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In 1983, RPG Diffusor Systems, Inc. introduced the first
commercial sound diffusor that offered uniform scattering over a
designable bandwidth. The QRD® has now been used in thousands
of projects in a wide range of venues. As with any technology, research
and experimentation lead to advances. The QRD® is a reflection
phase grating formed from the periodic repetition of a base shape,
consisting of a series of wells of depth based on the quadratic residue
sequence, separated by dividers. While periodicity is the basis of the
QRD®, it is also one of its limitations, because periodicity
causes lobing in specific diffraction directions. To minimize this
lobing, which compromises the uniformity of the polar response, RPG
developed the Modffusor™. By contrast to a QRD®
periodic array, a Modffusor™ aperiodic array is formed by
following the prescription of an optimal binary sequence, which
indicates when to use the asymmetric, optimized base shape or a flipped
version (rotated 1800 about the surface normal). The shape optimized
Modffusor offers significantly better performance than a low-prime,
number theoretic QRD® diffusor and the aperiodic modulation
minimizes lobing non-uniformity caused by periodicity. Thus, the
Modffusor™ offers the next generation of high performance
reflection phase gratings.

Problem

Quadratic Residue Diffusors (QRD®) owe their diffusing ability
to the phenomenon of diffraction from a periodic reflection phase
grating. The product of the number and width of the wells defines the
diffraction directions and the energy in these directions is equal due
to the fact that the quadradic residue well depth sequence has a flat
power spectrum. To cover wide areas, the QRD® is repeated. This
periodicity decreases uniformity by focusing the energy in the
diffraction directions (B), preventing uniform diffusion (C) from being
achieved.

Solution

To solve this problem, RPG patented a new modulated optimized diffusor
called a Modffusor™. The Modffusor embodies two patented RPG
inventions, namely Shape Optimization and a concept called Aperiodic
Modulation of a Single Asymmetric Base Shape. The optimized, asymmetric
base shape of the Modffusor, consists of 7 full wells and two
zero-depth, half-width wells on either end. Since periodicity, the
regular repetition of an element, reduces diffusive performance, RPG
utilized the Shape Optimizer to form an asymmetric, diffusively
optimized surface, that is no longer bound to the restrictions and
constraints of number theory. This optimized surface is now arrayed in
an aperiodic manner, using binary Code Division Multiple Access (CDMA)
modulation techniques. CDMA systems are used in mobile telephony to
enable multiple users to use the same transmission bandwidth. Of
interest here are so-called spread spectrum techniques. Spread spectrum
techniques take frequency (spectral) components and spread them over a
frequency bandwidth. If the lobes generated by a diffuser are viewed as
spatial frequency components, then when spread spectrum techniques are
applied, the lobes will be spread spatially. This is a significant
advance of QRD number theory technology, which directs scattered energy
into specific diffraction directions (grating lobes).
In the Modffusor,
the spread spectrum modulation of one asymmetric, optimized base shape
enables the scattered energy to be distributed in all directions (all
spatial frequencies). This is accomplished by assigning a binary zero
to the asymmetric, optimized base shape and a binary one to the flipped
shape (rotated 180° about the surface normal). Installation of
an array of Modffusors to cover a given surface area is accomplished by
following the prescription of an optimal binary sequence with good
aperiodic autocorrelation, provided by RPG. It there is a zero in the
sequence the base shape Modffusor is installed, and if there is a one
in the sequence the flipped version of the Modffusor is installed.
Using aperiodic modulation, the performance of the single optimal base
shape can be preserved, while covering an infinite area. The patented
half-width, zero-depth end wells provide seamless tiling and the
appearance of pseudo-periodicity and pseudo-symmetry, which is
aesthetically pleasing.

An example of how a generalized, single, asymmetric diffusor can be flipped according to the prescription of an optimal binary sequence (1 base shape, 0 flipped shape in red) to form an aperiodic diffusive surface with minimized lobing.

The base shape is installed when there is a
zero in the sequence and the flipped shape is installed when the
sequence value is a one. The joining of the two zero-depth half-width
wells gives the appearance of periodicity for a pleasing visual
appearance, however, acoustically the array is aperiodic with optimal
diffusive performance. The Modffusor represents the state-of-the-art in
diffusor design, overcoming all of the shortcomings of periodic,
number-theoretic QRDs.

Absorption

The Modffusor exhibits minimal absorption with a slight rise between 500 and 630 Hz, due to pressure gradient absorption between resonant and non-resonant wells. If a panel fabric is placed over the surface, then this resistive element increases the absorption significantly in this frequency region.

Diffusion

Diffusion coefficient comparison between a traditional QRD and the
Modffusor, reveals significant performance improvement, due to the
reduction of periodic lobing. A flatpanel response of comparable size is
also shown to indicate the Modffusor’s better low
frequency diffusion, as indicated by the onset of diffusion.

Installation

The Modffusor is typically mounted on a cleat and secured. For
installations that require a flush mount the units are framed out much
like an opening for a window.

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