But the question is, can computers generate excellent lens designs? Of course not. The real design actually comes from the human brain, just like a navigation instrument can help you find the right route only after you specify a clear goal for it. The commercial lens design system can certainly optimize the lens design for you, but if the starting point of the design itself is insufficient, then it is difficult for you to correct it. At present, computers are widely used in optical design departments, but it also shows that computers and their computer programs can not find all the answers for you.
Lens design is a creative work, and we must understand the characteristics of various optical aberrations with experience and keen insight.
First, let's look at some basic principles of lens design.
Any lens, whether new or old, can use the word "lens description" to distinguish the number of lenses, the type of glass, the radius of curved surface of lenses, the thickness of lenses, the distance between lenses, the diameter of each lens and so on. These are all parameters used to describe a shot in an all-round way. When the light emitted by an object passes through the glass surface, it will be refracted, as described in the physics knowledge we learned in the middle school physics textbook.
The amount of refraction of light depends on the refractive index of glass. If the lens designer can know the position and incident angle of light when it enters the front lens of the lens, he can accurately track the light path through the light theory system. Angle and distance can be calculated by sine and cosine of trigonometric function. Therefore, the path of light can be traced by simple plane geometry. We know that the energy emitted by any point light source is scattered and has no direction. Only a part of the energy passes through the lens, and the designer also assumes that the energy passing through the lens (those regarded as a series of independent rays) can trace the paths of those rays through simple mathematics.
The lens designer first traces a small amount of light from a certain point on the optical axis. Assuming that each object point will be formed at its corresponding point on the film plane, the light from the object will be converted into such a phase point and have the same relative position. This is a novel by Gauss. For those points close to the optical axis, designers can reasonably think that Gaussian imaging is quite accurate, which is paraxial optics. Although the calculation formula is quite simple (at least for experienced designers), these numbers are required to be calculated accurately to 5~8 decimal places.
Before the advent of mechanical and electronic computers, the only way to calculate these values was to use logarithmic tables. In the 1930s, only 50 such calculations could be made every day. Because it is easy to make mistakes, every number should be checked twice. For example, don't treat "7" as "9", but make sure that the handwritten font is neat and easy to recognize. I once had the opportunity to see Leitz's early design achievements in Solms. Those long numbers and carefully written fonts for easy identification and copying all show how hard the work was at that time. For example, for a lens design with 6 lenses, the surface of each lens needs to calculate 200 optical paths, and the calculation amount of the whole lens reaches 3000 optical paths, which takes 3 months to complete all calculations. Leitz's work and organization were amazing at that time (Leitz revealed it for the first time only recently).
The romantic idea that the lens designer poured into his design is naturally a mystery.
In actual design, the design supervisor is responsible for a group of workers, most of whom are women, who are responsible for a very important part of a large number of calculations. The design director guides the whole design. He drew the results from a large number of optical formulas known to his staff and decided whether to continue the original design or adjust the design. For any important photographic optics, the calculation of parallel optical axis optics is of little use.
For the design of large-aperture lens, it is very important to consider oblique light entering the lens because of the large amount of light, and it is very important to consider parallel light entering the lens to image in the central area, but it is of little significance for imaging far from the central area of the image field. The light entering the lens obliquely can be divided into vertical and horizontal parts. Those passing through the vertical plane are called tangential rays, and those passing through the horizontal plane are called radial rays. This part of the light path needs a special formula to calculate. However, these formulas are extremely complicated and complicated, and manual calculation is almost impossible. Even for modern electronic computers, this is not an easy task.
So in actual design, designers try to avoid those calculations (rays) or only do approximate calculations, which Leitz and Zeiss did. The final calculation is the result of compromise without exception, that is, there are known factors and unknown factors.
misdemean
As we all know, light is composed of colored light waves with different wavelengths, and when light enters the lens, light waves with different wavelengths have their own unique optical paths. We already know that the ideal light will inevitably be disturbed by the lens and produce aberration. The first element of lens design is to understand and control these aberrations. The offset between the corrected ray path and reality can be calculated by trigonometric geometric function, and the difference between them is called ray path difference, which is used to control aberration. Typical aberrations are spherical aberration, halo and light loss. In 1930s, although the object difference was quantified, it always became a puzzling factor in lens design.
Aberration equation is a multivariate equation, each element represents a known aberration, and its coefficient represents its importance and influence on image quality degradation. The sum of all aberrations can be summarized as follows: aberration = aSA+bC+cA(SA: spherical aberration; C = coma, halo; A = astigmatism, light loss; A, b, c: weighted values).
In the past, because the understanding of object difference required a lot of calculations, the understanding of object difference by optical designers was limited to some theoretical knowledge, and its practical application was very limited. Therefore, the knowledge about special optical path correction is not perfect. So it is not surprising that the debate between Sonnar of Zeiss and Summar of Lai Ci has continued since then. Only by starting with the design sketch can designers know how to roughly correct the lens design.
For designers, if they want to correct the aberration, they must be able to know what effect the specific aberration will have on imaging. The spherical aberration will affect the imaging of the central part of the image field, and the curvature of the image surface indicates the correction of the corner, and so on. However, this is still a simple statement. All aberrations will affect the whole picture. Aberration has only one function: the energy of light from a certain point of an object cannot be completely concentrated on its corresponding imaging point, but a fuzzy circle is formed, and the distribution of light in the fuzzy circle is not balanced, but irregular. In fact, the fuzzy circle is not a perfect circle, but an irregular shape. Its shape, the distribution of light in it and the exact position of the fuzzy circle on the imaging plane are all the results of aberration interaction.
Aberrations are various. For convenience, we can divide them into three categories: 3rd order aberration, 5th order aberration and 7th order aberration. "3", "5" and "7" represent the indices of the above aberrations in the equation. We are familiar with the third-order aberration, also known as Saidel aberration, whose name comes from the first person who described it comprehensively by mathematical methods. The name "third order" is really confusing: the third order aberration is the most important of all aberrations, and in this respect, it is the first order. At present, it is difficult to control all three aberrations at a satisfactory level. The point is: when you control all three aberrations, you will encounter five aberrations. Compared with third-order aberrations, they are more variable and more difficult to control. In this way, once the third-order aberration is well controlled, the fuzzy circle of imaging becomes very small, and new aberrations are produced. The influence of these new aberrations on the picture will make you more depressed. The result of aberration is usually the same: reducing contrast and blurring the whole picture. Aberration has a fatal effect on imaging, which is why MTF has become one of the powerful tools for modern lens design. MTF can tell you where your lens design needs to be improved.
Now we should understand why the old lens design is like that. First of all, there is a lack of theoretical knowledge about higher-order aberrations. In order to correct Saidel aberration well, designers will have to face a huge amount of calculation. Therefore, designers usually start with creative inspiration or previous fame and draw a rough sketch of the light path. If the sketch looks promising, continue to design. In order to achieve the results within a reasonable time and budget (limited funds at that time), the designer omitted some optical calculations, used approximation method when it was impossible to calculate accurately, and used optical glasses with precise characteristics.
Of course, Cedell aberration cannot be completely corrected, and designers will have to seek the balance of correction or minimize its influence. But even this balance itself has limited effects. Taking the double Gaussian structure as an example, the design itself has some oblique spherical aberration (OLA = oblique spherical aberration), but on the other hand, this structure can correct astigmatism well. Oblique spherical aberration is much more serious in radial direction than in tangential direction. In order to balance the radial spherical aberration, we need to accept a certain amount of third-order aberration, so that LOA is basically close to the tangent in the radial direction, but it also produces a certain degree of vignetting! Yes, very interesting phenomenon. In fact, many designs (old and new) use dark corners as design tools. Amateur lens test reports often criticize the dark angle phenomenon of some lenses, but they don't know that a certain degree of dark angle can improve the imaging quality.
The most notable example is Noctilux f/ 1.2 by Leitz. The dark angle of this lens is more serious than that of Canon 50/ 1.2, but the picture quality is much better when it is fully open. Therefore, the lens design geniuses of the older generation (Berek, Bertele) took two paths: First, we must first create a basic design with small aberration and this design can be corrected. Tessa is such an example. Designers have to consider many other variables at the same time, which is the first step of successful design.
The next and more important step is to make your design have enough production tolerance. Old designs such as Hektor 2.5/50 are too expensive because the tolerance of production and processing is too small.
Users must test several different versions to get satisfactory shooting results. It is not difficult to understand why serious photographers choose different lenses to test and use until they are satisfied. In order to balance the different aberrations in the design, a certain amount of residual aberrations must be retained. Not every designer can successfully or creatively find the best solution at hand. Therefore, from 1930s to 1960s, there was a heated debate about the taste and characteristics of Leitz and Zeiss' famous shots (real or imagined). Until today, optical design and calculation are not at the same level as users' expectations.
computer
Since computers began to intervene in lens design in 1950s (Leitz first used computers for lens design, and the machine name was Zuse, made in Germany), little change has taken place. You can calculate faster and do more complicated equations that distort light.
However, what the design lacks is a deep understanding of various aberrations themselves. The amount of light that can be calculated and needs to be calculated into the lens increases geometrically. The number of lenses (the limiting factor of previous design: the more lenses, the more calculations and changes) has increased, and more lenses have brought more freedom to designers. Because there are more lens surfaces to deal with the design, designers can control the aberration to a greater extent. More lenses also mean higher costs and often less production space. The new Leica Apo-Tele 3.4/ 135 has five lenses, which has real Apo correction ability, but its refraction of light is not infinite. We need more lenses to do better in this aspect, but with it, it will be more difficult to ensure the high-quality imaging quality and the production tolerance will be stricter.
With the powerful ability of modern computer and the further study of optical theory, today's understanding of fifth-order Saidel aberration has expanded to include more than 60 kinds of aberrations. Designers can't manipulate many variables of the lens at will. The diameter and weight of the front lens, the diameter of the lens bayonet and the position of the aperture are usually fixed and cannot be changed.
These limitations will affect the correction of many aberrations. Now the design requirements for new lenses are getting higher and higher. The new SummiluxR 1.4/50 needs two design goals: the image quality is significantly improved after the aperture is reduced, and the whole picture should achieve very good image quality when the aperture is fully opened. Neither of these two requirements was met by their predecessors.
Modern computers can track and calculate 200,000 rays per second, and the number of various parameters is increasing. For the design of six lenses, it takes many years for the computer to find all possible results, and the time required is astronomical-starting from 1, followed by 99 zeros.
The importance of computer to today's lens design lies in that it is an optimization tool, not a design tool.
Remember the aberration equation? Before imaging, we actually formed a diffusion zone. We can determine each deviated ray and calculate the fuzzy circle of the image. The fuzzy circle of understanding the state should be small, and all the lights and colors should be firmly gathered together. We can let the computer do this work (such as calculating the curvature, the required thickness of lenses and the distance between lenses) so as to get the smallest fuzzy circle range. It is relatively time-saving and labor-saving to do this work with the computer. Then the designer will optimize the choice. This is the most important use of computers. In fact, most optical design programs should be called optimization programs, and designers should decide which ones to optimize and to what extent. The result obtained is called the value function. There are thousands of optimization schemes, which we can show in three-dimensional space with maps-imagine you are sitting in a helicopter and observing the terrain of a place, and you will see plains, mountains and canyons.
Some places are high, some places are low, and the theoretical optimization equation is similar to that terrain. A merit value is actually the lowest point of the landform, or the bottom of the canyon. Let your computer explore the area until you find the canyon. Once the computer finds a canyon point, it will stop looking. You can let it continue to look for the next canyon bottom.
If you are not familiar with the terrain in this area (you don't know the optimization point, otherwise you can get the optimization point directly without the help of a computer), even if you have found the optimization point, you may know nothing.
What one knows is that many different manufacturers' lenses are very good and very close, which is attributed to the result of finding the optimization point by computer. All computers are looking for the same point, and eventually they will find one. A strategy with a rough tendency appears: if you don't find the best value you need, you can increase the number of shots to achieve a beautiful MTF map. You can't look for the best point endlessly, it will take thousands of years to calculate. So when the budget draws to a close, you must stop and stay on the original design. If an optical design is a very good design, then the MTF diagram obtained by this design is very beautiful. But the reverse is not the case. A good MTF diagram is by no means equal to a good design.
So we know Leica's design strategy: you need to master the design characteristics by studying the roots of optical design. Once you know whether a design has potential, you can wisely instruct the computer to search for optimization points in a specific area of the optimization diagram and stop when you find the ideal value you need.
Evolution of Leica lens
Knowing the general background knowledge of these lens designs, we can understand why modern Leica lenses have been improved and in what ways. From the beginning to the 1960s, the early Leitz lenses were actually designed by hand on the basis of incomplete understanding of advanced aberrations and glass parameters. The use of computer makes it possible to correct the residual aberration better, but in essence, the image quality (for distorted optics) lags far behind the central part (parallel optics). Optical design and product processing are completely separated, which leads to very strict production tolerance in design.
The second generation (Vollrath/Mandler era) is characterized by the use of optimal design. The importance of production tolerance has attracted people's attention. Optimal design is widely used to rationalize production and reduce costs.
The 1970s and 1980s were the times when Lai Ci struggled for survival. The continuous expansion of R system needs to be designed to minimize the production cost. Leica still retains some of the most famous lenses designed during this period. Notilux 1.0/50 and Summilux 1.4/75 are still considered as great designs, which can be said to be the last products of the era of manual design.
Optimization also brings choices. Now we have a better understanding of the design process, and the production of products can achieve the required production tolerance more harmoniously. Take APO- Hermary -R 2.8/ 100 as an example. If we only look at monochromatic aberration, it is not as good as the earlier 4/ 100. But in white light, the progress of 2.8/ 100 is enormous.
Now we have another problem. Each wavelength has its own image plane with the best contrast. But there is only one real image plane, and that is the movie plane. Therefore, the designer needs to find a compromise on his understanding of optical design in order to obtain the best imaging.
The third generation design (Kolsch period) from the end of 1980s to the present is characterized by seeking better optical design in the two major constraints of lens design: mechanical accuracy and acceptable cost. The design team led by Mr. K.K. lsch is composed of some very enterprising men and women. For them, the principles of optical design and production and processing are perfectly integrated. For example, the use of aspherical lenses requires more stringent production, processing and assembly accuracy than before. Aspheric lens is the only lens that needs to be sent to Solms for inspection.
Modern Leica lenses are designed to challenge the limits of film grain. If any design knows the principle, it is: the extremely high contrast performance of low-frequency space frequency (the ability to outline objects) and the Gao Fancha performance of high-frequency space frequency (the ability to record as fine details as possible). This performance itself is not easy to achieve, and it needs to be available in most areas of the image field under the condition of full aperture.
The difference between Zeiss and Leica is that Zeiss focuses on Gao Fancha's expression of low-frequency spatial frequency, rather than Gao Fancha's expression of high-frequency spatial frequency. Zeiss's design system of compensating production latitude is not feasible in Leica. Leica's design requirements imply strict correction of spherical aberration and dispersion, and require a deep understanding of the basic principles of lens design-let's call it optical characteristics. It may take you more than a year to fully understand what kind of effect a proposed design can achieve.
Without this understanding, designers will never find the optimization function of design.
A design that can record the high-frequency spatial frequency with good contrast requires a small tolerance. The reproduction of contrast in the smallest detail is extremely sensitive to the errors of focusing and machining correction. Leica lens was completed by a design team composed of optical engineers and mechanical engineers from the beginning. The engineer in charge of product production has the final say: if the production tolerance required by the design is unrealistic, then the optical designer will have to start all over again. At the beginning of this paper, I mentioned the total light energy passing through the optical system. Leica designers noticed that the light flow gradually relaxed from one lens to another (the original Leica designers noticed that the light flow relaxed from one lens to another). To avoid sudden changes in the optical path, for example, use a lens with a completely different refractive index from other lenses or a lens with a very large curvature change. What you see here is a Zen way. The surprise brought by these new design principles is shocking: the lens clearly reproduces the smallest detail that film can record. Even at full aperture, you can see this excellent performance from the center of the picture to the whole picture.