Calibration | 校准

2026-08-30 05:56 · 本文部分内容由AI辅助创作

📚 Calibration | 校准

Calibration is the process of comparing a measuring instrument's reading with a known standard or reference value. In A-Level physics, calibration is essential for ensuring that measurements are trustworthy and that experimental results can be compared with theoretical predictions.

校准是将测量仪器的读数与已知标准或参考值进行比较的过程。在 A-Level 物理中，校准对于确保测量可靠、使实验结果能够与理论预测相比较至关重要。

1. What is Calibration? | 什么是校准？

Calibration involves adjusting or checking an instrument against a standard. For example, a thermometer may be calibrated using the freezing and boiling points of water, which are fixed reference temperatures. The reading of the instrument is then adjusted so that it agrees with the known values.

校准涉及根据标准来调整或检查仪器。例如，可使用水的凝固点和沸点这些固定的参考温度来校准温度计，然后调整仪器的读数，使其与已知值一致。

A calibrated instrument produces readings that are directly traceable to a recognised standard, such as those maintained by national laboratories. This traceability is fundamental in all quantitative science.

经过校准的仪器产生的读数可直接溯源到公认的标准，例如由国家实验室维护的标准。这种可追溯性是一切定量科学的基础。

In practice, calibration often results in a correction that must be added to or subtracted from the raw reading. Alternatively, a calibration curve can be plotted to show the relationship between the instrument's output and the true value.

在实践中，校准通常会得到一个必须从原始读数中加上或减去的修正量。或者，可以绘制校准曲线，以显示仪器输出与真实值之间的关系。

2. Why is Calibration Important? | 为什么校准重要？

Calibration is important because all instruments are subject to manufacturing tolerances, drift over time, and environmental influences. Without calibration, measurements may be consistently wrong, leading to incorrect conclusions in experiments.

校准很重要，因为所有仪器都会受到制造公差、时间漂移和环境因素的影响。如果没有校准，测量可能会持续出错，导致实验得出错误结论。

For example, a voltmeter that reads 1.5 V when the true value is 1.45 V will give systematically high readings. This error will affect every voltage measurement in an experiment, potentially invalidating results.

例如，一个电压表在真实值为 1.45 V 时读数为 1.5 V，那么它的读数会系统性地偏高。这种误差会影响实验中的每次电压测量，可能使结果失效。

Calibration also allows different instruments to be compared. If two thermometers are calibrated against the same standard, their readings can be considered equivalent within the stated uncertainty.

校准还允许对不同仪器进行比较。如果两支温度计针对同一标准进行校准，那么在规定的不确定度范围内，它们的读数可被视为等效。

3. Accuracy, Precision and Calibration | 准确度、精密度与校准

Accuracy describes how close a measured value is to the true value. Precision describes how close repeated measurements are to each other. An instrument can be precise but inaccurate if it has a systematic error; calibration corrects such errors and improves accuracy.

准确度描述测量值接近真实值的程度。精密度描述重复测量值彼此接近的程度。如果仪器存在系统误差，则可能精密度高但准确度低；校准可纠正这类误差并提高准确度。

Accuracy | 准确度：nearness to the true value | 与真实值的接近程度。
Precision | 精密度：repeatability of readings | 读数的可重复性。
Calibration | 校准：reduces systematic error, improving accuracy | 减少系统误差，提高准确度。

Even after calibration, random errors remain. These are caused by unpredictable fluctuations and can be reduced by taking multiple readings and averaging, but not wholly eliminated by calibration.

即使校准后，随机误差仍然存在。这些误差由不可预测的波动引起，可通过多次读数并取平均值来减少，但不能完全靠校准消除。

4. Systematic Errors and Zero Errors | 系统误差与零误差

A systematic error affects all measurements in the same direction by a similar amount. One common type is a zero error, where the instrument does not read zero when it should. For example, a balance may show 0.05 g when empty, and a micrometer may read 0.01 mm with closed jaws.

系统误差以相同方向、相似大小影响所有测量。常见的一种是零误差，即仪器在应该读数为零时不为零。例如，天平空载时可能显示 0.05 g，千分尺在闭合时可能读数为 0.01 mm。

Zero errors are corrected by subtracting the zero reading from all subsequent readings, or by physically adjusting the instrument. Other systematic errors include thermal expansion, electrical resistance in leads, and parallax when reading a scale.

零误差的修正方法是从所有后续读数中减去零读数，或对仪器进行物理调整。其他系统误差包括热膨胀、导线中的电阻以及读取刻度时的视差。

Calibration can identify the magnitude of a systematic error at each point on the scale. A calibration curve then provides the correction needed at any intermediate reading.

校准可以确定标尺上每个点的系统误差大小。校准曲线随后为任何中间读数提供所需的修正。

5. Calibration Curves | 校准曲线

A calibration curve is a graph showing the relationship between the measured reading from an instrument and the known true value. The vertical axis often represents the true value, while the horizontal axis represents the instrument's raw reading. Alternatively, the correction can be plotted against the reading.

校准曲线是显示仪器测量读数与已知真实值之间关系的曲线图。纵轴通常表示真实值，横轴表示仪器的原始读数。或者，可以将修正量相对于读数作图。

For an ideal instrument, the calibration curve is a straight line through the origin with a gradient of 1. Real instruments deviate from this; the curve may have an intercept or a different gradient, or it may be curved.

对于理想仪器，校准曲线是穿过原点的直线，梯度为 1。实际仪器会偏离这一理想情况；曲线可能有截距或不同的梯度，或可能是弯曲的。

Once a calibration curve is drawn, it can be used to convert any future raw reading into a corrected value. This is especially useful when the response of the instrument is not linear.

一旦绘制了校准曲线，就可以将其用于将任何未来的原始读数转换为修正值。这在仪器响应非线性时尤其有用。

6. How to Construct a Calibration Curve | 如何绘制校准曲线

To construct a calibration curve, you need a set of known reference values and the corresponding instrument readings. The reference values are provided by standards, such as calibrated weights, standard resistors, or fixed-point temperature cells.

要绘制校准曲线，需要一组已知参考值和对应的仪器读数。参考值由标准提供，例如校准砝码、标准电阻或固定点温度单元。

For example, in an experiment to calibrate a spring balance, known masses are hung from the spring, and the extension is measured. The true force is calculated as F = mg, where g = 9.81 m s^-2.

例如，在标定弹簧测力计的实验中，将已知质量的砝码挂在弹簧上，并测量伸长量。真实力用 F = mg 计算，其中 g = 9.81 m s^-2。

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Instrument	Standard / Method	Typical Error
Thermometer	Freezing / boiling points of water	±0.1 °C
Voltmeter	Standard reference cell	±0.01 V
Top-pan balance	Standard masses	±0.001 g

Calibration | 校准