But they also must know what is practical in terms of available technology, materials, costs, design methods, etc. Optical engineers work in all areas of optics, using different techniques to design lasers, build telescopes, create fiber optics communication systems, and much more. As with other fields of engineering, computers are important to many perhaps most optical engineers. Computers are used with instruments, for simulation, in design, and for many other applications. So what is a lens? You might think this is a simple question -- just a curved piece of clear glass or plastic, right?
Well, right -- this is one type of lens, and the most common type at that most eyeglass and contact lenses are this type. To a lens designer, though, a lens is a more general device, basically any system that tries to collect and distribute light in a specifically desired way.
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This is closer to what we think of when we discuss interchangeable "lenses" for a 35 mm SLR single lens reflex camera e. If you cut one open don't try this at home, kids! We refer to these as lens elements, and the complete lens is more generally called an optical system. With this terminology, the lens designer today is more often called an optical designer, though the older term is still widely used, along with such whimsical descriptive names as "ray bender.
With this background, a lens or optical system can actually contain any number and combination of lens elements, mirrors, prisms, rotating polygon scanners, filters, diffraction gratings, holographic elements, and other sorts of optical components. The designer also has to think about what sort of light source will be used with the lens light bulbs, LEDs, lasers, stars, the sun, etc.
Also important is the type of "detector" detectors are devices that react to light, such as film, photodetectors, CCD arrays, or the unsurpassed human eyeball. So the modern lens designer may work on "lenses" that are a long way from your bifocals or pocket 35 mm camera although the compact lens in a pocket camera can represent some clever design and cost-effective engineering.
If a system uses light in some way including any system that uses laser beams , lens design is almost certainly involved. Some examples:. Now that we know what a lens is, how do you design one? The full details are a bit beyond the scope of this "gentle introduction," but we can outline the typical steps. Number of elements? Overall size? Pre-design often involves paper and pencil sketching, including rough graphical ray tracing, with thin lenses standing in for real lenses.
There are some graphical software tools that can really help in this stage, especially when pre-design tradeoffs "what-ifs" are needed, as they often are. Software comes into play here, since access to a database of existing designs can really speed up the selection process. Graphical and approximate methods can also be used to create a starting point "from scratch," if necessary. Aberration analysis may not be part of the spec, but it will probably be useful in the design process, especially in selecting variables for optimization.
Numerical methods are used to alter the variables in systematic ways that attempt to minimize the error function while honoring all constraints. Sometimes it goes smoothly, more often it doesn't, so changes are necessary, injecting designer guidance to resolve conflicts though some software is pretty smart about many types of optimization problems, no program is yet fully automatic, if only because some requirements and esthetic judgments may remain in the designer's head and not in the error function.
If it's not quite there, you may have to go back for some more optimization perhaps adding variables or changing constraints. You may even have to find a different starting point in some cases.
See "The Rest of the Story" below for a bit more on this subject. Model, analyze, optimize, and provide fabrication support for the development of optical systems with CODE V optical design software. What does this leave out? A lot of the "hard parts" of the design process, in fact. Incomplete or changing specifications.
Conflicting requirements. Dead-end solution attempts. Unrealistic schedules. Computer crashes. Nobody said it was easy! The fabrication defect made spherical aberration temporarily famous or perhaps infamous?
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In geometrical terms, the concept of aberration is pretty simple. Rays from a zero-dimension point object like a distant star imaged through a perfect lens will all focus to a single zero-dimension image point in reality, diffraction effects result in a small but finite size even for aberration-free imaging. If these rays go anywhere else, that is aberration.
Aberration can be expressed in various ways, most of which start out by tracing a number of rays through the lens to see where they go. The ray distribution can be plotted as a scatter plot we call this a spot diagram , or cross-sections of ray position data can be plotted ray trace or "rim ray" curves. To those trained in the art, the shapes and sizes of the resulting patterns can tell things about the amount and forms of aberrations that are present, and with this information, you can plan to correct or reduce the aberrations in various ways.
Aberration theory breaks down aberration into components terms of polynomials, actually , and can even assign "blame" for aberration to specific surfaces in the lens a strongly curved or badly made surface can contribute major amounts of aberration, but surface contribution information at least gives a clue how to proceed. Most optical surfaces are sections of spheres, since these are the easiest surface shapes to make. For a simple spherical-surface lens or mirror, rays at different heights on the surface are not bent to the same degree, so they focus at slightly different distances along the axis; this is SA.
With simple lenses, you can reduce SA by choosing the right lens form " lens bending ", as we say in the trade. With mirrors as in the HST , you can correct it by making the mirror a slightly non-spherical conic section but you have to create the CORRECT conic shape, which was HST's problem -- they built it perfectly against the wrong test standard! This can make lens design a bit challenging and leads to the next subject of optimization. The Hubble also illustrates the GOOD thing about aberrations: if you know what they are in detail, you can often correct them especially with a big enough budget!
If the optics are bending the light in the wrong way, elements can be reshaped or other elements added to cancel out the aberration, similar to the way that glasses correct myopic vision although myopia is not exactly an aberration -- the myopic eye actually has the wrong focal length, so an additional lens is needed to allow it to focus on the retina.
Remember that the goal of optimization is to take a starting lens of some sort and change it to improve its performance the starting lens should have a suitable number of optical surfaces of suitable types, since optimization can change only the values of the parameters, not the number or types of surfaces. Since optics is very precise distances of micrometers can make a big difference , we need to closely determine the values of all our variables at each step of the optimization. Let's consider local optimization first. What does "local" mean? If you have a lens model, an error function is something that correlates with its image performance, like spot size or RMS wavefront error -- smaller is better.
As variables are changed, the lens changes, ray trace values change, and the error function takes on new values. If you could plot these out, you would create a map of the hills and valleys of error function space in anywhere from one to 99 dimensions or more, depending on your variables.
In the admittedly silly sketch above, vertical distance represents the error function value lower is better , and horizontal position represents ONE of the variables in the lens for example, it could be the curvature of the front surface. Local optimization finds the lowest near-by region in the EFL, so if you are lucky or smart in choosing your starting point, you will do well by analogy, starting in Los Angeles might let you reach Death Valley using local optimization, but starting in New York would not -- you'd probably end up somewhere in New Jersey.
Does this analogy help? Maybe not, but the point is, with local optimization, your choice of starting point is very important. In our picture, local optimization will NOT get you to the lowest point -- it will roll you into one of the valleys to the right or left of the "You are here" starting point.
Now consider global optimization. This is an algorithm that somehow looks at the entire map of Error Function Land and eventually locates the lowest point regardless of where you started. Even if you start in Florida, global optimization will eventually get you to Death Valley, though depending on the methods used, it might take a really long time to actually get there, and you might be told about a lot of other low places along the way, some of which might be low enough for your purposes.
Silly analogy? Maybe, but the point to remember here is that global optimization considers the whole of "error function space," so your actual starting point is much less critical. In our picture, global optimization should take you to the desired low point. It is difficult even to measure very distant or too small an object.
In these cases, the magnification can be determined by measuring the distances p and q. In fact, for thin lenses, the ray passing through the lens center and which is not deflected fig. Verify this relation experimentally. As you bring the the lens towards the illuminated object, you come to a position in which the image is far away. If the lens object distance is equal to the focal length, the image will be formed at infinity, whereas an object placed at infinity will produce its own image at the focal point.
Furthermore, a lens placed at 2F from the object, will form the image at the same 2F distance. In this case, the magnification ratio is equal to 1. What is the focal length? This word comes from the Latin "focus" fire for the lens' property of concentrating the sunlight so much as to set fire to combustible objects.
The distance from the lens at which those objects must be kept has been named focal length. In optics this word is defined as the distance from the lens node we will see that later to the point at which a ray, which was initially parallel to the optical axis, intercepts the axis after being deflected by the lens.
To determine the focal length of a converging thin lens, use again your special optical bench. Arrange the illuminated object and the lens in such a way as to obtain a sharp image on the screen. Measure the p and q distances with the meter rule. The focal length is given by:. To obtain a better approximation, more measurements must be made to calculate the average value of the lens focal length. There is another way to indicate the focal length of a lens. In the fields of the production and the market of eyeglasses, instead of focal length people prefer speak of lens power, measured in diopters.
So, if you have to buy an eyeglass lens, you need to know its power. Focal length and power of a lens are bound to each other and you can easily pass from one to the other using this simple formula:. Equipment: a convergent lens with focal length included between 20 and 60 mm. The lens must be kept close to the eye. If it is planoconvex, keep the plane surface towards the eye. Approach the object until it becomes distinct. This experiment is very simple. But how does the lens magnify the object? The nearest distance of distinct vision with the naked eye is considered to be mm.
A normal adult man has difficulty seeing clearly objects closer than mm. Converging lenses allows us to approach the object well below this distance and to still see it clearly. As we approach the object we will see it larger fig. A human eye is able to work with parallel light from distant objects or with light of limited divergence objects not nearer than mm. Converging lenses reduce the divergence of rays coming us from an object nearer than mm, and allows us to still see it clearly.
The object to be observed must be placed between the front focus F2 and the lens fig. For convenience we assume that the optical center of the eye coincides with the back focus F1 of the lens. The distance of the eye from the lens is not important, but in practice we will keep the eye close to the lens. Let's consider an object point. Among all the rays leaving the object we shall take for convenience ray A parallel to the axis, which is deflected by the lens and passes through the back focus F1 and arrives at the retina.
We shall also take ray B passing through the lens center which is not deflected, and enters the eye where it is deflected by the cornea and intercepts ray A on the retina, forming an image point. The image formed on the retina is seen in a plane conventionally placed at a distance of mm from the eye. It is not a real image, in the sense that it cannot be recorded on film and for this reason it is called virtual.
This image is perceived the right way up, although in the eye it is upside-down. Even when we are not using lenses, the images formed in the eye are inverted. It is the brain that corrects this image. At the onset the A and B rays have a great divergence; on the other side of the lens, their divergence is reduced. If the object were placed in F2, the lens would make the A and B rays parallel, and to see the image clearly, the eye would focus at infinity. Finally, as we were saying, the magnifying lens reduces the divergence of the light coming from a close object.
The lens also allows the object to be viewed clearly and magnified even below mm. Notice that the same converging lens can be used both as a magnifier and as an image generator. Note that the lens producing images turns them upside-down, while the magnifying glass keeps them the correct way up. For example, a lens with 50 mm focal length will magnify 5 times. Hence, the lens of 50 mm focal length magnifies from 5 to 6 times, according to the eye's accommodation.
In a previous article, in which we talked about a little glass-sphere microscope, you could see to what extent a lens can magnify. However it is necessary to say that this is an extreme situation: normally a magnifying glass does not exceed 20 X. Now you are finally ready for the conclusive experiment, the one that should enable you to understand how some of the most important optical instruments work. Let's go back to the optical bench. However, this time replace the box with a translucent screen.
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You can make it with a card frame on which you have fixed a piece of white plastic taken from a plastic bag fig. Focus the image on the screen and you can observe the image appearing from behind the screen. You can also enlarge the image with a magnifying glass by taking the lens you used for the previous experiment and observing the image behind the translucent screen. As you can see, the image appears magnified.
So far there is nothing strange. While you continue to watch the upside- down image, try to move the screen a little. The image keeps steady. Oh, dear! Remove the screen.
conservadores2020.xtage.com.br/5598-conocer-a.php The image stays there. It is "floating" in the space. Therefore the screen was useless! It actually was! Not only is the image clearer and brighter, it is colored and in 3D too. There, you have built a telescope!