The four resolutions

Four separate questions describe how good a satellite picture is, and no satellite is best at all four.

The basics

Four separate questions describe how good a satellite picture is. How small a thing can be told apart from its neighbours is the spatial resolution. How many colours are measured is the spectral resolution. How often the same place is photographed is the temporal resolution. How many shades of brightness are recorded is the radiometric resolution. A road atlas and a street map of the same city differ in the first, and a black and white photograph differs from a colour one in the second. No satellite is best at all four, because each has a limited rate at which it can send data to the ground, and more of one usually costs some of another. Choosing data means deciding which of the four the job depends on.

Why it matters

The job decides which of the four matters most. Counting cars needs small pixels. Telling crops apart needs more colours. Watching a flood needs frequent visits. Seeing faint differences in water or in shadow needs many shades of brightness. Asking for the best of all four at once usually means asking for something no single satellite offers.

The same patch of ground, 16 metres across, drawn with 1 metre pixels and with larger ones. Each larger pixel is the average of the ground it covers, so small things such as the building blur away. The slider, where shown, sets the pixel size.

In depth

Spatial resolution is usually quoted as the ground sample distance (GSD), the distance on the ground between the centres of neighbouring pixels. For a camera looking straight down, with detector pitch $p$ , focal length $f$ and altitude $H$ , similar triangles give the GSD directly.

\mathrm{GSD} = \frac{p\,H}{f}

(1)

where $\mathrm{GSD}$ is the ground sample distance, in $\mathrm{m}$ ; $p$ is the detector pitch, the spacing between neighbouring detector elements, in $\mathrm{m}$ ; $H$ is the altitude above the ground, in $\mathrm{m}$ ; and $f$ is the focal length of the optics, in $\mathrm{m}$ .

A camera with 13 micrometre detectors and a 13 metre focal length, flown at 700 km, would have a GSD of 0.70 m. The GSD is a sampling interval and not a promise that every object of that size is visible. Blur from the optics and the atmosphere, and noise, set the real limit on what can be resolved [1]. Figure 1 shows one scene at three pixel sizes in panel (a).

Spectral resolution has two parts, the number of bands and the width of each. The resolving power of a band centred on wavelength $\lambda$ with width $\Delta\lambda$ is

R = \frac{\lambda}{\Delta\lambda}

(2)

where $R$ is the spectral resolving power, without unit; $\lambda$ is the central wavelength of the band; and $\Delta\lambda$ is its width, in the same unit as $\lambda$ , such as nanometres.

so a 10 nanometre band at 700 nanometres has $R = 70$ . Panel (b) of Figure 1 contrasts one wide band, four broad bands and sixty narrow ones.

Temporal resolution is the revisit interval described on the orbits page, shown in panel (c). The radiometric resolution is the number of distinguishable brightness levels, set by the number of bits $N$ the detector signal is recorded in.

L = 2^{N}

(3)

where $L$ is the number of distinguishable brightness levels, without unit; and $N$ is the number of bits each sample is recorded in.

One bit gives two levels, eight bits give 256 and twelve give 4096 (panel d). Extra bits only help if the sensor noise is smaller than one step, otherwise the lowest bits record noise. The trade-offs between the four follow from a fixed budget of light and of downlink capacity. Smaller pixels and narrower bands each collect fewer photons per measurement, and every added band, pixel or revisit adds data to send down [1].

(a) Spatial

(b) Spectral

(d) Radiometric

Figure 1. The four resolutions. (a) Spatial, one 16 m scene sampled with 1 m, 2 m and 4 m pixels. (b) Spectral, bands of different number and width. (c) Temporal, passes over one place for a single satellite and for several in the same orbit. (d) Radiometric, the number of brightness levels for 1, 2, 3 and 8 bits.

References

Rees, W. G. (2012) Physical Principles of Remote Sensing. Cambridge University Press. https://doi.org/10.1017/CBO9781139017411