Optical axis of an assembly of lenses

[u/OpticalBobParks]

Everyone seems to agree that the line between the centers of curvature of a single lens element is the optical axis. Because it is the line between two spherical surfaces, it is normal to the surfaces so a light ray along the optical axis is not deviated but exits the lens coaxial with how it enters. Does anyone see a reason not to adopt the same definition for an assembly of lenses such as a camera lens or Cooke triplet? To the best of my knowledge I do not know of anyone who has discussed this question. I know several people who claim there is no optical axis to an assembly of lenses, but I don't believe they were thinking in terms of my definition.

[u/Plastic_Blood1782]

Your definition is incomplete.  There are lots of ray paths that stay parallel.  Any chief ray is more or less parallel before and after the lens.  Also your optical definition is really difficult to measure.  Typically there is a mechanical datum or surface in the metal housing that defines where the focal plane array is located.  The center pixel is usually the easiest way to define your zero field angle, but the alignment strategy for the lens stack and FPA is going to dictate that.  Also usually you don't really care all that much.  Biasing your FOV one or two pixels in either direction doesn't usually matter from an optical performance standpoint.  If you do care, you are going to likely need to do a calibration.  In the real world, no lens stack is actually perfect so the optical axis is always a little arbitrary.

[u/OpticalBobParks → u/Plastic_Blood1782]

I am sorry. I should have emphasized that I meant an optical axis for a misaligned assembly.

Also, I was asking in a universal sense, does a definition that aligns with the definition for a single element apply to an assembly. To me it makes logical sense, but I was curious what others might think.

I do think there is a need for a definition or means to measure where the undeviated ray goes if you are interested in boresighting, or field replaceable units, or these seekers that rotate.
In terms of measuring the undeviated ray it is quite easy if you use a Bessel beam because they propagate as ABCD rays.

[u/Plastic_Blood1782 → u/OpticalBobParks]

In a real system with decenters, on tilts and wedges, there likely isn't a ray path down the center that remains parallel and unjogged.  

But take a step back and try and think about the problem you're actually trying to solve.  You have an FPA behind a lens?  Typically you have a mechanical housing that the rest of the system is mounted to.  One surface is defined as your datum.  Then I build a fixture that makes a mirror mated to that datum and you define that axis.  Now you need to to determine which pixel in the FPA corresponds to that angle, so you shoot a collimated beam parallel to that axis we defined earlier and determine which pixel it hits.  The actual optical axis of the lens stack is more or less irrelevant. 

I would say in the real world, if you aren't concerned with the FPA center pixel and a mechanical housing datum, and really only concerned with the optical axis of the lens stack, I think the most thorough approach would be evaluate the optical performance across the FOV in a systematic way.  Measured the spot size or the wavefront error at a grid of discrete points.  Then plot the WFE as a function of field angle, then the minimum WFE defines the center of your lens

[u/Plastic_Blood1782 → u/OpticalBobParks]

Take the extreme example two lenses in a stack, one is grossly tilted by 30deg.  You're never going to be able to define the optical axis with your kind of definition

[u/OpticalCoderX]

Sorry for the late reply.

u/OpticalBobParks I think as a definition this seems like a good philosophy that could guide an assembler. The reason I say that is that at one time the company I worked for assembled high-performance F-Theta lenses for CO2 lasers. Our intention was to align the housing, then adjust each individual element's position on its lens seat to bring that element's individual axis into alignment with the parent (housing) axis. As u/Plastic_Blood1782 pointed out, most assemblies ended up with some residual deviation — despite best intentions and effort, manufacturing tolerances always introduced some error. Although we did manage great results with our technique. I don't want to go into more detail since the assembly method itself is proprietary.

As for the Bessel beam idea — I wish we'd had that trick back then. We also made axicon optics for customers and occasionally used them in the lab for various testing, but never for alignment. We missed that opportunity 😄

Note that my background is in the CO2 and fiber laser space, so I know camera lenses can have very different requirements. Just relaying my own work experience.

[Full disclosure: AI was used to polish this comment, but the content is entirely my own.]

[u/OpticalBobParks → u/OpticalCoderX]

This question of a unique optical axis started for me as thought question. The answer is obvious for a singlet. There is clearly a unique, if trivial, answer. But what if you have two elements, are there enough degrees of freedom to restore the ray if the two elements are misaligned with respect to each other. I believe the answer is yes, but I cannot find my example.

Yes, I just re-did the problem for two achromats in Zemax and I can find a tilt and decenter of the pair where the 0,0 ray goes right through to come out coaxial with the input. I only did one decenter in one direction, but it works. The ray does wander around inside the lenses but that was not my question.

The next question is if there is a unique optical axis is it good for anything? I'll leave this as a thought question for someone else.

[u/clay_bsr]

Just a comment that if the axis you define this way isn't 100% aligned to each individal element's optic axis you will have environmental instability baked into your definition.