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Diffusion

Overview
Acoustic diffusion is the deliberate reflection of sound energy in a spatially near-uniformly distributed pattern and temporally uniform distribution to replace fixed-angle reflections which produce peaks and nulls in fixed patterns. Flat surfaces produce simple reflections, like light from a flashlight off a mirror. Because sound sources and reflective walls don't move, the direct sound paths add and cancel but the pattern within the room will remain relatively fixed -- though it's different for every frequency. Move your head a few inches and you hear big changes where none were expected. When the reflection distance is large, it sounds like echo or reverberation but Very Small Studios generally have no reverberation -- yes, reflections but they are too short to be called reverberation. When the reflection is much closer, flutter can be heard from hard surfaces and diffusion helps to redistribute these reflections and reduce flutter.

Reflections
Very Small Studios have problems with closely-spaced, flat, hard walls which easily reflect most frequencies and the spacing between walls sets the fundamental resonance frequency where the first reflection cancellations (nulls) are produced. This null frequency is repeated at integer (2x, 3x, 4x, etc) that frequency -- which produces a frequency response with a series of nulls separated by peaks. The frequency response curve has lots of "bumps" due to reflections adding and canceling so it looks like a "comb" -- hence the name "comb filtering. Comb filtering, caused by room resonance modes (which are related to the room dimensions) cause "coloration" of sound. With monitor speakers, which tend to be directional, this coloration can be severe because the directivity makes any comb filtering effects more stark. Killing all reflections leaves a "dead-sounding" room so, after fixing the worst low frequency room mode reflections using traps, adding diffusion (without attenuation) returns some of the "live-room" feel of reflections but diffuses those reflections to avoid peaks and nulls.

Scattering
If the surface were made "un-even", spatially it might be less "patterned" so less noticeable but the more scattered sound waves would all still have approximately the same phase relationship (arrival in time). They are scattered but not diffuse.


Diffusion
However, if in addition to scattering the sound waves, the different paths were delayed by different amounts, there would be both spatial (location) and temporal (time/delay) "scattering". This is diffusion. Diffused sound does not confuse the listener, does not cause large peaks and nulls and reduces detectable distortion. Diffusion also gives the listener the "feeling" that the room is larger than it really is and that the wall with the diffuser is further away than it physically is. The now-famous BlackBird Studios photo is a visually stunning example of room diffusion taken to the extreme. Some claim the room "feels" as big as all outdoors.


Skyline Diffusers of Studio C at Blackbird Studios, Nashville TN
( Designed by George Massenburg ) ( photo: blackbirdstudio.com )
(How to avoid bass traps by using VERY deep diffusers...)

Diffuser Types
  • Angled-Flat Diffuser: Flat surfaces added at angles to flat walls. More scattering than diffusion and more easily constructed in very large spaces.
  • Curved-Surface Diffuser: Sometimes called "poly-diffusers". Large, curved surfaces; sometimes arrays. Also best for large spaces. Just one or two produce scattering but little diffusion.
  • QRD (Quadratic Residue Diffuser): A mathematically-defined array of small, flat surfaces at many different depths which provides broadband spatial and temporal diffusion with scattering and octave or bore below the design cutoff frequency. Generally 1-dimensional but several diffusers can be arranged in an array with different orientations.
  • Skyline (2D) Diffuser: A mathematically-defined 2-dimentional array of flat surfaces raised above the supporting surface with no "walls" between the surface elements. However, the necessary depth and excessive weight of well-designed Skyline diffusers can be prohibitive for small rooms.
  • Fractal Diffuser: A mathematically-defined design which uses the self-similarity of fractals in an effort to 1) simplify construction and 2) provide much wider bandwidths. However, there is limited performance measurements and data to support its application in a very small studio.
  • PRD (Pseudo-Random Diffuser): Generally a mathematically-defined 2D array, similar in appearance to skyline diffusers, but based on pseudo-random number sequences. The concept is that randomness has fewer distinguishable patterns thus may provide more diffusion than scattering.
  • Others: There are a host of other designs which combine ideas from these basic concepts and make claims of superior performance. However, most have no respectable laboratory measurement data to back up the claims and some amount to nothing more than multiple "random" surfaces which may have some scattering but which likely do not produce diffusion.
Very Small Room Diffusers
Of all the designs, theoretically only the QRD, Skyline and Fractal diffusers have potential for the Small Room studio. On closer inspection, only the QRD diffuser is has practical application for the Very Small Room acoustic space.
  • While Fractal products are advertised, there is limited performance measurements and data for Fractal diffusers in small spaces.
  • Skyline diffusers have been successfully used (as in the photo above) and may even be the ultimate design for very large rooms. However, well-designed Skyline diffusers are very heavy (you can't just build them out of foam) and the design depth can be excessive which is not compatible with Very Small recording spaces.
QRD Diffusers
The QRD diffuser, therefore, appears to still be the best choice for Very Small Studios. The QRD:
  • Is technically the most understood and is precision designed from mathematical relationships
  • Has the most available measurement data and the most anecdotal performance reporting
  • Is technically complex to design and build, but can be constructed with minimal weight and cost
  • Allows some N-length designs can minimize the design depth
  • Can be designed for improved diffusion via maximal length coding techniques
  • Is readily designed using the QRDude WinPC application which is available free on-line
QRD Terminology
The free QRDude PC application does the number crunching and produces build measurements. The hard part is deciding the best combination of design variables to optimize the design solution for a Very Small Room. First, here is a list of QRD terminology:
  • Spatial dispersion
    • Multiple reflections of a sound wave in differing directions
  • Temporal dispersion
    • Multiple reflections of a sound wave with differing times (phase)
  • Scattering
    • The spatial dispersion of a sound wave
    • Does NOT assume any change in phase between the reflections
  • Diffusion
    • The Spatial AND Temporal dispersion of a sound wave
    • Diffusion is accomplished by multiple surfaces (wells) at differing distances from the source
  • Well
    • A single, 5-sided cavity, open toward the room, whose depth determines the phase of the reflected sound wave
    • All surfaces must be sealed to each other
  • Fin
    • A thin, but rigid, wall which separates two wells and forms one side of each well
    • Generally the fin should be as thin as possible while remaining rigid (does not easily vibrate with room sounds)
    • Rigid material of 1/8-in thickness is typical
  • Design Frequency
    • The lowest frequency at which "true theoretical diffusion" is possible
    • This is NOT a sharp cut-off. It is the transition frequency for diffusion being replaced by simple scattering
    • Scattering can be effective down another two octaves below this frequency
  • Scattering - Diffusion Crossover
    • Above the Design Frequency, an ideal diffuser provides primarily diffusion
    • Below the Design Frequency, the ideal diffuser provides less and less diffusion but still scattering
    • This is a result of the limited phase difference for a given well depth at lower and lower frequencies
    • This is why building diffusers to replace bass traps is impossible in Very Small Studios
    • This is also why the Blackbird Studio D (photo above) used VERY deep diffusers
  • HF Cutoff
    • The practical upper frequency limit for theoretical diffusion to exist
    • Again, it is not a hard barrier, it is just a design limit
    • Choice of materials can easily influence this limit
  • N
    • The number of wells in a single non-repeating sequence of well depths
    • Multiple sets of N-number of wells are assembled in a sequence to form a single diffuser
    • Only specific values of N can be used in the design: 3, 5, 7, 11, 13, 17, ... etc
    • For Small Rooms, anything over about 11 becomes impractical for reasons explained later
  • Depth
    • A Very Small Room studio has very little spare space and even a 6-in depth will be "felt" as an encroachment into the room
    • While diffusers of 3-in depth can be designed, they lack the necessary low frequency performance
    • The general rule is to design with as much depth as can be accommodated
  • Sections
    • In general, the more sections that can be assembled, the better the diffusion
    • However, just repeating the same section 10 times is not optimal -- see Barker Codes
  • Well Width
    • Well width is more flexible but does help define the overall length of the diffuser
  • Well Width/Depth Ratio
    • Ratios of 1/2 to 1/1 behave similarly and are more common with very large diffusers for large spaces
    • Low ratios allow covering a larger wall area without as much construction complexity
    • A ratio of 1/4 to 1/8 is typically considered the limit before the well develops additional losses
    • This ratio is not a hard limit like the 1/5 ratio of the QRDude application
  • Diffusion Lobes
    • Most practical diffusers do not produce uniform diffusion of the reflected sound
    • All diffuser reflect sound with a series of "lobes" of peak energy separated by nulls
    • As N increases so do the number of lobes and, generally, greater diffusion
  • Modulation
    • Changing one of a sequence of otherwise repeating N-length sections
    • The purpose is to 'disrupt' a repeating pattern and make the lobes less regular
    • This tends to improve the diffusion
  • Maximal Length Codes
    • Used to create modulation of a QRD
    • These are binary sequences of '1's and '0's with pseudo-random sequences
    • These codes are used in communication to 'spread' a signal's energy over a wide bandwidth
    • These codes are also useful to diffuser design
  • Barker code
    • A unique set of code sequences which can be applied to diffusers
    • The 5-length Barker Code is expressed as:  +1 +1 +1 -1 +1
    • The '+1' refers to a "normal" diffuser well-depth sequence (11 wells long for N=11)
    • The '-1' refers to an "inverted" diffuser well-depth sequence
    • The coded pattern provides some pseudo-random distribution effects on an otherwise uniform lobe pattern
    • This pseudo-random effect significantly improves diffusion in multi-section QRDs
Very Small Room QRD
For this Very Small Studio, a number of QRD design features are desirable:
  • An N=11 design because well depths are the same for 'normal' and 'inverse' variants
  • A 5-section, Barker-Code modulated sequence [+1 +1 +1 -1 +1]
  • Well-width of 1-in because foam sheeting comes cheap in this thickness
  • 1/8-in thick fins because Lauan hardwood ply is the cheapest, rigid, thin material (plastic is expensive, metal heavy)
  • 1/8-in thick hardboard is also cheap, but 4x8 Lauan ply is 12 lbs/sheet and 4x8 hardboard is 23 lbs/sheet
  • Design goal of 1 kHz 'design frequency' to get scattering down to 500 Hz
  • Max of 6-in depth due to space constraints
  • Anecdotal evidence suggests not to worry about the "theoretical listening distance" with this Very Small Studio size
  • Keep total weight down below 30 lbs for a 2x5-ft panel
  • Build 2 panels (5-ft wide, 2-ft high, fins vertical) and mount one the reverse of the other to increase modulation
  • Construct each panel as 5 sub-panels to make construction more modular

QRD Design Process

Notes from books by Cox and D'Antonio:
  • Experimental results show 1-in well width can be viable for well depths as much as 16-in
  • Narrow well absorption losses are not frictional
  • Resonance transfer between wells (one well resonant and the next one is not) cause most of the attenuation
  • Wells MUST be sealed to reduce absorption
  • Sealed wells refers to avoiding Helmholtz resonators formed by a gap to a hollow cavity below the well
  • ANY close-proximity cloth covering causes significant absorption [interferes with well-to-well resonance coupling]
  • Do NOT cover a QRD diffuser with fabric. Fabric can add 10 dB of attenuation.
  • If fabric covering is mandatory, then use very acoustically transparent material and keep it 3-5x the well-width out in front.
Given these guidelines, start with a value for N ...
  • N=5 requires very wide wells so, in small spaces, can't get enough periodicity to make QRD work properly
  • N=7 is better but still too few lobes and the inverse wells are deeper than the normal wells - for the same LF
  • N=7 / N=5 modulated requires wide wells because of the N=5
  • N=13 is physically longer per period but uses convenient 1-in wells - still allows Barker modulation
  • N=11 has same depth for Normal and Inverted, can use 1-in well width, can get to 6 kHz and down to 555 Hz scattering
  • Use 5-period max as grating lobes increase with periodicity - lobes have narrow nulls between
  • Wide well widths makes specular reflections worse, too narrow, below 1-in, starts to cause absorption with frictional losses
  • 1-in wells fits nicely with 1-in thick foam board spacing and 1.25-in width would be 75-in over-all length - too big
  • QRDude limits the well depth/width ratio to 5:1 but this is arbitrary. At 1 kHz, QRDude suggests 1.14-in well width
  • The Design Frequency was set to 1 kHz and use 5.5-in well depth but keep the 1-in well width due to materials
Newport's QRD
So, plug the numbers into QRDude then build a spreadsheet to view the combined data. These are the results:
  • N=11+4,6 design, 5-section, modulated with Barker Code [+1 +1 +1 -1 +1]
  • Scatter LF = 503 Hz
  • Diffusion LF = 1,006 Hz
  • HF Cutoff = 5,931 Hz
  • Fin Width = 0.125-in
  • Well Width = 1.0-in (ignore QRDude's suggested 1.14 limit)
  • Well Shift = -6
  • Period Width = 12.51-in
  • Max Well Depth = 5.51-in
  • Number of Sections = 5
  • Panel Inside Width = 12.25-in
  • Well Length ~= 2-ft
  • Total Width = ~62-in
  • Estimated weight = ~35 lbs
QRD Materials
  • 6ea 1/8-in 4x8-ft sheet Lauan hardwood ply
  • 5 ea 1-in thick 2x4-ft sheet EPS foam insulation
  • 1/2-gal carpenter's glue plus stain and polyurethane