# Diffuseness Quantification in a Reverberation Chamber and Its Variation with Fine-Resolution Measurements

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## Abstract

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## 1. Introduction

Category | Metrics | Reference | Measurement | Description |
---|---|---|---|---|

Homogeneity | The relative standard deviation of decay rate | ASTM C423-17 [1] | Decay rates or SPLs in multiple locations using fixed microphones or moving microphones. | Lower values of deviations across the sound field indicate higher diffuseness. |

Total Confidence Interval | ASTM E90-09 [19] | |||

The spatial standard deviation of the reverberation time | Bartel & Magrab [11], Davy [29] | |||

Spatial Uniformity | Wang et al. [13] | |||

Isotropy | The diffuseness estimate | Lokki [25] | Using spherical microphone arrays to analyze the direction of energy flow. | The isotropic sound energy from all directions means high diffuseness. |

Directional Diffusivity | Gover et al. [26] | |||

The spherical harmonic covariance matrix | Epain & Jin [27] | |||

Wavenumber spectrum | Nolan et al. [16] | |||

Indirect method | Number of peaks | Jeon et al. [23] | Analyzing the details of the impulse response. | Less fluctuation of impulse response in the early decay means higher diffuseness. |

Kurtosis | Jeong [15] | |||

Mixing time | Prislan [26] | |||

Degree of time fluctuation | Hanyu et al. [14,21] | |||

Maximum absorption coefficient | ISO 354:2003 [2] | Measuring the sound absorption coefficient with an increasing number of diffuser panels. | The optimum diffuse configuration is achieved when it produces the maximum absorption. | |

Reference absorber | Scrosati et al. [6] | Comparing the equivalent absorption area of the reference absorber with a minimum value. | The absorption correction factor can be used to quantify the reverberation chamber. |

## 2. Methods

#### 2.1. Diffuseness Metrics

#### 2.2. Measurement

#### 2.3. The Number of Measurement Samples Required for Diffuseness Quantification

## 3. Results and Discussion

#### 3.1. Diffuseness Quantification

#### 3.2. The Effects of the Number of Measurement Positions on Diffuseness Metrics

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A squared impulse response ((${p}^{2}\left(t\right)$), a Schroeder decay curve (${E}_{S}\left(t\right)$) and a squared decay-cancelled impulse response (${h}^{2}\left(t\right)$) measured in an empty reverberation room at 1000 Hz for DTF calculation.

**Figure 2.**

**Left**: A picture of the experimental setup in the reverberation room in Concordia Acoustics Lab.

**Right**: A 3-D model of the reverberation chamber. The diffusers hanging from the ceiling are indicated in light yellow. A steel rotating diffuser is located near the upper-right corner. The measurement grid spacing (X, Y) is 40 cm.

**Figure 3.**The measurement grid (11 × 12) used for the impulse response measurement. The distance between each microphone position was 0.4 m. 120 points were measured in total. Locations marked in red were removed to avoid getting too close to the sound source or rotating diffuser.

**Figure 4.**Diffuseness metrics of (

**a**) ${s}_{rel}$, (

**b**) ${\sigma}_{SPL}$ and (

**c**) $\mathrm{DTF}$ over 120 microphone positions measured in six diffuse conditions: (1) Empty, (2) Two hanging diffusers, (3) Four hanging diffusers, (4) Six hanging diffusers, (5) Rotating diffuser only, and (6) Rotating diffuser & six hanging diffusers.

**Figure 5.**The diffuseness metrics of (

**a**) ${s}_{rel}$, (

**b**) ${\sigma}_{SPL}$ and (

**c**) $\mathrm{DTF}$ were measured in two diffuser configurations: (1) Empty room and (2) Room equipped with six hanging diffusers as a function of an increased number of microphone positions at 125 Hz. The error bar presents the 95% confidence interval of the metrics computed using 50 repetitions of a subset of combinations randomly selected among the full data set of 120 microphone positions.

**Figure 6.**The 95% confidence interval of diffuseness metrics: (

**a**) ${s}_{rel}$, (

**b**) ${\sigma}_{SPL}$ and (

**c**) DTF measured in the empty room as a function of frequency with an increased number of microphone positions.

**Figure 7.**The coefficients of variation of diffuseness metrics: (

**a**) ${s}_{rel}$, (

**b**) ${\sigma}_{SPL}$ and (

**c**) DTF measured in the empty room as a function of frequency with an increased number of microphone positions.

**Table 2.**Diffuser configurations of the reverberation chamber, including the total surface area of the diffusers.

Diffuseness Condition | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 |
---|---|---|---|---|---|---|

Diffuser configuration | Empty room | Two hanging diffusers | Four hanging diffusers | Six hanging diffusers | Rotating diffuser | Rotating & Six hanging diffusers |

Total diffuser surface area (m^{2}) | 0 | 4.16 | 8.32 | 12.48 | 4.14 | 16.62 |

**Table 3.**The coefficient of variations (CV) of the diffuseness metrics at 100 Hz and 1000 Hz with a different number of measurement samples.

Metrics | Freq (Hz) | Number of Measurement Samples | |||||
---|---|---|---|---|---|---|---|

5 | 9 | 12 | 15 | 20 | 24 | ||

${\mathit{s}}_{\mathit{r}\mathit{e}\mathit{l}}$ | 100 | 26.06% | 18.73% | 15.01% | 9.50% | 8.98% | 7.27% |

1000 | 39.85% | 24.55% | 21.03% | 18.79% | 16.54% | 12.47% | |

${\mathit{\sigma}}_{\mathit{S}\mathit{P}\mathit{L}}$ | 100 | 34.07% | 21.14% | 17.59% | 14.68% | 12.02% | 7.64% |

1000 | 42.76% | 28.22% | 17.91% | 17.56% | 17.31% | 11.24% | |

DTF | 100 | 10.54% | 7.94% | 7.31% | 5.10% | 4.45% | 4.29% |

1000 | 6.11% | 5.20% | 4.11% | 3.52% | 3.09% | 2.39% |

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Zhang, S.; Lee, J.
Diffuseness Quantification in a Reverberation Chamber and Its Variation with Fine-Resolution Measurements. *Buildings* **2021**, *11*, 519.
https://doi.org/10.3390/buildings11110519

**AMA Style**

Zhang S, Lee J.
Diffuseness Quantification in a Reverberation Chamber and Its Variation with Fine-Resolution Measurements. *Buildings*. 2021; 11(11):519.
https://doi.org/10.3390/buildings11110519

**Chicago/Turabian Style**

Zhang, Shuying, and Joonhee Lee.
2021. "Diffuseness Quantification in a Reverberation Chamber and Its Variation with Fine-Resolution Measurements" *Buildings* 11, no. 11: 519.
https://doi.org/10.3390/buildings11110519