Thick Film Profilometry: When Sampling Hides Surface Ridges

Measurement purpose

Determine whether lateral acquisition preserves the required surface feature.

Specimens and conditions

Physical feature

Known region, expected spatial scale and height reference.

Surface preservation

Comparable state between scans, with any contact-induced change retained.

Equipment and records required

• Profile acquisition: Actual lateral coordinates, sample pitch and unresampled output available.
• Response confirmation: Appropriate reference feature or independent method for the required spatial scale.

Method sequence

1. Define

   Set the relevant feature scale and acquisition response.

   Record: Spatial measurement requirement.

2. Acquire

   Retain raw coordinates and assess potential folding.

   Record: Original profile and sampling conditions.

3. Challenge

   Repeat with justified finer spacing or shifted phase.

   Record: Registered comparison and supported geometry.

Decision and uncertainty

Accept geometry only when the method preserves its required spatial information.

Aliasing, probe response, missing data and processing can make different surfaces produce similar records.

Surface-metrology and drawing requirement owners.

Traceable outputs

Specify the feature that the profile must retain

Identify the dimensional question on the actual ceramic circuit: repeated print ridges, an overglaze transition, conductor-edge texture or a local depression. State its expected lateral scale and the height reference. A broad step between plateaus and a narrow periodic ridge pattern place different demands on acquisition. A method adequate for the plateau difference may not preserve the smaller structure between those plateaus.

Use the required function to choose the feature scale. If a contact or subsequent printed layer interacts with a local raised region, an average over the whole substrate may be irrelevant. Retain an overview that locates the profile relative to the printed pattern. The inspection should establish which surface information the customer needs, not simply select the instrument's fastest scan mode.

Read the physical sampling interval from the acquisition record

The lateral sample pitch is the physical distance between stored independent measurement positions along the scan. It is not the height increment shown by the instrument, nor necessarily the spacing of plotted pixels in an exported image. Software can draw many interpolated points between two acquired positions without adding measurements of the surface.

For a scanning instrument, confirm how position and acquisition timing determine the stored coordinates. For an imaging profiler, confirm object-space pixel spacing, any binning and the actual exported grid. Check whether filtering or decimation changed the retained pitch. A filename that says high resolution does not define any of these quantities. Keep the original coordinates and unresampled data when a dimensional decision depends on a small feature.

Apply the sampling condition to spatial frequency

For an ideal sinusoidal height variation with wavelength L, the spatial frequency is one divided by L. Uniform point sampling at pitch delta-x has spatial sampling frequency one divided by delta-x. To reconstruct a band-limited profile without ambiguity, its highest relevant spatial frequency must lie below half the sampling frequency, with practical margin for the real measurement response.

Equality at two samples per wavelength is a fragile boundary: a sinusoid can be sampled at its zero crossings and disappear. The condition also assumes that higher spatial frequencies are absent or appropriately suppressed before sampling. Real sharp edges are not single band-limited sinusoids. Their dimensional measurement requires a suitable response and enough measured points around the edge, not blind application of a two-point rule.

See how a real ridge pattern can become a false smooth trace

Consider the independent example z(x) = 2 sin(2 pi x/100) micrometres, with x expressed in micrometres. Its wavelength is 100 micrometres and its true peak-to-valley height is 4 micrometres. Sampling every 100 micrometres from x = 0 records only zeros. The stored points therefore look flat despite the unsampled ridges and valleys.

Sampling every 60 micrometres gives a spatial sampling frequency of 1/60 cycles per micrometre. The original 1/100 frequency folds to 1/60 minus 1/100 = 1/150 cycles per micrometre. An apparent 150-micrometre waveform can fit those samples, with the appropriate phase sign. That longer period is not a new physical surface feature; the acquired points cannot distinguish the two possibilities without additional information.

Separate sample spacing from the instrument's lateral response

A very fine exported grid cannot restore a feature that the probe or optics never resolved. A stylus may bridge a narrow trench, while an optical system may attenuate fine structure or lose data at a slope or reflective transition. Those are separate limitations from sampling pitch. Evaluate physical response and acquisition spacing together, using a suitable known feature where needed.

Likewise, reducing the pitch does not guarantee a better height result if it changes contact conditions, scan speed or optical acquisition quality. Keep those changes visible in the comparison. The correct question is whether the revised method preserves the feature required for the decision, not whether it produces the largest file or the most detailed-looking color map.

Challenge a suspect period with independent physical sampling

Repeat the same registered region at a sufficiently finer acquired pitch while retaining the original scan. Where the method permits, use a shifted starting position or a changed scan direction to test whether a supposedly absent feature depends on sample phase. A periodic artifact that moves in frequency when acquisition spacing changes is a reason to investigate aliasing, not proof of a particular manufacturing mechanism.

Keep the surface state stable between scans. If a contact method alters a soft coating or moves debris, differences may arise from changed material rather than changed sampling. An independent optical or sectioning observation can help, but it has its own access and resolution limits. Compare registered physical features and stated uncertainty rather than selecting whichever method gives the most visually convincing result.

Do not smooth or interpolate an alias into acceptance

Once high-frequency structure has folded into the stored band, a later digital smoothing operation cannot identify which physical frequency produced the samples. It may make the false longer-period profile look cleaner. Preserve unfiltered data and distinguish any filter used to define a roughness metric from the acquisition controls required to prevent aliasing.

If the customer only requires a band-limited surface quantity, document that bandwidth and how the instrument realizes it before sampling or through a validated complete method. Excluding a feature from the reported band is not evidence that the feature is absent. For a local-defect decision, a filtering choice that removes the relevant ridge or pit may invalidate the method even if the resulting roughness parameter is repeatable.

Report the retained spatial information with the result

The final record should state acquired sample pitch, coordinate calibration, lateral response, filtering and the spatial region examined. Include the original profile and confirmation evidence for any suspect periodic feature. Mark missing or unresolved regions instead of filling them invisibly. A smooth interpolated plot should never be the only retained evidence for a small-feature acceptance decision.

For a thick film circuit review, provide the feature drawing and the surface condition at measurement. ChipSimple can relate the profile question to the intended conductor, resistor or protective layer. The useful outcome is a measurement method that resolves the required geometry. Neither a dense grid nor a low roughness number establishes electrical insulation, adhesion or complete coverage without the corresponding functional evidence.