Acoustic Diffuser: How a Schroeder QRD Scatters Sound by Phase

Diffusion vs absorption

A room's sound-treatment panels usually do one of two very different jobs. Absorbers remove acoustic energy, converting it to heat in a porous or resonant material — useful for controlling excessive reverberation and echo. Diffusers do the opposite: they preserve almost all the acoustic energy but scatter it in many directions instead of reflecting it as one coherent, specular bounce, which controls flutter echo and comb-filtering coloration without deadening the room the way heavy absorption does.

The Schroeder diffuser: phase, not shape

Manfred Schroeder's 1975 insight was that you do not need a complicated curved surface to scatter sound — you need to control the phase of the reflected wavefront across the surface. A quadratic residue diffuser (QRD) is a series of narrow wells of different, carefully chosen depths cut into a flat panel; each well acts like a small closed organ pipe, reflecting sound with a phase delay set by its depth. Choosing the well depths according to a quadratic residue sequence makes the reflected wavefronts interfere in a way that spreads energy into a wide, statistically even fan of directions rather than one specular reflection.

s_n = n^2 mod N            (N prime; classic QRD sequence)
well depth d_n proportional to s_n, scaled so max depth = lambda_design / 2

n = 0, 1, 2, ... N-1  (well index across one period of the diffuser)

The prime N sets both the number of wells per period and, through the design wavelength, the bandwidth the diffuser works well over — larger N and deeper wells extend performance to lower frequencies, at the cost of a physically deeper panel.

The design frequency range

A QRD's useful range is bounded on both ends by geometry. The low-frequency limit is set by the deepest well: a well only diffracts effectively for wavelengths comparable to or shorter than about twice its depth, so below that frequency the panel starts acting more like a flat reflector. The high-frequency limit is set by the well width: once a wavelength becomes small compared to a single well's width, sound starts to see the well as a locally flat surface again and diffraction breaks down into simple reflection. Good QRD designs therefore pick well width and maximum depth together to bracket the target octave or two of room-problem frequencies, most often in the few-hundred-Hz to few-kHz range where flutter echo and comb filtering are most audible.

Reading the polar energy diagram

A diffuser's performance is usually shown as a polar energy response: send a fixed test signal at the panel from a fixed angle and plot how much reflected energy arrives at each angle around a semicircle. A flat, highly reflective panel produces a single sharp lobe at the mirror angle (specular reflection). A well-designed QRD spreads that same energy into a much flatter, near-hemispherical pattern with no strong single lobe — which is exactly the visual signature of good diffusion, since it means no listening position gets an unnaturally strong single reflected copy of the sound.

The diffusion coefficient

To turn a polar plot into one comparable number, room-acoustics standards (AES-4id, ISO 17497) define a normalised diffusion coefficient, essentially a measure of how evenly energy is spread across the measured angles relative to a flat reference surface, scaled from roughly 0 (all energy in one specular lobe, like a flat wall) to close to 1 (energy spread perfectly evenly across all angles). It is normally reported as a curve across frequency, since a diffuser's performance — bounded by the well-depth and well-width limits above — is never uniformly good at every frequency, and a panel's marketing spec usually understates how much the coefficient droops outside its designed band.

Frequently asked questions

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