JP3920194B2 - Ultrasonic measuring device - Google Patents

Ultrasonic measuring device Download PDF

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JP3920194B2
JP3920194B2 JP2002316171A JP2002316171A JP3920194B2 JP 3920194 B2 JP3920194 B2 JP 3920194B2 JP 2002316171 A JP2002316171 A JP 2002316171A JP 2002316171 A JP2002316171 A JP 2002316171A JP 3920194 B2 JP3920194 B2 JP 3920194B2
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fundamental
wave
frequency domain
waves
reflected wave
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JP2004147852A (en
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憲男 田川
正 守屋
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Japan Science and Technology Agency
National Institute of Japan Science and Technology Agency
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Japan Science and Technology Agency
National Institute of Japan Science and Technology Agency
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【０００１】
【発明の属する技術分野】
本発明は、超音波を用いて計測を行う分野に関する。
【技術的背景】
超音波を送信し、その反射波を受信することにより、反射した物体の画像を表示することは、例えば、医療の分野でよく行われている。
超音波による画像化手法の１つである、パルス圧縮方式に基づく画像化法では、送信系の物理的条件や、スタンドオフ領域の制限、あるいはドップラ計測の実現などの理由により、時間幅が狭く、かつ情報量の多い送信信号を用いる必要がある。ただし、圧縮性能（圧縮後のパルス幅や、サイドローブレベル、ＳＮ比等）も重視されることから、性能の保証されている基本的な符号化波形を足し合わせて合成送信信号とすることが多い。ダウンチャープ信号とアップチャープ信号を用いたものとして、例えば、特許文献１がある。
【０００２】
さて、合成送信信号が周波数帯域の異なる基本波を足し合わせたものであれば、受信信号を各周波数帯域に基づいて容易に分離できる。しかし、例えば、アップチャープとダウンチャープ、あるいは位相の異なるチャープを足し合わせた合成送信信号を用いる場合は、周波数帯域に基づく受信信号の分離ができない。
この場合の圧縮処理として、合成送信信号が対象物体から反射されて戻ってくる受信信号に対して、合成送信信号による相関計算を行ったのでは、通常、単一の基本波を送信信号として用いたときよりも圧縮性能が劣化する。したがって、各基本波による圧縮処理を行い、得られる複数の圧縮信号に対して適切な処理を施すことによって、圧縮性能の向上を目指すことが考えられる。
【特許文献１】
特開２００２−１３６５２２号公報
【０００３】
【発明が解決しようとする課題】
本発明の目的は、超音波の合成送信信号を送信し、その反射波を受信するパルス圧縮方式の計測器において、受信信号を、各基本波に劣化することなく分離を行うことができるようにして、各基本波ごとの圧縮受信信号を得ることにより、計測精度を高めた計測器を提供しようとするものである。
【０００４】
【課題を解決するための手段】
上記目的を達成するために、本発明は、複数の基本波を送信し、その反射波を受信し、圧縮して測定を行う超音波測定装置であって、複数の基本波からなる超音波を送信する超音波送信手段と、送信された超音波の反射波を受信する超音波受信手段と、前記受信した反射波を周波数領域での表現とするフーリエ変換手段と、前記周波数領域表現とした反射波から、異なる基本波間の周波数領域のスペクトル比を用いて、周波数表現の基本波の反射波を求める分離手段と、前記周波数表現の基本波に対応した反射波から、基本波の反射波を求める逆フーリエ変換手段と、前記基本波の反射波から、圧縮受信信号を得る基本波との相関手段とを備えることを特徴とする。
前記複数の基本波をｓ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、その周波数領域の表現をＳ（ｊ）（ω）とし、受信した反射波をｒ（ｔ）、その周波数領域の表現をＲ（ω）、周波数領域の基本波の反射波をＲ（ｊ）（ω）としたとき、
前記異なる基本波間の周波数領域のスペクトル比は、
【数６】

Figure 0003920194
であり、
前記分離手段は、Ｈ（ｊ）（ω）＝１＋Ｇ（ｊ）（ω）とすると、
【数７】
Figure 0003920194
により行うことができる。
【０００５】
また、前記複数の基本波を初期位相の異なる複数のアップ／ダウンチャープとして階層的に用い、複数のアップチャープ信号をｓｕ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、複数のダウンチャープ信号をｓｄ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、その周波数領域の表現をＳｕ（ｊ）（ω），Ｓｄ（ｊ）（ω）とし、受信した反射波をｒ（ｔ）、その周波数領域の表現をＲ（ω）、周波数領域の基本波の反射波をＲｕ（ｊ）（ω），Ｒｄ（ｊ）（ω）としたとき、
前記異なる基本波間の周波数領域のスペクトル比は、
【数８】
Figure 0003920194
および
【数９】
Figure 0003920194
（Ｇｕ，Ｇｄはｊに対して不変）であり、
前記分離手段は、Ｈｕ（ｊ）（ω）＝Ｇｕ（ｊ）（ω）＋１，Ｈｕ（ω）＝Ｇｕ（ω）＋１およびＨｄ（ｊ）（ω）＝Ｇｄ（ｊ）（ω）＋１，Ｈｄ（ω）＝Ｇｄ（ω）＋１とすると、
【数１０】
Figure 0003920194
により行うことができる。
【０００６】
【発明の実施の形態】
本発明の実施の形態を、図面を参照して説明する。
本発明では、パルス圧縮方式において、異なる基本波形間の周波数領域における比（スペクトル比）を利用して、周波数帯域による基本波成分の分離が困難な場合に、それを実現する方法を与える。
図１は、本発明の実施形態である超音波測定装置の構成を示すブロック図である。図１は計測器の特に受信部における分離圧縮フィルタ２００を示している。図１において、今、基本信号発生器１１２，１１４からの２つの基本波ｓ１（ｔ），ｓ２（ｔ）を合成器１２０により足し合わせて作成した、合成送信信号ｓ（ｔ）（パルス）を超音波振動子１３０から対象物１４０に対して送信する場合を考える。
【数１１】
Figure 0003920194
この関係を、フーリエ変換により周波数領域で表現すると
【数１２】
Figure 0003920194
となる。ここで、次の比を計算する。
【数１３】
Figure 0003920194
次に、反射体がＮ個存在するときの、式（１）の送信信号に対する反射（受信）信号ｒ（ｔ）を考えると、反射体１４２，１４４，１４６を区別する添字を iとして
【数１４】
Figure 0003920194
となる。
【０００７】
図１の分離圧縮フィルタ２００において、受信信号ｒ（ｔ）をフーリエ変換器２１０で、周波数領域における表現にすると、
【数１５】
Figure 0003920194
となる。ここで、適当な基本波を用いると、以下の関係と成る。
【数１６】
Figure 0003920194
このとき、Ｈ１（ω）＝１＋Ｇ１（ω）とすると、式（５）は、
【数１７】
Figure 0003920194
と書ける。この関係から、Ｈ１（ω）が０となるωが測度ゼロの集合であれば、そのようなωでの成分はゼロとおき、それ以外の成分について
【数１８】
Figure 0003920194
と、除算器２２２によりＨ１（ω）で除算することで、基本波ｓ１（ｔ）に対応する周波数表現の反射波Ｒ１（ω）を求めることができる。これを逆フーリエ変換器２３２で時間表現のｒ１（ｔ）とし、基本波としてアップ／ダウンチャープ信号を用いた場合等の必要なときに相関器２４２で基本波ｓ１（ｔ）との相関をとると、圧縮受信信号ｗ１（ｔ）となる。
同様にＨ２（ω）を求めることにより、基本波ｓ２（ｔ）に対する圧縮受信信号ｗ２（ｔ）を求めることができる。
【０００８】
上述では、基本波を２つの場合で説明したが、一般的に複数の基本波を用いた場合でも適用することができる。
この場合、複数の基本波をｓ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）とし、その周波数領域の表現をＳ（ｊ）（ω）とすると、上述の比であるＧ（ｊ）（ω）は、
【数１９】
Figure 0003920194
で求めることができる。これにより、Ｈ（ｊ）（ω）＝１＋Ｇ（ｊ）（ω）とすると、
【数２０】
Figure 0003920194
により、各基本波の受信信号を上述と同様に求めることができ、各基本波に対応する圧縮受信信号ｒ（ｊ）（ｔ）は、上述と同様に求めることができる。
【０００９】
また、階層的に、初期位相の異なる複数のアップ／ダウンチャープを足し合わせた送信信号を用いた場合でも適用可能である。図２（ａ）にアップチャープ信号、図２（ｂ）にダウンチャープ信号を示す。図２（ａ）に示すように、アップチャープ信号は時間Ｔの間に周波数ｆ１がΔｆ上昇してｆ２となる。図２（ｂ）に示すように、ダウンチャープ信号は時間Ｔの間に周波数ｆ２がΔｆ下降してｆ１となる。
アップとダウンを区別する添字をｕ，ｄ、初期位相を区別する添字をｊ（＝１，２，…，Ｍ）とすると、
【数２１】
Figure 0003920194
および
【数２２】
Figure 0003920194
（Ｇｕ，Ｇｄはｊに対して不変）から、Ｈｕ（ｊ），ＨｕおよびＨｄ（ｊ），Ｈｄを前述と同様に定義することで、
【数２３】
Figure 0003920194
として各成分を分離できる。
【００１０】
【実施例】
図３〜図５に、アップチャープ信号とダウンチャープ信号の２つの基本信号を送信した例を示す。図３は、合成送信信号ｓ（ｔ）（送信周波数１９〜２２ＭＨｚ，パルス幅１００μｓを、媒質内（媒質内音速１５００ｍ／ｓ）に距離をおいて設置している３つの反射体Ａ，Ｂ，Ｃ（反射率はそれぞれ、０．５，０．１，０．５）に対して送信し、各反射体からの反射波ｒ（ｔ）を受けていることを示している。
図４は、受けた反射波を示しており、図５（ａ），図５（ｂ）は、図１に示した構成で、上述のアップチャープ，ダウンチャープ信号の場合のように求めた圧縮受信信号ｗ１（ｔ），ｗ２（ｔ）を示している。図５（ａ），図５（ｂ）に示すように分離されて、圧縮受信信号ｗ１（ｔ），ｗ２（ｔ）が求められる。図５から分かるように、圧縮受信信号ｗ１（ｔ），ｗ２（ｔ）には、各反射体Ａ，Ｂ，Ｃからの反射が同じように明確に認められる。
【００１１】
【発明の効果】
本発明の分離圧縮フィルタの構成を用いることにより、周波数の重なった送信チャープ信号でも、明確に分離することができ、複数の送信信号を用いることにより、得られる情報量を増加させることで、Ｓ／Ｎ比を増加することができる。したがって、例えば、超音波の反射により画像を生成する場合でも、明瞭な画像を得ることができる。
【図面の簡単な説明】
【図１】本発明の実施形態である超音波測定器の構成を示すブロック図である。
【図２】アップチャープ波、ダウンチャープ波を示す図である。
【図３】実施例における反射体等を示す図である。
【図４】実施例における反射波（受信波）を示す図である。
【図５】実施例における圧縮受信波を示す図である。
【符号の説明】
１１２，１１４ 基本信号発生器
１２０ 合成器
１３０ 超音波振動子（超音波送受信器）
１４０ 反射体（測定対象）
２００ 分離圧縮フィルタ
２１０ フーリエ変換器
２２２，２２４ 除算器
２３２，２３４ 逆フーリエ変換器
２４２，２４４ 相関器[0001]
BACKGROUND OF THE INVENTION
The present invention relates to the field of measuring using ultrasonic waves.
[Technical background]
Displaying an image of a reflected object by transmitting an ultrasonic wave and receiving the reflected wave is often performed in the medical field, for example.
In the imaging method based on the pulse compression method, which is one of ultrasonic imaging methods, the time width is narrow due to the physical conditions of the transmission system, the limitation of the standoff area, or the realization of Doppler measurement. In addition, it is necessary to use a transmission signal having a large amount of information. However, since compression performance (compressed pulse width, side lobe level, S / N ratio, etc.) is also emphasized, basic encoded waveforms with guaranteed performance may be added to form a combined transmission signal. Many. For example, Patent Document 1 discloses a technique using a down chirp signal and an up chirp signal.
[0002]
If the combined transmission signal is a combination of fundamental waves having different frequency bands, the received signal can be easily separated based on each frequency band. However, for example, when using a combined transmission signal in which up-chirp and down-chirp or chirps having different phases are added, the received signal cannot be separated based on the frequency band.
As a compression process in this case, if a correlation calculation is performed on the received signal that is reflected from the target object and returned by the synthesized transmission signal, a single fundamental wave is usually used as the transmission signal. Compression performance is worse than when it was. Therefore, it is conceivable to improve compression performance by performing compression processing using each fundamental wave and performing appropriate processing on a plurality of obtained compressed signals.
[Patent Document 1]
JP 2002-136522 A
[Problems to be solved by the invention]
SUMMARY OF THE INVENTION An object of the present invention is to enable a pulse compression measuring instrument that transmits an ultrasonic composite transmission signal and receives the reflected wave to separate the reception signal without degrading each fundamental wave. Thus, it is intended to provide a measuring instrument with improved measurement accuracy by obtaining a compressed received signal for each fundamental wave.
[0004]
[Means for Solving the Problems]
In order to achieve the above object, the present invention provides an ultrasonic measurement device that transmits a plurality of fundamental waves, receives the reflected waves, compresses them, and performs measurement. Ultrasonic transmitting means for transmitting, ultrasonic receiving means for receiving reflected waves of the transmitted ultrasonic waves, Fourier transform means for expressing the received reflected waves in the frequency domain, and reflection in the frequency domain expression The fundamental wave reflected wave is obtained from the separating means for obtaining the reflected wave of the fundamental wave in the frequency expression using the spectral ratio of the frequency domain between the different fundamental waves from the wave, and the reflected wave corresponding to the fundamental wave in the frequency expression. Inverse Fourier transform means and means for correlating with a fundamental wave for obtaining a compressed reception signal from the reflected wave of the fundamental wave are provided.
The plurality of fundamental waves are s (j) (t) (j = 1, 2,..., M), the frequency domain representation is S (j) (ω), and the received reflected waves are r (t). ), The frequency domain representation is R (ω), and the fundamental reflected wave of the frequency domain is R (j) (ω).
The spectral ratio in the frequency domain between the different fundamental waves is
[Formula 6]
Figure 0003920194
And
When the separating means is H (j) (ω) = 1 + G (j) (ω),
[Expression 7]
Figure 0003920194
Can be performed.
[0005]
Further, the plurality of fundamental waves are hierarchically used as a plurality of up / down chirps having different initial phases, and a plurality of up chirp signals are used as su (j) (t) (j = 1, 2,..., M ), A plurality of down-chirp signals as s d (j) (t) (j = 1, 2,..., M), and the frequency domain representation as S u (j) (ω), S d (j) (Ω), the received reflected wave is r (t), the frequency domain representation is R (ω), and the fundamental frequency reflected wave is R u (j) (ω), R d (j) ( ω)
The spectral ratio in the frequency domain between the different fundamental waves is
[Equation 8]
Figure 0003920194
And
Figure 0003920194
(G u, G d are invariant to j),
The separation means includes H u (j) (ω) = G u (j) (ω) +1, H u (ω) = G u (ω) +1 and H d (j) (ω) = G d (j ) (Ω) +1, H d (ω) = G d (ω) +1
[Expression 10]
Figure 0003920194
Can be performed.
[0006]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described with reference to the drawings.
In the present invention, in the pulse compression method, a method for realizing the case where separation of fundamental wave components by frequency band is difficult by using a ratio (spectral ratio) in a frequency domain between different fundamental waveforms is provided.
FIG. 1 is a block diagram showing a configuration of an ultrasonic measurement apparatus according to an embodiment of the present invention. FIG. 1 shows a separation / compression filter 200 in the measuring device, particularly in the receiver. In FIG. 1, a combined transmission signal s (t) (pulse) created by adding two fundamental waves s 1 (t) and s 2 (t) from the fundamental signal generators 112 and 114 together by a synthesizer 120. ) Is transmitted from the ultrasonic transducer 130 to the object 140.
[Expression 11]
Figure 0003920194
If this relationship is expressed in the frequency domain by Fourier transform,
Figure 0003920194
It becomes. Here, the following ratio is calculated.
[Formula 13]
Figure 0003920194
Next, when the reflection (reception) signal r (t) with respect to the transmission signal of Expression (1) when there are N reflectors, the subscript that distinguishes the reflectors 142, 144, and 146 is i. 14]
Figure 0003920194
It becomes.
[0007]
In the separation compression filter 200 of FIG. 1, when the received signal r (t) is expressed in the frequency domain by the Fourier transformer 210,
[Expression 15]
Figure 0003920194
It becomes. Here, when an appropriate fundamental wave is used, the following relationship is established.
[Expression 16]
Figure 0003920194
At this time, if H 1 (ω) = 1 + G 1 (ω), Equation (5) is
[Expression 17]
Figure 0003920194
Can be written. From this relationship, if ω where H 1 (ω) is 0 is a set with a measure of zero, the component at such ω is set to zero, and other components are expressed as follows.
Figure 0003920194
Then, by dividing by H 1 (ω) by the divider 222, the reflected wave R 1 (ω) of the frequency expression corresponding to the fundamental wave s 1 (t) can be obtained. This is converted to r 1 (t) in time expression by the inverse Fourier transformer 232, and the correlation with the fundamental wave s 1 (t) is obtained by the correlator 242 when an up / down chirp signal is used as the fundamental wave. , The compressed received signal w 1 (t) is obtained.
Similarly, by obtaining H 2 (ω), the compressed received signal w 2 (t) for the fundamental wave s 2 (t) can be obtained.
[0008]
In the above description, the case where two fundamental waves are used has been described. However, the present invention can also be applied to cases where a plurality of fundamental waves are used.
In this case, when a plurality of fundamental waves are s (j) (t) (j = 1, 2,..., M) and the frequency domain is S (j) (ω), the above ratio is obtained. A certain G (j) (ω) is
[Equation 19]
Figure 0003920194
Can be obtained. Thus, when H (j) (ω) = 1 + G (j) (ω),
[Expression 20]
Figure 0003920194
Thus, the received signal of each fundamental wave can be obtained in the same manner as described above, and the compressed received signal r (j) (t) corresponding to each fundamental wave can be obtained in the same manner as described above.
[0009]
Further, the present invention can be applied even when a transmission signal in which a plurality of up / down chirps having different initial phases are added hierarchically is used. FIG. 2A shows an up-chirp signal, and FIG. 2B shows a down-chirp signal. As shown in FIG. 2 (a), the frequency f 1 is f 2 rises Δf between the up-chirp signal time T. As shown in FIG. 2 (b), the frequency f 2 is f 1 and Δf lowered during the down-chirp signal is a time T.
If subscripts distinguishing up and down are u and d, and subscripts distinguishing the initial phase are j (= 1, 2,..., M),
[Expression 21]
Figure 0003920194
And
Figure 0003920194
(G u and G d are invariant with respect to j) , H u (j) and H u and H d (j) and H d are defined in the same manner as described above.
[Expression 23]
Figure 0003920194
Each component can be separated as follows.
[0010]
【Example】
3 to 5 show examples in which two basic signals, an up-chirp signal and a down-chirp signal, are transmitted. FIG. 3 shows three reflectors A, B, which are provided with a combined transmission signal s (t) (transmission frequency 19-22 MHz, pulse width 100 μs, at a distance from the medium (sound velocity in the medium 1500 m / s). It is transmitted to C (reflectances are 0.5, 0.1, and 0.5, respectively), indicating that the reflected wave r (t) from each reflector is received.
FIG. 4 shows the reflected wave received, and FIGS. 5A and 5B show the compression obtained in the configuration shown in FIG. 1 as in the case of the above-described up-chirp and down-chirp signals. The received signals w 1 (t) and w 2 (t) are shown. The compressed received signals w 1 (t) and w 2 (t) are obtained by being separated as shown in FIGS. As can be seen from FIG. 5, reflections from the reflectors A, B, and C are clearly recognized in the same manner in the compressed reception signals w 1 (t) and w 2 (t).
[0011]
【The invention's effect】
By using the configuration of the separation and compression filter of the present invention, even transmission chirp signals with overlapping frequencies can be clearly separated, and by using a plurality of transmission signals, the amount of information obtained can be increased. The / N ratio can be increased. Therefore, for example, even when an image is generated by reflection of ultrasonic waves, a clear image can be obtained.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of an ultrasonic measuring instrument according to an embodiment of the present invention.
FIG. 2 is a diagram showing an up-chirp wave and a down-chirp wave.
FIG. 3 is a view showing a reflector and the like in the embodiment.
FIG. 4 is a diagram illustrating a reflected wave (received wave) in the embodiment.
FIG. 5 is a diagram illustrating a compressed reception wave in the embodiment.
[Explanation of symbols]
112, 114 Basic signal generator 120 Synthesizer 130 Ultrasonic transducer (Ultrasonic transceiver)
140 Reflector (measuring object)
200 Separation and compression filter 210 Fourier transformers 222 and 224 Dividers 232 and 234 Inverse Fourier transformers 242 and 244 Correlator

Claims (3)

複数の基本波を送信し、その反射波を受信し、圧縮して測定を行う超音波測定装置であって、
複数の基本波からなる超音波を送信する超音波送信手段と、
送信された超音波の反射波を受信する超音波受信手段と、
前記受信した反射波を周波数領域での表現とするフーリエ変換手段と、
前記周波数領域表現とした反射波から、異なる基本波間の周波数領域のスペクトル比を用いて、周波数表現の基本波の反射波を求める分離手段と、
前記周波数表現の基本波に対応した反射波から、基本波の反射波を求める逆フーリエ変換手段と、
前記基本波の反射波から、圧縮受信信号を得る基本波との相関手段と
を備えることを特徴とする超音波測定装置。An ultrasonic measurement device that transmits a plurality of fundamental waves, receives the reflected waves, compresses and measures,
Ultrasonic transmission means for transmitting ultrasonic waves composed of a plurality of fundamental waves;
An ultrasonic wave receiving means for receiving a reflected wave of the transmitted ultrasonic wave;
Fourier transform means for representing the received reflected wave in the frequency domain;
Separating means for obtaining the reflected wave of the fundamental wave of the frequency representation using the spectral ratio of the frequency domain between the different fundamental waves from the reflected wave of the frequency domain representation;
An inverse Fourier transform means for obtaining a reflected wave of the fundamental wave from a reflected wave corresponding to the fundamental wave of the frequency expression;
An ultrasonic measurement apparatus comprising: means for correlating with a fundamental wave that obtains a compressed reception signal from the reflected wave of the fundamental wave. 請求項１に記載の超音波測定装置において、
前記複数の基本波をｓ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、その周波数領域の表現をＳ（ｊ）（ω）とし、受信した反射波をｒ（ｔ）、その周波数領域の表現をＲ（ω）、周波数領域の基本波の反射波をＲ（ｊ）（ω）としたとき、
前記異なる基本波間の周波数領域のスペクトル比は、
Figure 0003920194
であり、
前記分離手段は、Ｈ（ｊ）（ω）＝１＋Ｇ（ｊ）（ω）とすると、
Figure 0003920194
により行うことを特徴とする超音波測定装置。The ultrasonic measurement apparatus according to claim 1,
The plurality of fundamental waves are s (j) (t) (j = 1, 2,..., M), the frequency domain representation is S (j) (ω), and the received reflected waves are r (t). ), The frequency domain representation is R (ω), and the fundamental reflected wave of the frequency domain is R (j) (ω).
The spectral ratio in the frequency domain between the different fundamental waves is
Figure 0003920194
 And
When the separating means is H (j) (ω) = 1 + G (j) (ω),
Figure 0003920194
 An ultrasonic measurement apparatus, characterized in that 請求項１に記載の超音波測定装置において、
前記複数の基本波を初期位相の異なる複数のアップ／ダウンチャープとして階層的に用い、複数のアップチャープ信号をｓｕ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、複数のダウンチャープ信号をｓｄ（ｊ）（ｔ）（ｊ＝１，２，・・・，Ｍ）、その周波数領域の表現をＳｕ（ｊ）（ω），Ｓｄ（ｊ）（ω）とし、受信した反射波をｒ（ｔ）、その周波数領域の表現をＲ（ω）、周波数領域の基本波の反射波をＲｕ（ｊ）（ω），Ｒｄ（ｊ）（ω）としたとき、
前記異なる基本波間の周波数領域のスペクトル比は、
Figure 0003920194
および
Figure 0003920194
（Ｇｕ，Ｇｄはｊに対して不変）であり、
前記分離手段は、Ｈｕ（ｊ）（ω）＝Ｇｕ（ｊ）（ω）＋１，Ｈｕ（ω）＝Ｇｕ（ω）＋１およびＨｄ（ｊ）（ω）＝Ｇｄ（ｊ）（ω）＋１，Ｈｄ（ω）＝Ｇｄ（ω）＋１とすると、
Figure 0003920194
により行うことを特徴とする超音波測定装置。The ultrasonic measurement apparatus according to claim 1,
The plurality of fundamental waves are hierarchically used as a plurality of up / down chirps having different initial phases, and a plurality of up chirp signals are represented by su (j) (t) (j = 1, 2,..., M), A plurality of down-chirp signals are represented by s d (j) (t) (j = 1, 2,..., M), and their frequency domain representations are represented by S u (j) (ω), S d (j) (ω ), The received reflected wave is r (t), the frequency domain representation is R (ω), and the fundamental frequency reflected wave is R u (j) (ω), R d (j) (ω). When
The spectral ratio in the frequency domain between the different fundamental waves is
Figure 0003920194
 and
Figure 0003920194
 (G u, G d are invariant to j),
The separation means includes H u (j) (ω) = G u (j) (ω) +1, H u (ω) = G u (ω) +1 and H d (j) (ω) = G d (j ) (Ω) +1, H d (ω) = G d (ω) +1
Figure 0003920194
 An ultrasonic measurement apparatus, characterized in that
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