ISO 16610-20:2015

Overview

ISO 16610-20:2015 - "Geometrical product specifications (GPS) - Filtration - Part 20: Linear profile filters: Basic concepts" defines the basic concepts and formalism for linear profile filters used in surface metrology. The standard explains how linear filters separate profiles into long‑wave and short‑wave components, how filters are represented and implemented in discrete measurement data, and the fundamental properties that filters must satisfy (e.g., phase correctness, normalization). ISO 16610-20 is part of the ISO 16610 series on GPS filtration and is a foundational reference for profiling, filtering and pre‑processing of extracted profile data.

Key topics and technical requirements

• Definitions and scope: Formal definitions for terms such as linear profile filter, phase correct filter, weighting function, transmission characteristic, and cut‑off wavelength.
• Discrete data representation: Profiles are modelled as uniformly sampled vectors; filtering is therefore treated in discrete form.
• Filter representation as matrices: Linear profile filters are represented by square matrices - non‑periodic filters by Toeplitz (constant diagonal) matrices and periodic filters by circulant matrices. For phase‑correct filters the matrix is symmetric.
• Weighting function and sampling: The weighting (impulse‑response) function can be continuous (e.g., Gaussian) or discrete; continuous weighting functions must be sampled at the same interval as the data and renormalized so sample weights sum to unity to avoid bias.
• Filter equations and convolution: Filtering is expressed as a matrix operation or discrete convolution (circular convolution for circulant matrices). The standard addresses invertibility (existence of inverse matrix) and implications for data reconstruction.
• Transmission characteristic & cut‑off wavelength: The transmission characteristic (Fourier transform of the weighting function) defines frequency attenuation; the cut‑off wavelength (50% amplitude transmission) is used to identify filters and as a recommended nesting index.
• Filter banks and multiresolution analysis: Structure for combining high‑pass/low‑pass filters to decompose a profile into multiple scales or resolutions.

Practical applications

• Surface texture and roughness analysis - separating waviness and roughness components before computing GPS surface parameters.
• Implementation of standard filters in measurement software and instrument firmware (Gaussian, spline, spline wavelets).
• Designing and validating filter kernels for profilometers, tactile probes, optical profilers, and data post‑processing tools.
• Multiresolution analysis for feature extraction and scale‑dependent inspection.

Who should use this standard

• Metrology and quality engineers working with surface profile measurement
• Instrument manufacturers and calibration laboratories
• Software developers implementing GPS filtration algorithms
• Researchers in precision engineering and surface characterization

Related standards

• ISO 16610-1 (Overview and basic concepts)
• ISO 16610-21 (Linear profile filters: Gaussian filters)
• ISO 16610-22 (Spline filters) and other parts in the ISO 16610 series covering robust and morphological filters

Keywords: ISO 16610-20, linear profile filters, GPS filtration, weighting function, transmission characteristic, cut-off wavelength, discrete convolution, Toeplitz matrix, circulant matrix, Gaussian filter, profile filtering.