Strain Gauges in Optical Engineering

This SPIE Tutorial Text excerpt discusses the use of strain gauges in optical engineering.

12 April 2017
Scott W. Teare

Cover of SPIE Press Book Strain Gauges in Optical EngineeringOf the wide range of electronics topics that might of interest to optical engineers, one that stands out relates to the use of electronic circuits for strain gauges, which can be used for structural health monitoring through deflection in materials. Why are these systems of interest?

While commercial packages can be purchased for these systems, they can actually be constructed with very little effort and cost, the result being that they can be easily adapted into inexpensive automated instruments supported by low cost micro-controllers. This approach places custom electronic systems in the hands of most scientists and engineers and at very low cost! Best of all, you didn't have to consult with "the guy" or the local electrical engineer to get your instrument to work. Here we offer a short explanation of strain gauges provided as rough excerpts from the SPIE Tutorial Text, Practical Electronics for Optical Design and Engineering.

As their name suggests, strain gauges are sensors that measure strain, or the displacement of a body compared to its original length, when subjected to an applied force.1,2 It is common when discussing strain to include the idea of stress, which is the force per unit area. Combining these two concepts in a simple fashion leads to the idea of stress being a result of strain!

Young's modulus is defined as the ratio between stress and strain and is a commonly quoted property of metals.3 This property is often used to discuss the elasticity of metals, that is to say, a stress applied to a metal will cause it to elongate, but the metal will return to its original length when the stress is removed. This is a mechanical property of the materials and one of great interest to optical engineers who are interested in high-precision alignments. Environmental changes ranging from temperature and pressure to irradiation by light to movements in a gravity field can all make small but measureable changes in an optical system. Other types of strain gauges are available, such as fiber optical gauges, which can be very useful; however, here we will restrict ourselves to the classical strain gauges. Strain gauges are remarkably sensitive devices and are commonly used in almost every science and engineering discipline.

Strain gauges are also remarkably simple devices1,2 and are really little more than foil electrodes sandwiched between two flexible plastic sheets. The strain gauge is effectively a long length of conductor folded up to provide a compact resistor. In use, one side of the plastic sheet is glued to the object that is to be measured such that any movement in the object translates into movement in the foil gauge. Wires attached to the solder tabs of the strain gauge provide an electrical connection that is used to connect to the detection circuit.

The strain gauge (Fig. 1) operates as a resistor whose resistance can be varied, making it similar to a potentiometer. In a strain gauge, the resistance change is induced by the small movements of the object causing the foil electrodes geometry to change. The movement causes the electrodes to become thinner and elongated or thicker and shorter so that the resistance of the strain gauge changes from the unstrained value. Strain gauges are available in a wide range of shapes, sized, and combinations, but in all of the various forms, the narrower lines in the pattern show the active region of the sensor.


Figure 1. Strain gauge showing the location of the solder contacts and alignment markers.

There are many combinations and geometries that combine individual strain gauges into single-sensor devices. Figure 2 shows a schematic view of the way a combination of four strain gauges might be placed onto a single sensor.


Figure 2. A quad strain gauge or full bridge showing how this device might be wired together to require just four external connections.

The foil electrode strain gauges are just one of many different types of strain gauge; there are also semiconductor, glass, and ceramic gauges, but for now we discuss foil gauges and how to work with them. These gauges are not particularly large, and the active area of a single gauge is typically between 2 and 12 mm.2

The gauge factor K of a strain gauge is a calibration of the change in electrical resistance (ΔR/Ro) of the strain gauge to the mechanical strain (ε = ΔL/Lo) and is also known as the strain factor.2 This can be stated mathematically as

K=(ΔR⁄R_o )/(ΔL⁄L_o )=(ΔR⁄R_o )/ε.(1)

Here Ro and Lo are the original resistance and length, respectively, and Δ indicates the change in those values under loading. The gauge factor for foil gauges is on the order of 2. Additional effects such as temperature can come into play, but we will ignore these.

Strain gauges are often used in devices that measure mass, such as a weigh scale. This is accomplished by creating a load cell, which is little more than a bar of metal with strain gauges attached. The force from the object to be weighed is place on the scale and deforms the load cell, then the change is converted into a mass. Strain gauge load cells are therefore transducers that convert the applied force into an electrical signal.

The operation of a strain gauge relies on the change in resistance caused by deformation, and this resistance change can be very small.1,2 The simplest way to measure the change in resistance is to use electrical voltage to generate a current and measure the change in voltage with the change in resistance.

The simple, low-cost, electronic circuits needed for using strain gauges make them an appealing first electronics experiment or an easy add-on to an existing project. Once you get into the habit of constructing your own electronics circuits, many of the other ideas in the SPIE Tutorial Text, Practical Electronics for Optical Design and Engineering, will be equally eye catching!


1. R. Djugum, Strain Gauges: Fabrication Processes and Techniques, VDM Verlag, Saarbrücken, Germany (2009).

2. "Measuring Strain with Strain Gauges," Application Note 078, National Instruments Corporation, Austin, Texas (1998).

3. F. W. Sears, M. W. Zemansky, and H. D. Young, University Physics, Seventh Edition, Addison-Wesley, Boston (1987).

SPIE e-book author Scott W. TeareScott W. Teare received a PhD in Physics from the University of Guelph, Canada and is currently professor of Electrical Engineering and Research Scientist at the Energetic Materials Research and Testing Center at New Mexico Institute of Mining and Technology in Socorro, New Mexico.

He regularly teaches university courses in optics, electronics, and MATLAB®. His primary research interests include adaptive optics and wavefront sensing; thin film optical filters; electrical and optical properties of energetic materials; and ballistics. He has authored or coauthored more than 100 technical papers, two other SPIE Tutorial Text Series books and has been awarded 4 patents.

He is a member of the Canadian Association of Physicists and the Royal Astronomical Society, and is a Senior Member of IEEE and Fellow of SPIE.

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