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From reading this interesting discussion below.

I went down a rabbit hole when I was figuring out where the object principal plane of a thick plano-convex lens is. I’ve been taught to find the principal planes like its described at RP Photonics, that is:

extrapolate the ingoing and outgoing rays such that they meet in a plane

However, when rays parallel to the optical axis enter through the plane face of the lens, the ingoing and outgoing rays will meet exactly along the convex face, which is not a plane.

Therefore, I believe the principal plane is defined as the plane coincident with the convex surface vertex. At least, this is what I’ve taken away when I used OpticStudio (surface 1 is the convex surface).

I also found this information here:

Plano-convex and plano-concave lenses have one principal plane that intersects the optical axis, at the edge of the curved surface, and the other plane buried inside the glass.

I can accept this definition, but I was curious, from a teaching perspective, to hear if someone can provide an explanation that would be compatible with the “traditional” explanation: find the plane where the in and out rays bend. I know we are at a boundary between paraxial and real optics and it might not make sense to ask this question, but I could imagine a student asking about this and all I could answer for now is that in this instance we choose the vertex of the convex surface as the principal plane and its a special case.

Take care all,

 

David

Hey David,

I think you’re on the right track with real vs paraxial rays.  When I encounter a basic question like this, I always like to go back to the fundamentals, namely how are the principal planes truly defined (not simply how are they calculated).

Principal planes (along with all the Cardinal Points) are defined using Gaussian optics.  From the Field Guide To Geometric Optics:

Gaussian optics treats imaging as a mapping from object space into image space.  It is a special case of a collinear transformation application to rotationally symmetric systems, and it maps points to points, lines to lines and planes to planes.

Therefore, when you take a real system and Gaussian reduce it (so you can use concepts like Lens Maker’s equation, reduced distances, magnification), there are no curved surfaces but only points, lines, and planes.  This is where thin lens and paraxial optics comes from.

From a calculation standpoint, I believe all the Cardinal Points in OpticStudio use paraxial ray tracing, so the curved surface is actually a plane.  Another way to think of it is you calculate the Principal Plane using parabasal rays that are so close to the optical axis the local curvature of the lens looks like a vertical plane.

Something that would be really nice from a teaching perspective is if OpticStudio had the ability to show Paraxial Layouts…then the calculation would become visually obvious.  

I agree with Michael.  The principal planes (and more generally the cardinal planes), are paraxial entities.  In a paraxial world, all lens surfaces are planes that have ray-bending optical power.  The planes reside at locations calculated relative to where the lens surfaces intersect the optical axis.  Paraxial ray tracing is very valuable; for example, the Seidel aberrations are computed by tracing the paraxial marginal and chief rays.  In Zemax, rays don’t have to be small-angle to be considered paraxial.  Instead, rays that are traced using linearized paraxial math (i.e., linearized Snell’s Law, again with lens surfaces represented as planes), are called paraxial. 

A good reference is Introduction to Lens Design, by J. M. Geary, Ch. 4 (Paraxial World).

Regards,

Jeff

PS: I also agree with Michael that having a paraxial ray trace layout window would be very nice!

Thanks @MichaelH and @Jeff.Wilde. You gave me a different perspective on this problem. I like the idea of using parabasal rays. I also find paraxial ray tracing to be extremely valuable and its interesting to see how paraxial ray tracing subtly integrates with real ray tracing into OpticStudio.

On a side note, @Jeff.Wilde have you ever considered sharing a curated reading list for optical design/engineering? You always have the right references and you point people to the exact chapter/section that they need. Your knowledge of the literature on this subject is a literal treasure trove for the community.

Take care,


David

@David.Nguyen

Thanks for your gracious comments.  I haven’t thought about putting together a reference list organized by topic.  Maybe that’s something I’ll work on in the future.

Speaking of references, I think most optical engineers know about the SPIE Field Guides.  They are very handy, concise handbooks chocked full of good information.  For example, the principal planes/points for a thick lens are succinctly described in the SPIE Field Guide to Geometrical Optics by J. E. Greivenkamp.

From this description it is clear that the principal planes (at P and P’) need not coincide with the physical lens surfaces.  However, for plano lenses (with one of the two surfaces being a flat), then one of the principal planes does coincide with a lens surface.  Here’s a nice figure from Fundamentals of Optics, 4th Ed. by Jenkins & White:

Regards,

Jeff

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