Temporal resolution (TR) refers to the discrete resolution of a

measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...

with respect to

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

. It is defined as the amount of time needed to revisit and acquire data for exactly the same location. When applied to

remote sensing Remote sensing is the acquisition of information about an physical object, object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring inform ...

, this amount of time is influenced by the

sensor A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a devi ...

platform's orbital characteristics and the features of the sensor itself. The temporal resolution is low when the revisiting delay is high and vice-versa. Temporal resolution is typically expressed in days.

Physics

Often there is a trade-off between the temporal resolution of a measurement and its spatial resolution, due to Heisenberg's uncertainty principle. In some contexts, such as

particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...

, this trade-off can be attributed to the finite

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

and the fact that it takes a certain period of time for the

photons A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that ...

carrying information to reach the observer. In this time, the system might have undergone changes itself. Thus, the longer the light has to travel, the lower the temporal resolution.

Technology

Computing

In another context, there is often a tradeoff between temporal resolution and

computer storage Computer data storage or digital data storage is a technology consisting of computer components and Data storage, recording media that are used to retain digital data. It is a core function and fundamental component of computers. The cent ...

. A

transducer A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another. Transducers are often employed at the boundaries of automation, M ...

may be able to record data every millisecond, but available storage may not allow this, and in the case of 4D PET imaging the resolution may be limited to several minutes.

Electronic displays

In some applications, temporal resolution may instead be equated to the sampling period, or its inverse, the refresh rate, or update frequency in

Hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

, of a TV, for example. The temporal resolution is distinct from temporal uncertainty. This would be analogous to conflating

image resolution Image resolution is the level of detail of an image. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies ...

with

optical resolution Optical resolution describes the ability of an imaging system to resolve detail, in the object that is being imaged. An imaging system may have many individual components, including one or more lenses, and/or recording and display components. E ...

. One is discrete, the other, continuous. The temporal resolution is a resolution somewhat the 'time' dual to the 'space' resolution of an image. In a similar way, the sample rate is equivalent to the pixel pitch on a display screen, whereas the optical resolution of a display screen is equivalent to temporal uncertainty. Note that both this form of image space and time resolutions are

orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...

to measurement resolution, even though space and time are also orthogonal to each other. Both an image or an oscilloscope capture can have a

signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in deci ...

, since both also have measurement resolution.

Oscilloscopy

oscilloscope An oscilloscope (formerly known as an oscillograph, informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing i ...

is the temporal equivalent of a microscope, and it is limited by temporal uncertainty the same way a microscope is limited by optical resolution. A digital sampling oscilloscope has also a limitation analogous to

, which is the sample rate. A non-digital non-sampling oscilloscope is still limited by temporal uncertainty. The temporal uncertainty can be related to the maximum frequency of continuous signal the oscilloscope could respond to, called the bandwidth and given in

. But for oscilloscopes, this figure is not the temporal resolution. To reduce confusion, oscilloscope manufacturers use 'Sa/s' instead of 'Hz' to specify the temporal resolution. Two cases for oscilloscopes exist: either the probe settling time is much shorter than the real time sampling rate, or it is much larger. The case where the settling time is the same as the sampling time is usually undesirable in an oscilloscope. It is more typical to prefer a larger ratio either way, or if not, to be somewhat longer than two sample periods. In the case where it is much longer, the most typical case, it dominates the temporal resolution. The shape of the response during the settling time also has as strong effect on the temporal resolution. For this reason probe leads usually offer an arrangement to 'compensate' the leads to alter the trade off between minimal settling time, and minimal overshoot. If it is much shorter, the oscilloscope may be prone to aliasing from radio frequency interference, but this can be removed by repeatedly sampling a repetitive signal and averaging the results together. If the relationship between the 'trigger' time and the sample clock can be controlled with greater accuracy than the sampling time, then it is possible to make a measurement of a repetitive waveform with much higher temporal resolution than the sample period by

upsampling In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of sample rate conversion, resampling in a multi-rate digital signal processing system. ''Upsampling'' can be synonymous with ''expansion'' ...

each record before averaging. In this case the temporal uncertainty may be limited by clock

jitter In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a signifi ...

References