​@CJ27 :  It would be helpful if you could attach a ZAR version of the model. 

Hi ​@Jeff.Wilde ,

Sure, here is the ZAR version of the model. 

Thanks for the comments and feedback.

 Hi ​@Jeff.Wilde,

Thanks a lot for the feedback. I did not know about the re-aligning option.

Well, what I was more wondering about is: Is it possible to beat the limitations in coupling efficiency for this lens configuration? (Given that the fiber and lens are fixed and aligned along the optical axis)

In my case, at the end, I want to design a lens which “corrects” for the possible object offsets in the transversal direction at the object plane. As you mentioned in your comment, for a 1 micron offset in the object plane, my stigmatic image point has a huge trasversal offset, at least for my case, in where I cannot perform any fiber re-alignement, i.e, the fiber and the lens are fixed in space and cannot be re-positioned.

When I read the wikipedia section on the Abbe sine condition (https://en.wikipedia.org/wiki/Abbe_sine_condition#Magnification_and_the_Abbe_sine_condition), there, at the end of the section, it is mentioned:

“This is another way of writing the Abbe sine condition, which simply reflects the classical uncertainty principle for Fourier transform pairs, namely that as the spatial extent of any function is expanded (by the magnification factor, M), the spectral extent contracts by the same factor, M, so that the space-bandwidth product remains constant.”

From this I understand that the Abbe sine condition and its implications on the image points height and NA, are some sort of “fundamental” limit, i.e, that if I want to mantain aplanatism (and get rid of linear coma) in my fiber coupling system, the fact that I am imaging the object ray bundle to a lower NA bundle (to match the fiber NA) implies that there is no way I can “squeeze” more Airy disks or image points closer to each other (since the magnification is the ratio of the image space NA to the object space NA).

Does this need to hold no matter what optical elements I include in between my “initial” source or object and my final image plane? ( meaning that this condition should satisfied for the overall system).  Or does this condition need to hold only for each local object and image planes associated to each cardinal lens?  

What do you think about this? Do you maybe have some suggestion on how could I improve the tolerancing of this ideal aplanatic fiber coupling system (again, in my case performing a fiber re-alignment is unfortunately not possible)

Thanks for the comments and feedback.!

Hi ​@CJ27 

Sorry, no free lunch.  You can reduce alignment sensitivity by broadening the spot size at the fiber input at the expense of lower overall coupling efficiency.

Regards,

Jeff

Hi ​@Jeff.Wilde,

I see, I got it now.

Any idea about other alternatives to improve the toleracing? What else could I compromise for in this case? (As an alternative to the spot size at the fiber input) I could sacrifice other things to compensate for the toleracing accuracy in this case. 

If all you want to do is collect light, you could use a multimode fiber with a larger core size.  However, if you must use SMF for some reason, then you are most likely stuck with tight tolerances.