PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen,
Germany

Design of a new testing chamber to determine the absorption,diffusion and scattering coefficients
Peter D’ANTONIO 1; Melanie NOLAN 2; Efren FERNANDEZ-GRANDE 3; Cheol-ho JEONG4RPG Acoustic Systems, LLC, USA

12, 3, 4

Acoustic Technology, Department of Electrical Engineering, Technical University of Denmark, Denmark

ABSTRACTThis presentation describes a design for a new 285 m3 testing chamber that will allow themeasurement of the random incidence absorption coefficient, according to the current revision of ISO
354, the scattering coefficient, according to ISO 17497-1, the diffusion coefficient, according to ISO
17497-2 and the normal incidence low frequency absorption coefficient, according to ISO 10534-2.
Both dome-shaped boundary diffusors and hanging convex panels are used to provide satisfactory
diffusivity, which is verified using a 200 mm reference absorber. The isotropy of the incident sound isevaluated with a new SOund Field Analysis Recorder (SOFAR) and quantified by an analysis of thewavenumber spectrum. As desired, a scattering coefficient or diffusion coefficient apparatus can bebrought into the rev room to measure these data. A reflection free volume is provided in the chamber
for boundary method diffusion coefficient goniometer measurements. A new FDTD simulation
program will be described to determine the diffusion and scattering coefficients of any 3D surface inthe near and far field. A steel and concrete lined low frequency impedance tube measuring 0.60 m x
0.60 m x 5.8 m long and 7 tons will be used to measure absorption from 25-250 Hz.
Keywords: Coefficients, Measurements, Isotropy

1. INTRODUCTION

This paper describes the planned Acoustical Research Center (ARC), which is a private testing anddevelopment lab at RPG to determine the absorption, scattering and diffusion coefficients according
to ISO standards. The ARC will include a 285 m3 reverberation room, a low frequency impedance tube
to extend measurement of the normal incidence absorption coefficient down to 25 Hz, a scattering
coefficient apparatus to determine the random incidence scattering coefficient and a boundary planegoniometer for testing samples at 1:5 scale. Since this is not a commercial facility, we had toeconomically modify a non-ideal space. As of this writing the ARC is nearing completion and thehope is to provide experimental measurements at the ICA conference in Aachen.
The random incidence absorption coefficient is an essential parameter is acoustical design and yet
more than 100 years after the reverberation room method was suggested, we are still not able tomeasure it accurately. While the intra-lab precision is high in most laboratories, the accuracy is
uncertain and the lack of agreement among labs is not acceptable. Therefore, the ISO 354 (1) standard
is under continual development and revision. Much more recently, a scattering coefficient, measured
in a reverberation chamber and subject to its limitations, has been enshrined as ISO 17497-1 (2) tocomplement the absorption coefficient in geometric computer models. The new lab will utilize therevised ISO approach to evaluating diffusivity with a reference absorber. We also plan toexperimentally measure the degree of isotropy of the incident sound with a new SOund Field Analysis
1 dr.peter.dantonio@gmail.com; pdantonio@rpgacoustic.com
2 melnola@elektro.dtu.dk
3 efg@elektro.dtu.dk
4 chj@elektro.dtu.dk

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Recorder (SOFAR), which will measure thousands of impulse responses in proximity to the reference
absorber to determine the wavenumber spectrum. The wavenumber spectrum is then expanded into a
series of spherical harmonics, and the moments from this expansion are used to characterize theisotropy of the wave field, according to a method developed by Nolan (3).
The sound diffusion coefficient is determined with a new boundary method goniometer according
to ISO 17497-2 (4). The diffusion coefficient, d, is a measure of the uniformity of the reflected sound.
This is used in diffuser design and allows acousticians to compare the effectiveness of surfaces andgive performance specifications. Using the polar responses obtained from the goniometermeasurements, a correlation scattering coefficient can also be determined by a method proposed by
Mommertz (5). The method correlates the scattered pressure polar responses from a test surface and areference flat surface. The difference between the definitions of the scattering and diffusion
coefficients may appear subtle, but it is significant (6).To extend the low frequency capability of thetest chamber to measure the normal incidence absorption coefficient down to 25 Hz, a 7 tonsteel-faced concrete impedance tube measuring 0.6 m x 0.6 m x 5.8 m was installed in the room.
Following this experimental testing and simulation overview, we will briefly mention the potential ofmetamaterials in developing the next generation of absorbers and diffusers for architectural acoustics.

2. TEST CHAMBER DESIGN
2.1

Existing space

Figure 1(left) Existing space; (right) Rendered rev room rotated counterclockwise 90 degrees with thefront wall in Fig. 1 (left) on the left
The existing space, shown in Figure 1 (left), was formerly used as a blast room for a chemicalcompany. The room had a concrete floor and three permanent cinderblock walls. The short wall had a“garage-style” corrugated metal door and one of the long walls had a window. The roof, which had tobe replaced, was fitted with panels that would open from the impact of an explosion. The volume was
503 m3 and the goal was to partition the room into a test chamber and a control room. The capabilityof utilizing suggested dimensional ratios was not possible due to the existing walls and the only
dimensional variables were shortening the long wall and adding a ceiling close to the existing ceiling
trusses. Due to weight issues, the new ceiling, consisting of two layers of 16 mm drywall and was
attached to 406 mm spaced 51 mm x 152 mm planks resting on the lips of the ceiling trusses. The
corrugated door was removed and filled with cinderblock, as was the window. To determine theoptimal location of the new wall in the long dimension, a cuboid image method (7), called the Room
Sizer, was utilized to find dimensional ratios with the lowest standard deviation in the modal
frequency range. The floor, walls and ceiling surfaces were sealed and painted to minimize porosity.
The rendered, renovated rev room, with diffusing surfaces, impedance tube and reference absorber, isshown in Figure 1 (right).
2.2 Dimensions, diffusive clouds and domes
The length, width and height of the rev room are 7.89 m, 6.27 and 6.07 m, respectively, with avolume of 300.3 m3 and surface area of 270.8 m2. To achieve the necessary diffusivity in the chamber,(15) 1219 mm x 1524 mm overhead, transparent vinyl, 6.4 mm curved convex clouds, (20) 610 mm x
305 mm hemispherical domes and (21) 864 mm X 356 mm spherical cap domes were randomly
distributed, as seen in Figure 1 (right). The additional surface area added to the room by the domes,

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clouds, speakers, and impedance tube is 87 m2 , yielding a ratio of diffusor surface area to adjusted,
increased room surface area (358 m2 ) of 24%. The adjusted room volume, reduced by the volumes ofthe domes, (3) JBL SRX835P speakers and the impedance tube is 285 m3. The clouds are curved alongthe 1524 mm direction, forming a convex surface with a cord length of 1067 mm and a height of 460
mm, to diffuse low frequencies. To further improve diffusion at low frequencies, the clouds arearranged in a two-dimensional (2D) primitive root (PR) sequence. Not all one-dimensional (1D) PR
sequences can be converted into a 2D array via the Chinese Remainder Theorem (6). To convert a 1D
to a 2D PR array, the two factors must be coprime, meaning they have no common factors other than
1. A PR sequence based on a prime N, has (N-1) sequence values. The closest primes to 15 are 13 and
17. An N=17 PR sequence has 16 elements for which there are no two coprimes. Therefore, we
selected N=13, with coprimes of 4 and 3, forming a 4x3 array. To provide 15 clouds, we selected themost suitable 5 x 3 array from the larger periodic array, starting with the 6th sequence value, toaccommodate the cloud heights with other items in the room. The distances of the base of the convex
shapes from the ceiling are equal to the ratio of the sequence values/maximum sequence value
multiplied by the maximum displacement of roughly 3 m. This primitive root arrangement of theceiling clouds provides diffusion below 100 Hz.
2.3 ISO 354 experimental diffusivity evaluation
After measuring the empty rev room, Table 1 summarizes the 3-step, sequential addition of domes
and clouds to evaluate the equivalent absorption area and compare with the values required in therevised standard. The measured equivalent absorption of the reference absorber shall be equal to or
larger than the values in Table B2 (1) for the octave bands of 250 Hz and above. The correction factor
g, which is equal to the required absorption divided by the measured absorption, is determined inoctave bands, but applied to all third octave bands in the octave for samples under test.
Table 1. Three step diffusivity evaluation with domes and clouds
Domes

Clouds2

Step Length Wall SA m
1
2
3

#
4
2
2
8

2

2

SA m Opposite Wall SA m

0.61 # 0.86
0.29 3 0.4
0.29 3 0.4
0.29 2 0.4
8

#
1
1
1
3

2

2

SA m Width Wall SA m

0.61 # 0.86
0.29 1 0.4
0.29 2 0.4
0.29 1 0.4
4

#
3
3
3
9

2

2

SA m TD# TD SA 1.2 x 1.5 m

0.61 # 0.86
0.29 3 0.4
0.29 4 0.4
0.29 2 0.4
9

#
15
15
11
41

5.12
5.34
3.74
14.2

2

TC SA m TSA m TD+C2

SA m
5 3.725 3.725 3.7215

18.6 23.72
18.6 23.94
18.6 22.34
55.8
70

56

For example, in Step 1 the following diffusers are added to the room: (4) 0.61 m domes with asurface area (SA) of 0.29 m2 (after subtracting the base which is included in the room’s surface area),(3) 0.86 m domes with a SA of 0.4 m2 on the long wall of the rev room; (1) 0.61 m and (1) 0.86 m dome
on a short area of the opposite wall; (3) 0.61 m and (3) 0.86 m domes on the width wall and (5) convex
1.2 m x 1.5 m clouds with a total cloud surface area (TC SA m2 ) of 18.6 m2. The total surface area
(TSA m2 ) for Step 1 is 23.72 m2. The combined dome and cloud surface area is 70 m2, with 41 domes
and 15 clouds, totaling 56.
2.4 Experimental measurement of the isotropy coefficient
In addition to the ISO diffusivity test, we will investigate an experimental measure of the isotropyof the incident sound on the sample with a method proposed by Nolan (3). The method consists ofexpressing an arbitrary sound field on an array of sensors as the superposition of a set of plane waves.
The magnitude of the wavenumber spectrum is subsequently expanded into a series of sphericalharmonics and the moments of this spherical expansion are used to characterize the isotropy of theincident sound field. A wave field is termed isotropic if the wavenumber vectors of the incident planewaves are uniformly distributed over all angles of incidence. Consequently, all the energy of theangular spectrum resides on the monopole moment of its spherical harmonic expansion. This will not
be the case if the contributing waves cover just a partial section of the solid angle, as the higher-ordermoments would characterize the wave field. This quantity is suggested as a potential isotropy
indicator.

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A conceptual approach to measuring the sound field necessary to determine the isotropy
coefficient is shown in Figure 2. The device is called a SOund Field Analysis Recorder (SOFAR) andis placed in close proximity to the reference absorber in the rev room. The device consists of a
movable gantry containing 32 microphones spaced 25 mm apart located within a frame, which allows
accurate displacements of the gantry every 25 mm parallel to the reference absorber. 32 impulse
responses are recorded at each of 32 positions for a total of 1,024 impulse responses in the firstmeasurement plane. The frame supporting the gantry is moved up 25 mm and an additional 1,024
impulse responses are measured. This data collection is repeated in two additional upward planes
separated by 25 mm for a total of 4,096 impulse responses. The 32 electret microphones are connected
to preamps connected to A/D converters, which are input into a computer running the data collection
process. The impulse responses are processed to provide the needed pressure responses.

Figure 2. SOFAR concept illustration
A prototype of the SOFAR is in development. The device consists of 4 vertical elements to whicha rectangular frame is attached. The left and right legs of the frame contain rectangular plates to which
the gantry containing the 32 mics is attached. The frame containing the mic gantry is mechanicallyadjustable vertically. The leg on the right side contains a stepping motor and encoder to automaticallyadvance the gantry by 25 mm after each data collection for the 32 positions. The frame is thenmechanically lifted 25 mm higher for the next cycle of impulse response measurements and repeated
at two additional heights above the sample. Thus, generating the 4,096 impulse responses which are
fitted to determine the magnitude and phase of the wavenumber spectrum.

3. DIFFUSION COEFFICIENT GONIOMETER

There have been continuing advances in 2D goniometer data collection over the years. From 1983
to 1993, impulse response data were collected with a TEF analyzer using one microphone, which was
manually repositioned every 5 degrees, after each impulse response measurement. In 1994, scaled
measurements were made with the first boundary plane goniometer, utilizing 37 fixed mics every 5
degrees. In 2011, new hardware and software were added to collect 32 simultaneous impulse

Figure 3. Ellipsoid illustrating the reflection freezone in the rev room for goniometer measurements
responses. This was accomplished using (4) MOTU 8Pre preamps and a hard disk recording program.
To obtain the impulse responses, the recorded signals are deconvolved with the MLS stimulus. 32
channels of the scattered energy are recorded. The simultaneously collected data are then processed as

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described in ISO 17497-2 (4 ). The location of the goniometer in the rev room, along with its
transparent ellipsoidal reflection free zone, are shown in Figure 3.
In an effort to develop a 3D diffusion coefficient simulation program, we re-examined datacollected in 1998 at Salford University. In Figure 4 (left), we show the 13 specified positions for thesource loudspeaker according to ISO 17497-2 and a schematic illustration, Figure 4 (center), showing
two concentric hemispherical arcs capable of being rotated about the vertical axis. The inner arc
contains 32 microphones separated by 5 degrees and the outer arc contains the speaker, which is able
to assume the 13 angles of elevation and azimuth. Figure 4 (right) shows a 3D goniometer in an
anechoic chamber built in 1998 at Salford University (8). A sample is located at the origin.

Figure 4. Left: ISO 17497-2 loudspeaker positions, 3D schematic goniometer, actual goniometer
apparatus
An extensive set of measurements were made on the 2D (blue) and 3D (red) goniometers and the
diffusion coefficients were also simulated with a boundary element program (green BEM). The
comparison for a square based pyramid are shown in Figure 5. The exceptional accuracy of the BEM
calculation, compared to the 3D and 2D goniometer measurements, suggested that the diffusion
coefficient could be numerically simulated. For an asymmetric sample, the measurement requires 936(360/5x13) measurements, i.e. 72 measurements with 5 degree increments for each of the 13 speaker

Figure 5. Comparison of measurements and predictions at 4
kHz for a square based pyramid
positions. This yields 34,632 (936 x 180/5 microphones) impulse responses. The measurements take4-5 hours and suggest the need for a numerical simulation.
An FDTD Diffusion Coefficient Calculator (DCC) program to virtually simulate full scale, 3D
scattering surfaces, in the near and far field, without any physical prototype, was developed as part ofHassan Azad’s Ph.D. thesis (9). The FDTD solver used is called ParallelFDTD and is accessible
through its developer’s GitHub account. It uses the standard rectilinear, SLF (standard leapfrog)
FDTD scheme for the calculation of the sound pressures inside the domain and NFTFF
transformations to determine the far field polar responses. One of the most signiﬁcant advantages of
FDTD is its ability to be programmed in a parallel manner, which makes it suitable to be run on many
parallel computing engines, such as General-Purpose Graphical Processing Units (GPUs) on the AWS
cloud.

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Figure 6. Virtual diffusion coefficient schematic
The agreement with BEM and experimental measurements is excellent. In Figure 6, we show aschematic of the DCC in a virtual room with the 13 microphone positions (black dots) and themicrophone arc with 37 microphones in two of the 72 positions.

4. SCATTERING COEFFICIENT MEASUREMENT

A full scale scattering coefficient apparatus can also be placed in the rev room for ISO 17497-1
measurements. A photo of the device’s rotation framework, the reflective base and several periods of
600 mm x 600 mm square 2D primitive root samples, surrounded by “eyebrows”, is shown in Figure
7.

Figure 7. Scattering coefficient apparatus. Left: rotating framework; middle: reflective base; right:
square 2D primitive root sample

5. LOW FREQUENCY IMPEDANCE TUBE

To extend the absorption coefficient range below 100 Hz, we developed a 0.6 m x 0.6 m x 5.6 m, 7
ton impedance tube, fabricated from steel covered concrete. Figure 8 (left) shows the sample lid in the

Figure 8. Low frequency impedance tube
open position. Figure 8 (middle) shows the lid closed and Figure 8 (right) shows a membrane absorberwith the movable measurement mic in one of three positions in front of the sample. The transfer

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function, reflection factor and the normal absorption coefficient are determined from the impulse
responses determined at 2 microphone position. Then by overlapping data from microphone pairs(1,2; 1,3; and 2,3) the normal incidence absorption coefficient and complex surface impedance can be
determined from 25 Hz to 250 Hz.

5.

FUTURE DEVELOPMENTS

Figure 9. Temporal and spatial
characteristics of acoustical surfaces
A schematic of the top three existing acoustical surfaces and a new Returner, are illustrated in
Figure 9, along with their temporal and spatial response,. The Reflector redirects incident sound in the
specular direction, in which the angle of incidence equals the angle of reflection. The Absorberattenuates incident sound. The Diffuser uniformly distributes incident sound and the Returner
redirects incident sound back to the direction of incidence, like a boomerang. The Returner is formed
from three mutually perpendicular polygons.
While these surfaces provide acousticians with useful devices to design spaces, they have
limitations. Today, the burgeoning field of metamaterials offers the possibility of a new generation ofultra-thin, subwavelength innovative acoustic materials, which provide extraordinary acousticalcharacteristic to move beyond the behavior of naturally occurring materials. Metamaterials derive
their properties not from the properties of the base materials, but from their newly designed structures,very similar to the original reflection phase gratings. The material properties of interest for acoustic
metamaterials are the effective mass density and the effective bulk modulus. By optimally designingsurfaces with the appropriate sign and values of these variables, a host of novel properties can beobtained. One approach particularly suited to developing broad bandwidth perfect absorbers andbroadband diffusers utilizes coupled periodic arrays of Helmholtz resonators, at scales that are smaller
than the wavelength of the phenomena they influence. Various approaches to produce perfectabsorption (10, 11) or broadband diffusion (12, 13) optimize appropriate phenomena to produce thedesired performance, namely taking advantage of slow sound, thermal and viscous losses, acoustic
dispersion, rainbow-trapping and critical coupling.

6. CONCLUSION

As of this writing, we are in the process of completing the final commissioning of a new Acoustical
Research Center (ARC) at RPG, which will allow the measurement of the normal and random
incidence absorption coefficient and the scattering and diffusion coefficients according to ISO
standards. Since the lab is still in development, this paper is limited to a description of the design andgoals. It is the hope to present experimental measurements at the time of the conference. The rev room
contains both spherical cap domes and suspended convex clouds spaced from the ceiling in a primitiveroot sequence to provide low frequency diffusion below 100 Hz. Measurements will be madeaccording to (1) to obtain the scaling factor, g, to reduce the inter-lab variance. A described SOFAR
device, which is in prototype design, will be used to experimentally determine the randomness of theincident sound on the reference sample, using the wavenumber spectrum. A low frequency normal

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incidence, impedance tube is described to extend the frequency range of the rev room down to 25 Hz.
When desired, a scattering coefficient or diffusion coefficient apparatus can be brought into the rev
room to measure these data. A new FDTD diffusion coefficient calculator is described allowing
predictions on virtual samples in the near and far field. Lastly, a brief discussion is offered on theimportance of the burgeoning field of metamaterials to provide the next generation of sound absorbers
and diffusers.

ACKNOLEDGEMENTS

D’Antonio would like to thank RPG and its employees for providing the space for the Acoustical
Research Center and for the difficult task of converting a previously unsuitable space into afunctioning reverberation room. D’Antonio would also like to thank Lea Ann Pelleschi for all of the
CAD drawings and animations.

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