📚 Ultrasound Scanning | 超声扫描
Ultrasound scanning is an imaging technique that uses high-frequency sound waves above the human hearing range to produce real-time pictures of internal body structures. In CIE A Level Physics, this topic links wave properties such as reflection, refraction, attenuation, impedance and the Doppler effect to a practical medical application. Understanding how ultrasound is generated, transmitted and detected helps explain both the physics principles and the design choices made in clinical scanners.
超声扫描是一种利用高于人耳听觉范围的高频声波实时显示人体内部结构图像的成像技术。在 CIE A Level 物理中，该主题将反射、折射、衰减、阻抗和多普勒效应等波动性质与实际医学应用联系起来。理解超声波的产生、传播和检测方式，有助于解释其物理原理以及临床扫描仪中的设计选择。
1. What is Ultrasound? | 什么是超声波？
Sound waves with frequencies above about 20 kHz are called ultrasound. Medical ultrasound imaging typically uses frequencies between 1 MHz and 15 MHz because this range provides a useful compromise between resolution and penetration depth in soft tissue. The upper limit of human hearing is about 20 kHz, so ultrasound is completely inaudible, and the wavelength in tissue is of the order of millimetres, which is comparable to the size of the structures we wish to image.
频率高于约 20 kHz 的声波称为超声波。医学超声成像通常使用 1 MHz 至 15 MHz 的频率，因为这一范围在软组织中的分辨率与穿透深度之间提供了有用的折中。人耳听觉上限约为 20 kHz，因此超声波完全听不见，而其在组织中的波长约为毫米量级，与我们要成像的结构尺寸相当。
Ultrasound is a longitudinal mechanical wave, not an electromagnetic wave. It therefore requires a medium to travel through, and it cannot propagate through a vacuum. In soft tissue the speed of sound is approximately 1540 m s⁻¹ and is almost independent of frequency, which is a key simplifying assumption in A Level calculations.
超声波是纵波机械波，不是电磁波。因此它需要介质传播，无法在真空中传播。在软组织中声速约为 1540 m s⁻¹，且几乎与频率无关，这是 A Level 计算中的一个关键简化假设。
| Wave type | 波的类型 | Frequency range | 频率范围 | Typical use | 典型用途 |
| Infrasonic | 次声 | below 20 Hz | earthquake waves | 地震波 |
| Audible | 可听声 | 20 Hz – 20 kHz | human speech | 人声 |
| Ultrasonic | 超声 | above 20 kHz | medical imaging | 医学成像 |
2. Generating and Detecting Ultrasound | 超声波的产生与检测
Ultrasound is produced and detected using a piezoelectric transducer, usually a thin slice of quartz or a lead zirconate titanate ceramic. When an alternating voltage is applied across opposite faces of the crystal, the crystal changes shape at the frequency of the applied voltage. If that frequency matches the natural frequency of the crystal, resonance occurs and a large-amplitude ultrasound wave is emitted.
超声波由压电换能器产生和检测，通常是一薄片石英或锆钛酸铅陶瓷。当在晶体相对两面施加交变电压时，晶体以所加电压的频率改变形状。若该频率与晶体的固有频率匹配，就会发生共振，并发射出大振幅的超声波。
The reverse piezoelectric effect is used for detection: when an ultrasound wave strikes the crystal, it forces the crystal to vibrate, generating a small alternating potential difference across it. The same crystal can therefore act as both transmitter and receiver, switched rapidly between the two roles by the control electronics.
检测则利用逆压电效应：当超声波打到晶体上时，迫使晶体振动，从而在晶体两端产生微小的交变电势差。因此同一块晶体既可作发射器也可作接收器，由控制电路在两个角色之间快速切换。
The crystal must be cut to a specific thickness so that it resonates. The fundamental resonance condition is that the thickness equals one half of a wavelength:
d = λ / 2 and therefore f = c / (2d)
晶体必须切割成特定厚度才能共振。基本共振条件是厚度等于半个波长：d = λ/2，因此 f = c/(2d)。
⁴ m = 0.50 mm. A very thin crystal is required, which is one practical engineering constraint on producing very high frequencies.
例如，若声在晶体中的速度为 4000 m s⁻¹，所需频率为 4 MHz，则所需厚度为 d = 4000 / (2 × 4 × 10⁶) = 5.0 × 10⁻⁴ m = 0.50 mm。频率越高，晶体必须越薄，这是制造超高频率时的一个实际工程限制。
3. Reflection, Refraction and Attenuation | 反射、折射与衰减
Ultrasound imaging depends on echoes. When a wave meets a boundary between two media of different acoustic impedance, part of the wave is reflected and part is transmitted. The reflected pulse returns to the transducer, and the time delay between emission and detection gives the depth of the boundary. This is exactly the same idea as pulse-echo ranging used in radar and sonar.
超声成像依赖于回声。当声波遇到两种声阻抗不同的介质之间的界面时，一部分被反射，一部分透射。反射脉冲返回换能器，从发射到检测的时间延迟给出界面的深度。这与雷达和声呐中使用的脉冲回波测距原理完全相同。
Refraction occurs when the wave crosses a boundary at which the speed of sound changes. Since the wave enters the new medium at an angle, the direction of travel bends, in accordance with Snell's law. In soft tissue the speeds of sound in different organs are similar, so refraction is small, but at boundaries involving fat and muscle the effect can produce image distortion (an artefact).
当声波穿过声速发生变化的界面时会发生折射。由于声波以一定角度进入新介质，传播方向发生偏折，遵循斯涅尔定律。在软组织中不同器官的声速相近，因此折射很小；但在脂肪与肌肉等界面处，这种效应会造成图像畸变（伪影）。
Attenuation is the gradual loss of intensity of the ultrasound beam as it travels through tissue. It is caused by two processes: absorption, in which wave energy is converted into internal energy of the tissue, and scattering, in which the wave is redirected in many directions by small irregularities. The intensity decreases exponentially with distance.
衰减是超声波束在组织中传播时强度逐渐损失的现象。它由两个过程造成：吸收，即波的能量转化为组织的内能；以及散射，即波被微小的不均匀结构向各个方向重新导向。强度随距离按指数规律下降。
4. Acoustic Impedance | 声阻抗
The acoustic impedance Z of a medium is the product of its density and the speed of sound in it. It measures how much the medium resists the passage of a sound wave and determines how strongly the wave is reflected at a boundary.
介质的声阻抗 Z 等于其密度与其中声速的乘积。它衡量介质对声波通过的阻碍程度，并决定声波在界面上被反射的强弱。
Z = ρ c
The unit of acoustic impedance is kg m⁻² s⁻¹. Note that this is not the same as the SI unit of pressure; the combination arises because density (kg m⁻³) is multiplied by speed (m s⁻¹). Typical values encountered in CIE questions are shown below.
声阻抗的单位是 kg m⁻² s⁻¹。注意它与压强的 SI 单位并不相同，因为该组合来自密度（kg m⁻³）与速度（m s⁻¹）相乘。CIE 题目中常见的典型值如下表所示。
| Medium | 介质 | Density ρ / kg m⁻³ | Speed c / m s⁻¹ | Z / kg m⁻² s⁻¹ |
| Air | 空气 | 1.3 | 330 | ≈ 4.3 × 10² |
| Fat | 脂肪 | 940 | 1470 | ≈ 1.38 × 10⁶ |
| Soft tissue | 软组织 | 1040 | 1540 | ≈ 1.60 × 10⁶ |
| Blood | 血液 | 1060 | 1570 | ≈ 1.66 × 10⁶ |
| Bone | 骨 | 1900 | 4080 | ≈ 7.75 × 10⁶ |
A useful rule of thumb: the larger the difference in Z across a boundary, the greater the fraction of the incident intensity that is reflected, and the smaller the fraction that passes through to reveal deeper structures. Small differences produce weak echoes, which is why soft tissue to soft tissue boundaries give faint outlines, while soft tissue to bone gives a very strong echo.
一条实用的经验规律：界面两侧 Z 的差别越大，被反射的入射强度比例越大，能透过去显示更深处结构的比例越小。差别小则回声弱，这就是软组织与软组织之间界面轮廓模糊、而软组织与骨之间回声极强的根本原因。
5. The Intensity Reflection Coefficient and Coupling Gel | 强度反射系数与耦合剂
The fraction of the incident intensity reflected at normal incidence is called the intensity reflection coefficient α, and it depends only on the two acoustic impedances:
在垂直入射时，被反射的入射强度所占比例称为强度反射系数 α，它只取决于两种介质的声阻抗：
α = (Z₂ − Z₁)² / (Z₂ + Z₁)²
and the transmitted fraction is (1 − α). Because the impedances are squared, it does not matter which medium is labelled 1 and which is labelled 2; the value of α is the same.
而透射比例为 (1 − α)。由于阻抗是平方的，哪一侧被标为 1、哪一侧标为 2 并不影响结果，α 的值相同。
Consider the boundary between air and skin. Taking Zair ≈ 4.3 × 10² and Ztissue (1.60 × 10⁶ − 4.3 × 10²)² / (1.60 × 10⁶ + 4.3 × 10²)² ≈ 0.999. In other words, about 99.9% of the intensity is reflected at an air– ft tissue must be smeared on the skin: it fills the space between the transducer and the skin and displaces the air, allowing ultrasound to pass into the body.
考虑空气与皮肤的界面。取 Z_空气 ≈ 4.3 × 10²、Z_组织 ≈ 1.60 × 10⁶ kg m⁻² s⁻¹，则系数约为 (1.60 × 10⁶ − 4.3 × 10²)² / (1.60 × 10⁶ + 4.3 × 10²)² ≈ 0.999。也就是说，约 99.9% 的强度在空气–皮肤界面上被反射，几乎无法进入人体。因此必须在皮肤上涂抹声阻抗接近软组织的耦合剂（水基凝胶）：它填充换能器与皮肤之间的空隙并排走空气，使超声波能够进入体内。
For the same reason, internal gas pockets such as the lungs and bowel are barriers to ultrasound, and air bubbles in the coupling gel must be avoided. The gel performs the same function as an impedance-matching layer: it makes the change in Z gradual rather than abrupt, so transmission is maximised. The jelly is also harmless, inexpensive, and does not irritate the skin, unlike oil-based alternatives.
同理，肺、肠等体内含气部位是超声波传播的屏障，耦合剂中的气泡也必须避免。凝胶的作用与阻抗匹配层相同：使 Z 的变化变得平缓而非突变，从而最大化透射。相比油性替代品，凝胶无害、廉价且不刺激皮肤。
6. Attenuation and the Exponential Decay Law | 衰减与指数衰减定律
Because of absorption and scattering, the intensity of a parallel beam of ultrasound falls exponentially with depth. If I₀ is the incident intensity and I is the intensity after travelling a distance x through the medium, then
由于吸收和散射，平行超声波束的强度随深度按指数规律衰减。若 I₀ 为入射强度，I 为在介质中传播距离 x 后的强度，则
I = I₀ e−μx
where μ is the attenuation coefficient of the medium, measured in m⁻¹. The quantity μx must be dimensionless, so x must be in metres. The attenuation coefficient increases with frequency, roughly in proportion to f for soft tissue, so high-frequency ultrasound is attenuated much more rapidly than low-frequency ultrasound.
其中 μ 是该介质的衰减系数，单位为 m⁻¹。μx 必须是无量纲的，所以 x 必须以米为单位。衰减系数随频率增大，对软组织大致与 f 成正比，因此高频超声的衰减比低频超声快得多。
In clinical practice, attenuation is often quoted in decibels per centimetre. The decibel level is defined as
在临床实践中，衰减常以每厘米分贝数表示。分贝值定义为
attenuation / dB = 10 log₁₀(I₀ / I)
ss x½ is the distance over which the intensity falls to half its original value; setting I = I₀ / 2 in the exponential formula gives ln 2 = μ x½, so x½ = ln 2 / μ ≈ 0.693 / μ.
对软组织，典型值约为 0.5 dB cm⁻¹ MHz⁻¹，因此 5 MHz 的声束每传播 1 cm 约损失 2.5 dB。半值厚度 x½ 是强度降为原来一半所经过的距离；在指数公式中令 I = I₀/2 得 ln 2 = μ x½，故 x½ = ln 2 / μ ≈ 0.693 / μ。
7. A-Scan and B-Scan Modes | A 型扫描与 B 型扫描
An A-scan (amplitude scan) displays the received echoes as a graph of signal amplitude against time on a cathode-ray tube or digital display. The x-axis can be calibrated in depth because the time delay t corresponds to a depth d given by
A 型扫描（幅度扫描）把接收到的回声显示为信号幅度随时间变化的曲线，显示在示波管或数字显示屏上。由于时间延迟 t 对应深度 d，可由下式把横轴标定为深度：
d = c t / 2
The factor of two appears because the pulse must travel to the boundary and back again. A strong peak on the trace indicates a boundary with a large impedance mismatch, such as the front and back surfaces of the eye, and A-scans are widely used in ophthalmology to measure the axial length of the eye before lens surgery, and in non-destructive testing to detect cracks inside metal castings.
系数 2 的出现是因为脉冲必须往返传播。轨迹上的强峰表示存在阻抗失配较大的界面，例如眼球的前后表面。A 型扫描广泛用于眼科测量人工晶体植入前的眼轴长度，也用于无损检测中以发现金属铸件内部的裂纹。
A B-scan (brightness scan) records the amplitude of each echo as the brightness of a dot on a two-dimensional display. The transducer is swept across the body surface, and the brightness of each dot depends on the strength of the echo. The result is a cross-sectional image, which is what most people picture when they think of a pregnancy scan or an abdominal scan. Real-time B-scanning uses a linear array of many small transducers switched electronically in sequence, producing many frames per second so that moving structures such as a beating heart can be observed.
B 型扫描（亮度扫描）把每个回声的幅度记录为二维显示屏上光点的亮度。换能器在体表扫过，每个光点的亮度取决于回声的强度。结果是横断面图像，这正是大多数人想到孕检或腹部检查时脑海中的画面。实时 B 超使用由许多小换能器组成的线阵，通过电子方式依次切换，每秒产生多帧图像，从而可以观察心脏搏动等活动结构。
| Feature | 特征 | A-scan | A 型扫描 | B-scan | B 型扫描 |
| Display | 显示方式 | amplitude against time | 幅度–时间 | brightness (2-D image) | 亮度（二维图像） |
| Beam | 声束 | single fixed direction | 单一固定方向 | swept across a plane | 在平面内扫掠 |
| Typical use | 典型用途 | eye length, flaw detection | 眼轴、探伤 | foetal imaging, heart | 胎儿成像、心脏 |
8. Resolution and the Trade-off with Frequency | 分辨率与频率的权衡
Resolution is the ability to distinguish two nearby structures as separate. For ultrasound, the wavelength sets the limit of resolution, and the wavelength is related to frequency and speed by the wave equation:
分辨率是指把两个相距很近的结构分辨开的能力。对超声而言，波长决定了分辨率的极限，而波长与频率、声速由波动方程相联系：
c = f λ so λ = c / f
Since structures smaller than about one wavelength cannot be resolved, increasing the frequency improves the spatial resolution and produces a sharper image.
取 c ≈ 1540 m s⁻¹，2 MHz 声束的 λ ≈ 0.77 mm，而 10 MHz 声束的 λ ≈ 0.15 mm。由于小于约一个波长的结构无法被分辨，提高频率可改善空间分辨率，使图像更清晰。
However, higher frequency also means a larger attenuation coefficient, so the beam penetrates less deeply. This is the central design trade-off of ultrasound scanning: high frequency for shallow structures with fine detail (for example the eye or superficial blood vessels at 7–15 MHz), and low frequency for deep structures (for example the abdomen or a foetus at 2–5 MHz). There is no single best frequency; the operator chooses the probe according to the depth and size of the structure of interest.
然而，频率越高衰减系数越大，声束穿透深度越小。这就是超声扫描核心的设计权衡：对浅表且细节丰富的结构使用高频（例如眼部或浅表血管，7–15 MHz），对深部结构使用低频（例如腹部或胎儿，2–5 MHz）。不存在唯一最优频率，操作者需根据目标结构的深度与大小选择探头。
A second limitation is that the axial resolution (along the beam) is also limited by the pulse duration: a shorter pulse gives better depth resolution but contains a wider range of frequencies. Lateral resolution (across the beam) depends on the width of the beam and can be improved by focusing, just as light can be focused with a lens.
第二个限制是轴向分辨率（沿声束方向）还受脉冲持续时间限制：脉冲越短，深度分辨率越好，但包含的频率范围越宽。横向分辨率（垂直声束方向）取决于声束宽度，可以通过聚焦改善，正如可以用透镜聚焦光一样。
9. The Doppler Effect and Blood Flow Measurement | 多普勒效应与血流测量
The Doppler effect is the change in observed frequency when there is relative motion between a source and an observer. In medical ultrasound, the source is the moving blood cells and the observer is the stationary transducer (or vice versa). When blood moves towards the probe, the reflected frequency is higher than the emitted frequency; when it moves away, the reflected frequency is lower.
多普勒效应是指声源与观察者之间存在相对运动时，观察到的频率发生变化的现象。在医学超声中，声源是运动的血细胞，观察者是静止的换能器（或反之）。当血液朝向探头运动时，反射频率高于发射频率；远离时则低于发射频率。
The Doppler frequency shift Δf for blood flowing at speed v at an angle θ to the beam is given by
血液以速度 v、与声束成 θ 角流动时，多普勒频移 Δf 由下式给出：
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