reflection reflection phase gratingsphase gratingsthe first, quantifiable, sound diffusor

RPG Diffusor Systems, 651-C Commerce Drive, Upper Marlboro, MD 20774Phone 301-249-0044 Fax 301-249-3912 email info@rpginc.com web www.rpginc.com

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Sound is attenuated by absorp-tion, re-directed by reflection anduniformly scattered by dif-fusion, as shown in thetemporal and spatialresponses above.Absorbing and reflectingsurfaces are common-place, however, it wasn’tuntil 1983 that RPG intro-duced the first, designablesound diffusing surface,based on mathematicalnumber theory. This tech-nology revolutionizedarchitectural acoustics andpioneered the passive,digital acoustics era.

In addition to this pioneer-ing technology, RPG also devel-

oped a measurement technique toevaluate the performance of thesenew surface treatments. The first3-dimensional goniometer tomeasure the directional diffusion

coefficient is shown above. A redconical sample is at the origin, themicrophones are located on theintermediate semicircle and thedirectional source loudspeaker islocated at a given azimuth andelevation. Sound from any inci-dent direction is backscatteredand collected at 5 degree inter-vals on the surface of a hemi-sphere, by rotating the semicircu-lar microphone arc. As describedin the AES-4id-2001 informationdocument, the backscatteredimpulse responses at each obser-vation angle are isolated from

room interference, correct-ing for speak-er/microphone responseand transforming into thefrequency domain. 1/3-octave polar responsesare derived from the fre-quency responses and adiffusion coefficient,bound between zero andone (uniform diffusion),describing the uniformityof the polar responses isobtained.

The first surfaces intro-duced were formed from

divided wells with depths basedon quadratic residue number the-ory and were called QuadraticResidue Diffusors or QRDs. The1- dimensional QRD-734 is basedon a prime 7 number of divided

Diffractal is pictured above, show-ing a high frequency diffusor nest-ed into a mid-frequency QRD 734.The diffusion response is extend-ed by bootstrapping the mid-fre-quency diffusion response of theQRD 74 with the diffusionresponse of the nested andscaled replica high frequency dif-fusor, forming a second genera-tion Diffractal. Third generationDiffractals have also beeninstalled offering broad bandwidthdiffusion.

To address the non-uniformity ofspatial lobing problems resultingfrom periodic repetition of a diffu-sor, as in a wall paper pattern,RPG patented an approach calledthe “Aperiodic Modulation of aSingle Asymmetric Base Shape”.Up to this point QRDs were sym-metrical and contained a mirrorsymmetry about the centerdivider. RPG developed a propri-etary program called the ShapeOptimizer which allowed diffusordesign without relying on numbertheory with its constraint of primenumber of wells with quantizedwell depths, providing specularscattering a the prime multiple ofthe design frequency. The ShapeOptimizer allowed the design ofsymmetric or asymmetric diffu-sors, with non-quantized welldepths. The concept of modula-tion of an asymmetric shape wasthen employed, because now anasymmetric shape could assume

cally as opposed to a directionalhemi-disc for a 1D diffusor. Thewooden (top) Omniffusor andclear Omniviewsor (bottom) areshown above. Asymmetric, opti-mized, 2D diffusors in the form ofa GRG Omniffusor (top) and aEPS Skyline (bottom) can also beaperiodically modulated.

wells, shownbelow andscatters sounduniformly inthe direction ofthe depth vari-ation, asshown in thepolarresponse.Special trans-parentDiviewsors

were added to provide diffusion

with a view. To address projectswith limited available surfacedepth, 1” deep high frequencyFlutterFree diffusive molding

devices were added.Never content with the status quo,RPG has been involved in contin-ually evolving the phase grating toexpand frequency bandwidth limi-tations, due to limited depth andwell width, improve uniformity,which is compromised by quan-tized wells depths and periodicrepetition.

To increase the frequency rangeover which the diffusor scattersuniformly, RPG patented the dif-fusing fractal or Diffractal, whichconsists of nested diffusors ofsmaller and smaller scale, as in afractal. A first generation

a different shape by flipping oninstallation. These two configura-tions were assigned a binary zeroand binary one and installedaccording to the prescription ofan optimal binary sequence.Modulation can be explained with

the following graphic. The baseshape indicated with a binary 1,can be flipped to form a binary 0and a surface can be tiledaccording to the prescription ofan optimal, non-repeating, aperi-odic, binary sequence, whichoffers uniform scattering and miti-gates all of the negative effects ofperiodicity. An example of the firstModulated Optimized Diffusor

(Modffusor) is shown below. Thistechnique has also been utilizedto improve the bandwidth andspatial response by developingFlutterFree-T, shown to the leftbelow FlutterFree.

RPG alsodeveloped 2-dimensionaldiffusors,which havedepth varia-tion in twodirections andscatter sounduniformly orhemispheri-