In 1983, RPG Diffusor Systems, Inc. introduced the first commercial sound diffuser 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™ 875. By contrast to a QRD® periodic array, a Modffusor™ 875 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 180deg about the surface normal). The shape optimized Modffusor™ 875 offers significantly better performance than a low-prime, number theoretic QRD® diffuser and the aperiodic modulation minimizes lobing non-uniformity caused by periodicity. Thus, the Modffusor™ 875 offers the next generation of high performance reflection phase gratings.

Problem
Quadratic Residue Diffusers (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 diffuser called a Modffusor™ 875. The Modffusor™ 875 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™ 875, 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™ 875, 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 Modffusor™ 875s 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™ 875 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.

Type “0” Unit	Type “1” Unit

An example of how a generalized, single, asymmetric diffuser 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 Modffusor™ 875 represents the state-of-the-art in diffuser design, overcoming all of the shortcomings of periodic, number-theoretic QRDs.

Absorption
	The Modffusor™ 875 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™ 875, reveals significant performance improvement, due to the reduction of periodic lobing. A flat panel response of comparable size is also shown to indicate the Modffusor’ 875's better low frequency diffusion, as indicated by the onset of diffusion.

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The First Modulated Optimized Sound Diffuser From The Acoustical Industry’s Leading Innovator

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