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Acoustic Holography

Content:

  • Which criteria are most important for accurate sound source localization?
  • What is near-field acoustic holography?
  • What are the advantages & disadvantages of using near-field acoustic holography?
  • How can the disadvantages be overcome?
  • How can near-field acoustic holography be combined with simulation techniques?
  • More information about near-field acoustic holography


Near-field acoustic holography: a modern sound source localization technique

Finding out the exact source of a sound is a tough challenge for any acoustics engineer. Since the early 90’s, a number of methods, based on microphone arrays, have matured and are used throughout numerous industries. In general, the methods fall into three categories: near-field acoustic holography, beamforming, and inverse methods. Depending on the test object, the nature of the sound and the actual environment, engineers will have to select one method or the other. What that means for the near-field acoustic holography (NAH) technique is described in more detail below.

Which criteria are most important for accurate sound source localization?

These are two important criteria to assess the validity of sound source localization methods:

  • Spatial resolution is the ability to separate 2 sound sources. This is usually expressed in centimeters. It represents the closest distance between two sources, where they still appear to separately and do not merge into a single source. The lower the spatial resolution, the better the source localization.
  • Dynamic range expresses sound level differences in dB between real sound sources and their surrounding mathematical artifacts inherent to the sound source localization techniques. The higher the dynamic range, the better the source localization.

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Figure 1: Spatial resolution (left) and Dynamic range (right).

What is near-field acoustic holography? 

Near-field acoustic holography, also called NAH, is a technique where the microphone array is placed relatively close to the sound source – in the near field. It provides good results over the entire frequency range. Near-field acoustic holography was introduced in the mid-eighties, and industrialized in the mid-nineties. It has by now become a well-known technique.

The near field can be described as the area that is closer to the sound source than one or two wavelengths of the highest frequency. So if 3400Hz is the highest frequency of interest, then the near field would be within 10-20cm of the sound source.

Near-field acoustic holography measures sound pressure by arranging several microphones in a rectangular planar array. Microphones are regularly spaced both horizontally and vertically. The sound pressure in the plane is then back-propagated to the actual surface of the object. The spacing between the microphones determines the half-wavelength of the maximum frequency, and the size of the array determines the half-wavelength of the minimum frequency. The spacing also determines the spatial resolution: a coarsely spaced array cannot accurately localize sources on the fine mechanics of a small object.

The process to propagate this measured pressure field in one plane to another plane can be divided in 3 steps: 

  • I. The first step is the transformation of the acoustical pressure field on the array from the spatial domain to the wave number domain by means of a Spatial Fourier Transform
  • II. The second step is back-propagation of the different waves to the new defined plane, using the Dirachlet Green function. In order to optimize the spatial resolution so-called evanescent waves have to be included. These are near-field standing waves that occur only very closely to the sound source and decay exponentially. If too few are included, the spatial resolution is not optimal. Including too many evanescent waves, blurring of the hologram can occur. A special Wiener Filter is usually implemented in the standard algorithm to define the optimal number of evanescent waves. 
  • III. Finally, the last step is transforming the acoustics signal back from the wave number domain to the spatial domain by means of an inverse Spatial Fourier Transform.
The differences between various industrial implementations of the original near-field acoustic holography formulation lie in the exact implementation of the second step which is crucial to obtain a good spatial resolution.
 
Near-field acoustic holography requires that the array’s dimension matches the object size since it back-propagates sounds perpendicularly to the array’s surface. The array dimension in turn determines the number of required microphones and measurement channels. The array width depends on (1) the size of the object and (2) the minimum frequency of interest. For objects that are too big to reasonably match the size of an array, it is possible to use near-field acoustic holography to perform measurements in different patches, until the full surface of the object is covered. In that case, the object’s condition has to be stationary. If the condition is not stationary, it should at least be a repeatable transient condition, such as a run-up in function of rpm, or a repeatable impulsive noise, such as a door slam. If the minimum frequency of interest requires an array, which is far wider than the object, near-field acoustic holography still allows using an array that is of the same width as the test object. This yields correct source localization, at the expense of less reliable source quantification.
 
The spacing between microphones will be determined by (1) the maximum frequency of interest and (2) the granularity of the sound sources. If the maximum frequency is very high, the spacing becomes very small. Microphones that are placed too close to each other can cause interference in the respective sound fields. The recommended relative position of microphones should therefore not be less than 2.5cm. If the granularity of the sound sources is small (i.e. all the small components in a door lock), then the microphone spacing should be adapted to this, even if this is not needed for the maximum frequency. Too few points on the hologram do not let accurately pinpoint which component is the sound source. In both cases, the ideal number of microphones sometimes outnumbers the availability of transducers and acquisition hardware.

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Figure 2: Small air pump, air intake and air outlet analyzed with NAH.

Figure 2 shows an example of a small 12cm wide air pump. The hologram size is 27cm x 27cm, derived from 3cm spacing resulting in a maximum frequency of 5700Hz. Based on critical frequencies found in the spectrum, the various holograms pictured below show the rotating pump itself (left, 1150Hz), the air outlet (middle, 430Hz), and the air intake (right, 715Hz). This example demonstrates that it is possible to propagate to frequencies with a half-wavelength larger than the hologram size, as is the case for the middle hologram (½λ≈40cm). This still allows correct localization at the expense of less reliable quantification results. Besides that, with small structures, it is important to take the granularity of possible sound sources into account, and match microphone spacing accordingly. In this case, the 3cm spacing matches the size of the different small pump components.

What are the advantages and disadvantages of using near-field acoustic holography?

Near-field acoustic holography has following major advantages.  

  • Spatial resolution is independent of frequency. It equals the microphone spacing in the hologram. 
  • Using the Dirachlet Green function allows propagation from the measured pressure field to a velocity field. This method supports sound intensity calculations and, therefore, sound power for different zones or components. This means that the sound sources can not only be localized, but also quantified.
The near-field acoustic holography method is a very precise engineering tool for source localization. However, it has some disadvantages:

  • Near-field acoustic holography can only propagate to a surface that is parallel to the measured surface. The size of the propagated plane has to be identical to the measured plane. To localize a source on a complete vehicle, the measurement plane has to span the complete vehicle. For stationary applications and repeatable transient applications, such as slow engine run-ups or door slams, the data can be acquired in batches. As a result, it is possible to perform near-field acoustic holography measurements with a 20 to 30-channel data acquisition system.
  • The spacing between the microphones is defined by either the desired spatial resolution or the wavelength of the highest frequency one wants to analyze. So an increasing maximum frequency implies closer spaced microphones. From a practical standpoint, near-field acoustic holography is therefore limited to analyze higher frequencies because of the large amount of data that needs to be acquired. Also, at small microphone spacings, the sound pressure as measured by one microphone starts to get disturbed by the close presence of its neighboring microphones in the sound field.
How can the disadvantages be overcome?

As already indicated, for repeatable transients conditions, or transient conditions that rely on the rotational speed of an engine, near-field acoustic holography can measure in different patches. The other main disadvantage can be overcome by using a dedicated acoustic beamforming technique called near-field focalization.

Near-field focalization is an acoustic beamforming technique – which is a far-field sound source localization technique – that uses measurements in the near field. The same near-field acoustic holography measurement can therefore be reprocessed with this technique. In the near field, the sound waves do no longer arrive at the microphone as planar waves, but as spherical waves. The original beamforming back propagation can therefore be reformulated to deal with these waves. For acoustic beamforming and thus also near-field focalization, the spatial resolution is not constant anymore over the entire frequency range, but is proportional to the wavelength λ. Near-field focalization improves that spatial resolution to 0.44 λ.

When compared to near-field acoustic holography, there is no benefit of using focalization in the lower frequency range. However, there is a break-even point at which the spatial resolution of near-field acoustic holography is equal to focalization. Above that frequency, focalization improves spatial resolution. In fact, at the near-field acoustic holography frequency limit, near-field focalization improves spatial resolution by a factor of 2. Obtaining the same accuracy with near-field acoustic holography would mean that the spacing between the array microphones should be decreased by a factor 2. This translates to 4 times more microphones and requires a larger number of transducers and measurement channels, which increases hardware investments and maintenance costs. Using near-field focalization after the break-even point for near-field acoustic holography data means improved results at a lower cost.

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Figure 3: Spatial resolution versus frequency for different techniques

How can near-field acoustic holography be combined with simulation techniques?

Inverse Numerical Acoustics (or INA) is a method which reconstructs the surface normal velocities on a vibrating structure from the sound measured in the near field around the structure. This is of particular interest when the structure is rotating or moving, too light or too hot to be instrumented by accelerometers. The use of laser vibrometers is often of no remedy due to the complex shape of the source. The retrieved surface normal velocities can afterwards be used to carry out source ranking for different panels of the structure and to predict the pressure in the far field.
 
INA is a unique and hybrid solution as it combines experimental sound pressure data in the near field, measured by a microphone array for near-field acoustic holography, with Acoustic Transfer Vectors (ATVs) obtained from simulation: the technique is based on the inversion of transfer relations, which are for example obtained from an acoustic Boundary Element Model (BEM) formulation. Typically only a limited set of microphone points are used in the near field pressure measurements which means the INA problem is usually underdetermined, resulting in a non unique solution for the surface vibrations. Using Singular Value Decomposition (SVD) with appropriate truncation, the most physically meaningful solution can be extracted.

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Figure 4: INA-computed volume velocities on the left, measured on the right.

Summary 

As a general rule, near-field techniques are preferred solutions for sound source localization. When possible, they provide the best results in terms of dynamic range and spatial resolution. The combined near-field acoustic holography and near-field focalization approach delivers optimal results, as near-field acoustic holography is the most suitable technique in the low and mid frequency range, and near-field focalization most appropriate for higher frequencies.
 
As seen, there are some cases where combined near-field acoustic holography and near-field focalization is not practical: (1) it is not possible to measure in the near field, (2) the array size becomes too big, or (3) it is not possible to measure in patches due to rapidly changing operational conditions. In these cases, an acoustic beamforming solution will be chosen.

More information about near-field acoustic holography:
 
Go to the LMS International Acoustic Testing page to learn more about the LMS Test.Lab Array-based Holography and Focalization
 
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LMS Test.Lab Array-based Holography and Focalization