# Image Z Coordinate Clarification

I'm trying to understand 3D image reconstruction, and want to clarify how we can find a z image coordinate.

Is the z coordinate for image coordinates (x,y,z) the focal length since that's the distance to the focal plane? If so would using z=(fx+fy)/2 from K = cv.calibrateCamera() work (K~camera matrix)? Normally images are in normalized coordinates (x',y',1) where z=1. Do I multiply (x',y',1)*z (where z=f), or just use z=1?

Some additional questions if anybody can answer them:

From GPU Parallel Computing of Spherical Panorama Video Stitching, it states "x, y, z are coordinates of Cartesian coordinate system in image pixels", where spherical coordinates are calculated by theta=arccos(z/sqrt(x^2+y^2+z^2)), phi=arctan(sqrt(x^2+y^2)/z) and I assume I can just use regular pixel coordinates after centering them at (0,0). Is this correct?

Additionally from a Szeliski paper, Creating Full View Panoramic Image Mosaics and Environment Maps: "we map world coordinates p =(X; Y;Z) ...to 2D spherical screen coordinates (theta,phi) using: theta=arctan(x/z), phi=arctan(y/sqrt(x^2+z^2)". What does he mean by "world coordinates". Does this mean the image plane in world coordinates as nowhere in the paper does it call for real world object point positions?