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A Novel Coordinate Measurement System Based on Frequency Scanning Interferometry

Published: Thursday, February 18, 2016 - 08:33

I n this article, we present a wide angle, frequency scanning interferometer (FSI) system capable of measuring the absolute distance to multiple targets simultaneously.

A spatial light modulator has been integrated into the FSI sensor head, projecting multiple beams towards targets. Absolute distance measurements of up to 6.8-m range have been achieved with high signal-to-noise values. Design of the optical system has allowed targets with angular range of ± 55˚ off-axis to be measured. So far up to 10 targets have been measured simultaneously at distances ranging from 1.5 m to 6.8 m, and at off-axis angles of ±30˚. For increased practicality and usability a stereo vision system with target detection software has been developed and integrated allowing tracking of multiple targets over the measurement volume.


Accurate, traceable measurement is a key requirement for efficient manufacturing and assembly. For dimensional measurement of components and assemblies up to a few meters in size, the coordinate measuring machine (CMM) is the most commonly used measuring tool. The most accurate CMMs can achieve expanded uncertainties of the order of a few micrometers per meter, i.e., a few parts in 106. For larger components, structures, or facilities, large-volume metrology (LVM) tools such as laser trackers, laser radar, photogrammetry, laser scanners, theodolites, total stations, and hydrostatic levels are required[1]. Typical measurement ranges of these tools are from approximately one meter to several tens or hundreds of meters, and they are used in a wide range of applications such as aerospace manufacturing and assembly, civil engineering, particle accelerator alignment for science, and beam therapy systems[2], and manufacturing of energy generation systems (civil nuclear[3], wind and fusion research[4]).

Apart from photogrammetry (specifically multi-camera videogrammetry), which can achieve an uncertainty of around a few parts in 105, all these LVM tools measure a single point in space at one time, though rapid sequential measurement is possible using laser scanners and laser radar. The relative uncertainty of the measured points ranges from around 5 × 10-6 (static target measured using a laser tracker), to 5 × 10-5 (the most accurate laser scanners).

Figure 1: Example of a measurement network using a laser tracker that was re-positioned many times to cover a large volume and navigate between obstacles.

The highest accuracy currently achievable is obtained when instrument(s) are deployed in a multi-station network, as illustrated in figure 1, where each station measures points common to other stations to build a data set with redundant data that allows for statistical analysis of the observations and hence some blunder detection and uncertainty estimation. Although commercial software exists to implement this capability using single-point measuring systems like laser trackers, currently, the only commercial system that offers this ability by design is iGPS[5], which uses a number of transmitters to locate a number of receivers within the measurement volume pseudo-simultaneously at relatively low data rates. The length measurement uncertainty achievable with iGPS depends on the deployment, but uncertainty of the order of 0.19 mm in a 10 m x 10 m x 2 m volume is achievable[6].

There are no LVM tools more accurate than iGPS, which can measure three dimensional locations of multiple points simultaneously and with the higher data rate required for high-speed automation—the nearest existing capability is found in multi-channel linear interferometer systems such as those used on the ATLAS detector at CERN[7] or the Multi-Line system[8] from Etalon AG[9]—though these are 1D measuring systems monitoring independent linear dimensions in parallel.

Under a European Metrology Research Programme[10] project (“LUMINAR”[11]), the National Physical Laboratory in the UK is developing a novel coordinate metrology system that combines a variation of FSI—a high-accuracy absolute distance measurement technique—with the inherent self-calibration, monitoring, and uncertainty estimation ability of multilateration[12],[13]. The system is capable of simultaneously measuring the distance to multiple targets from multiple sensors to provide the simultaneous 3D location of the targets and six-degree-of-freedom (6DOF) measurements of rigid bodies fitted with multiple targets. The new measuring system instantly builds a measurement network and exploits the inherent data redundancy associated with multilateration together with robust numerical algorithms to provide rigorous real-time uncertainty evaluation and diagnostic information. Another important feature of this development is the adoption of a stable length reference in the form of a gas absorption cell to provide traceability to the realization of the definition of the SI meter[14],[15],[16], so no additional scale factor or system calibration is required.

In previous research[12], we presented a diverging-beam FSI system with a measurement volume of approximately 0.3 m x 0.3 m x 0.3 m, with each sensor having a range of approximately 1 m and a field of view (FoV) of approximately ± 15°. The fundamental range limit of that system was set by the signal-to-noise ratio that could be achieved with that sensor design. In this article, we present a new design of sensor that increases the measurement range and FoV significantly beyond that previously reported. This new sensor will enable a system with a measurement volume of at least 5 m x 5 m x 3 m to be realized.

In the “Frequency scanning interferometry” section, we describe the basis of classical FSI, which is a technique that can be used to determine absolute distances between a sensor and a single target. We then explain how we have developed what we refer to as wide-field FSI, in which we can determine, simultaneously, absolute distance to multiple targets from a single sensor. In “The new sensor head design” section, we describe a new sensor prototype to measure absolute distances to targets greater than 5 m, with a FoV of up to 110°. In the “Results” section, we present some the results of some initial testing of the new sensor, and in the final section, “Conclusions and future work,” we consider the findings and chart the course of upcoming efforts.

Frequency scanning interferometry

Classical frequency scanning interferometry
Frequency scanning interferometry (FSI) is an absolute distance measurement technique that combines a conventional interferometer, usually an optical fiber interferometer, with a tunable frequency laser rather than a stabilized fixed-frequency laser[17]. Different FSI technologies exist, some relying on phase information for high-precision measurements, however, these systems can only measure the absolute distance to a single target per measurement. Methods that rely on frequency detection for distance estimation sacrifice precision, but grant more flexibility, such as allowing lower signal-to-noise limits, and the ability to measure multiple targets simultaneously[18].

Figure 2: Schema of one channel of a conventional multichannel frequency scanning interferometry system.

A schematic representation of a frequency scanning interferometer system can be seen in figure 2. Light from a tunable laser is first amplified by an erbium-doped fiber amplifier (EDFA) before being split into several measurement channels using a fiber splitter. For each measurement channel, the light is directed by optical fibers via a fiber circulator to a sensor head containing a collimating lens. The end of the fiber is located at the focal point of the lens. The end of the fiber reflects 4% of the light back into the fiber, forming a reference beam, which is directed towards a photodiode via additional fibers. The fiber end in the sensor head performs the function of a beam splitter in a conventional interferometer. The majority of the light from the fiber emerges as a diverging beam which is collimated by the lens.

A retroreflecting target placed within the collimated beam reflects the light back towards the lens, which focuses it back into the fiber. This beam, the measurement beam, combines with the reference beam reflected from the fiber end to produce an interference signal on the photodiode, according to equation (1).

(Equation 1)

Here, f0 is the optical frequency of the swept laser at time t = 0, A is the magnitude of the signal, α is the tuning rate of the laser, and τ is the time is takes for the light to travel to the target and return back into the fiber.

(Equation 2)

(Equation 3)

The frequency of the interference signal, fbeat is directly proportional to both the tuning rate of the laser and the total out and return distance, D, to the target and inversely proportional to the speed of light, c. Accordingly, as seen in equations (2) and (3), it is possible to determine the range to the target from measurement of the frequency of the interference signal.

Wide-field frequency scanning interferometry
In classical FSI, only one target is located within each collimated beam, i.e., one target per sensor head. We previously reported[12] on a simple modification of replacing the collimating (positive) lens with a diverging (negative) lens, thereby using the light from the fiber to illuminate a much larger volume, namely a cone centered on the axis of the lens, as seen in figure 3. With this arrangement it is possible to locate several targets within the cone of illumination. To avoid the directionality of traditional cube-corner retroreflectors, we instead use spheres (10 mm and 16 mm in diameter, respectively) made from S-LAH79 glass of refractive index n = 1.956, which function as omni-directional retroreflectors. With these hardware changes, each sensor head can illuminate multiple targets and each target can be illuminated by multiple sensor heads simultaneously.

Figure 3: Schema of a wide field FSI sensor head. R1 … R3 are omni-directional retroreflectors in the field of illumination of this and other sensors. Click here for larger image.

Where there are multiple targets in the FoV of a sensor head, the interference signal at the detector, previously given by equation (1) is now given as a sum of all of the target interference signals, as expressed in equation (4).

(Equation 4: Click here for larger image.)

By taking the Fourier transform of the detector interference signal, the frequency of each of the multiple targets can be recovered (as seen in figure 4). If the rate of tuning of the laser, α, is known then the distance, D, to each of the targets can be determined from the frequency peaks in the Fourier transform using equation (3). This is the fundamental principle of how our wide-field, multi-target distance measurements are made.

Figure 4: Typical frequency spectrum showing three targets detected as the three spikes located at ranges between 1 × 104 and 2 × 104 (arbitrary frequency units). The spikes and noise at ranges below 0.5 × 104 come from back reflections in other optical components and the fibers.

We have previously presented results using divergent-beam FSI to measure target distances operating at volumes of about 0.3 m x 0.3 m x 0.3 m. This is close to the maximum working volume[19] achievable with a divergent beam system, while keeping the device eye-safe. Divergent-beam FSI will always be limited due to the amount of light “thrown away” in the projected beam. To operate in excess of volumes of the order 10 m x 10 m x 5 m, a new method of distributing the limited quantity of light is required.

The new sensor head design

A new sensor is being developed to overcome the range and FoV limitations of the original sensor described above. It features a spatial light modulator to generate and steer individual measurement beams to each target, thus greatly improving the signal-to-noise ratio, and a vision system to guide the beam steering.

A picture of the new sensor design incorporating a spatial light modulator (SLM) and stereo cameras can be seen in figure 5. The FSI laser illumination is delivered to the sensor optics via optical fiber. The SLM can be seen towards the upper middle of the image. The cameras are clearly visible on either side of the SLM and optics. Some representative FSI beams have been superimposed on the image for illustration purposes.

Figure 5: The new sensor head showing stereo cameras on either side of the SLM system. FSI beams have been superimposed on the image for illustration purposes.

Beam steering with a spatial light modulator
SLMs induce a spatially variable modulation across a light beam, modulating either the phase or the amplitude (or in some cases both). Through this modulation they are able to form an arbitrary image from an input beam with a plane wave front. By integrating an SLM into each sensor head we are able to direct multiple near-collimated beams simultaneously from each sensor head to multiple targets over large distances and over a large FoV. Furthermore, the SLM can be reprogrammed in near real time, allowing the individual beams to be steered.

A liquid crystal on silicon (LCOS) SLM is used to modulate the phase of the beam. The SLM used for the FSI measurements is a reflective, electrically addressed spatial phase modulator, the Hamamatsu X10468-08[20]. This device has 800 x 600 pixels, which allows individual beams to be directed in an angular grid of 800 by 600 directions.

The angular and radial range achievable using an SLM-based FSI system is dependent on the optics used to direct the beams. The current optical setup for projecting spot patterns can be seen in figure 6. A collimated laser beam is directed through a polarizing beam splitter (PBS) and quarter wave plate onto the SLM. The phase-modulated beam reflected by the SLM then passes back through the quarter wave plate, which ensures it is reflected by the PBS through a first lens, which generates a pattern of spots depending on the phase modulation imparted by the SLM. Each spot is then effectively the source of a near-collimated beam that is directed by a second lens to a target. The number of beams and the direction of each beam are determined by the spot pattern produced by the SLM. Multilateration achieves best results when targets are arranged within a large angular range, so the optical system ideally requires a FoV of ± 45˚.

Figure 6: Optical set up used to project multiple SLM spot patterns to targets. The FSI beams are emitted through the 3.5-mm focal length lens at the bottom of the image.

FSI measurements are made by directing nearly collimated beams towards targets. The required spot patterns must be converted into phase distortion maps for the LCOS, as seen in figure 7. This is achieved using the iterative Gerchberg-Saxton (GS) algorithm[21]. The algorithm relies on the fact that if the required spot pattern is known, then the phase distribution required at the source to produce that spot pattern at the image can be obtained through the Fourier transform. By iterating between the source and image plane, a convergent solution to the required phase pattern can be found.

Figure 7: The beam profile incident upon the SLM is used along with the required spot pattern to generate the phase pattern required by the SLM. Click here for larger image.

A downside to this technique is that it requires an initial estimate of the target locations before being able to determine the required spot pattern. A possible solution to this could be to perform a raster scan of the FoV (using the SLM to raster the beam) to locate targets. In practice this is a lengthy operation (on the order of tens of seconds) and not an optimum solution. For this reason a stereo vision system was developed to provide initial estimates of target locations.

Stereo vision to guide beam steering
To estimate a coarse location of the targets to within less than 1 cm in 3D space, a stereo vision system has been incorporated into the sensor. Two cameras are used to estimate the X, Y, and Z positions of each target in the sensor’s coordinate system. The cameras used for the initial proof of concept experiment were borrowed from another project. They have a FoV of approximately 40° and use through-the-lens laser illumination at 635 nm to provide high-contrast images of the retroreflecting spheres.

The two cameras are situated either side of the SLM with slight angular inclination to each other to provide a stereo perspective (see two sample stereo pair images in figure 8). The cameras were calibrated using stereo calibration software in LabVIEW and a calibration grid of known dimensions. Various grid orientations and inclinations were required to achieve accurate depth estimates. The stereo calibration information is used to rectify the images and custom target detection software determines the central pixel values of the targets. These values, combined with the calibrated focal length and stereo baseline of the system, allow the target coordinates (Xi, Yi, Zi) of the ith target to be calculated.

The target coordinates were transformed into SLM (xi, yi) spot pattern coordinates using direct linear transformation (DLT)[22]. This method is ideal as it can determine the orientation of the SLM image plane without the need for approximate initial SLM orientation parameters.

(Equation 5)

(Equation 6)

The transformation equation of the DLT is given by equations (5) and (6), where L1-11 are calibration parameters and 1 ≤ iN, where N is the number of targets. Equations (5) and (6) can be re-arranged to give:

(Equation 7)

(Equation 8)

If six or more reference points are known (N ≥ 6), equations (7) and (8) can be solved.

To calibrate the vision system, target locations (Xi, Yi, Zi) were estimated with the stereo system, while SLM beams were traced onto the targets using a photosensitive infrared (IR) viewing card. The optimum SLM (xi, yi) values were then found by measuring the FSI target peak amplitudes and adjusting the (xi, yi) values until the greatest amplitudes were found. The process was repeated for six targets, allowing initial calculation of the DLT parameters. These parameter estimates were then improved as more targets were found.

Figure 8 shows example stereo images of our laboratory with a number of targets highlighted. The stereo vision system potentially allows tracking of multiple targets at video frame rates.

Figure 8: Stereo vision system detecting eight targets (green-numbered red circles) distributed across the laboratory at distances ranging between 4.5 m and 6.8 m.

Employing a stereo vision system also provides other benefits. When multiple FSI sensors are used to measure multiple targets simultaneously, the stereo vision system will help solve the correspondence problem, i.e., which sensor-target distance corresponds to the same target distance measured by another sensor. Furthermore, it is possible that targets off-axis from the SLM exhibit some form of length-measurement distortion. Knowledge of target angular location from the SLM image plane will allow these systematic effects to be adjusted for in the multilateration solution.


The key parameters of interest when testing the new sensor are the distance range over which it can successfully detect targets and measure their range, and the angle of the field of view. We have performed initial tests of both these parameters.

Absolute range tests
Due to line-of-sight limitations in the current laboratory setup, the maximum distance achievable during testing was ~7 m. Ten targets were distributed across the laboratory, as seen in figure 8. Spheres of 10-mm and 16-mm diameter were used in the measurements. When using the old divergent-beam FSI system, a common signal-to-noise (SNR) value over a range of 0.3 m to 1 m for 16-mm diameter spheres was of the order 102 to 5 × 102. Using the SLM-based FSI system, typical SNR values of 105 to 106 were achieved at distances of up to 6.69 m. As the SNR does not appear to drop off significantly with distance, we are confident that range measurements at distances greater than 10 m are achievable.

Angular range tests
The FoV of the SLM system is determined by the focal length of the objective lens. We have experimented with two different focal lengths: 3.5 mm and 6.5 mm. Using the 3.5-mm lens we have achieved a FoV of ± 55° and successfully measured the distance to targets in excess of 45° off axis. Figure 9 shows the signals obtained from seven targets obtained simultaneously with ranges between 1 m and 2.5 m and off-axis angles up to > 45°.

Figure 9: Seven targets measured between 1 m and 2.5 m. The maximum angular range achieved was > 45˚ off-axis.

Figure 10: Target FSI peak at > 45˚ off-axis from the SLM.

Figure 10 shows a detailed view of the data obtained around one of the peaks shown in figure 9 corresponding to a target that was 45° off axis. The individual data points (plot 0) follow a clear sinc profile as expected indicated by the good fit of the data to a sinc function (plot 2). The x-axis in figure 10 corresponds to distance. The location of the peak, indicated by the red line, shows that this target was at a distance of 1.227525 m from the sensor.

Conclusions and future work

Simultaneous range measurement to multiple targets from multiple sensors with interferometric accuracy and a built-in quantum scale reference (gas-cell) offers the tantalizing prospect of a high-accuracy, self-calibrating coordinate measurement system with inherent traceability to the SI. Realization of such a system could provide a step change in reliability and end-user confidence in applications requiring high accuracy and flexibility, and open up new possibilities for metrology-assisted machining and assembly or machine tool calibration. The National Physical Laboratory has been developing a system based on a combination of FSI and multilateration to explore these possibilities. In this article, we have described a prototype sensor that greatly extends the operating volume of our previous design and opens up the possibility of realizing a coordinate measurement capability over a volume of > 5 m x 5 m x 5 m. However, further development is required.

The next steps include the following:
• Improvements to the optical system beyond the current proof-of-principle setup, to allow the FSI and vision system to share the same optical axis. This will allow a single camera to be used in place of the current stereo system, thus simplifying and shrinking the sensor design and reducing the cost.
• Improvements to the data-processing algorithms and software to increase processing speed to facilitate real-time tracking of targets.
• Production of at least four of the new sensor heads and testing of the multi-sensor system.


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About The Authors

Mike Campbell’s picture

Mike Campbell

Michael Campbell is a higher research scientist at the National Physical Laboratory (NPL), the United Kingdom’s national measurement institute. Since joining NPL, Campbell has been undertaking research in large volume metrology, focusing on the design and implementation of frequency scanning interferometry to measure 3D coordinates.

Ben Hughes’s picture

Ben Hughes

Ben Hughes is a principal research scientist at the National Physical Laboratory (NPL), the United Kingdom’s national measurement institute. He worked in NPL’s dimensional metrology group more than 27 years ago on the development of instrumentation for high-accuracy, traceable instruments and measurement techniques for dimensional and coordinate measurement. Hughes currently leads NPL’s research activities in large-volume coordinate metrology. Hughes is chair of the European Portable Metrology Conference, author of more than 25 metrology papers, and holds several patents.

Dan Veal’s picture

Dan Veal

Dan Veal is a senior research scientist at the National Physical Laboratory (NPL), the United Kingdom’s national measurement institute. Veal’s research interests include photogrammetry (where he holds a patent), laser trackers, large volume metrology, and applying dimensional metrology to other challenging projects. He leads the micro-vibration measurement area of NPL, which applies interferometry to the tracking of assemblies in real time in six degrees of freedom for ground-based satellite testing facilities.