Resolution

The resolution of a measuring instrument is the smallest variation of a physical quantity that the instrument is capable of detecting and displaying.

Discover FizziQ

How to measure it in class

With the FizziQ app, it is possible to compare the resolution of different smartphone sensors.

Steps:

Open FizziQ and select the atmospheric pressure sensor. Observe the number of decimal places displayed and deduce the sensor resolution (for example, 0.01 hPa).
Make very small height variations (stand on a chair, raise your arm) and observe if the sensor detects these changes.
Repeat the operation with the light sensor and acceleration sensor. Note the resolution of each sensor.
Compare the resolutions obtained and discuss: which sensor has the best resolution? Is this resolution sufficient for the planned experiments?

Scientific activities on this topic

Several experiments easily achievable with a smartphone, tablet, or computer allow exploring the resolution of measurement sensors.

1: Evaluating sensor quality - Analysis of sensor precision: https://www.fizziq.org/en/activities/evaluate-the-quality-of-a-sensor/
2: Uncertainty - Analyzing measurement uncertainties: https://www.fizziq.org/en/activities/uncertainty/
3: Altimeter - Create an altimeter with an atmospheric pressure sensor: https://www.fizziq.org/en/activities/altimeter/

Learn more

Resolution and digitization

In a digital sensor, resolution is directly related to the number of bits in the analog-to-digital converter (ADC). A 10-bit ADC divides the measurement range into 1,024 levels. A 16-bit ADC offers 65,536 levels, or 64 times better resolution for the same range. Modern smartphone pressure sensors typically use 24-bit ADCs.

Spatial and temporal resolution

The concept of resolution extends beyond measuring instruments. In imaging, spatial resolution refers to the smallest visible structure. An optical microscope achieves a resolution of approximately 200 nm, limited by the wavelength of light. The temporal resolution of an oscilloscope determines the fastest signals it can capture.

Resolution and background noise

In practice, the useful resolution of a sensor is often limited by background noise rather than the digital converter. If random noise is plus or minus 0.1 degrees C, displaying a resolution of 0.01 degrees C provides no useful information. Effective resolution is therefore the maximum between digital resolution and noise level.

Orders of magnitude

Resolution of a smartphone accelerometer: approximately 0.001 g. Resolution of a smartphone barometer: approximately 0.01 hPa. Resolution of a civilian GPS: approximately 1 to 3 m in horizontal position. Resolution of a laboratory temperature sensor: 0.001 degrees C.

Formula

For an analog-to-digital converter, resolution is calculated by:

R = (V_max - V_min) / 2^n

Meaning: R: converter resolution (in the unit of the measured quantity) V_max: maximum value of the measurement range V_min: minimum value of the measurement range n: number of bits of the converter

Application examples

A kitchen scale graduated to the gram cannot weigh 0.5 g of salt
A medical thermometer displaying to the tenth of a degree has a resolution of 0.1 degrees C
A smartphone GPS with 1 m resolution cannot distinguish two positions 50 cm apart
A digital stopwatch displaying hundredths of a second has a resolution of 0.01 s
A car speedometer graduated every 5 km/h has a resolution of 5 km/h

FAQ

Q: Are resolution and precision the same thing? A: No. Resolution is the smallest detectable difference. Precision measures the dispersion of results around the true value. An instrument can be resolved but imprecise.

Q: How to know the resolution of a smartphone sensor? A: It can be estimated by observing the smallest variation displayed by FizziQ during micro-changes, or by consulting the sensor’s technical documentation.

Q: Can the resolution of a sensor be improved? A: The hardware cannot be modified, but multiple measurements can be averaged to detect finer variations than the nominal resolution.

Q: Why does a sensor sometimes display more decimal places than it actually measures? A: The digital display may show decimals from internal calculations, but these additional digits are not significant if the sensor does not have the corresponding resolution.

Q: Does resolution depend on the quantity measured? A: Yes. The same smartphone may have excellent resolution in pressure (0.01 hPa) and mediocre resolution in luminosity (1 lux).

Precision - Sensitivity - Uncertainty - Sensor - Analog-to-digital converter - Measurement noise - Significant figures