Hi Hugo,

First, the Grid Phase will always be an approximation to a real lens, but based on how you set it up, it can be a really good approximation.  Although in OpticStudio, we trace “rays” through the system, the ray is always going to be the normal to a phase front at any point in space.  When the ray hits a surface, the ray bends and thus the phase front changes.  So, using a Grid Phase rather than a “real” lens can represent this bending.

A few things to note:

• The Grid Phase can only be a plane, so if your lens has high curvature, then rays that hit towards the edge of the lens will not be represented well with a Grid Phase (they will have lateral shift)
• The Grid Phase is represented by units of radians, not nm, so you will need multiple Grid Phase (in a multi-config) to represent a polychromatic system
• The Grid Phase will only be a “snapshot” for a specific field/set of fields (if the Grid Phase is close to the Stop, you will probably need a different Grid Phase for each field point).  The farther a new field point is from the field point used to calculate the Grid Phase, the more error you will introduce.
• If the lens is thin enough, you can get by with using only 1 Grid Phase, but if the lens is thick, then you’ll need to create a Grid Phase for the front surface and another Grid Phase for the rear surface.  Just like with a lens, rays exiting the rear surface will bend a different amount based where they hit the rear surface (controlled by the thickness).

With that said, to answer your questions:

1. Yes, but there are several limitations to consider and this will only be an approximation.
2. Implementing the correct dz/dx, dz/dy, and d2z/dxdy might not be necessary for a well behaved lens (like your plano-convex lens).  If these derivatives are blank, OpticStudio will calculate these derivatives using a finite difference bicubic interpolation so the Grid Phase will still be smooth and continuous.  However, if the phase between pixels will not be well represented by a bicubic curve, then you should provide the derivatives directly.
3. I would use direct ray tracing to ensure the phase is correct.  This could be either a Single Ray Trace or something like a Spot Diagram.  Paraxial calculations (like EFL) and wavefront calculations might take extra effort to be correct and are not necessarily tied directly to the phase pixels in the Grid Phase file.

One question I have is why are you trying to replace a lens with a Grid Phase?  Are you trying to hide the exact prescription of the lens file?  If so, a Black Box will be more accurate and easier to implement.