雙頻諧波影像(dual-frequency harmonic imaging)同時發射中心頻率為f0　與2f0　之雙頻組合波形並接收其產生的二次諧波(second harmonic)與互調變諧波(inter-modulation harmonic)進行成像，故在發射端與接收端均可完整利用探頭頻寬，但雙頻諧波信號的低訊雜比（signal-to-noise ratio, SNR）仍為其成像品質的主要限制。前期研究中發展了一特殊啾聲編碼波形（chirp）用以改善雙頻諧波影像之訊雜比，但該波形經脈衝壓縮後仍會因影像頻帶之間的互干擾而殘留軸向旁瓣訊號（range side-lobe）。本研究中提出軸向旁瓣反相消除法（range side-lobe inversion, RSI）以抑制該啾聲編碼波形之軸向旁瓣，藉由設計編碼波形的發射相位來達到軸向旁瓣反相效果，再與原編碼波形進行結合以消除雙頻啾聲編碼之軸向旁瓣訊號。我們進一步探討格雷編碼中影像頻帶互干擾問題，並與具備正交特性之高位元格雷編碼進行比較。實驗結果顯示啾聲編碼波形在使用軸向旁瓣反相技術後可以提供較佳之壓縮品質與旁瓣抑制效果，而格雷編碼應用方面效果亦然，並且高位元正交格雷編碼驗證其成像品質也得到有效的提升。

Dual-frequency (DF) tissue harmonic imaging effectively utilizes the system bandwidth for frequency compounding and has been proposed to detect the harmonic signal at two independent frequencies. In DF harmonic imaging, the second harmonic signal at second harmonic (2f0)　frequency and the inter-modulation harmonic signal at fundamental (f0) frequency are simultaneously generated for imaging. Therefore, the signal bandwidths are determined by the pulse length of the components respectively for the DF harmonic signal two spectral peaks with center frequencies at f0 and 2f0. Though particular chirp-encoded excitation can achieve high signal-to-noise ratio (SNR) for penetration together with wide signal bandwidth for resolution, it suffers from the range side lobes cause by the mutual interference between two imaging bands. In this study, range side lobe inversion method (RSI) is to fire an auxiliary chirp to change the polarity of the range side lobes, the range side lobes can be suppressed in the combination of the original chirp and the auxiliary chirp. The advantage of the phase encoding of complementary Golay pairs was taken to alleviate the mutual interference, and a new orthogonal encoded method for multi-bits Golay code has been developed to further suppress the range side lobes interference from the incorrect coded Golay pairs. The experiment result shows that, with the RSI method, the quality of pulse compression in DF harmonic imaging improves. And the comparison between multi-bits Golay code shows that orthogonal encoded method can avoid interference between two imaging bands.

[1] 沈哲州，醫用超音波影像課程講議，國立台灣科技大學，台北(2013)

[2] Lin, C.H., and Shen, C.C., “Chirp-Encoded Excitation for Dual-Frequency Ultrasound Tissue Harmonic Imaging,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 59, No. 11, pp.2420-2430 (2012).

[3] 巫祈，「用於雙頻組織諧波影像之格雷編碼波形」，碩士論文，國立台灣科技大學，台北(2012)

[4] Flax, S. W., and O’Donnell, M., “Phase-Aberration Correction Using Signals from Point Reflectors and Diffuse Scatterers: Basic Principles,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 35, No. 6, pp.758-767 (1988).

[5] O’Donnell, M., and Flax, S. W., “Phase-Aberration Correction Using Signals from Point Reflectors and Diffuse Scatterers: Measurements,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 6, pp.768-774 (1988).

[6] Li, P. C., and O’Donnell, M., “Phase Aberration Correction on Two-Dimensional Conformal Arrays,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 42, No. 1, pp.73-82 (1995).

[7] Krishnan, S., Rigby, K. W., and O’Donnell, M., “Improved Estimation of Phase Aberration Profile,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 44, No. 3, pp.701-713 (1997).

[8] Beyer, R. T., and Letcher, S. V., Nonlinear acoustics. New York, NY: Academic Press, 1969.

[9] Haran, M. E., and Cook, B. D., “Distortion of Finite Amplitude Ultrasound in Lossy Media,” Journal of the Acoustical Society of America, Vol. 73, No. 3, pp. 774–779 (1983).

[10] Burckhardt, C.B., “Speckle in Ultrasound B-Mode Scans,” IEEE Transactions on Sonics and Ultrasonics, Vol. 25, No. 1, pp. 1-6 (1978).

[11] O’Donnell, M., and Silverstein, S.D., “Optimum Displacement for Compound Image Generation in Medical Ultrasound,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 4, pp. 470-476 (1998).

[12] Silverstein, S.D., and O’donnell, M., “Speckle Reduction Using Correlated Mixed-Integration Techniques,” Proceedings of SPIE - The International Society for Optical Engineering, Vol. 768, pp. 168-172 (1987).

[13] Li, P. C., and O’Donnell, M., “Elevational Spatial Compounding,” Ultrasonic imaging, Vol. 16, No. 3, pp. 176-189 (1994).

[14] Biagi, E., Breschi, L., Vannacci, E., and Masotti, L., “Multipulse Technique Exploiting the Intermodulation of Ultrasound Waves in a Nonlinear Medium,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 56, No. 3, pp. 520–535 (2009).

[15] Nowicki, A., Wojcik, J., and Secomski, W., “Harmonic Imaging Using Multitone Nonlinear Coding,” Ultrasound in Medicine and Biology, Vol. 33, No. 7, pp. 1112–1122 (2007).

[16] Li, P. C., and Shen, C. C., “Effects of Transmit Focusing on Finite Amplitude Distortion Based Second Harmonic Generation,” Ultrasonic Imaging, Vol. 21, No. 14, pp. 243-258 (1999).

[17] Takeuchi, Y., “Coded Excitation for Harmonic Imaging,” Proceedings of the IEEE Ultrasonics Symposium, Vol. 2, pp. 1433–1436 (1996).

[18] Chiao, R. Y., and Hao, X. H., “Coded Excitation for Diagnostic Ultrasound: A System Developer's Perspective,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 52, No. 2, pp. 160–170 (2005).

[19] Misaridis, T., and Jensen, J. A., “Use of Modulated Excitation Signals in Medical Ultrasound. Part II: Design and Performance for Medical Imaging Applications,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 52, No. 2, pp. 192–207 (2005).

[20] Misaridis, T., and Jensen, J. A., “Use of Modulated Excitation Signals in Medical Ultrasound. Part II: Basic Concepts and Expected Benefits,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 52, No. 2, pp. 192–207 (2005).

[21] Song, J., Kim, S., Sohn, H.Y., Song, T.K., Yoo, YM., “Coded Excitation for Ultrasound Tissue Harmonic Imaging,” Ultrasonics, Vol. 50, No. 2, pp. 613–619 (2010).

[22] Chia, R.Y., Hao, X., “Coded Excitation for Diagnostic Ultrasound: A System Developer’s Perspective,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,, Vol. 52, No. 2, pp. 160–170 (2005).

[23] Prieur, F., Denarie, B., Austeng, A., Torp, H., “Multi-Line Transmission in Medical Imaging Using the Second-Harmonic Signal,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 60, No. 2, pp.(s): 2682 - 2692 (2013).

[24] Park, J., Li, X., Zhou, Q., Shung, K.K., “Combined Chirp Coded Tissue Harmonic and Fundamental Ultrasound Imaging for Intravascular Ultrasound: 20–60 MHz Phantom and Ex Vivo Results,” Ultrasonics, Vol. 53, No. 2, pp. 369–376 (2012).
[25] Arif, M., Cowell, D.M., Freear, S., “Pulse Compression of Harmonic Chirp Signals Using the Fractional Fourier Transform,” Ultrasound in Medicine and Biology, Vol. 36, No. 6, pp. 949–956 (2010).

[26] Nowicki, A., Trots, I., Lewin, P.A., Secomski, W., Tymkiewicz, R., “Influence of the Ultrasound Transducer Bandwidth on Selection of the Complementary Golay Bit Code Length,” Ultrasonics, Vol. 47, No. 1-4, pp. 64–73 (2007).

[27] Tseng, C.C., “Signal Multiplexing in Surface-Wave Delay Lines Using Orthogonal Pairs of Golay's Complementary Sequences,” IEEK Transactions on Sonics and Ultrasonics, Vol. su-18. No. 2, pp. 103-107 (1971).