3D Shape Sensing of Elongated Objects Using Fibre Bragg Gratings

  • Karsten Hoehn
  • Andrew Olsson


Navigating in GPS deprived areas can be a challenging task, especially when the environment doesn’t offer sufficient visual clues for stereo camera matching. This paper describes the development of a 3D shape sensor based on optical fibres and the resulting “Sensor Wand”. The intension was to develop a Wand that could be easily deployed in small holes like drill holes for mining or geo-technical applications and determine their 3D shape, which is a vital information for Drill and Blast Engineers in mining, or a geo-technical assessment in civil applications. Initially the expected response of the Wand was modelled for a number of configurations. A Wand was then manufactured to verify the simulated results. The mechanical manufacturing proved itself to be significantly more complex than originally anticipated. As a result, the sensor accuracy was below expectation. Improvements to the manufacturing process were identified to increase the performance of the next generation of the Sensor Wand.


3D shape sensing Fibre optic sensing Fibre bragg grating FBG 

1 Introduction

Meaningful navigation requires the knowledge of the current location and pose. In many applications this information can be derived from Global Positioning Systems, Inertial Navigation Units, (stereo) cameras, or a combination of these systems. However, there are applications where it is neither practical nor even possible to utilise these traditional localisation systems. Such examples include medical, underwater and downhole sensing in the oil, gas and mining industries.

The Commonwealth Scientific and Industrial Research Organisation (CSIRO) through its Minerals Resources Business Unit developed a 3D shape sensor based on Fibre Bragg Gratings (FBGs) embedded in optical fibres that can be used in these challenging environments.

2 Sensing Concept

An FBG is a wavelength selective reflector, with the nominal reflected wavelength depending on the grating constant. Additionally, the reflected wavelength is subject to external influences like temperature and strain as they alter the grating constant. An FBG can therefore be looked at as an optical strain gauge. We have incorporated a number of these FBG sensors a deflection sensor wand. Based on the knowledge of the various strains along the length of the wand the 3D shape of the sensor wand can be reconstructed in real-time (Fig. 1).
Fig. 1

Principle of “triangulation” and “deflection”

There are some commercial and pre-commercial systems available to measure the 3D shape using fibre optics, such as
  • the Luna Fibre Optic Shape Sensor [1], which has an extremely high spatial resolution as it uses Rayleigh backscatter to determine the strain along the length of the sensor. Because of this sensing principle it has a limited sensor length of 1.5 m and is very expensive; and

  • the Fraunhofer Fibre Optical 3D Shape Sensor (FibreNavi) [2], which requires a highly sophisticated optical setup to burn the FBGs into the fibre.

The CSIRO design uses a simple configuration utilising four optical fibres with FBGs embedded in a linear arrangement. These fibres are available off the shelf and then were embedded in a glass-fibre composite tube.

3 Simulations

3.1 Static Model and Simulations

An initial static model was set up to investigate the sensor performance. It is capable of computing a straight, an arced, or a sinusoidal sensor layout, both in the x and y plane (the depth is given by the z value). Additional measurement noise can be added in the form of normal distributed random error with a configurable standard deviation. An example calculation with blue for the theoretical curve and red for the reconstructed path using 1 pm signal noise is shown on Fig. 2. The plot on the right shows the error versus measurement length or depth.
Fig. 2

Simulated shape reconstruction for an arced (R = 100 m) Sensor Wand, which is also buckled into a helix (pitch = 8 m), with 0.5 m spacing between stages and 1 pm normally distributed measurement error

This figure shows that the reconstruction fits very well initially, but drifts at the “turning points”. The reconstruction algorithm assumes a constant curvature between sample points, however, this is not a valid assumption for a sinusoidal or helical path.

The same calculation can be performed with a spacing of 0.1 m between the stages and the results are shown in Fig. 3. This finer spacing reduced the total error at the end of the path by 20%.
Fig. 3

Simulated shape reconstruction for an arced (R = 100 m) sensor wand, which is also buckled into a helix (pitch = 8 m), with 0.1 m spacing between stages and 1 pm normally distributed measurement error

3.2 Dynamic Model and Simulations

It is worth noting that the above simulations use a static model that can be seen as a “snapshot”. In reality the sensor will progress into the hole and so it is possible to measure the defection at a given depth multiple times, which will reduce all random and not systematic errors. Therefore a dynamic model was developed to simulate the progression of the Sensor Wand through the hole and compare the new readings with the old measurements. Averaging of the repeated deflection angle measurements was used to combine the consecutive readings.

A series of images generated by a simulation of a shorter wand going through a deeper hole is shown in Fig. 4. These graphs show the theoretical path section in blue, the reconstructed sample points as crosses and the fitted path as a dotted, red line. The Deflection Sensor length used in this computation is 2 m, the hole depth is 20 m and no signal noise was added. Longer sensor configurations can be computed, and the dimension are only reduced for illustration purposes.
Fig. 4

Progression of the sensor wand through a deeper hole

The Sensor Wand measures deflection, which is a relative parameter, therefore the algorithm needs a start point and direction for the absolute 3D shape determination. These values can be assumed to be known at the beginning of the hole. Once fully submerged the algorithm uses its previous estimated path to determine these values.

3.3 Initial Discussion

The Sensor Wand model is designed to simulate the result one would get by inserting the wand into a hole. It computes the reconstructed 3D shape of the hole and the deviation of the theoretical path as a function of the following input parameters:
  • Depth of hole

  • Theoretical or design hole shape

  • Measurement interval

  • Measurement noise

  • Distance between FBG stages

  • Number of FBGs per stage

  • Sensor geometry

  • Interrogator resolution

The model has been used with various input parameters to identify the influence of particular parameters and their error contribution. We observe that when the interrogator resolution is reduced the error will grow, and that once it reaches 100 pm, the interrogator resolution becomes the dominant error contribution factor. Reducing the Sensor Wand length also increases the error. Reducing the distance between the FBG stages on the other hand reduces the error as demonstrated in Figs. 2 and 3. If the interrogator resolution is increased again to a value of 1 pm, which is achievable with state-of-the-art interrogator systems, the resulting error returns back to the original size of around 5–6 cm.

The heavy oversampling, which happens when a point in the hole is measured again by a consecutive FBG stage, is responsible for the good performance even for a short Sensor Wand.

Unfortunately the fabricated Sensor Wand, which was constructed during this project showed a number of imperfections. Therefore it was not possible to verify the simulated data with the measurements. However, the measurement results show qualitatively the expected behaviour.

4 Sensor Wand Performance

4.1 Testing

The Sensor Wand was manufactured and tested on a surveyed rail track at the Queensland Centre for Advanced Technologies. Some images from our field-test studies are shown in Fig. 5. The image on the right shows the calibration jig, which is used to calibrate the “zero-strain” wavelength values of the non-deflected FBGs. Furthermore, the jig contains an encoder wheel to determine the penetration depth of the Sensor Wand. The testing was conducted on different sections of the track with curvatures between 30 and 200 m radius. Additionally, the sensor was tested on a straight section of the track.
Fig. 5

Sensor wand testing on surveyed track

4.2 Algorithm

The wavelength and peak level values for each FBG were recorded during the testing and stored in a hierarchical data format grouped by penetration depth. A recording of 18.5 m depth in 25 cm steps resulted in a data file containing roughly 2.5 million values. The data processing was conducted in Matlab. The first task after reading in the data was to apply a filter to remove double peaks and outliers.

Furthermore, the filter verifies that the peaks are within the expected wavelength range. Values which differ by more than ±1 nm from the factory calibration, corresponding to roughly 0.5 mƐ, are tagged to be ignored during processing. Reasons for incorrect wavelength values could be glitches in the interrogator, resulting in some peaks not being recorded, or temporary “over-stretching” of some FBGs during manual handling.

The next step is the data pre-processing. During this step the algorithm searches for the FBGs that are already in the hole and computes the mean values from the recorded data sets. At the same time, the on-the-fly calibration values are generated for the FBGs currently in the calibration jig.

Finally, the deflection algorithm uses the mean FBG wavelength and the calibration values to compute the 3D shape, which accumulates up as the Sensor Wand progresses deeper into the hole.

4.3 Initial Results

The 3D reconstruction of a straight track section from a manually recorded data set is shown in Fig. 6. Obviously the reconstructed path is not straight and shows a significant deflection in the “y” direction.
Fig. 6

3D reconstruction of test 3 (straight section, manual recording)

To investigate the reason for the deflection of the reconstructed path, the calibration values and the final wavelength values for the fully penetrated Sensor Wand were compared. Theoretically, both values should be equal as no deflection force is applied during the on-the-fly calibration, and when fully submerged in the hole.

The wavelength difference between the straight Sensor Wand and the calibration values are plotted in Fig. 7. The results vary substantially from zero, indicating that the Sensor Wand is NOT force free when laid out straight. The 3D reconstruction of the above data set was repeated, but instead of the “on-the-fly” calibration, the “forced-straight” values were used to in the deflection algorithm. To avoid a circular reference, the forced-straight values from a repeated measurement series were taken. The result of this reconstruction is shows in Fig. 8, an almost perfect straight line at the beginning with a slight curve at the top. The maximum deflection, or error in this case is less than 6 cm over 18.5 m.
Fig. 7

Comparison between the straight and the calibration wavelength

Fig. 8

3D reconstruction of test 3 (straight section, manual recording) using the forced-straight calibration

The forced-straight calibration can also be applied to the other recordings. The reconstruction of a bent track part is shown in Fig. 9. This figure shows a good correlation in the y plane, however the reconstructed shape still deviates significantly in “x”. This deviation may be affected by the fibre misalignment issues which occurred during the manufacturing as the FBGs were not aligned radially, two of the four fibres had a constant offset, and the entire Sensor Wand contained a twist. Additionally, the FBGs were not aligned longitudinally, but showed an offset of several millimetres. Therefore the algorithmic assumption that all FBGs are within one cross-section plane was not fulfilled. Consequently we enhanced the reconstruction model to correct for the misalignment.
Fig. 9

3D reconstruction of a bend track section using the forced-straight calibration

The enhanced model can be used to reconstruct the test data from Fig. 9. The result is shown in Fig. 10. The resulting error is reduced significantly, however, still not to expectations. The enhancement uses only a first order approximation of the misalignment and future Sensor Wands will need to be better characterised to determine these misalignments better, in case they can’t be avoided during production.
Fig. 10

3D reconstruction of test in Fig. 9 using the enhanced model

5 Discussion

All results were heavily influenced by the fibre misalignment and this artefact dominates the plots. Given the limitations of the constructed Sensor Wand these results are very promising nevertheless. The algorithms developed as part of this project managed to reconstruct the 3D shape of the Sensor Wand and reduced some of the errors introduced by the artefacts in the wand. However, the measurement accuracy did not meet the expectations from the simulations due to the wand artefacts.

Future Deflection Sensor Wand developments should take potential residual stresses in the composite material into account; and if possible, optimise the design to reduce these stresses. Furthermore, it is important to characterise the actual location of the FBG along the tube so that the compensation algorithm can use the correct position offsets rather than a first order estimate.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CSIRO Mineral Resources Business UnitQueensland Centre for Advanced TechnologiesPullenvaleAustralia

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