Troubleshooting TOFD Cursor Curves and Scan Geometry

A curve that looks parabolic may be a beam-envelope cursor or a point-diffractor time trace; those are different quantities and require different parameter sets. Identify which one the instrument displays before changing probe spacing, focal laws, or cursor settings.

Identify what the cursor represents

Start by locating the curve relative to the live A-scan or encoded data. A software cursor, beam-envelope overlay, and measured indication can occupy similar areas on a screen, but only the last represents an acquired ultrasonic response. A geometric beam cursor describes a selected beam boundary; a TOFD tip indication plots arrival time against scan position.

Use this decision path:

1. Check whether the curve moves or changes when you move the measurement cursor, change its display mode, or select another software overlay. If so, it is a display aid, not a flaw response.
2. Check whether the curve is tied to an acquired amplitude response in the encoded scan. If it follows a repeatable signal as the probe pair moves, analyze it as a possible ultrasonic indication.
3. Compare it with the lateral wave, backwall response, and known reference reflectors. Their travel-time patterns help distinguish an indication from a beam display.

The word “cursor” is not enough to determine the correct model. Instrument cursor terminology varies, so use the trace’s relationship to the acquired signal and scan axes as the deciding evidence. Check: record whether the plotted item is an overlay, beam boundary, or acquired response before proceeding.

Establish probe geometry and scan coordinates

Lock down the coordinate system before interpreting curvature. In a conventional TOFD arrangement, a transmitter and receiver sit on opposite sides of the inspection zone. The scan moves the pair along the weld while the instrument records signal time against position. A point diffractor at depth therefore sees changing source-to-tip and tip-to-receiver path lengths as the pair passes it.

Record the acoustic geometry, not just the outside dimensions of a probe holder. For each probe, identify the relevant wedge exit point or modeled beam origin, the pair separation, the scan direction, and the scan datum. Record whether a reported separation is measured between probe centers, element centers, or wedge exit points; those are not interchangeable in a ray-path calculation.

• Set the scan-position zero at a documented feature, such as the weld centerline or a reference reflector.
• Measure the transmitter-to-receiver spacing using the points that the instrument’s acoustic model uses.
• Record the assumed refracted path, material sound velocity, wedge path, and time zero from the actual setup or calibration.

For phased-array wedges, the selected focal law determines the active elements and beam direction. Use the actual law and calibrated path model rather than inferring the sound path from the wedge’s appearance. Snell’s law relates incidence and refraction through the wave velocities; a desired refracted angle depends on the wedge and test material. Check: verify that a known reflector appears at the expected scan position and travel time with the recorded datum, spacing, and acoustic path.

Apply the cone-slice model to a beam envelope

A small-element beam can be approximated as a cone for a simple geometric explanation of a curved beam envelope. As the probe moves past a point, the point enters and leaves the selected beam boundary. A scan plane cutting that idealized cone can produce a conic curve; under the appropriate cut geometry, that section is a parabola.

This approximation is useful for understanding why a beam-boundary display can curve as the probe scans. It is not a universal equation for a TOFD tip indication. Also, a precise conic-section statement matters: a plane parallel to a cone’s generator produces a parabolic section. A plane parallel to the cone axis does not generally produce a parabola.

A real ultrasonic beam has a pressure distribution rather than a hard wall. For a circular element, diffraction shapes the field; an idealized field description can involve Bessel-function behavior. The boundary shown by software therefore depends on which pressure or amplitude level the display treats as the edge, as well as on the probe and material. Changing the displayed boundary level can change the visible envelope without changing a flaw’s location.

Use the cone model only after confirming that the plotted curve is a beam envelope or a deliberately simplified geometric cursor. Check: confirm the instrument is displaying a beam-boundary tool, not a time-of-flight indication, before fitting a conic to it.

Calculate the idealized beam-edge parabola

For a cone with axis coordinate X, radial coordinate r, and half-angle α, the ideal boundary is r = X tan(α). A section parallel to a generator and offset from it can be written in a local coordinate system as:

y² = 4p(X − Xv)
|p| = |h| tan(α) / 2

Here Xv is the section’s vertex, h is the signed offset of the section plane from the reference generator in the chosen coordinate system, and p is the vertex-to-focus distance. The sign determines which way the parabola opens. This expression comes from the ideal cone geometry; it does not determine a physical TOFD beam edge until the cone axis, half-angle, section plane, and display threshold have been defined.

For a scan image, map the physical coordinates to the displayed axes. The screen may plot scan position horizontally and time or depth vertically, not the two spatial coordinates X and y used by the conic equation. Consequently, fitting y² = 4pX directly to an image can give a meaningless p unless the axis mapping and scale are known.

Do not estimate a beam angle from the cursor alone if the instrument’s beam model or threshold is unknown. Read the probe data and setup values used by the instrument, then compare the calculated envelope with the display. Check: confirm the equation’s axes and units match the cursor axes, and that the fitted vertex and opening direction agree with the displayed boundary.

Predict point-diffractor TOFD timing

A point-tip response has a separate geometric model. In a simplified homogeneous material model, place the transmitter and receiver symmetrically about the moving pair midpoint, separated by acoustic distance L. Let x be the midpoint’s scan offset from the diffractor, z its perpendicular depth, c the applicable material wave velocity, and t₀ any fixed system or wedge-time offset. The predicted arrival is:

t(x) = t₀ + [√((x − L/2)² + z²) + √((x + L/2)² + z²)] / c

This equation assumes straight paths in one uniform material, a fixed probe separation, a point diffractor, and no changing wedge contribution. Use the relevant acoustic exit points for L. If wedge paths or refraction change with scan position or focal law, calculate those paths separately using the instrument’s calibrated model instead of hiding them inside a constant t₀.

The arrival time is lowest when the pair midpoint passes directly over the diffractor. Near that minimum, the curve can be approximated by a parabola:

R = √((L/2)² + z²)
t(x) ≈ t₀ + 2R/c + [z² / (cR³)]x²

This is a local approximation near the trace apex, not a claim that the full travel-time curve is an exact parabola. The separation, tip depth, sound velocity, and time offset set the predicted curvature and vertical placement. Multiple tip diffractors at different depths can produce distinct traces. A displayed curve that matches this timing pattern is a stronger candidate for a diffraction trace than a beam-envelope cursor, but timing alone does not identify the reflector type.

Check: compare the predicted apex position and time with a known reflector in the reference scan; if they disagree, recheck the coordinate datum, exit-point spacing, velocity, and wedge/time-zero contribution before interpreting the curve.

Configure paired phased-array probes as transmit and receive

Two phased-array probes can provide separate transmit and receive functions, but “phased array” describes the probe technology, while TOFD describes the inspection approach and the signals being interpreted. A paired-PA setup does not become TOFD simply because the probes face one another. The acquisition must preserve the intended transmitting and receiving paths and record the relevant arrival times across the scan.

Set up the pair from the actual instrument and procedure capabilities:

1. Assign which probe transmits and which receives, and confirm the instrument supports the required acquisition and encoded time display.
2. Select focal laws that create the intended paths in the wedge and test material. Confirm the wave mode and velocity used by the time model.
3. Calibrate time zero and position against a reference reflector using the same probe separation, wedges, laws, and material path used for inspection.
4. Inspect the lateral-wave and backwall regions to confirm the acquired signals occupy the expected time windows before scanning the weld.

A conventional single-element TOFD arrangement and a two-PA arrangement can differ in element selection, steering, focusing, and acquisition configuration. Those differences affect beam coverage and path calculations; they do not change the basic need to identify diffraction arrivals by their acoustic path and scan-time behavior. No universal focal-law angles or settings follow from the phrase “two PA probes.” Check: confirm the live A-scan and encoded reference response show the intended transmitting and receiving paths for the selected laws.

Distinguish TOFD responses from pitch-and-catch signals

Pitch-and-catch describes using separate transmitting and receiving elements; it does not specify whether the received energy came from reflection, diffraction, or transmission through the inspected volume. TOFD is associated with detecting diffracted energy from reflector tips, but TOFD records can also contain reflected signals. The probe arrangement alone cannot classify a response.

Observation	Likely interpretation path	What to verify
Signal arrival moves with scan position in a pattern predicted for a tip.	Test as a possible diffraction indication.	Compare the arrival-time curve with known tip geometry and the calibrated path model.
Signal is tied to a strong reflecting boundary or reflector face.	Consider a reflected response, including a backwall or root response in a TOFD setup.	Check the expected reflected path and whether it overlaps the tip arrival.
Received amplitude drops as the pair scans across a discontinuity.	Consider a transmission or shadow effect in a pitch-and-catch arrangement.	Compare with a clean section and track the received amplitude as well as timing.

Amplitude alone is not a reliable classifier. Diffracted signals may be weak, but reflections can also vary with reflector orientation and position within a beam. A large planar reflector can return strong energy without producing separately resolved upper and lower tip responses. Use the reference block and expected path geometry to distinguish these cases.

Check: classify a response only after comparing its arrival time, scan-position behavior, and amplitude pattern with the known reflectors and paths in the actual setup.

Check surface and backwall masking before sizing

TOFD displays commonly show a near-surface lateral or creep-wave arrival near the top of the time range and a backwall-related reflection later in time. The lateral wave can obscure shallow indications; the backwall or root response can overlap or mask indications near the far surface. Other reflected waves may appear later as well. A clean-looking gap between these strong arrivals is not proof that every defect in that region is detectable.

Use the scan display to identify, rather than assume away, overlap:

• Locate the lateral-wave and backwall-related arrivals on a clean reference area.
• Compare suspect indications against these arrivals across adjacent scan positions. A response that merges into a strong arrival may be masked, not absent.
• Check both upper and lower tip responses when the procedure uses them for vertical extent sizing. If one tip is unresolved, do not infer a complete height measurement from the visible tip alone.
• For a suspected root or backwall indication, compare the response with the reference geometry and the reflected backwall path before assigning it to a tip.

TOFD can reveal root or backwall defects, but a reflected backwall indication may mask them in some configurations. The practical result is a coverage limitation to document and resolve through the governing inspection procedure or an approved complementary method, not a reason to re-label every backwall response as diffraction. Check: confirm the near-surface and backwall zones are identifiable on the reference scan and that any masked or unresolved region is handled by the applicable procedure.

Prove the setup in an end-to-end reference scan

Use a reference block with known reflector geometry to verify the complete chain: probe arrangement, laws, sound path, position encoding, time calibration, and display interpretation. A software cursor can look convincing while the acquisition path is wrong, so the proof must use acquired responses rather than the appearance of the overlay alone.

1. Set the transmitter-receiver spacing, scan datum, focal laws, and wave-velocity model to match the intended inspection setup.
2. Acquire a clean-area scan and identify the lateral-wave and backwall-related arrivals.
3. Scan the known reflector through its full length. Confirm its indication tracks scan position and compare the measured arrival-time curve with the geometric prediction.
4. Check that the reference reflector’s known location and depth are recovered using the instrument’s calibrated axes and procedure.
5. Repeat the reference scan after any change to probe spacing, wedge, focal law, velocity, time zero, or encoder datum.

Keep beam-cursor fitting and TOFD indication fitting separate in the record. A beam-envelope equation describes a selected idealized field boundary; the point-diffractor equation describes a travel-time response. Do not use a cursor fit as a substitute for depth or flaw sizing under the inspection procedure.

Check: accept the setup for production only when the reference reflector is detected at its expected position and time, the relevant surface/backwall arrivals are identified, and the same geometry reproduces the result on a repeat scan.

FAQ

Stop changing focal laws or cursor parameters if the reference reflector does not reproduce at the expected position and time, or if the instrument cannot acquire the intended separate transmit and receive paths. Escalate the setup to the equipment manufacturer’s official support channel and the inspection procedure authority before using the data for acceptance or sizing.