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# Resolution and Accuracy of Measurements

Posted on 2010-04-26 as part of the Photonics Spotlight (available as e-mail newsletter!)

Abstract: The article explains the difference between resolution and accuracy of a measurement, and describes an example case where the accuracy can be much higher than the resolution of a detector chip.

Ref.: encyclopedia article on photodiodes

There is often a confusion between the terms resolution and accuracy of a measurement. Well, there is some relation between these terms. However, it is important to understand the difference:

• The resolution of a measurement is mostly relevant for digital readings: it tells in which steps the measurement result can change.
• The accuracy tells how well the result matches reality.

## High Resolution, Low Accuracy

Obviously, a measurement could be totally inaccurate despite a high resolution. For example, the instrument's calibration may be wrong, or the reading may be influenced by strong noise influences, and a high resolution doesn't help against such types of errors.

As this is not totally obvious for many consumers, it is possible to sell cheap photo cameras with many megapixels (i.e., a high spatial resolution) which are not suitable for taking accurate pictures. In some cases, the quality of the optics is insufficient to make it worthwhile to use so many pixels. A large number of pixels can even be detrimental, particularly under conditions of low illumination, where detector noise becomes a problem.

## Low Resolution, High Accuracy

Perhaps surprisingly, there are some cases where the accuracy of a result can be higher than the resolution of the apparatus used. As an example, consider a photodiode array which is used for the measurement of the position of some light point. We can consider the resolution to be the spacing of the detector elements. If the measurement method is simply to take the position where the highest recorded optical intensity is recorded, then the measurement error (without any noise or calibration errors) can be up to half the spacing of the detector elements. However, we may instead fit a curve (for example, a Gaussian) to the readings, and in that way determine the position with a much higher accuracy. This works well if the diameter of the light spot corresponds to a few detector spacings and the noise influences are weak. The accuracy can then be much better than the detector spacing. One may, however, refuse to identify the resolution with that detector spacing in such a case because the calculate position results can indeed vary in much smaller steps. We actually have two types of resolution: the resolution of the intensity measurements and the resolution of numerical results calculated from these values.

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