There is a number of conventions for specifying coordinates in Spherical polar coordinate system: ($r$, $θ$, $φ$), ($r$, $φ$, $θ$), ($\rho$, $\theta$, $\phi$) and even ($r$, $\psi$, $θ$).
The article in citizendium states:
The notational convention introduced above (θ for the colatitude angle, φ for the azimuth angle) is used universally in physics. It is in accordance with advice of the International Standards Organization (ISO 31-11, which, however, advises the use of ρ instead of r ). In mathematics—especially in the older and the European literature—the convention is very widespread, too. To quote a few prestiguous mathematical books that apply it: Abramowitz and Stegun (p. 332), Whittaker and Watson (p. 391), Courant and Hilbert (p.195), and Kline (p. 527). Until the 1960s this convention was used universally, also in mathematical textbooks, see e.g. the 1959 edition of Spiegel (p. 138).
Somewhere in the 1960s it became custom in American mathematical textbooks to use a notation in which φ and θ are interchanged, see e.g. Kay (p. 24) and Apostol (p. 419). This was done in order to not confuse students by changing the meaning of the Greek letter θ in the transition from 2D to 3D polar coordinates...
The article at mathworld.wolfram.com summarizes a number of conventions used by various authors.
The questions are:
- What notation convention is more "standard" for physics and especially photometry and computer graphics?
- Can I use ($r$, $θ$, $φ$) symbols to specify radial, azimuthal and polar coordinates?