Fraunhofer diffraction

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.