Principal planespdf

The second type of UV laser is a gas laser, the excimer laser. The wavelength of this laser depends on the type of gas mixture used. The beam generated isn’t round but has a rectangular shape with an intensity distribution more or less constant over the cross section of the beam that falls off sharply at the edges. Masks can be used to generate specific spot geometries. Process details can be as small as a few microns, while the distance between focusing optics and workpiece can be as large as 50 to 100 mm. Holograms may also be used to generate specific beam energy patterns.

I agree with Michael.  The principal planes (and more generally the cardinal planes), are paraxial entities.  In a paraxial world, all lens surfaces are planes that have ray-bending optical power.  The planes reside at locations calculated relative to where the lens surfaces intersect the optical axis.  Paraxial ray tracing is very valuable; for example, the Seidel aberrations are computed by tracing the paraxial marginal and chief rays.  In Zemax, rays don’t have to be small-angle to be considered paraxial.  Instead, rays that are traced using linearized paraxial math (i.e., linearized Snell’s Law, again with lens surfaces represented as planes), are called paraxial.

In 1995 Hans van Esdonk left the Philips Center of Manufacturing Technology where he had been a specialist in the application of excimer lasers. His company, Excilas, serves companies in southeast region of the Netherlands in addition to companies in other European countries, Asia, and the U.S. The company prefers to work in projects with well-defined phases and deliverables.

Principal planeslist

I went down a rabbit hole when I was figuring out where the object principal plane of a thick plano-convex lens is. I’ve been taught to find the principal planes like its described at RP Photonics, that is:

Like all other types of lasers ultraviolet lasers are suited for a specific field of applications. They are well suited for applications on a micro scale with high quality results. This has opened a wide range of new applications for which there is no alternative technology. It is certain that in the future we will see a number of new applications that we haven’t even thought of today. The relatively low processing rate, compared to visible and infrared laser radiation, will challenge the laser manufacturers to develop lasers with higher average powers. This will help to reduce the costs of the technology.

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From a calculation standpoint, I believe all the Cardinal Points in OpticStudio use paraxial ray tracing, so the curved surface is actually a plane.  Another way to think of it is you calculate the Principal Plane using parabasal rays that are so close to the optical axis the local curvature of the lens looks like a vertical plane.

I think you’re on the right track with real vs paraxial rays.  When I encounter a basic question like this, I always like to go back to the fundamentals, namely how are the principal planes truly defined (not simply how are they calculated).

Principalplane in Mohr's circle

Plano-convex and plano-concave lenses have one principal plane that intersects the optical axis, at the edge of the curved surface, and the other plane buried inside the glass.

The main services the company provides are laser engraving of precision tools; direct laser marking of metals, glass, and synthetics; application research in new methods to compliment conventional manufacturing technologies; development of ultraviolet-based production process; and preventive maintenance of ultraviolet laser systems. According to the director of the company, Marco Bak, the company can also take full process responsibility.

From this description it is clear that the principal planes (at P and P’) need not coincide with the physical lens surfaces.  However, for plano lenses (with one of the two surfaces being a flat), then one of the principal planes does coincide with a lens surface.  Here’s a nice figure from Fundamentals of Optics, 4th Ed. by Jenkins & White:

The Dutch company Lasertec, located in Barendrecht near the city of Rotterdam, will celebrate its 10th anniversary this year. As one of the first companies to use solid-state ultraviolet lasers it has broad experience in development of special processes. Over the years it has built working relations with specialists in design and manufacturing of production units and also with the manufacture of synthetics. Through these relationships the company can supply customers with turnkey solutions.

Principalplane formula

The company has two excimer lasers. They can be filled with different gas mixtures to choose the best wavelength for a specific application.

Principal planesexamples

Many of these applications require the user to have proper know how about UV lasers and also about optics and the material to be processed. Manufacturers of UV lasers and specific companies with facilities for application research are helping industry to develop new processes using these lasers.

Thanks @MichaelH and @Jeff.Wilde. You gave me a different perspective on this problem. I like the idea of using parabasal rays. I also find paraxial ray tracing to be extremely valuable and its interesting to see how paraxial ray tracing subtly integrates with real ray tracing into OpticStudio.

Speaking of references, I think most optical engineers know about the SPIE Field Guides.  They are very handy, concise handbooks chocked full of good information.  For example, the principal planes/points for a thick lens are succinctly described in the SPIE Field Guide to Geometrical Optics by J. E. Greivenkamp.

What isprincipalplane in Optics

What makes them so well suited for marking synthetics and glass and for creating safety features on ID and credit cards? Again the short wavelength is important because the small spot size allows penetration into the material where chemical and or physical transitions will result in changes that can be observed either by the naked eye or under special light or with proper magnification.

However, when rays parallel to the optical axis enter through the plane face of the lens, the ingoing and outgoing rays will meet exactly along the convex face, which is not a plane.

Therefore, when you take a real system and Gaussian reduce it (so you can use concepts like Lens Maker’s equation, reduced distances, magnification), there are no curved surfaces but only points, lines, and planes.  This is where thin lens and paraxial optics comes from.

Therefore, I believe the principal plane is defined as the plane coincident with the convex surface vertex. At least, this is what I’ve taken away when I used OpticStudio (surface 1 is the convex surface).

Thanks to his Philips background, van Esdonk has an extended network of high-tech partners so the company is well suited to serve other companies in finding an optimum solution for production problems. The service may range from application research through design and development of production systems to transfer of know how.

Thanks for your gracious comments.  I haven’t thought about putting together a reference list organized by topic.  Maybe that’s something I’ll work on in the future.

Gaussian optics treats imaging as a mapping from object space into image space.  It is a special case of a collinear transformation application to rotationally symmetric systems, and it maps points to points, lines to lines and planes to planes.

In structuring of surfaces these lasers fill the gap between lithographic techniques as used in integrated circuit (IC) fabrication and mechanical micromachining and micro-spark erosion.

Principal planesexplained

Principal planesandprincipalstresses

On a side note, @Jeff.Wilde have you ever considered sharing a curated reading list for optical design/engineering? You always have the right references and you point people to the exact chapter/section that they need. Your knowledge of the literature on this subject is a literal treasure trove for the community.

Something that would be really nice from a teaching perspective is if OpticStudio had the ability to show Paraxial Layouts…then the calculation would become visually obvious.

Principal planes (along with all the Cardinal Points) are defined using Gaussian optics.  From the Field Guide To Geometric Optics:

I can accept this definition, but I was curious, from a teaching perspective, to hear if someone can provide an explanation that would be compatible with the “traditional” explanation: find the plane where the in and out rays bend. I know we are at a boundary between paraxial and real optics and it might not make sense to ask this question, but I could imagine a student asking about this and all I could answer for now is that in this instance we choose the vertex of the convex surface as the principal plane and its a special case.

According to van Esdonk, beside an interest from the micromachining industry there is an increase in interest in biomedical applications where the short wavelength and the short pulses of ultraviolet lasers are of benefit.

The third type of UV laser is the metal vapor laser. The copper vapor laser is mainly used although vapors of several other metals can also be suitable. Copper vapor lasers generate radiation at 511 nm and 578 nm wavelength. Frequency mixing and doubling are use to generate ultraviolet radiation with 255 nm, 271 nm, and 289 nm wavelength. The beam shape is Gaussian, which makes the laser well suited for the same range of applications as the solid-state ultraviolet laser.

The word “laser” can mean different things to different people, depending on their experience or specific knowledge. They may be familiar with one of the industrial applications like drilling, cutting, or welding. Perhaps they know about eye corrections by laser or have visited a laser light show. But I wonder how many know that the marks on drugs they may be using are made by laser, that advanced safety features on ID and credit cards are made by laser, or that eyeglasses have almost invisible marks made by laser. The lasers used for these applications are ultraviolet (UV) lasers that generate light with wavelengths in the range of 150 to 400 nm.