Diffraction#Single-slit diffraction

As optical gap or slit diaphragm is referred to in optics, a diaphragm with a narrow, elongated, generally rectangular opening. Slit diaphragms are often used to select desired Lichtspektralanteile, to hide unwanted light or for beam shaping.

• 4.1 monochromators and spectrometers
• 4.2 beamforming
• 4.3 Picture area
• 4.4 Phototechnik

Technical structure

Slit diaphragms are implemented as light transmission in a planar support. In the laboratory, formerly a blackened with soot, for example glass plate (possibly in a slide frame ) was used on a pointed object ( scalpel, knife) the blackening in the desired passband shape ( line, rectangle, ... ) has been removed. Today, the diaphragm usually made of metal plates, which are often diluted in a wedge shape towards the gap is performed ( such as the blade of a pair of scissors ), as an adjustable air-gap (see figure top). In order to avoid reflections at the edge of the diaphragm and to a well defined position of the slit to allow the space, the diaphragm blades usually as thin sheets (maximum a few millimeters thick ) will be executed.

To avoid stray light and glare are not translucent parts are mostly kept matt black, occasionally roughened.

The second pair of metal plates, the height of the gap opening can often be an additional factor. As the width of the gap is generally done by hand by set screws, as is adjusted more than once per measurement. Continuous adjustment that would make a servo drive needed, rarely occurs.

Intensity distribution behind slit diaphragms

General

If a slit aperture used for beam shaping and its opening with coherent light all illuminated, so diffraction effects can play an important role. To describe these effects, the light must be considered in the framework of wave optics. The strength and visibility of these effects depends largely on the Fresnel number, which describes the ratio of the width of the gap wavelength of the incident light and the observer distance from the gap:

The intensity distribution can be calculated with the diffraction integral. It is assumed that spreading from each point of the gap from a spherical wave. The diffraction integral then calculates the sum of all these spherical waves. The following figure shows (numerical ) results for different distances ( Fresnel numbers) of the observer from the gap:

Also for the diffraction phenomena in the optical gap is considered the Babinet's principle, therefore, the resulting diffraction pattern is the same as a straight wire.

Near field

For large Fresnel numbers, the intensity distribution is the indicated in dark gray gap shape well again. The fluctuations on the plateau of the intensity distribution are due to diffraction at the slit edges forth. In this regime ( Geometrical Optics ) diffraction effects are usually negligible. Depending on the width of the gap, this regime can also occur at a great distance from the gap. For example, when green light ( ) for a wide gap is not given for the distance.

Far-field

For narrow gaps with a gap width D in the vicinity of the wavelength (eg D = 10 · λ = 5 microns ) is, however, the far-field image (here) very close already behind the slit (in the example about d = 1.25 mm), and practically is then observed only that. The most striking feature of this remote field is its strong broadening compared to the gap width, which is indicated in the above figure 1 by the two differently scaled graphs for. The diffraction pattern in the far field is calculated using the Fraunhofer approximation for the diffraction integral ( see there). This results in the diffraction pattern as a Fourier transform of the shape of the orifice passage. An example is shown on the right.

Often it is sufficient to restrict the viewing of a plane parallel to the propagation direction of light. Then you can calculate the image that an observer is behind the gap. Looking at this at an angle to the optical axis ( see Figure 3, right ), we obtain:

For small distances from the optical axis allows the distribution of the intensity along an axis parallel to specify the cleavage plane approximation:

This distribution is also a function as a gap (see also sinc function si (x), and sinc ( x) ) and is shown in the bottom right of Figure 4. Some properties ( minima ) of these one-dimensional intensity distribution can also be derived graphically. You have for rapid estimations ( the distance between the two minima close to can be used as a measure of the size of the diffraction pattern ) and as instructive application of the principles of diffraction at an aperture very great importance:

To do this, follow the Huygens principle and assumes that each point of the diaphragm assumes a spherical wave. These waves propagate independently and interfere with the observers. The observers now see the gap at an angle φ (see Figure 2 right). If the path difference 2s ( see Figure 2, right) between the rays of the gap edges precisely the wavelength λ, so you can split the beam into two sub-beams. For each sub-beam of the first bundle is found then always exactly one partial beam bundle in the second, with a relative path difference of λ / 2 These two beams interfere destructively and thus cancel each other out. Thus, the total intensity is extinguished and we observe an intensity minimum. The same reasoning applies if the path difference between the outer beams is an integer multiple of n? Wavelength; dividing then only in accordance with more sub-bundle n. Even then found for each beam in each sub-bundle a partner with path difference λ / 2 This cancellation condition is therefore ( with the path difference s ):

We speak each order from minimum nth.

For the maxima there is no simple derivation. Can be calculated by the extremes of the sinc function, which are listed in detail in the article to the sinc function.

The intensity of these peaks decreases rapidly for large angles. The zero-order maximum is found at φ = 0, that is on the optical axis.

Especially the condition for the minimum may be used to estimate the widening of the intensity distribution after a gap. As shown above, the far field distribution is much wider than the slit itself, the opening angle may be as defined and obtained, for example, for a gap having a width of 10 wavelengths ( D = 10λ, for example, 5 microns to green light) to about α = 11.5 °. The light beam thus widens very quickly behind the slit. For a gap of 1000 wavelengths (eg, 0.5 mm for green light ) width arises, however, only α = 0.1 ° and you have to watch the gap to a very great distance, to observe a noticeable broadening.

By means of this formula, for example, the wavelength of light incident to a known gap can be measured by measuring the angular separation of the minima of order n. Well can be closed with a known wavelength to the width of the gap vice versa.

Wide and narrow column

With the often taken classification solely on the basis of the ratio of slit width to the wavelength λ in wide column ( where the near field dominates, so diffraction effects can be neglected ) and narrow gaps ( where the far-field dominates ) must be handled with care. This distinction is in fact, was as shown above, not dependent on the gap width but the Fresnel.

In practice, this inaccuracy, however often leads to problems because of a wide gap almost all the near field is observed, while the far-field would be recognizable only in a big distance from the gap. On a narrow gap, however, the near field is visible only in exceptionally small distance from the gap, in practice one usually seen, the far field.

Polarization effect

Since the jaws of the gap usually made ​​of metal, it can also influence the light falling through. The conductive metal includes an electric field parallel to its surface and absorbs short by this component of light. The component of the light that is polarized perpendicular to the metal surface is substantially not affected. A partial polarization with a preference for the E -field component It is made ​​across the gap. However, this is a small effect, which decreases sharply with increased Spalbreite and finds no practical application. At precision measurements it may need to be included in the analysis.

Application

Monochromators and spectrometers

In physics slit diaphragms are mainly used in spectrometers and monochromators. There they are used to select a portion of the previously split the light spectrum ( see figure at right ). A dispersive element such as a diffraction grating or a prism is first used to split the incident light spectrally. Then a spectral range of the light is selected by the other areas are hidden by a slit diaphragm. In monochromators can be as light can be generated from an arbitrary and defined spectral range. In spectrometers such a specific wavelength is selected, with which the following measurement is performed. The entire spectrum can be recorded by means of gradually moving the gap or rather rotation of the dispersive element. In the optical test apparatus, the slit also serves as a secondary light source for the other beam path.

Similarly, the slit diaphragm is used as a secondary light source directly in front of the dispersive element to provide on its input side for a defined arrangement and shape of the light source. To this end, the aperture of a broadband ( white ) is irradiated light source is focused, for example, by a concave mirror optics at roughly the gap.

In this use, as a beam stop diffraction effects would interfere at the gap though. Therefore, one chooses the gap width is always large enough so that diffraction effects are not relevant consequence. This in turn limits the achievable wavelength resolution, which is why an optimal intermediate value is desirable.

Beamforming

Slit diaphragms are generally used for beam shaping. They are used extensively illuminated from behind and form a rectangular beam adjustable scale. May be prevented that light falls on portions of an optical configuration in which it would be disturbed by scattering or unwanted reflections. This principle applies eg light -plate microscopy ( SPIM). Here an adjustable gap formed a rectangular beam that is then focused by a cylindrical lens to a light sheet. More simply, the application gap in the ultra-microscope in which an illuminated optical gap with a single condenser lens is shown in a sample. Particles that pass through the light sheet thus formed can be detected by their stray light.

Often the width of such aperture is manually adjustable. In monochromator applications is the width while the wavelength range used or the required intensity adjusted ( for example, resolution is sacrificed by a wider stance to achieve more intensity and thus a better signal -to-noise ratio). Also the height of the unused Gap is executed often adjustable, again Assure defined conditions during beam.

In the beamforming column are usually so broad that a single slit diffraction pattern is not visible. Diffraction is, however, still be seen at the edges of the gap, resulting in a widened fall of the edge intensities ( see picture of the wide gap at the top).

Picture area

Conversely panels are often used to narrow frames. Thus, for example, a small area can be cut from a microscope image, and are then mapped to only a portion of an image sensor. With the help of additional optics, the same image can then be mapped somewhat offset again. If both cuttings sent by different optical filters, so you can record the same section simultaneously in several spectral ranges, without having to use multiple cameras.

Phototechnik

With cameras wide slit diaphragms find a greater distance (about 0.8 to 1.0 mm) in panoramic cameras and in technical applications. They are seen here as transition to electronic line camera. Overexposed is each a slit-shaped neckline, roughly analogous to the focal plane shutter, but the film (or film clip through the lens movement ) is moved during recording.