Acoustic holography essentially assumes that sound on a hologram (plane) is perfectly coherent. This is simply because acoustic holography exhibits how the sound pressure, or other acoustic variables of same frequency look like in the plane of interest. It is noteworthy that any two pure tones are coherent. However, this is, in the strict sense, very ideal assumption in reality. We always meet the signals that share the same band of frequency but not perfectly coherent. If the pressure signals that we measure to construct the hologram are not perfectly coherent or poorly coherent, then the way to implement acoustic holography must be appropriately reformulated. This is the key motivation of this thesis.
The reformulation assumes that a hologram consists of multiple coherent fields at the frequency of interest. That is because non-coherent sound is the result of multiple independent sources but an individual source produces coherent sound. This assumption leads to two problems: How many coherent fields do we need for a good hologram? Does each coherent field have a physical meaning? The first question is practically related with the number of references in step-by-step measurement. Its answer is that we need references as many as independent sources. However, it is difficult to know the number of independent sources in the sound field of low coherence. The second question requires decomposing a hologram or predicted sound pressure distribution, for example, into those due to individual sources. Otherwise, it is practically difficult to understand a holography result. This is simply because it is the summation of results due to individual sources. To separate the contribution of individual sources to the measured pressure or predicted information, conventional methods have to place the sensors near sources. As a result, they require prior information on source positions. However, it contradicts one of the important goals of acoustic holography. It is noteworthy that we often use acoustic holography to identify the source positions.
The first objective of this thesis is to establish step-by-step measurement in the sound field of low coherence. This thesis shows that the measurement result converges to the true one as the number of references increases. In order to check whether the number of the references is sufficient, this thesis proposes to check the convergence as the number of references increases. This thesis also shows that the source converges more rapidly as it transmits higher energy. This implies that we can see important sources in spite of the insufficient references. The reference positions do not seem to be important in the sound field of low coherence. Measurement noise, which is the other cause of low coherence, slows down the rate of convergence and generates a spatial random error due to insufficient average number. As an example of the sound field of low coherence, acoustic holography for the wind noise of a car is performed.
The second objective is to propose an applicable source decomposition method for acoustic holography. The proposed method uses the maximum pressure on a source plane. This is similar to the conventional methods measuring signals near sources. However, the proposed method uses signals predicted by acoustic holography. Therefore the proposed method does not require prior information on source positions. A six-speaker and vortex shedding experiment verify the proposed method. The proposed method is also applied to acoustic holography for the engine and wind noise of a car.
