data cube

The phrase data cube (also spelled datacube) refers to a three-dimensional array of data values, as might be stored in a computer. Each such value can be a single number or can be some fixed set of numerical values such as three numbers that together represent a vector. Data cubes have uses in astronomy such as storing spectral data associated with a portion of the sky. Often data cubes encompass huge amounts of data.

A data cube is analogous to a (two-dimensional) table but covers three dimensions. Printing a data cube on paper might be accomplished with a series of tables, using a table for each interval within the third dimension. A (2D) table, for example, is adequate to store some record of the surface temperature across a plot of land, storing the temperatures at points evenly spaced across the plot. A data cube (3D) could store the temperature values throughout the volume of a room, similarly distributed at one centimeter intervals over each of the three dimensions.

A data cube's three dimensions may be associated with the three spatial dimensions, but data cubes are also useful for other organizations of data. For example, in astronomy, two spatial dimensions over a portion of the celestial sphere are straightforward to collect and represent, but often data is collected over some non-spatial third dimension, i.e., a series of values from each of the locations on the celestial sphere. Wavelength or frequency is a common third dimension, such as data from integral field spectrographs. Another common third dimension is redshift (comprising redshift space), for data from redshift surveys. Yet another is radial velocity derived from Doppler shifts e.g., from Milky Way groups of clouds, comprising position-position-velocity space, P-P-V space, i.e., how much material is detected at each possible radial velocity at each point on the celestial sphere. In all these cases, the data cube is a natural way to store the data after just a bit of processing.

In the language of spectrography, the term spaxel (for spatial pixel or spectral pixel) is used for the column of values within a data cube that refer to a particular position within an image, i.e., to that image-location-point's entire spectral energy distribution (SED). The spectrograph's sensor (e.g., CCD) is two-dimensional and has pixels, whose layout generally does not match the two dimensions of the celestial sphere being observed, so having a separate term is useful.

The term voxel (for volume pixel) is used for a single element within a data cube, likely coined and most frequently used for data cube elements representing values over three spatial dimensions. But the term is perhaps reasonable for other 3D data, any of which could be thought of as some kind of abstract space (e.g., P-P-V space).