[5] In physical theory of surface and interface roughness, and especially in the study of shape conformations of membranes, it is usually called the Monge gauge,[6] or less frequently the Monge representation.
[8] Typically, the reference plane represents the average surface so that the first moment of the height is zero, =0.
The Monge gauge has two obvious limitations: If the average surface is not plane, then the Monge gauge only makes sense on length scales smaller than the curvature of the average surface.
And the Monge gauge fails completely if the surface is so strongly bent that there are overhangs (points x,y corresponding to more than one z).
The term obviously refers to Gaspard Monge and his seminal work in differential geometry.