Hi Ruik,

First, the “magnification” that OpticStudio reports is either PMAG (paraxial mag, finite conjugate) or AMAG (angular mag, infinite conjugate).  Both of these calculations only consider a parabasal +y ray and there is no x component.  Also, many of OpticStudio’s calculations are paraxial, which means OpticStudio “unfolds” a system with Coordinate Breaks and calculates values on a “straight” system so there is no rotation; the PMAG/AMAG calculation are paraxial calculations and don’t consider Coordinate Breaks.

Case A (assuming only a +y component) is how OpticStudio calculates the magnification.  For Case B, in real life, it doesn’t matter that the image surface is rotated, it's how big does the object “appear”, so assuming that SQRT(X’*X’ + Y’*Y’) = SQRT(X’’*X’’ + Y'’*Y'’), then the magnification value for Case A & Case B would be the same.  For Case C, the magnification is always calculated from the Image Surface local vertex, so a smaller y-image size would have no affect on a magnification calculation. 

The diagram that you are showing is more like a distortion mapping, not a magnification calculation.  If you want a more complex Distortion Map besides the built-in Grid Distortion that comes with OpticStudio, then you’ll need to create this yourself.

Hi Ruik,

Michael’s answer is spot-on as always. 

I like to think of it this way: in paraxial optics, there is a single ‘focal length’ for a lens at a given wavelength. As you progress to third-order aberration theory you see that focal length becomes a function of pupil size (spherical), pupil orientation (astigmatism) and so on. In general focal length is a function of conjugate location, pupil orientation, pupil size etc.

I agree that the various distortion plots are good proxies for non-constant magnification, particularly magnification as a function of field. But look on the Analysis tab at the PAL/Freeform features Power Pupil Map and Power Field Map. These are not restricted by paraxial assumptions and will give you the actual focal length of your system for any field/pupil combo.

• Mark