The ISO 3274 standard specifies that the primary profile should not contain the nominal form of the workpiece. The form component must therefore be removed prior to any other metrological operation.

When the form is just a line segment or a plane, this action is called **leveling**. When the form is non-planar, it is called **form removal**.

So how do I go about leveling or removing form from my measured surface?

Nominal form is the geometric form intended by the designer of a mechanical workpiece. Usually it is a planar form or a rotary form (cylinder, cone, sphere).

Surface texture specifications are made in reference to a flat surface, regardless of geometrical form, so the metrologist must apply an operation to flatten the profile or the surface before carrying out metrological analysis. This operation consists in modeling a shape and associating it with the cloud of measured points in order to subtract form.

In the case of a non-manufactured object, there is no nominal form, but it can still be useful to remove natural form.

On a 2D contact profilometer, the scanning axis along X gives the reference and defines the origin of heights. This reference is usually provided by a high precision steel rod on which pads slide to move the sensor and the stylus during scanning. Any straightness deviation from this reference is injected into the measured profile as a height bias.

Some profilometers can calibrate this straightness deviation by measuring a reference glass flat and saving a straightness profile that is then subtracted from any subsequent measurement.

With a 3D optical profiler, the reference depends on the optical technology. In the case of a vertical scanning device, the alignment and linearity of the device influence the reference. The reference mirror of an interferometer also influences the height reference. In general, any disturbance is mapped during a calibration routine done in the factory or sometimes by users. See also ISO 25178-700.

The metrologist should align the workpiece with measurement axes as closely as possible. For example, on a contact profilometer, the sample is positioned as horizontally as possible and aligned along the X axis, which is itself aligned on the internal reference of the instrument. This guarantees that heights are correctly recorded along the Z axis of the instrument which is very close to the Z axis of the workpiece. The leveling operation then subtracts the remaining fractions of degrees of the residual slope.

When measuring a surface, for example with a confocal microscope, the sample will be placed horizontally to ensure that the vertical scanning axis is as perpendicular as possible to the sample plane.

On a profile, the reference line is defined by leveling or form removal, and therefore depends on the association method. By default, the least squares line is associated with the profile. It becomes the horizontal reference of the primary profile, and defines the origin of heights. Similarly on a surface, the mean plane is calculated by the F Operator.

Local structures and geometrical features may affect this reference by deviating from the associated plane.

Association is an operation that configures a mathematical model in order to best fit a real workpiece, usually represented by a cloud of points. Models are geometrical forms (line, plane, portion of a sphere, of a cylinder, of a cone, polynomial, etc.)

Association methods used in surface texture metrology are:

**Least squares**, simple or total, constrained or not;

**Minimum zone**.

The default association method for surface texture metrology is the least squares association. This is the best method if surface texture is globally random (stochastic), without any particular structure or geometrical shapes.

When using Mountains® software, exclusion of structures can be manual or automatic, and allow the calculation to take into account only a subset of points of the profile or the surface when estimating the nominal form.

In the case of the surface below, the groove is not centered, which alters the calculation of the least squares plane, leading to incorrect leveling.

The solution consists in excluding the groove from the calculation by selecting it in the Leveling or Form removal operator dialog and to exclude this area from the calculation. The excluded area is marked in gray below.

In other cases, structures can be automatically excluded (least-squares plane is calculated correctly only from points on the flat plane).

A surface with several planes at different heights may be leveled using the Partition and level operator that segments the surface using watersheds and pruning algorithms.

In more complex cases, when the different planes are affected by a general curvature that needs to be removed, it is necessary to use the multi-plane leveling function. This will assess curvature but ignore edges and heights.

Above. Multi-plane leveling is particularly useful in applications such as inspection of micro-systems having undergone thermal drift, sheet-metal embossing or height measurement of ink on a non-rigid material (bank notes etc.)

- This article is based on extracts from the Digital Surf Surface Metrology Guide: Leveling and Form removal
- ISO 1101: GPS - Geometrical tolerancing - Tolerances of form, orientation, location and run-out
- ISO 17450-1: GPS - General concepts - Part 1: Model for geometrical specification and verification
- ISO 17450-2: GPS - General concepts - Part 2: Basic tenets, specifications, operators, uncertainties and ambiguities
- ISO 22432: GPS - Features utilized in specification and verification

This text was first published in the Surface Newsletter, Spring 2017.