Criteria and considerations for the hottest lens d

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Standards and considerations of lens design

today's lens design (or what optical designers call optical path design) seems to be a piece of cake: thousands of design patents are displayed in the lens database, and many of them are published. It seems that you can start with the general design idea, and then use the high-speed computer system to optimize your design sketch to achieve the goal you actually want to achieve

but the question is, can computers generate a good lens design? Of course, it is impossible. The real design actually comes from the human brain, just as the navigation instrument can help you find the right route only after you specify a clear target for it. Commercial lens design system can certainly optimize lens design for you, but if the starting point of 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 without exception that computers and computer programs themselves cannot find all the answers for you

lens design is a highly creative work, which must be based on experience and keen insight to understand the characteristics of various optical aberrations

first, let's look at some basic principles of lens design

for any lens, whether new or old, the term "lens description" can be used to distinguish the number of lenses, the type of glass, the radius of the surface of the lens, the thickness of the lens, the distance between the lenses, and the diameter of each lens. These are parameters used to comprehensively describe a lens. When the light from an object passes through the glass surface, the light will be refracted, as described in the physics knowledge we learned in the middle school physics textbook

the amount of light refraction depends on the refractive index of the glass. If the lens designer can know the exact incident position and angle of light when it enters the lens in front of the lens, he can accurately track the light path through the light theory system. The angle and distance can be calculated from the sine and cosine of the trigonometric function. Therefore, through simple plane geometry, the path of light can be traced. We know that the energy emitted by any point light source is scattered, and there is no direction to speak of. Only part of the energy passes through the lens, and the designer also assumes that the path of those rays can be traced by simply calculating the energy passing through the lens (which is regarded as a series of rays that are independent of ABS)

the lens designer first tracks a small amount of light from a point on the optical axis. What is assumed here is that each object image point will form a corresponding point on the film plane, so the light from the object will be transformed into such a phase forming point, and have the same relative position. This is Gaussian phase. For those points close to the optical axis, designers can have reason to believe that Gaussian imaging is quite accurate, which is called paraxial optics. Although the calculation formula is quite simple (at least for experienced designers), the calculation of these numbers is required to be accurate to 5-8 decimal places

before the advent of mechanical and electronic computers, the only way to calculate these values was with the help of logarithmic tables. In the 1930s, there were only 50 such calculations per day. Because it is easy to make mistakes, each number must be checked twice. For example, don't regard "7" as "9", and ensure that the handwritten font should be neat and easy to recognize. I once had the opportunity to see Leitz's early design achievements in Solms. Those long strings of numbers and carefully written fonts for easy recognition and copying showed how hard the work was at that time. For example, for a lens design with 6 lenses, 200 light paths need to be calculated on the surface of each lens, and the calculation amount of the whole lens reaches 3000 light paths, which takes 3 months to complete all calculations. It is amazing how Leitz worked and organized at that time (it was only recently that Leitz revealed for the first time)

the romantic idea that the lens designer poured into his design is naturally a mystery. In real design, the design director 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 computing work. The design director guides the whole design. He obtains the results from a large number of optical calculation formulas he knows, and decides whether to continue the original design or adjust the design. For any important Photographic Optics, the calculation of parallel optical axis is not very useful

for the design of large aperture lens, due to the large amount of light entering, it is very important to consider the light entering the lens obliquely. Considering the light entering in parallel is very important for the imaging of the central area, but it is not of much significance for the imaging far away from the central area of the image field. The light entering the lens obliquely can be divided into two parts: vertical and horizontal. Passing through the vertical plane is called tangent light, and passing through the horizontal plane is called radial light. This part of the optical path needs special formulas to calculate. However, these formulas are extremely complex and cumbersome, and manual calculation is almost impossible. Even for modern electronic computers, it is not an easy thing

therefore, in real design, designers try to avoid those calculations (radial light), or only carry out approximate calculations, which Leitz and Zeiss do. The final calculation without exception is the result of compromise, that is, there are known factors and unknown factors


we all know that light is composed of colored light waves of different wavelengths, and when light enters the lens, light waves of different wavelengths have their unique optical path. We already know that ideal light is inevitably disturbed by the lens to produce aberration. The first element of lens design is to understand and control these aberrations. The corrected light path and the actual offset can be calculated through the trigonometric geometric function. The difference between the two is called the light path difference, which is used to control the basis of aberration. Typical aberrations include spherical aberration, halo and loss of light. In the 1930s, although the object difference was quantified, it always became a perplexing factor in lens design

The equation of

aberration is a multivariate equation. Each element represents a known aberration, and its coefficient represents its importance and its influence on the decline of imaging quality. The sum of all aberrations can be summarized as: aberration = asa+bc+ca (SA: spherical aberration; c=coma, halo; a=astigmatism, loss of light; a, B, C: weighted value)

in the past, because the understanding of the object difference requires a lot of calculation, the understanding of the object difference of optical designers is only limited to some theoretical knowledge, while the practical application is very limited. Therefore, the knowledge about the correction of special optical path is not perfect. So it's no surprise that the debate about whether zennar of Zeiss is better or worse than Leitz's summar will continue from then to now. Only from the design sketch can the designer know how to roughly correct the lens design

for the designer, if he wants to correct the object difference, he must be able to know what effect the specific aberration will have on the imaging. Spherical aberration will affect the imaging of the central part of the image field, and the degree of image plane bending explains the correction of the corner, and so on. However, this is still a simple statement. All kinds of aberration will affect the whole picture. There is only one effect of aberration: the energy of light from a certain point of the object cannot be completely concentrated on its corresponding imaging point, but forms a fuzzy circle, and the distribution of light in the fuzzy circle is not balanced, but irregular. In fact, the blur circle is not a perfect circle, but an irregular shape. Its shape, the distribution of light in it and the exact position of the blur circle on the imaging surface are the result of the joint action of all aberrations

there are many kinds of aberrations. For convenience, we can classify them into three categories: Level 3 aberrations, level 5 aberrations, and level 7 aberrations. "3", "5", "7" represents the index of the above aberrations in the equation. We are familiar with the third-order aberration, also known as Seidel aberration. Its name comes from the first person who described it comprehensively by mathematical method. The naming of "level 3" is really confusing: Level 3 aberration is the most important of all aberrations. In this regard, it is the first level. At present, it is very difficult to control all three kinds of equal aberration to a satisfactory level. The key to the problem is: when you control all the third-order aberration, you will encounter interference from the fifth order aberration. Compared with the third-order aberration, they are more variable and difficult to control. The result is that once the level 3 aberration is well controlled and the blur circle of the image becomes very small, new aberrations appear again, and the impact of these new aberrations on the picture will make you more depressed. The result of aberration is usually the same: reduce the contrast and make the whole picture blurred. The influence of aberration on imaging is fatal, which is why MTF has become one of the powerful tools in 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 that way. First of all, for high-level aberration, there is a lack of theoretical knowledge. In order to correct Seidel aberration well, designers will have to face huge computational work. Therefore, designers usually draw a rough sketch of the light path from the creative inspiration or previous famous. If the sketch looks promising, continue designing. In order to achieve the results in a reasonable time and budget (the funds were very limited at that time), the designer omitted some optical calculations, used the approximation method when accurate calculation was impossible, and used those optical glasses that had accurately mastered their characteristics

of course, Seidel aberration cannot be completely corrected, and designers will have to seek the balance of correction, or try to reduce their influence. But even the effect of this balance itself is limited. Taking the double Gauss structure as an example, the design itself has a certain amount of oblique spherical aberration (ola=objective spherical aberration), but on the other hand, this structure can well correct astigmatism. The performance of oblique spherical aberration in radial direction is much worse than that in tangent direction. In order to balance the radial spherical aberration, we need to accept a certain amount of third-order aberration to make the loa basically close to the tangent in the radial direction, but then there is a certain degree of vignetting! Yes, it's a very interesting phenomenon. In fact, many designs (including new and old designs) use dark corners as a design tool. Amateur lens test reports often criticize the dark angle phenomenon of some lenses. However, a certain degree of dark angle can improve the imaging quality

the most remarkable example is Leitz's noctilux f/1.2. The dark angle of this lens is more serious than cannon 50/1.2. However, when it is fully open, the picture quality is much better than cannon. Therefore, the genius of the older generation of lens design (Berek, bertele) took two paths: first, to be the first

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