 3 40 mm long that are capable of sensing ranges up to 2 mm. The devices are well suited for applications requiring high resolution and repeat accuracy, and their 0.35 ms response time is fast enough for even the most high-speed measuring applications.

Despite their excellent repeat accuracy, resolution, and speed, the common 3%-4% linearity exhibited by these sensors occasionally presents problems. To combat this, some manufacturers specify the measured value even further by providing polynomial functions, mathematical descriptions of the sensor's characteristic curve that permit programming of common control units with very precise measuring and regular algorithms. A typical polynomial function based on the measuring characteristics of a 12 mm tubular inductive distance sensor is:

distance = a + b (lout) + c (lout)2 + d (lout)3 + e (lout)4

where lout = line out

measuring range = 0-2 mm, 0-20 mA (lout)

The following coefficients are available:

a = -0.144334; c = -0.00782; e = -7.27311 × 10-6; b = 0.151453; d = 0.00040

This equals a distance of 0.4638 mm with a measured value of, for example, 5 mA (lout).

Linearity problems can also be solved using sensors with integrated microprocessors. This digital signal-processing method enables a considerable linearization of the characteristic output curve, significantly decreasing linearity error. This becomes especially evident in absolute distance measurement. For example, a linearized sensor type M12 with a 0-4 mm measuring range achieves a maximum linearity error of less than ±0.4%, a tenfold improvement over non-microcontroller versions.

Ultrasonic Sensors

Some sensors offer distance measurement via ultrasonic transmission. Based on the speed of sound through air, ultrasonic sensors measure distance by calculating the time required for the sound to return to the sensor, and offer resolutions up to >0.3 mm.

Applying converters based on the reversible piezoelectric effect makes one-head systems possible where the converter serves both as transmitter and receiver. The transceivers work by transmitting a shortburst ultrasonic packet. An internal clock starts simultaneously, measuring propagation time. When the object reflects the sound packet back to the sensor, the clock stops. The time elapsed between transmitting the packet and receiving the echo back is the basis for calculating distance. Complete control of the process is realized by an integrated microcontroller, which allows for excellent output linearity.

The major benefit of ultrasonic distance sensors is their ability to measure difficult targets-solids, liquids, granulates, powders, and even transparent and highly reflective materials that cause problems for optical sensors. In addition, analog output ultrasonics offer comparatively long ranges, in many cases >3 m. They can be made very small too; some tubular models are only 12 mm in dia. and 15 × 20 × 49 mm square-bodied versions are available for limited-space applications.

Ultrasonic devices do have some limitations. Foam and other attenuating surfaces may absorb most of the sound, significantly decreasing measuring range. Extremely rough surfaces may diffuse the sound excessively, decreasing range and resolution. However, an optimal resolution is usually guaranteed up to a surface roughness of 0.2 mm. Ultrasonic sensors emit a wide sonic cone, limiting their usefulness for small target measurement and increasing the chance of receiving feedback from interfering objects. Some ultrasonic devices offer a sonic cone angle as narrow as 6º, permitting detection of much smaller objects and sensing of targets through narrow spaces such as bottle necks, pipes, and ampoules.

Optical Sensors

There are many ways of optically sensing distance: laser interferometers, diffuse sensors with and without fiber optics, and time-of-flight sensors. Each has its own strengths and weaknesses. Interferometers offer nanometer resolutions and long sensing ranges, but are expensive and require complex peripherals and optically efficient targets. Analog-output diffuse sensors and fiber-optic amplifiers can be programmed to offer rough distance measuring, but because they operate on the intensity of received light they are at the mercy of target color and reflectivity. Time-of-flight sensors, typically lasers, feature long measuring ranges and self-contained packages, but rely on propagation time and have somewhat limited resolution, just 3-5 mm over their measuring range.

Most machine applications require specifications somewhere between nanometer resolution and 50 m ranges. The sensors must often contend with target properties that are less than ideal: small size, varying color, difficult surface characteristics, and target speed. Triangulation-based laser distance sensors (see Figure 6) are the standard for industrial machinery applications.


Figure 6. Laser-based triangulation displacement sensors project a collimated beam that reflects off the target and passes through a lens that focuses the reflected beam onto a receiving element. These sensors are the standard for industrial machinery applications.

In triangulation, a laser light source projects a collimated beam that reflects off the target and passes through a lens that focuses the reflected beam onto a receiving element. Any change in distance between sensor and target immediately changes the angle of the returning light, thereby changing the position of the beam on the receiving array. The receiving element and the microcontroller combine to output the measured values as analog signals.

The major benefit of laser-based distance sensors is the combination of high resolution and comparatively long ranges. While many sensor manufacturers offer versions with <1 mm resolution and ranges of >1 micron, the highest resolution specs usually are possible over relatively small windows and at shorter ranges. So a 1 micron resolution and a 1 m sensing distance will not happen simultaneously.

To limit the effects of signal noise, all laser measurement sensors perform an internal sampling, sometimes called integration or averaging. During sampling, sensors take multiple readings and average them, resulting in smoother, more accurate outputs. Higher resolutions require the integration of a greater number of samples, which often increases response time proportionally with any improvement in resolution. While 1 micron resolution is possible, it comes with a response time as slow as 100 ms-rarely usable in a dynamic application.

In contrast, the Baumer Electric OADM laser displacement sensor family's <900 µs response time is an absolute high, regardless of resolution and target color. The OADMs offer up to 2 micron resolution at <900 µs on even matte black targets. On an ideal target such as matte white ceramic, response times can be as fast as 250 µs with no decrease in resolution. An advanced receiving element capable of subpixel resolution, combined with intelligent microprocessors, provides consistent response times at all resolutions.

Laser distance sensors are also undergoing a process of miniaturization. Where the industry standard has for years been a multiple-component system consisting of a sensing head and external control unit, new products such as the OADM 12 offer completely self-contained body sizes as small as 12 × 37 × 34 mm. These one-piece sensors are considerably smaller than the sensing head alone of previous multiple-component versions, require no external controller, and offer 2 micron resolution and 250-900 µs response times. The very good price-performance ratio of optical sensors satisfies applications from tuning the chassis of a Formula 1 racing car to tracking laser exposure heads in digital printing procedures with resolutions of 2 microns.

Choosing the Right Sensor

Before you specify or buy a displacement sensor, you should have the answers to these 10 questions:

  • What is your target material?
  • What is your range to target?
  • What resolution do you require?
  • What are your physical mounting needs?
  • How much space can you allocate to the sensor?
  • What output signal is required (e.g., 0-10 VDC, 4-20 mA, RS-485)?
  • How fast is the target moving?
  • What is the necessary response time?
  • What degree of environmental protection is required?
  • What are the connection requirements (e.g., cable, quick disconect)?

With this information, and a basic understanding of the operating principles of inductive, ultrasonic, and optical noncontact displacement sensors, you will be able to make the best selection for the job at hand.

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