Transverse ray-intercept fan plot

[pfxxx]

I need help understanding the transverse ray-intercept fan plot. Please see the scanned pages of my book if anything is not clear.

scanned pages on transverse ray-intercept fan plot:
https://docs.google.com/viewer?a=v&...NTNkOS00ZDE4LWIzZTEtZmM0NTYxMmM1ZWFi&hl=en_US

diagram of chief ray and marginal ray:
https://docs.google.com/viewer?a=v&...YTVmMS00NWQ3LWJlYjAtYTg5MjFiYjIxYTY0&hl=en_US

According to the book:
p50: A ray fan is a collection of rays from one object point that all lie in one plane. For a ray fan plot, this plane is made to pass through the center of the entrance pupil...

rays of one object point
Question 1: so that means these rays arrive at the lens with different incident angles?
pass through the center of the entrance pupil
Question 2: so that means the point and plane in consideration are on the meridional (tangential) plane?

p50: As a given ray in the fan passes through the lens on its way to the image surface ... [it] passes through the entrance pupil at a particular zone height (called P).
When the ray intercepts the image surface, it generally falls some small but non-zero distance away from the chief ray. This transverse distance from the chief ray is the ray height error or abberation, Δh, corresponding to the pupil zone height.

This is where things get interesting:
By looking at the diagram of chief ray and marginal ray, you can tell that any ray passing through the lens at certain height (P) between the center of the lens and edge of the lens will surely land between where the chief ray and marginal ray land on the image surface. In other words, that ray will obviously land on some distance away from the edge of the image field, defined by the chief ray.

Question 3: Why then, is the difference between where this ray and the chief ray lands on the image surface callled an aberration? This is the point I cannot get.

Not only that:
The book assume an object point.

Question 4: Where is this point located? Unless it is located on the optical axis, I cannot see how there can be a symmetry on the transverse ray-intercept fan plot. I do not think rays above and below the chief ray have a symmetrical relationship about the chief ray for transverse aberration.

Question 5: Different object points have different heights from the optical axis (assume they all lie at the same distance away from the lens). Then the rays originating from these points will have different incident angles when passing through the lens at the same zone height (P). That being said, each object point (with its unique height) will have its unique transverse ray-intercept fan plot. Thus to cover the all possibility, a 3D plot must be made (height of object point, zone height, and transverse aberration). However, this is not what I see. I only see 2D plots of the aberration (p53).

One interesting thing: on p53 the transverse ray-intercept fan plots at different angles are shown. Spot diagrams of a lens are shown in the same manner (at different angles). This along with the symmetry of the plots bring me to this suspicion:

The transverse ray-intercept fan plot are made for object points located on the optical axis, with the plane of the ray fan lying on the meridional plane. The angle mentioned is the angle between the optical axis and the marginal ray (thus, different angles for different object distances). Since the point is on the optical axis, there is a symmetry about the optical axis of the radiated rays, which explain the symmetry on the transverse ray-intercept fan plot.

Not only that, because the object point lies on the optical axis, the chief ray coincides with the optical axis. Thus, all the rays originated from this object point should end up at one same point if perfect imagery occurs (on axis, at the image plane). Thus, the deviation from this point is rightly named transverse aberration.

---> I am getting this right? This is the only way I can see that can explain the symmetry and why this Δh is an aberration.

---> If so, then how do you assess the quality of a lens for points that are not on axis? It seems like people only make the assessment for on axis points only (assume my explanation above is correct). My guess it that because it would make things so complicated, and the Δh defined above is no longer an aberration.

 

[eljose79]

---> One last thing, in the 3D plot, the height of the object point is the incident angle of the ray. Thus, the angle is the independent variable?

Thank you for reaching out for help understanding the transverse ray-intercept fan plot. I am happy to assist you in understanding this concept.

Firstly, to answer your questions:

1. Yes, the rays in a ray fan arrive at the lens with different incident angles. This is because they originate from one object point and are directed towards different points on the entrance pupil.

2. Yes, the point and plane in consideration are on the meridional (tangential) plane. This is because the chief ray and marginal ray are both on this plane.

3. The difference between where a ray and the chief ray land on the image surface is called an aberration because it represents the deviation of the ray from the ideal image point. In an ideal lens, all rays from an object point would converge at one point on the image surface. However, due to imperfections in the lens, some rays may deviate from this ideal point, resulting in aberrations.

4. The object point mentioned in the book is located on the optical axis. This is because, as you correctly pointed out, only for points on the optical axis is there a symmetry in the transverse ray-intercept fan plot. For points off the optical axis, the symmetry is broken and the plot becomes asymmetric.

5. You are correct in your understanding that each object point will have its unique transverse ray-intercept fan plot. However, for simplicity, the book only shows 2D plots of the aberration for points on the optical axis. For points off the optical axis, the 3D plot you mentioned would be necessary to fully understand the aberration.

Regarding your suspicion, it is correct that the transverse ray-intercept fan plot is made for object points located on the optical axis, with the plane of the ray fan lying on the meridional plane. This allows for the symmetry and also simplifies the plots. However, it is still possible to assess the quality of a lens for points off the optical axis by using more advanced techniques such as wavefront analysis.

In summary, your understanding of the transverse ray-intercept fan plot is correct. The angle mentioned in the plots is the angle between the optical axis and the marginal ray, and the height