The basic ABCD formulation is quite common and you can find many references for it including Wikipedia: Ray Transfer Matrix Analysis.

The case with Tilt/Decenter is only slightly more complicated. While I had seen the ABCDEF approach somewhere, I worked it out for myself when creating Raylab.

I can’t immediately find a reference which describes it now. I have not looked at the paper “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems” by Anthony A. Tovar and Lee W. Casperson. But the abstract suggests it might provide the precise details of this approach. Note that the matrices used in Gaussian Beam Propagation are the same as the matrices used in Ray Transfer Analysis.

The basic idea is that in addition to (x2;u2) = [A B; C D] * (x1; u1) there can also be constant terms added by various optical components. We handle this by growing the matrix to include E, F, and adding a 1 at the end of the x,u vector… So:

(x2; u2; 1) = [A B E; C D F; 0 0 1] * (x1; u1; 1)

If something adds a slight offset to the ray, it will have an E term: [1 0 E; 0 1 0; 0 0 0]

If something adds a slight tilt to the ray, it will have an F term: [1 0 0; 0 1 F; 0 0 0]

To handle a standard optical element (say a lens) which is off-center, we combine several matrices:

1. Matrix to offset the ray by an amount corresponding to the off-center position of the lens.

2. Matrix for the lens.

3. Matrix to change back the offset.

In effect, this is changing reference frames… We start in our global frame, transition to the lens frame, apply the lens matrix, and transition back to the global frame.

You do something similar for tilt.

The 3rd option in Raylab for Ray Transfer Matrix Relative to a Reference Ray is much more complicated. My reference for this was “Ray Techniques in Electromagnetics” by George A. Deschamps. Particularly section III.A. “Tracing of a Pencil” which culminates in equations 42-45. The notation in this paper was quite different than what I was familiar with. So I followed his approach while rederiving the equations in notation I could understand and relate to Raylab. The final result involves the angle of incidence and local curvature of the surface at the point where the reference ray hits it.

With all of these approaches, you also have to pay attention to some signs getting flipped when you encounter mirrors and when rays are traveling backward.

Hope this helps.

Kamyar

I am wondering, is it possible to get a short overview of the calculation method (formulas) used in Axial Analysis with Tilt/Decenter where you calculate the (E and F) when a tilt or a decenter is added.

I have gone through different books but couldn’t grasp the idea of how you are implementing it in your Matrix analysis. It would be really helpful if you could provide some insight.

Thanks in advance

]]>As for editing the prescription, I’d like it edit it in the spreadsheet mode rather than per surface.

]]>I have looked at MTF before and was not quite sure how to compute it for arbitrary lens systems. It would need further study on my part.

I am unclear what you mean by editing the prescription. RayLab already lets you edit all the lens surface parameters. ]]>

… What you say is indeed quite logical.

.

MichaelG. ]]>

In theory (i.e. mistakes on my part not withstanding) RayLab is taking a similar approach to units as Zemax. That is you can use whatever units you want as the Lens Units so long as you remain consistent.

As with Zemax, Lens units are the primary unit of measure for the lens system. Lens units apply to radii, thicknesses, apertures,

and other quantities, and may be millimeters, centimeters, inches, meters, etc.

Being consistent means that Lens Power has units of 1/Lens Units. So if all your dimensions are in mm, then power is in 1/mm.

The only thing which has a prescribed unit is wavelength which is in nm.

]]>A quick question:

What ‘unit of measure’ does RayLab use for Lens Power ?

… I am confused.

I have just ‘created’ the Thorlabs plano-convex lens LA1131-633

https://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=5383

This has a nominal focal length of 50mm and a nominal power of +20 Diopter … RayLab shows a focal length of 49.9mm [which is fine], but expresses the Lens Power as .020

Obviously, I can multiply RayLab’s number by 1000

… but I am keen to understand why it is expresed that way.

Thanks and Best Wishes

MichaelG.

Thanks for the prompt reply.

… I have sent you an eMail.

MichaelG.

]]>It has been a while since I looked at that model and I am hard pressed to say why Magnification is -51.3 instead of -40.

RayLab is reporting the Paraxial Magnification calculation, and I do know that Zemax also calculates -51.2 as the Paraxial Magnification for this model.

It may be that there is some aspect of the 40x objective specification from the patent which I am missing. For example, I just noticed that the patent mentions the presence of the 0.17mm cover slide, which is not included in the model.

Another possibility is that there is a difference between how magnification is defined for a microscope objective and the way paraxial magnification is defined. For one thing the paraxial magnification depends of the distance of the object from the lens. If I increase the distance between the object and first lens surface to 1.556mm we get -40x for paraxial magnification value. I am not exactly sure how Microscope objective magnification is defined. If you do, let me know.

]]>