HIGH END DIY triplet projection lens - diyAudio

JCB,

What makes it high end is that it is optimized to the point where it can no longer be improved without making the system more complex by adding more elements or by adding aspheric surfaces. This lens if built to spec would outperform any four element system that you could put together without going through the same computer optimization. In years past it took engineers months doing hundreds of calculations to approach a design like this but a computer can do millions of calculations in only a second or two.

We can also do a computer optimization for a four element lens design also. In fact by modifing this design by making the final lens into a cemented doublet we can make a tessar lens with somewhat better performance.

What I am saying is that using trial and error by mixing four lenses together is realistically going to be very difficult because you don't have enough lens values or time to look at every combination. Granted you could build the lens with stock lenses but it would perform lower than an optimized one of simpler design.

So we have the option of building a non optimized lens out of stock components or of starting with an optimized design and perhaps trying to find stock lenses for a couple of the lenses and leave one lens variable open for a custom made lens. Trying to optimize the design that way.

If you have a way to communicate with me your lens configuration I will model it and we will see how good it is. Perhaps it can be optimized with only one custom lens or something.

Hezz

There are so many optical systems that are out there.

Goto CLZ to know more.

Why is one lens type used over the other?

What lens design for do I need for this system?

What lens design alternatives should I consider?

Can I use this lens somewhere else?

What if we don’t know where to start with the lens design, when only given a specification sheet?

Overview

This is an Ultimate Guide of lens design forms, the optical systems that are used in our world.

The basic lens design forms are in here, and we can take a deep look into the development of lens design. But the not all the lens designs are simple lenses, we will look at newer and important lens design forms as well.

You’d be surprised to see what lenses are related to one another, and how we can break down seemingly complex lens design into parts from different lens forms.

I can’t catch all of the design forms, but let me know in the comments if you want to know more about a subject, or if you feel there is a lens form missing.

N.B. A few primers before you read on:

I may repeat the same explanations from time to time. This is because of the web and ebook format, where I feel it isn’t quite as easy to go back a few pages and re-read the material and immediately come back to the place you left off. I’ll provide links within the Guide, but I’ll also try to make it an easier read without saying “I said this already lookie over here”

There is a lot in here, so feel free to navigate around with the table of contents below.

If you’re interested, you can get the PDF version too.

Table of Contents

• Motivation and introduction to the General Theme
  • About this guide
  • What you will learn in this guide
  • Who this guide is for
  • Who this guide is NOT for
  • Who am I?
• Background

• Pattern recognition

• Imaging lenses: Classic imaging lenses and the dawn of lens design

  • The singlet lens: The first lens that deserves your attention
    • The two landscape lenses
  • The doublet lens: More to it than meets the eye
    • The Harting formula
  • The Petzval lens: The first systematically designed lens
  • The Cooke triplet and anastigmat lenses: The first “complete” lens
  • The Tessar lens: A commercial success that started an era
• Coffee break: Higher order aberrations

• Imaging lenses: The evolution of lens design that leads to diversification

  • The Ernostar lens: Evolution from the triplet still used today
  • The Sonnar lens: Bertele’s genius in lens design
  • The Double Gauss lens: The winner of the standard lens on a photographic camera
  • The symmetric wide angle lens: The quest for Field of View
  • The Telephoto lens: The telephoto lens: The term that is confusing for photographers(but not lens designers)
  • The Retrofocus / Reverse telephoto lens: The practical solution to wide angle lenses on SLRs and digital sensors
• Imaging lenses: Specific use lens systems
  • The Fisheye lens: Testing the limits of Field of View
  • Zoom lenses: How we can get many focal lengths in one lens system
  • Afocal lens systems: manipulating rays to get them to behave the way we want
    • Comment on conversion lenses: they are afocal too!
  • Telecentric lens systems: when and where we need straight rays
  • Reflective optic lenses: Changing the direction of light
• Coffee break: Some cool lens design names

• Imaging lenses: The eye and the lens design forms that use our vision

  • The eyepiece: The lens form that helps us see more than the naked eye
  • The telescope lens: The first steps to the dream of space travel
  • The microscope lens: The quest to enlarge the microscopic world
• Imaging lenses: Modern use cases based on new lens design forms
  • The stepper lens: A mastership in lens design
  • Laser beam printers and laser scanners: f-theta lenses and their seagull like shape
  • The Aspherical lens: an addition to the spherical shape that opens up possibilities
  • The freeform lens: Thinking of optical lens design in three dimensions
  • The mobile lens: Taking aspherical lenses to the extreme
  • Laser applications: The new age of optical lens design
  • Diffractive optics:
• Illumination lenses: A totally different approach to optical lens design
• Bonus: A list of interesting applications of lens designs not mentioned thusfar
• Lens design forms and the principles of optical lens design
• References
• Comments

Motivation and introduction to the General Theme

As an optical lens designer, there were times I used to think that “I can get the performance that I need for this system with the software, but I want to understand what I am doing”.

Nowadays, we are required to deliver high performance (not necessarily high quality) lens designs in a short amount of time. Non-intuitive lens design systems like aspherical lenses and off-axis lenses too. Lens design with computational software like Zemax and CodeV are the norm now.

Sometimes, I see myself punching in the parameters that are needed for a lens design, and I can press a button to get the desired performance of the system. In an extreme sense, I can turn my brain off and use the software to get the desired outcome. I try to catch myself every time I do so. I’m a scientist, researcher, engineer, and genuinely interested in the process of lens design. From my own experience, the time I realized that I was merely punching out lens designs like a machine, I realized that I had a hard time designing different systems when I needed to.

This did not make me a well-rounded lens designer, and frankly, it was a lot less fun!

So I hit the books. Thankfully, there are a multitude of books on lens design, starting with the optics theory, optical system design, manufacturing technology, and yes, lens design methods too.

I got mentors in different fields to help me with lens designs that I wasn’t familiar with.

I quickly found that knowledge from books is applicable in many situations, but to use the information in a meaningful way, I had to figure out how to apply them to different situations on my own.

In order to truly understand the material, I needed to connect the dots of the knowledge I gained from reading all of those books, and create a web of lens design knowledge to be able to catch everything that is thrown at me.

What I’ve done over the years is distilled the text book material from my favourite books into the usable concepts, in a logical format that shows each piece of the lens design puzzle and process.

This logically lead to writing this Guide, and it’s what I would have wanted at my fingertips when doing a lens design early in my career or when I was learning lens design. But make no mistake, I myself will be looking back at this Guide often as a reference for designing different lens designs as I go forward in my lens design career.

About this guide

This Guide provides the lens design forms of various lens designs from simple lenses to complex lenses, and is intended to provide many examples of the lens designs that we use today. By becoming familiar with the essential lens design forms, we can use them to our advantage during lens design.

The examples in this Guide provide a birds-eye view of the various lens design forms and why certain lens combinations are used, to help visualize typical lens designs and even complex lens designs.

This helps us become more efficient in our lens design process. I call this training your Pattern Recognition skills for lens design.

What you will learn in this guide

We will look into lens design forms and see when and where to use specific lens designs, techniques of lens designs, with plenty of examples.

Who this guide is for

• People who want an overview of the essential lens design forms
• People who want applicable lens design forms for reference for their lens designs
• People who are starting out in lens design as a reference for lens design forms
• People who are self-taught in optics to a certain degree, and want to get more familiar with lens design forms

Who this guide is NOT for

• People who want a quick fix to a specific optics and lens design problems
• People that don’t need to be well-rounded as a lens designer
• People that are happy with letting the computer software do the work for them
• People that are okay with becoming a lens design zombie

Who am I?

Hi, I’m Kats Ikeda, Ph. D, and my expertise is optical lens design, non-imaging / illumination lens design. I have enjoyed a lot of product development based on optics and lens design. I love nerding out on optics and lens design talk.

Background

Optical lens design is made up of many disciplines, one of which is imaging lenses. Depending on the desired outcome, which are the specifications of the lens, there are similarities and differences for each lens design. The similarities can be grouped up as a Lens Design Form.

A lens design form can be a combination of positive optical power and negative optical power lens elements that share characteristics with each other.

Part of the lens design form is from the configuration, as it is important to be able to see the configuration of the lens and decipher what it means. That includes what lenses to use where, the spacing of the lenses, the number of lenses, the material of the lenses, the optical power of the lenses, and so on.

Another part of lens design form is from the history of lens design, as there are different needs in different eras, and the technology associated with each era is different. The needs are fulfilled by different lens designers of the day, with the technology available to them at the time. New lens design forms are therefore approved by other lens designers if they use them in their lens designs.

Each topic will have the following format:

1. History and background of each topic: For example, in the Tessar chapter, I talk about how the lens design can be viewed as a Protar and Unar or that optically we can think of the Tessar as an evolution of the triplet.
2. Essentials for lens design, what you need to know: to proceed with the lens design. For example, for the Cooke Triplet, we need to know how the aberrations are controlled.
3. Where you can use knowledge used in other lens designs: For example, there is a link between Double Gauss lenses and stepper lenses. Also, there is a relationship with Zoom lenses and Retrofocus lenses and Telephoto lenses.
4. Tips and tricks: We look into useful techniques we can use to facilitate the lens design process.
5. Master the specsheet: Clues in the specification sheet (or specsheet) to figure out when to use a lens design form.
6. Real-world examples: Actual lens design specs designed by me or from patents. Lots of images and ray diagrams of the lens design form. (The patented examples belong to the inventor and assignee of the patent, and my design is for educational purposes only. I can’t be responsible for any legal ramifications if you use any of these designs in a product you’re going to sell)

Pattern recognition

On a basic level, when we can understand the lens design form of a lens design, we can look at the various properties of the lens and we can figure out the if the performance is good or not, or if the rays are behaving the way that we want.

Some of the lens design properties I’m talking about are the lens diagram, the type of glass used, and the rays passing through the lens system.

For the lens diagram, we can get an idea of the shape of the lens, even without the hard numbers for the curvature of the thickness of the lenses and the spacing between the lenses. We can see if a lens is a strong convex and causing unneeded problems, or if a combination of lenses is needlessly either too close or too far away to be meaningful in the lens design.

For the type of glass used, we can get an idea if the combination of glass types are beneficial to decreasing the aberrations if they are cancelling out to give an overall good performance.

For each surface, we can see if the rays passing through the surface is bending back and forth in a needless way, or if there are strong refractive surfaces that hinder the performance of the lens.

With a good eye for lens design, we can think “Hmmm, this lens is so-and-so, that surface is so-and-so” and really get a feel for the lens design simply by looking at the lens diagram and the rays, and with an idea of the refractive indices and dispersion of the glass. No complex calculations, no expensive software, no building and testing the lens performance.

With this “lens design pattern recognition”, it is possible to decipher more complex lens surfaces, even with aspherical lenses! It’s like a secret weapon.

With a good eye for evaluation of the aberration correction of any lens design form, we can use that knowledge to improve the lens design by further improving the aberrations or decreasing the aberrations and achieve a better lens design.

Looking at the above statements, you can see that I really value the ability to be able to “look” at a lens and figure out its good parts and bad parts. The lens diagram and ray paths are necessary to do this. Before computer-aided lens design, the lens design giants would rely on their intuition and eye for lens design. For some historic lens designer, sometimes pattern recognition trumps even aberration theory.

For example, lens design genius and lens design hero of mine, Ludwig Bertele knew about aberration theory, but supposedly never used the theory for his lens designs. Bertele relied on ray tracing the lens system, looking at the performance, and changing the shape/index/thickness of the lens design to get better performance. The fact that Bertele invented many innovative lens designs during his time (in the s) with this method is nothing short of extraordinary and speaks to his lens design intuition and lens design ability. This is called the ray tracing method or the change table method, the latter because the performance of the lens after raytracing would be displayed in a table, and the lens designer would look at how the little changes to the lens design affect this performance table.

Another lens design hero of mine, Nikon’s Zenji Wakimoto, also used ray tracing and pattern recognition for his many lens designs. In his Nikon days, he designed the Nikkor 50mm F1.4 lens and other lenses like the Nikkor-N Auto 24mm F2.8, Nikkor-SC 8.5cm F1.5, and Nikkor-PC 10.5 cm f/2.5. Wakimoto eventually designed the Ultra Micro Nikkor, while at Nikon. The Ultra Micro Nikkor had extremely high resolution and was the start of stepper lens design. Zenji Wakimoto also invented many innovative lens designs without computer-aided automatic lens design optimization and used ray tracing and the change table. Much like Bertele, he would change the lens design slightly, raytrace the optical lens system, look at the results of raytracing and change the lens again.

As an aside, both Bertele and Wakimoto didn’t write any books or academic papers and document their findings. They seemed to be more interested in actually doing lens design than writing about it. Shame for lens design nerds like me.

In any case, these lens design geniuses don’t use software optimization and produced many many innovative lens designs. That’s not to say we shouldn’t use computers for our lens design, that would be ridiculous. But I do think that we can incorporate their philosophy of pattern recognition and “looking” at a lens design to make the process easier for us. Maybe we can’t get to the level of Bertele or Wakimoto as far as intuitive lens design, but we have the history of their lens designs and lens designs inspired by the many lens designers since then, on our side.

It seems as though pattern recognition, an ability that humans and not machines possess, is a good way to pursue lens design, as demonstrated by my lens design heroes. In spite of that, a lot of lens design books and textbooks that I have read rely heavily on the derivations of mathematical equations, without actual lens design data and figures and graphs, especially lens design diagrams. A schematic diagram is not good enough in my opinion, I want to see the rays passing through the system.

It’s a lot of work to put data together, and I’ve tried to do that in this guide. I list many lens design forms, illustrate the lenses and show the rays passing through the lenses.

Let’s get to the meat of the Guide!

Imaging lenses: Classic imaging lenses and the dawn of lens design

To start off, we look at classic lens design forms in the dawn of lens design. These classic lenses may look simple given the more complex lens designs we have today.

Lens design was more conceptual in the early days of lens design since computational lens design had not been developed. Ray tracing and aberration theory was invented during this period. By examining the examples of relatively simple lens designs, it is actually easier to dissect why the lens designs are the way they are.

See also:
Ball lens - Wikipedia

The history of lens design is an evolution of new lens designs given the concepts and advancements in technology, and it’s great to start where it all began.

The singlet lens: The first lens that deserves your attention

1. History and background

In all honesty, a singlet lens looks really simple.

You may be thinking,

“What? Designing a singlet lens? A piece of cake!”

which is true, of course, but I want to dig a bit deeper since everything is simplified in a singlet lens. So much so that the merits and demerits of the lens are clear, and we can use this knowledge to our advantage in the bigger picture of lens design, and by proxy more complex systems. After all, a multi-lens system is a string of singlets when you think about it.

“Lens”, named from lentils, can be traced back to the 7th century, may or may not have been used as a burning lens, may or may not have been used as a reading lens, but by the 13th century spectacles were made, and in the 16th century optical microscopes and telescopes used lenses.

Truthfully, a singlet it the simplest lens form there can be, and it doesn’t need any explanation for even a novice lens designer. But to truly understand the singlet, and its limitations is the first step to understanding lens design.

Let’s take a look at the concepts.

2. Essentials for lens design

You might have seen the lensmaker’s equation early as high school, and this is the essence of the performance of the lens.

For a thin lens,

$$
\frac{1}{f} = (n-1) \left[ \frac{1}{R_1}-\frac{1}{R_2} \right].
$$

Where \(f\) is the focal length, \(n\) is the index of refraction, \(R\) is the radius of curvature of the lens (enumerated by surface).

For a thick lens with some thickness \(d\),

$$
\frac{1}{f} = (n-1) \left[ \frac{1}{R_1}-\frac{1}{R_2}+\frac{(n-1)d}{n R_1 R_2} \right].
$$

Where \(f\) is the focal length, \(n\) is the index of refraction, \(R\) is the radius of curvature of the lens (enumerated by surface).

For imaging properties, we can use an even simpler equation like the following:

$$
\frac{1}{f} = \frac{1}{d_1} + \frac{1}{d_2}
$$

Where \(f\) is the focal length, \(d_1\) is the distance from the object to the lens, and \(d_2\) is the distance from the lens to the image.

As simple as the singlet is, there are multiple lens forms associated with the singlet.

From left to right: Positive rear meniscus lens, positive plano-convex lens, bi-convex lens, positive convex-plano lens, positive front meniscus lens.

From left to right: Negative front meniscus lens, negative plano-concave lens, bi-concave lens, negative concave-plano lens, negative rear meniscus lens.

3. Where you can use knowledge used in other lens designs

Since every other lens design form is a combination of multiple singlets, there isn’t too much to say here. What you know about the singlet applies everywhere. For example, you may see any number of combinations of the positive or negative lenses in a lens system.

It’s good to know the limits of a singlet, because we can then know when a singlet isn’t enough in a lens design.

4. Tips and tricks

The singlet is a lens system with a single positive lens, and the stop is on the surface of the lens. As simple as this lens is, it has characteristics that teach us the advantages and disadvantages of a single lens.

• Although the spherical aberration cannot be fully corrected to zero, the smallest possible spherical If the radius of curvature ratio of the front radius to the rear radius is 1:-6. This means that any other configuration that you are thinking of is at the expense of the spherical aberration.
• The coma is also close to zero.
• The longitudinal chromatic aberration cannot be corrected. The positive lens only has positive power, which causes the chromatic aberration depending on the index of refraction of the material.
  
• Astigmatism can only be controlled by changing the size of the aperture stop. Thus the speed of the lens is determined by how much Astigmatism we can allow.
• The Petzval sum, i.e. the field curvature, cannot be fully corrected. The Petzval sum is dependent on the sum of the lens power divided by the index of refraction. A singlet lens has only one lens power and one index of refraction, so the Petzval sum is always non zero.
• The distortion can’t be corrected because there is no way to achieve symmetry about the stop in the design with one lens.
• The transverse chromatic aberration can’t be corrected because there is no correction with one material.

5. Master the specsheet

Again, there isn’t too much to say here.

\(R_1\), \(R_2\), \(t\).

If you want to go a level deeper, I recommend trying to draw the lens by hand. Don’t underestimate this step, you can learn so much from the application, even if it is as simple as a hand-drawing.

6. Real-world examples

Camera Obscura

[Camera obscura(https://en.wikipedia.org/wiki/Camera_obscura) the first camera system.

The Camera Obscura literally means “dark room”, and is said to be named by Johannes Kepler.

I made one during summer vacation one time, and I used a pinhole instead of a lens made of glass.

Kodak Hawkeye
The famous lens for a camera that I know is the Kodak Hawkeye, and it was riddled with aberrations.

FujiFilm Quicksnap
A more modern example, is Fujifilm’s QuickSnap(写ルンです).

(via Fujifilm)

The QuickSnap is interesting because if we look at the innards of this camera, the film is curved a bit on the image plane (far left). This accounts for the field curvature, since it cannot be corrected with a landscape lens, we curve the image instead.

(via Fujifilm)

Bonus: Two types of singlets, the telescope objective and landscape lens

There are basically two types of singlet lenses.

One, the telescope type objective, that I explain in detail in my Ultimate Guide to Spreadsheet Lens Design.

(Look at 4. Tips and tricks above for the rundown on the advantages and disadvantages)

Two, there is the landscape lens, used for photography. For a landscape lens, things are a bit different.

Probably the first real camera lens, used in the Camera Obscura, which is basically a box with a lens that formed an image. It was first used for sketching and painting.

There are two different lens forms for the landscape lens. The rear meniscus form in the image above, and a front meniscus form is shown below.

Landscape lenses are solved by determining the minimum field curvature while the coma is zero.

What we can expect is:

• The positive lens and the stop are separated, and the meniscus lens corrects astigmatism and coma.
• However, the spherical aberration is completely out of whack, and the only way to minimize it is to make the aperture smaller.
• The distortion can’t be corrected because of the asymmetry about the stop.

The landscape lens is an excellent example to illustrate that there are multiple solutions to a lens design. Even a lens as simple as the landscape lens has two solutions, called the rear meniscus form and the front meniscus form. If you optimize with a plano-convex lens with the stop in front of the lens Zemax will give you the rear meniscus form. If you optimize with a plano-convex lens with the stop in behind the lens, Zemax will give you the front meniscus form. Optimization from a flat surface, and it can fall to either lens form, depending on the optimization parameters we set in the form of a merit function.

The basic lens design method for a landscape lens is as follows:

1. Make a rough meniscus lens and choose the position of the aperture stop
2. Take an F-number about twice the speed than needed (set F8 if we’re designing an F16 lens)
3. Raytrace the FOV at about 70%, use bending to make minimize the aberrations
4. Set the optical systems to the desired F-number
5. Move the stop position to find the best location that minimizes the aberrations
6. Finish the design off with a few more points in the FOV, and we’re done

Although the design method is straightforward, it covers the basics and a good rule of thumb to follow, and will be useful when we look at more complex systems.

A few things to note in the design:

• To minimize astigmatism and coma, the stop and the lens are separated.
• The spherical aberration is impossible to correct given this situation. Since the spherical aberration is dependent to the F-number of the system, the only way to correct the spherical aberration is to make the aperture smaller and decrease the spherical aberration.
• In both the front or rear meniscus case, since there is only one lens on either side of the stop, the distortion and transverse chromatic aberration cannot be corrected.

Let’s take a qualitative look at the performance of the lens design for the two meniscus forms.

As far as optical performance, the rear meniscus is a bit better.

• The MTF is better since the spherical aberration is smaller
• The surface curvature is weaker
• The distortion is barrel distortion, perhaps more unobtrusive to the human eye

But the front meniscus form is dominant in the single-lens camera for ages.

So what gives? Why are we choosing an optically inferior lens?

1. The overall length of the lens is shorter, due to the higher curvature of the lenses. In our example, it is about 20% shorter. Remember, this is the balance of the smallest field curvature at zero coma.
2. With the lens on the outside, the stop (and therefore the shutter mechanism) is protected from any outside dirt from the lens itself.
3. Aesthetically, the camera has a lens in front, which is more appealing than the peculiar shutter and aperture stop sticking out. We see an aperture stop, normal people see a hole.
4. Since plastic lenses were invented, the stronger meniscus curvature for the front meniscus form is no more expensive to manufacture than a weaker curvature of the rear meniscus form, unlike with glass lenses.

The dominance of the front meniscus lens form for inexpensive cameras is a lesson that good optical performance is not always the be all end all of lens design.

Once you can design a singlet telescope objective and a singlet meniscus landscape lens, you’ve entered the gate as a lens designer, in my opinion.

If you want more information on landscape lenses, I have more information with a blogpost I wrote about the history of the landscape lens.

Do you want to design this lens? I have more information with my Ultimate Guide to Lens Design Using Spreadsheets with complete calculations on how to calculate the performance of a lens without complex software, but spreadsheet programs such as Excel.

So much to write about for a simple singlet lens system. To me, this is why lens design is fascinating