# Optical illustration

In optics, optical imaging is the generation of an image point from an object point by combining light emanating from the object point by means of an optical system. An image is the totality of all individual pixels that represent all object points.

A real image can be captured on a screen. The light is really united there. A virtual image seems to float in space. With a ray-optical construction, rays are also combined in pixels. When observing, the light seems to come from the virtual pixels.

The optical system can consist of lenses, mirrors, diaphragms or the like. consist. Only the points in each case on an object plane are mapped in a specific image plane. The further away the object points are from this object plane, the less sharp they appear in the image plane. In most real optical systems, the tolerable distance from the object plane - the depth of field - is very small.

## Optical systems

In addition to lenses and mirrors , diaphragms with punctiform openings produce optical images. They can therefore be used alone as optical systems - for example as pinhole cameras - for imaging. More complex systems are made up of several optical components .

In order to reduce aberrations, lenses often consist of several types of lenses of different types of glass, but they always act like a converging lens . Collecting lenses and objectives produce a reversed, upside-down image, for example on film in a photo camera .

By means of an inverting prism or another imaging converging lens, the image generated by the lens can immediately be rotated again to convert the intermediate image e.g. B. in the viewfinder of the camera or for projection in the enlarger or slide projector correctly laterally and upright. The distance between two lenses corresponds roughly to the sum of their focal lengths. It must be increased if a close object is to be viewed.

The principle of an astronomical telescope consists in viewing the image produced by the objective with a magnifying glass or an eyepiece . This magnifying glass or eyepiece only creates an image on the retina together with the eye lens. Therefore, the images of an astronomical telescope and also those of a microscope that works in the same way are upside down. Binoculars and many stereo microscopes therefore often have erecting prisms, which often also serve to shorten the overall length.

## Optical imaging with individual lenses and spherical mirrors

The idealizing beam optics usually start from an infinitely distant point light source. The rays coming from there run parallel to each other. If the imaged object is not at infinity, but at the distance of a finite object distance , the image is generated in the associated image distance , which is always greater than the focal length for the converging lens. The image plane is curved.

The further considerations apply to a so-called paraxial beam path . Strictly speaking, all considerations only apply to a very narrow area around the optical axis . The lenses are idealized into infinitely thin planes and the color of the light is neglected . This simplification is important because the focal length is different for each color.

The same principles apply to mirrors as to lenses. When looking at the images, you just have to be aware that the direction of the rays should actually be reversed on every mirror surface.

A converging lens focuses incident light rays parallel to the optical axis into the focal point , which is the distance , the focal length , from the lens; conversely, light emanating from the focal point and falling through the lens is deflected into a bundle of parallel light rays. ${\ displaystyle f}$

Construction of a real image on a converging lens

In general, objects can be mapped with the help of a converging lens. In this case, referred to the distance of the object from the lens (also called object distance) and the distance of the image from the lens (focal distance). If the lens is thin, the lens equation holds${\ displaystyle S_ {1}}$${\ displaystyle S_ {2}}$

${\ displaystyle {\ frac {1} {S_ {2}}} + {\ frac {1} {S_ {1}}} = {\ frac {1} {f}}}$.

This way of speaking expresses that an object that is at a distance from a lens of the focal length is displayed on a screen that is at the distance on the other side of the lens. The prerequisite is that is. A camera works according to this principle; In this case, the screen is the film to be exposed (or, in digital cameras, the semiconductor layer to be exposed) on which the so-called real image is mapped. ${\ displaystyle S_ {1}}$${\ displaystyle f}$${\ displaystyle S_ {2}}$${\ displaystyle S_ {1}> f}$

However, if the object is between the focal point and the lens (i.e. ) then goes negative; the image is then virtual and appears in front of the lens. Although a virtual image cannot be displayed on a screen, it is visible to an observer looking through the lens without any further aids. A magnifying glass works according to this principle. ${\ displaystyle S_ {1} ${\ displaystyle S_ {2}}$

Construction of a virtual image on a converging lens

The magnification of a lens is through

${\ displaystyle M = - {\ frac {S_ {2}} {S_ {1}}} = {\ frac {f} {f-S_ {1}}}}$

where is the magnification factor. A negative here means a real and upside-down image; a positive one means a virtual image that is upright. ${\ displaystyle M}$${\ displaystyle M}$${\ displaystyle M}$

The above formula can also be used for diverging lenses. However, such lenses produce virtual images in all cases.

Construction of a virtual image on a diverging lens

The calculation (modeling) of real optical systems from a large number of lenses or mirrors is of course incomparably more complex, but is carried out in the same way as the procedure for individual lenses.

## Image errors

Of aberrations is called when the different light rays emanating from the object point, not all are focused in a pixel.

The most important aberrations are spherical and chromatic aberration .

Spherical and chromatic aberrations are corrected by systems made of several lenses of different types of glass, spherical aberrations are corrected by aspherical lenses or gradient lenses.

Mirror optics have no chromatic aberration. The spherical aberration of a spherical mirror can be corrected with a correction glass plate that Bernhard Schmidt invented. The so-called Schmidt telescope (also Schmidt mirror) developed by him therefore has a particularly large field of vision.

A glass plate ( plane plate ) creates an offset of the image plane or a blurring that increases as the opening angle increases.

## Process similar to optical imaging

### Quasi-optical images

In general, a quasi-optical image can also be achieved with other types of radiation ( microwaves , X-rays , millimeter waves , terahertz radiation , ultraviolet , infrared radiation ) if an image can be generated by refraction or reflection on curved surfaces (e.g. X-ray telescope , radio telescope ).

In the electron optics is focusing beam deflection of electrons by means of magnetic or electric fields. Analogous to optical lenses, there are accordingly electron lenses consisting of fields, but these have strong imaging errors. They are used as imaging lenses in image intensifiers and transmission electron microscopes , but also for focusing in cathode ray tubes and electron guns .

The shadow cast also does not represent an optical image in the strict sense . Here, a sharp image is guaranteed by the fact that practically only one beam emanates from an object point, so that no optical system is required to combine the light. This can be done by a defined light source (point-like or with parallel light). The object is in the beam path and absorbs part of the light. In contrast to the illustration, basically every plane behind the object is suitable as a projection plane. This is z. B. used in X-ray diagnostics . Another possibility is the direct resting of the object on the projection plane, e.g. B. with contact copies.

## history

Simple forms of optical imaging can already be found in the great outdoors: spots of light that are visible under a canopy of leaves on the ground do not take the shape of the holes, but that of the light source . That is, in sunshine they are round (except for partial solar eclipses , in moonlight they take on the shape of the crescent moon.)

In a first abstraction, this observation leads to the development of the camera obscura : In a darkened room, one wall of which has a small hole, an image of external reality is created on the back. This well-known phenomenon is also reflected in the allegory of philosophy .

The image that is generated in the camera obscura is brighter the larger the hole. However, as the size of the hole increases, so does the sharpness of the image. This dilemma can be resolved by focusing the light using a converging lens . Each converging lens has a focus (focal point), which is defined by the fact that in it the light of an imaginary, infinitely distant, point-shaped light source is reunited into one point. Extended objects lead to a two-dimensional image in the focal plane defined by the focal point . This can easily be traced on a sheet of paper with a magnifying glass and the light of a structured light source (incandescent lamp, daylight in the window cross).