Sine laws of spherical singlets

[difalcojr]

index2 should equal 2.
Try a marginal ray, maybe. y-axis height is 0.5 for the marginal ray. Everything else the same.

 

[Drakkith]

Ah, I found the issue. The result was actually in engineering notation, but the number of digits after the decimal was so high the e-6 was hidden off to the right inside the text box. So it's very, very close to zero, close enough to agree with your analysis.

 

[difalcojr]

Did it work for both the paraxial and the marginal ray? Ray angles set at zero degrees with the horizontal, and the exit angles the same?

 

[Drakkith]

Just did a ray trace with an initial ray angle of 0.1 and ray height of 0 (hits the first surface in the center). The resulting exit angle was about 0.0999939. The difference from 0.1 is easily attributable to me only using 4 or 5 digits for the input values.

Did it work for both the paraxial and the marginal ray? Ray angles set at zero degrees with the horizontal, and the exit angles the same?

Yes, the first trace was a parallel ray with an angle of 0. The exiting angle was -1.4082972487512724E-06. Or very, very close to zero.

 

[difalcojr]

Terrific! That's good news. You can get a number even closer to zero maybe if you keep lowering the initial ray angle too. So, you have ray trace solfware for thick lenses too. Excellent.
That's two points on the planar wave, exiting with the same angle, the wave reduced in half its size. All the other rays between horizontal axis and marginal ray will do the same if you check. Thanks.

 

[difalcojr]

Here's a last, spider-legged diagram and values. A good test for your software now.
Let me explain how to read this. It is to show ray/wave magnifications and optical path lengths. Under the minimum conditions. At the point when each wave starts to enter the lens, and at the point when each wave finally exits the lens. Same waves as from the other sequences shown. Marginal rays incoming, marginal rays outgoing. Here's some values you can check for the marginal and arbitrary rays. Minimum magnification ratios.

TYPE...............................ANGLE......................MAGNIFICATION.............................................................................................................
converging.......................30.................................10.24:1...........................................................................................................................
converging.......................15....................................3.97:1..........................................................................................................................
planar..................................0...........................................2:1...........................................................................................................................
diverging..........................15..............................................1:0.92.................................................................................................................
diverging..........................30..............................................1:1.71.................................................................................................................
diverging..........................45..............................................1:3.41.................................................................................................................

Hope this chart posts OK to read.
For optical path lengths only the lens itself needs be figured to get the OPL. This formula works at the minimum condition for the lens:

Minimum OPL=(radius1+radius2)(index1). Its value for the lens index of square root of 2 equals 2.4142...
This value is constant for every wave shown.

 

[difalcojr]

Just did a ray trace with an initial ray angle of 0.1 and ray height of 0 (hits the first surface in the center). The resulting exit angle was about 0.0999939. The difference from 0.1 is easily attributable to me only using 4 or 5 digits for the input values.Yes, the first trace was a parallel ray with an angle of 0. The exiting angle was -1.4082972487512724E-06. Or very, very close to zero.

So, I know you are probably super busy with other projects, and I've overloaded everyone with this, and especially you and hutchphd. And it's the weekend now, and it's been 2 weeks with this problem.
When you get a chance, or anyone else please, even teachers needing a student project, maybe, set up this lens model with those easy equations given. Use the diagram for the plane model. Ray trace some different angled rays through the model lens. Convince yourselves that the incoming and outgoing angles are the same for this model's shape and choice of indexes.
I truly expect someone in this forum to be able to confirm or disprove my contention that this model has zero SA. It's only geometrical optics and very easy, right? Thks.

 

[Drakkith]

I managed to slap together a quick design in Optical Ray Tracer (which I've never used before) but either limitations in the software or my own inexperience with it forced me to eyeball things. I was able to get the rays entering the second lens to look close to parallel. You can try it yourself, you just have to fiddle with the thickness of the first lens and the x-position of the 2nd lens to get the distances between the elements correct. Unfortunately it wasn't as easy as just inputting the values we had above, for reasons I don't know.

I basically set up two lenses, the first with asymmetric curvatures, setting the curvature of the 2nd surface (the 'left sphere' in the program) to 0.70710798, the curvature of the 1st surface of the second lens to -0.70710798, and making the 2nd lens very thick. The radius of each lens should be small, something like 0.5 or so. Smaller than the smallest radius of curvature. The second lens should have an x-position that puts it very, very close to the last surface of the first lens with only a tiny gap in between.

 

[Gleb1964]

I'd say do a full raytrace before trying to consider what the system would be good for. SA might be fully corrected for, but what about other aberrations?

There is free OSLO EDU raytracing software which is limited up to 10 surfaces for free educational version.

 

[difalcojr]

I managed to slap together a quick design in Optical Ray Tracer (which I've never used before) but either limitations in the software or my own inexperience with it forced me to eyeball things. I was able to get the rays entering the second lens to look close to parallel. You can try it yourself, you just have to fiddle with the thickness of the first lens and the x-position of the 2nd lens to get the distances between the elements correct. Unfortunately it wasn't as easy as just inputting the values we had above, for reasons I don't know.

I basically set up two lenses, the first with asymmetric curvatures, setting the curvature of the 2nd surface (the 'left sphere' in the program) to 0.70710798, the curvature of the 1st surface of the second lens to -0.70710798, and making the 2nd lens very thick. The radius of each lens should be small, something like 0.5 or so. Smaller than the smallest radius of curvature. The second lens should have an x-position that puts it very, very close to the last surface of the first lens with only a tiny gap in between.

Valiant effort! Here's the model diagram again, explicitly, if you want to check that software against this one.

 

[difalcojr]

There is free OSLO EDU raytracing software which is limited up to 10 surfaces for free educational version.

Should only need two surfaces, thankfully.
Trace a planar ray through the planar model with the values shown in the last post's diagram, and trace any diverging or converging ray angle through it too. See if the input and output ray angles will be the same.
I have my doubts still on existing software being able to do thick lens, trigonometric tracing, as this requires.

 

[difalcojr]

You may find this treatment interesting (shaping aspheric second surface) .
https://royalsocietypublishing.org/doi/epdf/10.1098/rspa.2014.0608

From what I can tell the family of aspheric model lenses free from all orders of spherical aberration as shown in the article, is akin to this family of spherical model lenses free from all orders of spherical aberration.
A modern, aspheric singlet and a classic, spherical singlet. Both with zero SA. They could be paired together, possibly.
The spherical model here is exceedingly simple, while the modern physics aspheric model is the opposite. From a geometrical optics point of view, the aspheric model seems similar to Descartes' ovals.
The family photo of spherical models is shown in that large array in a previous post here. If you turn those pictures sideways, you will see how highly groomed their "haircuts" are. An ordered universe.

 

[berkeman]

It turns out that the OP is trying to use PF for peer-review of his work, so this thread is closed per the PF rules.