Fraunhofer diffraction

Light can bend around things.

This is called diffraction. It happens when light hits an object. Some light scatters around the edges. This makes light and dark stripes.

You can see these stripes far away. This is a special way to look at light. It is named after a man named Fraunhofer.

A lens can help you see the patterns too. The light travels in straight lines to the lens. Then the lens shows the pattern clearly. It is fun to see how light moves!

Light can bend around objects. This is called diffraction. When light hits an edge, it scatters. This creates patterns of light and dark bands.

Scientists use a special rule for far-away patterns. This is the Fraunhofer diffraction equation. It models light when the source is very far away. It also works when the light is viewed far away. We call this the far field.

In the far field, light waves act like flat sheets. These are called plane waves. Because the light is so far, the waves look parallel. This makes the math easier to solve.

You can use a lens to see these patterns. A positive lens, which is a focusing lens, helps. It gathers the parallel rays. The lens brings them together on a focal plane. This shows the diffraction pattern clearly.

Different shapes make different patterns. A tiny hole makes a circular pattern. This is called an Airy pattern.

A narrow slit makes a pattern of many stripes.

Have you ever noticed light and dark bands near a shadow? This happens because light can bend around the edges of objects. This bending is called diffraction. Scientists use a special rule to model this called the Fraunhofer diffraction equation. This equation helps us understand how light waves spread out. It is very useful for looking at light patterns from far away.

To understand how this works, we look at light as waves. Every point on a light wave acts like a tiny new source. These tiny sources create many small wavelets. When these wavelets meet, they add together or cancel each other out. If two waves are in phase, they make a bigger wave. If they are in opposite phases, they cancel out to zero. In the far field, these waves arrive almost parallel to each other.

This way of looking at light is named after Joseph von Fraunhofer. He did not actually create this specific math theory himself. However, scientists named the equation to honor his work in optics. The math is a simpler version of a rule by Kirchhoff. It works best when the light source is very far away. It also works when the viewing area is very far away.

There are specific numbers that tell us when this rule works. This is called the Fraunhofer condition. For example, imagine a tiny circular hole that is 0.5 mm wide. If you use a laser with a 0.6 μm wavelength, you must look from far away. You would need a distance greater than 1000 mm to see this pattern. A lens can also help you see these patterns clearly. A positive lens focuses these parallel rays onto a focal plane.

Different shapes create very different light patterns. A narrow rectangular slit creates many light and dark stripes. If the slit is smaller, the bands get wider. A circular hole creates a pattern called an Airy pattern. This pattern has a bright central disk called an Airy disk. This disk can limit how clearly an imaging system sees things. Some special filters can even remove the extra rings from these patterns.

Fraunhofer diffraction is a way to model how light waves spread out when they hit an object. This phenomenon occurs when plane waves, which are waves with flat fronts, hit a diffracting object. Scientists observe the resulting pattern in the far-field region. This means the pattern is viewed at a very long distance from the object. It can also be seen at the focal plane of an imaging lens. Understanding this process is vital for optics and imaging technology.

To understand this, we must look at the Huygens–Fresnel principle. This principle suggests that every point on a wavefront acts as a source of spherical secondary wavelets. The sum of these many tiny wavelets determines the shape of the wave at any later time. When these waves meet, they undergo superposition. This means they add together or cancel each other out. If two waves are in phase, they have the same phase and create a larger amplitude. If they are in opposite phases, they cancel each other out to zero amplitude.

Calculating the exact wave amplitude is difficult. It involves adding many waves with different amplitudes, phases, and polarizations. The Fraunhofer diffraction equation is a simplified version of Kirchhoff's diffraction formula. It works when both the light source and the viewing plane are effectively infinitely distant from the aperture. In this state, the incident light acts as a plane wave. This means the phase of the light is the same at every point on the aperture. At the observation plane, the phase varies linearly with position. This makes the math much more straightforward.

There is a specific requirement called the Fraunhofer condition for this model to be valid. This condition depends on the distance between the aperture and the observation plane. It also depends on the distance between the aperture and the light source. For example, consider a circular hole with a 0.5 mm diameter. If you use laser light with a 0.6 μm wavelength, the viewing distance must be greater than 1000 mm. A positive lens can also be used to create this effect. The lens focuses parallel rays onto a focal plane, which acts as the far-field plane.

Different aperture shapes produce unique diffraction patterns. A narrow rectangular slit creates a pattern with a central maximum of intensity. This is followed by a series of peaks that decrease in intensity. The angle between the first two minima depends on the width of the slit. If the slit is smaller, the angle of the diffraction bands becomes larger. For a 0.5 mm slit with 0.6 μm light at 1000 mm, the central band is 2.4 mm wide.

A rectangular aperture creates a different pattern of horizontal and vertical fringes. A circular aperture produces what is known as the Airy diffraction pattern. This pattern features a bright central disk called the Airy disk. The size of this disk is an important factor in imaging. It can limit how well an imaging system resolves two objects that are close together.

Some apertures have a Gaussian profile, such as certain photographic slides. These produce a diffraction pattern that is also a Gaussian function. Unlike rectangular or circular apertures, a Gaussian profile has no secondary rings. This can be achieved through a process called apodization. In this process, a Gaussian filter covers the aperture to smooth the pattern. This is useful because a single-mode laser beam can maintain its Gaussian profile as it travels.

Fraunhofer diffraction connects many ideas in physics and engineering. It explains how light behaves when it encounters obstacles or small openings. This knowledge helps scientists design better lenses and imaging tools. It also helps us understand the limits of how clearly we can see the world. From tiny microscopic slits to large telescope lenses, these principles govern how light reaches our eyes and sensors.