It should be fairly easy to generate a double-pass grin lens path.  After inserting the mirror, just make sure the return surface thicknesses are all negative, including the return grin thickness.  If any curved surfaces are involved, then the radii signs will need to be flipped too (for aspheres, the make double-path tool should do the trick).  Here is an example with a plano grin lens (lambda = 660 nm). 

Regards,

Jeff

Hi Jeff, 

Thanks for your insights and suggestions. I have a couple of questions:

1. Besides any thicknesses/curvatures, none of the parameters in the GRIN lens have to switch their signs like positive to negative and vice versa correct?
2. When I attempt to run the GRIN lens, I get the following Seidel plot for the spherical aberration:

   

   Why are the spherical aberrations for surfaces 6 and 7 for the return beam not being taken into account? Here is what the asphere Seidel diagram looks like for comparison:

   

1) I’ve only tried reverse propagation through radial gradient grin lenses, and for those none of the coefficients need to have their signs changed. Can’t comment on axial gradient lenses w/o spending a little more time.

2) The Seidel aberrations are not supported for grin lenses.  According to the help documentation:

However, any of the analysis features that rely on real ray tracing should be okay though, like the spot diagram, PSF, fiber coupling, etc.

Hi Jeff,

Thanks for the help and feedback. I will look into real ray tracing analysis tools for the GRIN lens.

Gradient index formulas where with a dependency in Z (gradium 3,4,5 and 7), are not simply reversed as other surfaces, as the origin of the index defining polynomial is changing from one face to another. You need to re-compute all coefficients containing Z after a change of coordinates  (a flip and a translation by the length of the GRIN). That should not change the maximal degree of the polynomial, but your length needs to be fixed.

In practice, the grin propagation steps may also not be aligned in both directions, as they start at the entrance, so you could accumulate errors along the way if the length is not exactly a multiple of the step size. If the steps are small enough, that is less of an issue. However, I remember an eye model that used a gradient index with a big step, so it was not possible to reverse it.

Hi Ray,

Thanks for your suggestions and feedback. The GRIN lenses that I am currently testing with are off-the-shelf lenses from Edmund Optics with one lens having a maximum step size of 0.02 mm and the other having a maximum step size of 0.1 mm. Would these step sizes be considered small enough for the GRIN propagation? The lenses use gradient 5 as the surface and it seems like the nz terms are all zero:

Would I have to modify these terms in particular? Would the nr^2 and nr^4 terms have to change or are those values fixed? 

Hi Trevor,

There does not seem to be any z component, although the negative sign on the Nz1 & Nz3 may mean it’s just the numerical precision in the editor that makes it so. Radial terms do not need modification for flipping. If the Nz terms are all really zero, there is no problem with the step being as big as the lens thickness or bigger. 

Hi Ray,

Thanks for your help and feedback. I will consider these points when modeling the GRIN lenses.