Compatibility Table
35mm Format Lens	35mm Format Imager Size	No FOV Crop
"X-Format"* Lens	"X-Format" Imager Size	No FOV Crop
"X-Format" Lens	35mm Format Imager Size	Vignetting**
35mm Format Lens	APS-C Format Imager Size	Physical FOV Crop

* "X-Format" is meant to be any format SMALLER than a 35mm format, with a lens matched to it. For example, Nikon's DX lenses and Olympus 4/3 lenses, are matched to their sensors, and have sensors smaller than 35mm format.

** The reason why I mention vignetting, is because if you put a lens with a smaller image circle on a larger imager of a different format, there will be vignetting. Nikon mentions this fact with their DX lenses. The same would hold true for any lens with an image circle smaller than 36mm x 24mm in size (35mm format).

As you can see by the above table, the term "FOV Crop" is limiting to only a specific situation. Now, let's create a table with FOVEF, and see how compatible it is...

FOVEF Compatibility Table
35mm Format Lens	35mm Format Imager Size	FOVEF of 1x
"X-Format"* Lens	"X-Format" Imager Size	FOVEF of Nx
"X-Format" Lens	35mm Format Imager Size	FOVEF of Nx
35mm Format Lens	APS-C Format Imager Size	FOVEF of Nx

As you can see by the above table, FOVEF does indeed solve all forms of lenses and imagers in all possible combinations. In the first case, you have a FOVEF of 1x (or none), because there is no equivalency factor. In the second case, there is a FOVEF factor, and this number will depend on the size of the format and lenses in comparison to a 35mm system.

For example, in the case of Nikon, their DX lenses produce a FOVEF of around 1.5, and the Olympus Four Thirds system, has a factor of 2. In the case of a smaller lens being put on a larger imager, you will get vignetting, but there will be a field of view equivalency factor of the area which is captured by the imager. In the case of a larger lens being put on a smaller imager, the same is true. Now remember, the only reason FOVEF exists, is because we're comparing it to another system (normally a 35mm system). If we had matched lenses on matched sensors and did not compare them, theoretically we wouldn't need FOVEF. But since we have been so used to using 35mm systems, this is the system we compare it to when smaller sized imagers and non-35mm lenses are introduced.

Instead of thinking in terms of a "crop", we are now thinking in terms of what a particular image looks like if we had a 35mm system. We are also getting more accustomed to using the angles of view of a given lens. Once we learn what a given lens AOV is, it will be much easier for us to understand what each format can offer our photography interests.