A measured height map contains more than surface roughness. Part shape, fixture alignment, waviness, fine texture, and measurement noise can all contribute. Useful reporting states the aperture, lateral sampling, reference geometry, removed terms, spatial filters, and treatment of missing points before quoting a single number.
Separate surface form from texture
Surface form describes the overall geometry. Surface form error (SFE) is departure from a specified nominal or reference form over a declared aperture. Waviness and roughness describe longer and shorter spatial-scale texture after a defined separation. Their boundaries depend on the specified filters and nesting indices; they are not universal frequency bands.
Remove fixture tilt or fit a nominal surface only when the measurand permits it. Removing a quadratic shape can conceal bow that the drawing actually limits. Filtering does not distinguish unwanted noise from legitimate fine structure without a justified bandwidth; edge effects, gaps, and instrument lateral resolution also matter.
State the statistic and its reference
For a residual height map relative to its declared mean/reference, peak-to-valley is the maximum minus minimum. Mean-centered root-mean-square height describes distributed variation:
The displayed expression assumes a mean-centered, equally area-weighted surface. Profile analogues use after the required profile processing. “Peak-to-peak” often denotes the same range, but does not specify the filtering. Areal is maximum peak height plus maximum pit depth on the defined scale-limited surface.
PV is sensitive to isolated extremes. Minimum-zone flatness instead minimizes separation between two enclosing parallel planes and still includes outliers. A proprietary robust PV statistic is a separate construction; it is not automatically equivalent to either quantity.
Robust PV, RMS, and declared data treatment
ZYGO’s published PVr method combines the PV of a fitted 36-term Zernike surface with an RMS-based residual contribution. It separates a smooth fitted contribution from unresolved residual structure; it is not the minimum separation of two planes enclosing every measured point. Report the software’s actual definition and fitting aperture rather than labeling a percentile range or another custom statistic “PVr.”
The calculator below reports sampled profile PV and mean-centered RMS, with optional straight-line removal. It does not implement standardized roughness filtering, ZYGO PVr, or certified minimum-zone flatness. A percentile span would be another explicitly defined statistic, not a substitute for these quantities. No statistic repairs invalid points automatically. Preserve raw data, explain masking, and investigate whether an isolated peak is noise, contamination, or a real defect.
Raw RMS about zero includes the mean offset: . A residual surface after piston, tilt, or form removal is a different measurand from the original map. Report both the permitted removals and the resulting statistic.
Describe wavefront shape with Zernike modes
Wavefront error is optical-path departure from a reference wavefront. Zernike polynomials describe this shape over a circular pupil: piston is a constant offset; tilt is a ramp; defocus is radially quadratic; astigmatism and coma describe other distinct shapes. Coefficients need a stated normalization, indexing convention, units, and pupil.
Connect surface error with optical error
SFE and wavefront error both use length units, but describe different quantities. In air, reflective surface departure produces approximately , with incidence angle measured from the surface normal. For a homogeneous, near-normal plane-parallel plate of phase refractive index , local thickness variation produces approximately:
Thus surface form errors can contribute to transmitted wavefront error (TWE), but both surfaces, their registration, refractive-index inhomogeneity, and ray deflection matter. One surface’s SFE cannot determine TWE by itself.
Relate fitted modes to GD&T without confusing the specifications
A plane fit can describe level and tilt, while low-order curvature can describe bow or optical power. These are useful geometric interpretations, not replacements for drawing requirements. Flatness is a form tolerance independent of a datum; parallelism relates orientation to a datum; profile tolerances compare a surface with the specified nominal geometry under their stated datum conditions. Straightness applies to a defined line element or axis, rather than the entire areal map.
For a plate with front and back heights measured along the same axial direction, the local material replaces an equal thickness of air. Relative to a nominal plate, that replacement changes optical path by . This approximation assumes uniform phase index, small slopes, near-normal propagation, and common pupil registration. A shared surface ripple on both faces can produce little thickness variation even though each surface has form error; conversely, index variations can distort the transmitted wavefront without changing external geometry.
With orthonormal Zernike modes over a complete uniformly weighted unit disk, mean-removed wavefront RMS is the square root of the sum of squared non-piston coefficients. A clipped pupil, nonuniform weighting, missing data, or another normalization changes that relation. Removing tilt or defocus must be permitted by the optical test specification; removal changes the reported wavefront error.
Iris Optics can define surface and wavefront measurands, select defensible filtering and fitting conventions, and connect geometric inspection with the optical performance that the assembly must deliver.