利用微氣泡衰減估測微氣泡大小分佈

Abstract

微氣泡分佈是一種顆粒大小和數量的分佈，不同顆粒大小的微氣泡有著不同的共振頻率，此共振頻率會讓微氣泡在該頻率下會有最強的回波訊號，傳統上估測微氣泡大小的方法有很多種，迭代近似法、非線性雙頻率估測法等，然而這些方法只能估測分佈較大的微氣泡分佈，對於欲估測小顆微氣泡分佈有許多的限制，今我們使用的方法欲改良上述所說無法求得微氣泡分佈較小的限制，所估測的微氣泡半徑介於1um-10um。 本研究模擬如何利用微氣泡衰減以反矩陣的方式來估測微氣泡分佈，使用的微氣泡分佈模型為瑞利分佈，以掃頻的方式來模擬發射不同頻率的窄頻pulse下其單顆微氣泡的反射訊號和頻譜上強度的變化，並使用bubblesim模擬散射訊號和計算出散射截面積，消光截面積和微氣泡衰減，再套入衰減關係式來利用反矩陣和奇異值分解方法來計算微氣泡大小分佈。 最後探討在實際情況下探頭和雜訊對於估測微氣泡衰減的影響和困難度，探頭會讓其中心頻以外的發射訊號減弱，加上受到雜訊影響SNR會變的很低，近而讓估測出來的微氣泡衰減失去原本的曲線特性，因此我們必須調整這兩個參數讓得到的衰減曲線符合實際情況，最後才能探討使用奇異值分解估測微氣泡分佈的準確性。

Bubble size distribution is a distribution of particle size and number of different particle size. Each bubble size have different resonant frequency. And the resonant frequency of bubble will make strong scatter signal at that frequency. Estimate the bubble size distribution can help to decide what the frequency of transmit signal will produce strongest scatter signal. In traditional, there are many methods to estimate bubble size distribution, ex: iterative approach and linear double frequency. However, these methods can only estimate the distribution of larger bubble distribution. If want to estimate the distribution of small bubble there will be many limitations. The method we use is to improve the restriction of the estimation small size distribution(1um~10um). In this study, we use the inverse matrix to estimate the bubble size distribution. We assume the distribution follow the Rayleigh distribution. We use frequency sweep to transmit narrowband pulse signal and see the single bubble scatter signal. Then we use bubblesim to calculate scatter cross section, extinction cross section and attenuation. Use the relationship between attenuation and extinction cross section and inverse matrix, SVD method to calculate the bubble size distribution. Finally, we discuss the probe and noise impact and the difficulty of estimating the attenuation of bubble in the real situation. The probe will make the transmit signal weaken except the center frequency. And under the noise effect the transmit signal SNR will become very low. Then let the bubble attenuation loss original curve characteristic. Therefore, we need to adjust these two parameter to let the attenuation curve accord with real situation. Final, explore the accuracy method of use singular value decomposition to estimation bubble distribution.