Paraxial ray tracing: fixing image/height w/o knowing stop location

In summary: However, if one wants to know the aberration values for a specific object or lens, then one should aim the rays at the STOP.Geary mentions in section 5.4 that "the stop starts to become important...when the optical system isn't an idealised linear model." This is where the stop becomes relevant in the context of paraxial rays. When using a non-optimal design, one may find that other components "clip" the ray bundle. In this case, it is important to aim the rays at the stop to ensure that all rays from the object reach the stop.
  • #1
TL;DR Summary
Text book (Geary) describes paraxial ray tracing using stop location (marginal ray at height of stop, chief ray through center of stop) to fix image and image height. Example problems across the net use axial/edge rays of arbitrary initial angles. Stop not specified. Why the difference?
In recent coursework, I was taught that one locates the image and identifies the image height using the marginal and chief rays. These descriptions are:

Marginal ray: that ray traced from [top or bottom] of the object, through the outermost edge of the stop. The place where that ray crosses the optical axis is where I will find the image.

Chief ray: that ray traced from [top or bottom] of the object, through the center of the stop. The height of that ray at the image location (defined by marginal ray) is the height of the image.

In an attempt to practice this, I looked for some solutions to replicate (unfortunately, my recent coursework required some ray tracing, but getting the actual solutions for my flawed coursework was difficult or impossible).

I replicated this ray trace on slide 9-9 and 9-10 (two thin lenses in air):

I can get the same result as the author. However, there is no mention of a stop. Instead, the two rays used to find image/height are launched at arbitrarily small angles. I have seen this elsewhere also. Why?

Tangential question: most resources refer to "stop" when describing system chief and marginal rays. However, does this actually mean entrance pupil? In other words, if the stop is the final component in the system (e.g., stop is exit pupil or "XP"), must I trace this backwards to image that XP as an entrance pupil ("EP") to use that to locate my system chief and marginal rays?

Geary seems to say this explicitly on page 46 (section 5.4): "Suppose we are given the triplet with a buried stop shown in Figure 5.11. We want to trace the marginal and chief ray through the system. But to do that we need to aim the marginal ray at the edge of the entrance pupil and the chief ray at the center of the entrance pupil..."

But other resources on the interwebs seem to contradict or ignore this. For example, this publication seems to use the physical stop to define chief and marginal rays, NOT the EP:

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  • #2
For paraxial rays it doesn't matter what angle you launch at, so you just pick your favourite. Every ray from the tip of the object will go through the tip of the image; every ray from the on-axis point of the object will go through the on-axis point of the image. For the purposes of this construction you can completely ignore the stop - a ray that doesn't pass through the stop would have ended up in the same place as one that did.

Where the stop starts to become important is when the optical system isn't an idealised linear model (i.e. anything real and non-trivial). Then you need to know which part of each lens/mirror/whatever is in use for an object of interest because it affects the aberration. It's been decades since I did any optical design, so caveat emptor, but I recall that you would typically try to ensure that the stop was the limiting factor in what angles of rays were accepted, but in a non-optimised (or just plain lousy) design you may find that other components "clip" the ray bundle. So I'd say the marginal ray in this context is the most extreme ray from a given point that can make it through the system. You shouldn't need too much trial and error to find the marginal ray if you guess wrong initially - it's a linear system.

As I say, it's been a while since I did optical design, so see what others say too...
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  • #3
I see. In that case, perhaps the use of paraxial ray tracing to locate the EP or XP is probably just an exercise.

Thanks for your time, much appreciated!
  • #4
Since my last post, I think I better understand why one would want to conduct a PRT using system marginal and chief rays through pupils.

Many aberration values can be computed using ray heights and angles resulting from a PRT of marginal and chief rays. Tracing rays in this way will also reveal the image location and height.

If one ONLY needs to know the image location and height, one can use PRT with arbitrary initial angles.
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1. What is paraxial ray tracing?

Paraxial ray tracing is a method used in optics to predict the path of light rays through an optical system. It involves tracing a limited number of rays near the optical axis, assuming that they are close to the paraxial (or central) ray, and using this information to determine the characteristics of the image formed by the system.

2. How does paraxial ray tracing help in fixing image and height without knowing the stop location?

Paraxial ray tracing allows us to calculate the image position and height without knowing the exact location of the stop (the aperture or opening that controls the amount of light entering the system). This is possible because paraxial rays are assumed to be close to the central ray, which passes through the center of the stop.

3. What are the limitations of paraxial ray tracing?

Paraxial ray tracing is only accurate for rays that are close to the optical axis and do not deviate significantly from it. It also does not take into account aberrations (distortions) caused by imperfections in the optical system, which can affect the accuracy of the predicted image position and height.

4. How is paraxial ray tracing used in lens design?

In lens design, paraxial ray tracing is used to determine the basic parameters of a lens, such as the focal length, image distance, and magnification. This information is then used to optimize the design and minimize aberrations.

5. Can paraxial ray tracing be used for all types of optical systems?

No, paraxial ray tracing is most accurate for simple optical systems with spherical surfaces, such as thin lenses. It may not be suitable for more complex systems, such as those with aspherical surfaces or multiple elements, where aberrations and deviations from the paraxial approximation are more significant.

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