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Freedom251 › Blog › field mapping

How to Measure and Verify a Magnetically Sculpted Field

By Freedom251 Team · · 12 min read

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To verify a magnetically sculpted field, turn the intended shape into a measured vector field: define the coordinate system, volume, operating condition and tolerances; use a calibrated probe whose range and geometry fit the field; scan a planned grid or path; record position, orientation and background; then compare measured components with the target map and report uncertainty. A single gaussmeter reading can confirm a local value, but it cannot prove a three-dimensional field shape.

What “sculpted field” means in a measurement plan

A sculpted magnetic field is deliberately nonuniform. Its useful description is not “the magnet is strong here,” but a field value assigned to every relevant location and operating state. Before taking a reading, decide whether the target is magnetic flux density B (tesla or gauss), magnetic field strength H (ampere per metre), or a derived quantity such as a gradient, force or direction. Do not mix B and H in the same acceptance calculation.

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Define the spatial target

Write down the coordinate origin, the positive x, y and z directions, and the volume or surface to be verified. Specify the component that matters: for example, Bz on a plane, the full vector (Bx, By, Bz) throughout a gap, or the field magnitude along a trajectory. If a simulation supplied the design, preserve its coordinate convention and sampling locations so measured and calculated values can be compared at matching points.

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Also state whether the target is static or time-varying, and define the intended condition: coil current, magnet position, temperature, duty cycle, nearby ferromagnetic parts and any mechanical load. A field map without those conditions is not reproducible.

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Set tolerances before measuring

An acceptance rule might limit the absolute error in each component, the magnitude error, the angular error, or a gradient error. State the rule mathematically and identify the region where it applies. For example, a design may allow a component residual of no more than 2 percent at every grid point, while permitting a larger error outside the working volume. The tolerance must be wider than the combined measurement uncertainty if a pass/fail result is to be meaningful.

Why one reading cannot verify a three-dimensional shape

A peak reading tells you only the field at one probe location and orientation. It does not reveal where the field changes sign, how rapidly it varies, whether transverse components are present, or whether the peak moved from its designed position. Probe stand-off and active-area size can also average a small feature and make a local maximum appear lower.

Verification therefore requires a planned set of points, a line scan, a surface map or a volume grid. The sampling must resolve the smallest feature that matters. There is no universal spacing: a millimetre-scale gradient needs a much denser grid than a field that changes over tens of centimetres.

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Choose a sensor that matches the field

Selection depends on field strength, directionality, feature size, stand-off, bandwidth, temperature and the uncertainty you can tolerate. Confirm the current calibration status and the complete probe specification rather than relying on a meter’s headline range.

Measurement need Practical sensor category What it provides Important limitations to check
Local DC field strength at accessible points Hall-effect gaussmeter Pointwise field value, usually with a specified probe orientation Range, accuracy, active area, tangential or axial geometry, stand-off, temperature coefficient and calibration traceability
Weak field or full vector components Three-axis fluxgate magnetometer Components along three sensor axes, useful when direction and low fields matter Offset drift, crossfield error, axis sensitivity, orthogonality, noise, bandwidth and usable field range
Fast-changing field AC-capable calibrated probe or another bandwidth-matched sensor Time-dependent amplitude, waveform or phase when supported AC/DC mode, bandwidth, RMS versus peak behavior, sensor response and synchronization
Very strong, very weak or unusually fine features Specialist calibrated instrument or facility Measurement within a regime selected for the application Do not extrapolate beyond the specified range; verify probe loading and spatial resolution

Hall-effect gaussmeters

A Hall probe is a practical choice for local field mapping. As one concrete example, the Magnaflux Bell 5170 datasheet lists a tangential probe, a 0–200 G (0–20 mT) range, selectable Gauss, tesla and A/m units, and ±3 percent accuracy. Those figures describe that particular model and datasheet, not a universal performance level. Check availability, calibration date, range selection and whether its tangential geometry matches the component you intend to measure.

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Probe geometry is as important as the meter. Find the active sensing area and the distance from the probe tip to that area. A probe that is large compared with the field feature spatially averages it; a long tip can place the sensitive element farther from the intended coordinate than the fixture indicates. Record the orientation convention supplied by the manufacturer and use it consistently.

Three-axis fluxgates

A three-axis fluxgate is appropriate when the vector direction or weak-field behavior is important and the field lies within the instrument’s usable regime. The National Physical Laboratory’s guidance discusses offset drift and crossfield error. Each axis may require sensitivity and orthogonality calibration, and the three outputs may need correction before they are treated as an orthogonal vector.

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Do not assume that three displayed numbers are an accurate vector. Check the sensor’s axis alignment, zero stability, cross-axis response and temperature behavior. NPL also describes calibrated Helmholtz-coil systems for generating known fields during instrument gain calibration; such a calibration can establish response without relying on an unknown permanent magnet.

When to use a specialist method

If the field is far outside a probe’s range, contains features smaller than the probe’s active area, or requires formal material-property characterization, use a method designed for that regime. A sensor operated beyond specification can saturate, drift or silently report a plausible but wrong value. Choose another calibrated method rather than extrapolating.

Control the coordinate frame and environment

Use a repeatable fixture

Fix the magnet or assembly and the probe in a documented, nonmagnetic coordinate frame. A rigid fixture is preferable to hand placement when tolerances are tight. Define a datum, mark the scan axes, and control the probe’s stand-off with a spacer or stage. Record whether the probe is tangential, axial or otherwise oriented at every point.

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Control nearby influences

Remove ferromagnetic tools, fasteners and temporary supports from the measurement volume. Identify current-carrying cables, motors and switching equipment that can add a field. If an item cannot be removed, record its position and operating state and include it in the test configuration. A small change in a steel fixture can alter a deliberately shaped field enough to look like a design error.

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Measure the background

With the device under test in the same mechanical arrangement, take a background reading with the source disabled when that is safe and physically representative. Keep the meter orientation unchanged. For a time-varying environment, record the background over the same time window or phase condition. State whether the reported map is raw, background-subtracted or corrected by a model; never subtract an unmeasured or differently oriented background by assumption.

Step-by-step field-mapping procedure

  1. Write the target specification. Name B or H, units, coordinate origin and axes, mapped volume or surface, operating state, relevant component(s), sampling locations and pass/fail tolerances. Preserve the design map’s coordinate and unit conventions.
  2. Confirm the instrument. Record manufacturer and model, probe or sensor serial number, calibration certificate and date, selected range, units, mode, resolution, bandwidth and temperature conditions. Verify that the expected field stays inside the specified range.
  3. Build and document the fixture. Establish the datum and probe orientation, set the stand-off, and use nonmagnetic hardware where possible. Photograph or draw the setup if another operator must reproduce it.
  4. Stabilize the operating condition. Set coil current, magnet position, temperature and duty cycle. Wait for the defined settling time. If the field changes with time, record timestamps or phase so readings can be aligned.
  5. Measure the background. With the source disabled or in the defined reference state, collect readings at representative points and orientations. Keep the same range and meter orientation used for the active scan.
  6. Scan the planned points. Move through the grid, line or surface in a known order. At each point record x, y, z, probe orientation, reading, units, instrument state, operating condition and any anomaly. Do not replace the planned scan with a search for the maximum.
  7. Repeat check points. Revisit selected points, including a low, high and central value, after part of the scan or at the end. The spread estimates repeatability and can reveal fixture movement, drift or operator errors.
  8. Apply declared corrections. Subtract or otherwise correct for background only according to the documented method. Apply axis, offset, temperature or calibration corrections supplied for the instrument, and retain the raw data.
  9. Compare with the target. Interpolate only when the method is stated. Compare measured and intended components at matching coordinates, calculate residuals and uncertainty, and evaluate the predeclared tolerance.

Design the grid or path intelligently

Start from the smallest field feature that must be verified: a pole edge, null, narrow peak, gradient transition or working gap. Use enough points across that feature to show its shape rather than merely touching its endpoints. Add denser sampling where the design changes rapidly and wider spacing in smooth regions. A line scan can validate a one-dimensional requirement, but it cannot establish behavior away from that line.

For a volume map, document the number of planes, points per plane and spacing in each direction. For a surface map, state the surface height and normal direction. If access forces an irregular path, record the actual coordinates rather than treating nominal stage positions as measurements.

Compare measurements with the intended field

Use component-wise residuals

At each coordinate, calculate a residual such as rx = Bx,meas − Bx,target, and similarly for the other components. Report the residual map, not only a maximum value. Where useful, also report magnitude and direction: |B| and the angle between measured and target vectors. A magnitude match can hide a direction error, while a component residual can expose a cancellation that magnitude conceals.

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State how any interpolation, smoothing or filtering was performed. Filtering can make a map look cleaner while removing a real feature; retain an unfiltered view for acceptance decisions unless the specification explicitly permits processing.

Quantify uncertainty

Include instrument accuracy or calibration uncertainty, repeatability, positioning error, stand-off error, background variation, temperature effects and any correction uncertainty that materially affects the result. Report the uncertainty convention, such as a stated coverage factor, and keep it attached to the result. If the tolerance is close to the uncertainty band, classify the outcome as indeterminate or require a better measurement rather than calling a marginal pass.

Check coordinate and polarity errors first

A disagreement can originate in the magnetic assembly, the ambient field, probe calibration, probe stand-off, fixture movement, polarity convention or a mismatch between simulation and measurement coordinates. Before redesigning the magnet, verify the origin, axis handedness, sign convention, units and sensor orientation. Re-measure a reference point after correcting each suspected setup error.

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Dynamic, thermal and repeatability effects

For a changing field, define whether the target is instantaneous, averaged, RMS, peak or phase-resolved. Confirm that the meter’s AC/DC mode and peak or RMS behavior match that definition. A slowly updated display may miss a transient even when its nominal range is adequate. Synchronize the scan with the drive waveform when phase matters, or record time series at representative points.

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Record temperature of the magnet, sensor and relevant electronics when they can drift. Repeat a subset of points after warm-up and after the scan. If current, position or temperature is part of the operating state, include its measured value with every map or with a clearly defined run-level record.

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What large-system validation teaches

The CMS detector field-map validation described measurements from a dedicated field-mapping machine, 22 flux loops and 82 three-dimensional Hall sensors installed on return-yoke blocks, followed by comparison with a three-dimensional model. The lesson is independent measurement and model comparison at the scale of the system, not a required sensor count for a small magnet. A small assembly can use far fewer points, but it still needs a documented coordinate frame, independent measurements and an explicit comparison.

Do not confuse field mapping with magnet-material characterization

Mapping asks, “What field exists at these locations in this assembly and operating state?” Material characterization asks about intrinsic or specified properties of a permanent-magnet material, often with demagnetizing corrections and a different magnetic circuit. IEC TR 63304:2021 addresses DC magnetic properties of permanent magnet materials in an open magnetic circuit using a superconducting magnet, including self-demagnetizing corrections. That technical report is not an everyday procedure for checking the field shape around a finished assembly.

Instrument and method comparison criteria

When evaluating more than one candidate instrument, compare the following items against the target tolerance and smallest feature:

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  • Usable field range and overload behavior.
  • Accuracy, resolution, noise and calibration traceability.
  • One-axis output versus true three-axis vector output.
  • Active-area dimensions, probe geometry and minimum stand-off.
  • DC and AC bandwidth, including peak, average and RMS definitions.
  • Temperature coefficient and zero or offset drift.
  • Cross-axis error, sensitivity matching and axis orthogonality.
  • Ease of positioning and repeatability of the fixture.
  • Potential disturbance or spatial averaging caused by the probe.

IEEE’s P3599 project page identifies planar-Hall sensor characterization measures including sensitivity, linearity, full-scale range, hysteresis, temperature dependence, offset, noise, bandwidth and dynamic range. The page listed the project as an Active PAR and gave PAR approval as 2025-06-19; it is not a published final standard. Use those categories as questions for a datasheet or calibration report, not as evidence that every sensor meets a common limit.

Common failure modes and fixes

Symptom Likely cause Corrective action
Peak value changes when the operator moves the probe slightly Uncontrolled position, angle or stand-off Use a rigid nonmagnetic fixture, mark the datum and record the active-element location.
Map looks smoother and weaker than the simulation near an edge Probe active area or stand-off averages a fine feature Use a smaller suitable probe or reduce stand-off; verify the sensor’s sensitive-element geometry.
Three-axis vectors rotate between repeated runs Axis misalignment, offset drift or crossfield error Check zero and orientation, apply the instrument’s axis corrections and repeat after thermal stabilization.
All points have a similar offset Ambient field, zero error or polarity convention Measure background in the same orientation, verify calibration and check sign and axis definitions.
Only the highest readings are recorded Maximum-search substituted for a planned map Return to the defined grid or path and retain every coordinate and component.
Results differ when current or temperature changes Operating condition was not controlled or documented Record current, temperature and time; specify the condition and repeat after stabilization.
Instrument display appears normal but the field is outside the expected regime Range exceeded, saturation or unsupported extrapolation Stop using that result and select a calibrated method with an appropriate range.

What to put in the verification record

A defensible report lets another operator reproduce the map and understand its limits. Include:

  • Target definition: B or H, units, coordinate frame, mapped region, operating state and tolerances.
  • Assembly identity and configuration, including current, temperature and nearby magnetic or electrical items.
  • Instrument and probe identities, calibration information, range, mode, bandwidth and corrections.
  • Fixture drawing or description, probe active-element position, orientation and stand-off.
  • Background procedure and raw background readings.
  • Complete point data with coordinates, components, timestamps and anomalies.
  • Repeat measurements and the method used to estimate repeatability.
  • Plots or tables of measured components, target values, residuals and uncertainty.
  • A pass, fail or indeterminate decision for each stated criterion, with the criterion shown beside the result.

The National Physical Laboratory’s best-practice guide is practical guidance for generating and measuring DC magnetic fields in its stated 1 nT to 1 mT range. That range belongs to the guide’s scope and is not a claim that one instrument covers it all. Use the guidance as context, then select equipment and acceptance limits for your actual field.

A concise decision checklist

  • Is the target a defined map of B, H or a derived quantity?
  • Are origin, axes, volume, sampling locations and operating conditions written down?
  • Does the sensor cover the expected range and resolve the smallest feature?
  • Are probe orientation, active-element position and stand-off repeatable?
  • Was background measured in the same setup and orientation?
  • Were all planned points, not just peaks, recorded with units and timestamps?
  • Were repeatability and relevant uncertainty sources estimated?
  • Were measured components compared with the target at matching coordinates?
  • Are residuals and tolerances reported without hiding coordinate or polarity errors?
  • Is the conclusion limited to the mapped region and operating condition?

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