6DOF Electromagnetic Tracker Construction HOWTO
A basic 6DOF (six degrees of freedom) electromagnetic tracker contains the following parts:
- Transmitter contains three colocated orthogonal coils.
- Receiver contains three colocated orthogonal coils.
- Driver electronics provides three sinewaves at distinct frequencies through three series-tuning capacitors to the three transmitter coils.
- Operating frequencies are typically 30 Hz to 15000 Hz. 1000 Hz, 1300 Hz, and 1600 Hz are a good starting point. Higher frequencies give higher induced voltages, lower frequencies reduce error-causing eddy-current effects.
- Data-acquisition electronics measures the currents in the three transmitter coils, and measures the voltages induced in the three receiver coils. The voltage preamps should have 2 nV/sqrt(Hz) or lower input noise. The ADC sampling rate must be high enough to capture the driver frequencies.
- A six-ADC electronics can measure all the currents and voltages continually and simultaneously.
- A four-ADC electronics can use one channel to measure the three currents periodically over time (The currents change slowly as the transmitter coils warm up.), and three channels to measure the three voltages continually and simultaneously.
- A single-ADC electronics can measure the currents and voltages sequentially, but this gives poor dynamic performance due to inconsistent data sets.
- The receiver coil voltages must be measured simultaneously if dynamic accuracy is needed. Sequential voltage measurements give inconsistent data sets, which are hard to interpolate between. This is analogous to the interlace artifacts seen in digital television.
- If the measurements are inconsistent, the algorithm will make errors in both position and orientation, attempting to minimize the total error.
- Signal-processing software converts the current and voltage measurements into measurements of the HFluxPerI coupling from each transmitter coil to each receiver coil. This gives a 3x3 matrix HFluxPerIMeasured.
- C. L. Dolph, "A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level," Proc. IRE, Vol. 35, pp. 335-348, June, 1946. The original Dolph-Chebyshev window article. This window is capable of 140 dB rejection of out-of-band signals.
- Each component of HFLuxPerIMeasured is the H flux through one receiver coil, divided by the current I in one transmitter coil. HFLuxPerIMeasured has units of meters, and is a geometrical property of the coils' sizes, shapes, number of turns, positions, and orientations.
- Algorithm software converts HFluxPerIMeasured to estimated receiver position and orientation, using direct-solution algorithm in Raab's 1981 paper.
- Frederick H. Raab, "Quasi-Static Magnetic-Field Technique for Determining Position and Orientation", IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-19, No. 4, October 1981, pages 235-243.
- File:Dry0097.c is a simulator program containing an implementation of Raab's algorithm. The straight-line-segment models require triple-precision floating-point calculation at large distances.
Much elaboration and extension is needed to give high accuracy with high convenience, but the above is the basic idea.
For example, U.S. Patent 4,109,199 describes the use of a calibration coil in the receiver to continually calibrate the gains of the electronics.
More elaborate algorithms provide higher accuracy at the expense of much more computation. See U.S. Patents 5,307,072 and 7,096,148 and 7,835,779 for examples.
Straight-line-segment models are very accurate for rectangular and square coils, but require better-than-double-precision floating-point accuracy. X86 double precision is actually better than double precision, using 80 bits for internal calculations. The physically-accurate analytical equations suffer from numeric problem: small difference of large terms.
Better than 1 millimeter P95 accuracy is achievable, as reported in Nafis etal 2006 paper:
- C.A. Nafis, V. Jensen, L. Beauregard, P.T. Anderson, "Method for estimating dynamic EM tracking accuracy of Surgical Navigation tools", SPIE Medical Imaging Proceedings, 2006, preprint can be found [here].
Pete reported a 6DOF tracker using four-coil transmitter and four-coil receiver in his Ph.D. dissertation. Transmitter and receiver were each built from four triangular printed-circuit boards assembled into a tetrahedron. Each board contained a single triangular coil made of straight-line segments:
