See also: Focusing

In Optical, the focusing is the operation which consists in concentrating ray S coming from a point in another point. When one is very far from the object observed that amounts concentrating the parallel rays between them of the same point. This is done either using Miroir S, or using lenses.

Interest of focusing

Focusing consists in obtaining a clear image of an object. The term “image” is to be in the broad sense taken characteristic information on the object.

Indeed, the information emitted by the object (for example the light which it diffuses) leaves in general in all the directions, they “are diluted” in space. If one wants to collect a sufficient quantity of information (to have sufficient signal, of luminosity), one thus needs reconcentrer this information, while separating what comes from such or such point from the object. It is the goal of focusing there. The image is clear if the information allotted to a point of the object comes well from this point and not from another. The image is fuzzy if information coming from several points mixes.

There exist two types of phenomena for which focusing is useful:

• in the case of the Diffraction, for example for the analysis by diffraction on a crystal, or for the analyzes spectral by dispersion wavelength;
  chaque point of the diffracting crystal emits in all the directions, and one wants to collect all the rays having the same deviation; it is thus necessary to concentrate these rays, whatever their point of origin, in the same point;
• in Photography and Astronomy, one wants to observe objects located close or “very” distant (in general of stars in the second case);
  pour the remote objects, the rays (luminous, radio or x-rays) which emit these objects arrive parallel, the fact of collecting these rays on a large surface then to concentrate them in a given point allows to have more signal.

In the case of the focusing of parallel rays, the rays concentrate in a plan named the focal plane . Each point of the focal plan represents a direction of rays. The focal plan represents a dual Espace real space.

Stigmatism

The optical systems are not perfect. It is in general only about one approximate focusing (parafocussing) , valid if one is under the conditions of Gauss (the ray strikes near the optical center, and with a weak slope).

In the case of a perfect focusing, rays resulting from a point of the object observed convergent towards a single point of the image. One speaks about Stigmatisme, the optical system is known as “stigmatic”.

If focusing is imperfect, the rays all do not converge, and a point of the object becomes a spot on the image, the image is fuzzy. There is not any more a Bijection between the points of the object and those of the image. One speaks about astigmatism. Let us note that the Astigmatisme is also an eye trouble (see the article Ophtalmologie).

Image of the darkroom

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It is difficult to illustrate the subject with at the same time clear figures (close objects to have a reasonable scale) and geometrically exact (deviation of the rays). The illustrations of this part are thus to regard as explanatory diagrams similar to those which one would trace by a show of hands on a table.

A simple experiment to include/understand focusing is the principle of the Darkroom: it is about a box of which one of the east coasts bored of a hole, and of which the other constitutes a screen. Striking rays an object (coming from the Sun, a bulb…) are reflected by each point of the object in all the directions (diffusion), therefore a point of space (in particular that where the hole of the darkroom is located) receives rays coming from the various points of the object. On the other hand, all the luminous rays striking the screen necessarily pass by the hole, one thus concludes from it whom each point of the screen receives from the rays coming only from the direction of the hole.

Let us suppose that one makes two holes now, and that a mirror deviates the rays passing by each hole, the screen being then between the holes. While positioning the mirrors well, one can manage to make converge the rays coming from the same point of the object observed on a single point of the screen. Thus, there will be twice more intensity. On the other hand, it is not possible to make converge strictly all the rays. Certain points will be slightly duplicated, one will have like two slightly shifted images, a blur. It is thus seen that focusing is a compromise between the luminous intensity and clearness.

The fact of adapting the system to make converge as well as possible the rays is called the “Mise at the point”. Generally, one manages to have a clear image of an object parallel with the plan containing the two holes, and it is necessary to adapt the position of the mirrors according to the distance from the object to the darkroom. The part of space giving a clear image is called the “Depth of field”.

So now there are not two points but a whole opening, one needs a mirror curves correspondent with small plane mirrors put side-by-side. In this case, one focuses rays coming from a close object by a mirror. For the imagery of a close object, this situation has currently only little concrete application, because it would be necessary to be able to deform the mirror to adapt to the position of the object, and in particular to its distance from the objective (one finds the problem of the blur). This system however is used for an object of curiosity sold in the stores of scientific discovery or “jokes and traps”: it is about a papered box of a curved mirror on which one poses an object; the rays are focused on the opening of the box, with the result that when the mirror is looked at, one with the impression which the object is above the opening, suspended in the vacuum, and imperceptible. On the other hand, the curved mirrors are used to focus the objects located “ad infinitum”, for example in the Télescope S (see below).

In the case of the room with two holes, one can also deviate the rays using a prism. The result is appreciably the same one: there is a profit of luminosity at the price of a light blur, the rays not converging all exactly.

If one puts holes side-by-side in a continuous way, it is necessary to replace the prisms by a curved prism, i.e. a lens.

Focusing of rays coming from the infinite one

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Danslecasde the instruments optical, the image given by the objective is in general observed via a Oculaire, of which the goal is to give an image “ad infinitum” (that makes it possible the eye to slacken the muscles charged with the Accommodation, which presents a better comfort of observation). If the objective focuses the light, the instrument is overall afocal.

Principle and interest

When an optical system observes objects which are close, the luminous rays coming from an object are not all parallel, and from the parallel rays necessarily do not come from objects which are in the same direction (compared to the optical axis).

On the other hand, when the objects are very distant such as for example stars in the sky, then the rays resulting from a point and which arrive in the optical system are all parallel between them, and their direction is the direction of the object compared to the optical center. One can note it in a simple way: if one closes an eye then the other, or if one moves of a step in any direction, one always sees the stars at the same place. That proves well that what imports, it is the direction observed and not the positioning of the observer except for a few meters (what is not the case for the objects close to the observer).

Thus, by selecting a direction of rays, one selects also a direction in the sky, therefore an object.

Therefore, if one puts a screen on the focal level of a lens or a curved mirror, each spot will thus correspond to the collected light coming from the same direction coming from the same object (or aligned objects). Rather than to put a screen, one in general puts a mirror, which takes less place and makes it possible to lengthen the optical way, therefore the enlarging of the image. The larger the opening of the optical instrument is, the more one will collect light, the more the intensity will be important, but the more one will move away from the conditions of Gauss, the less focusing will be perfect (fuzzy image).

In addition, if an obstacle stops partially the opening of the optical instrument, that will decrease the visualized intensity, but will not deteriorate the image, since it is enough to take rays coming beside the obstacle (do not forget only the direction of the rays counts). Thus, the presence of a small mirror in front of the opening of the large mirror in the telescopes of Newton and Cassegrain does not obstruct the formation of the image. The presence of the sensor in front of the mirror of a parabola of television does not obstruct the reception of the waves.

Examples

Optical telescopes

The Télescope S use parabolic or spherical mirrors to focus the light coming from the stars. As the focal plan is in front of the mirror focalisator, therefore on the arriving way of the rays, the considered rays are deviated by another mirror, which makes it possible to have an image of the focal plan of the first mirror. This image of the focal plan is observed thanks to an optical device called Oculaire.

In the case of the telescopes known as of Schmidt-Cassegrain, the first mirror is bored in its center, the rays are returned behind the mirror through the hole. The second mirror, hyperbolic, is perpendicular to the optical axis of the telescope.

In the case of the telescopes known as of Newton, the rays are returned on the side by a tilted plane mirror with 45  ° compared to the optical axis of the first mirror.