Source: https://jmrplens.github.io/phonometry/materials/diffusers/ # Diffusers and surfaces Where the [Absorbers](https://jmrplens.github.io/phonometry/absorbers/) subsection asks how much energy a material removes from the field, this one asks what a *surface* does with the sound it returns: how much it throws off the specular direction and how evenly it spreads it. Two guides walk that ground, and a third family of surface measurements — pavements characterised where they lie — has its own subsection nested inside this group. [Diffusers and Their Coefficients](https://jmrplens.github.io/phonometry/materials/diffusers/) is the measurement and design core: the random-incidence **scattering coefficient** $s$ of ISO 17497-1, measured on a reverberation-room turntable, the **diffusion coefficient** $d$ of ISO 17497-2, measured on a free-field goniometer, the Schroeder quadratic-residue design rules with the Fraunhofer far-field prediction that grades a well-depth sequence before it is built, and the closing argument for why the two coefficients must never be swapped. [Metadiffusers](https://jmrplens.github.io/phonometry/materials/metadiffusers/) shrinks the Schroeder diffuser by an order of magnitude: slits loaded by Helmholtz resonators slow the sound until a 2 cm panel reproduces the reflection phases of wells 27 cm deep, with critical coupling supplying the perfectly absorbing `0` state that ternary sequences need. The published quadratic-residue design is evaluated end to end, transfer-matrix chain to FDTD cross-check. [Surfaces measured in place](https://jmrplens.github.io/phonometry/surfaces/) takes the absorption question outdoors, to the surfaces that have no sample: it covers the ISO 13472-1 subtraction technique and the ISO 13472-2 spot tube, and the decision between them. The neighbours are close: the diffuser panels are surface relatives of the [metamaterial absorbers](https://jmrplens.github.io/phonometry/absorbers/metamaterial-absorbers/) built from the same slit and resonator cell, the scattering coefficient feeds the room predictions of [Room acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/), and the road methods serve the outdoor-noise interest of [Environment and transport](https://jmrplens.github.io/phonometry/environment/). ## Pages in this section - [Diffusers and Their Coefficients](https://jmrplens.github.io/phonometry/materials/diffusers/): the ISO 17497-1 scattering and ISO 17497-2 diffusion coefficients, Schroeder design and the far-field prediction model. - [Metadiffusers](https://jmrplens.github.io/phonometry/materials/metadiffusers/): deep-subwavelength Schroeder diffusers from resonator-loaded slits, with slow sound and ternary sequences. ## See also Pages elsewhere on the site that this section leans on: - [Surfaces measured in place](https://jmrplens.github.io/phonometry/surfaces/) and its guide [In-situ Road-Surface Absorption](https://jmrplens.github.io/phonometry/surfaces/road-absorption/): the ISO 13472-1 subtraction technique and the ISO 13472-2 spot method. ## What this section does not cover Both prediction models here are **design estimates, not measurements**. The Fraunhofer far field the diffuser and metadiffuser pages share loses accuracy at low frequency, at grazing angles and over strongly absorbing surfaces, and it ignores edge diffraction, so it grades a well-depth sequence before it is built and does not replace an ISO 17497-2 measurement; the metadiffuser model is locally reacting on top of that, with no coupling between wells. Only the quadratic-residue depth sequence has a dedicated helper — primitive-root and modulated arrangements are discussed as design guidance and enter through the explicit depth or reflection arguments. The inverse problem, solving resonator geometries for a target phase profile, is not automated: the workflow matches phases by evaluation. On the measurement side the library reduces the data but does not run the rig: the ISO 17497-1 turntable and the ISO 17497-2 goniometer supply the reverberation times and the polar response, and what is implemented is the arithmetic that turns them into a coefficient.