 # Interference and Diffraction

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Interference and Diffraction
Introduction to Physical Optics Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

What is Light? To understand physical optics, let’s review how we think about and measure light, which is part of electromagnetic radiation. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Gamma Rays Ultraviolet Rays X Rays Light Infrared (IR) Microwave Radio wave 10-15 m 10-6 m 10-2 m 103 m EM radiation is made up of an electric field and a magnetic field. Particle-wave duality of EM radiation. Light as a particle Light as a wave (physical optics) Includes x-rays as well as light, IR (heat) and radio waves. Electromagnetic radiation is everywhere around us. It is the light that we see, it is the heat that we feel, it is the UV rays that gives us sunburn, and it is the radio waves that transmit signals for radio and TVs. EM radiation can propagate through vacuum since it doesn’t need any medium to travel in, unlike sound. The speed of light through vacuum is constant through out the universe, and is measured at 3x108 meters per second, fast enough to circle around the earth 7.5 times in 1 second. Its properties demonstrate both wave-like nature (like interference) and particle-like nature (like photo-electric effect.) Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Optics Optics contains two areas of study:
Geometrical Optics Physical Optics Recall: Geometrical optics, or ray optics, is the study of light that travels as a “ray,” in straight lines. Light rays passing through lenses and bouncing off mirrors Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

What is Physical Optics?
Physical optics, or wave optics, is the study of how light interacts with objects similar in size to its wavelength. Light energy travels as a wave (not a ray). Wave optics concerns the characteristics of light such as wavelength, intensity, phase, and orientation. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Wavelength Wavelength is the distance between two identical points on a wave. (,lambda) One way of describing light is by its wavelength. Wavelength is the distance between the two identical points on the wave. The wave must be steady (no change in the oscillation and no change in its velocity) for it be possible to measure the wavelength. Wavelength is also shorthanded to a Greek letter Lambda. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Frequency Frequency is the number of cycles per unit of time. (, nu)
The same exact wave can be described using its frequency. Frequency is defined as the number of cycles of the waves per unit time. In the case shown, the frequency would be 1.5, since there are exactly one and a half complete cycles of the wave in the given time. The frequency is inversely proportional to its wavelength. Frequency is denoted by Greek letter “nu”. Frequency is the number of cycles per unit of time. (, nu) It is inversely proportional to the wavelength. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Wavelength and Frequency Relation
Wavelength is proportional to the velocity, v. Wavelength is inversely proportional to the frequency. eg. AM radio wave has a long wavelength (~200 m), therefore it has a low frequency (~KHz range). In the case of EM radiation in a vacuum, the equation becomes Wavelength and frequency are related to one another by the wave’s velocity. Wavelength is proportional (wavelength increases if velocity increases), and wavelength is inversely proportional to frequency (wavelength decreases if frequency increases). An AM radio wave has a large wavelength, so it has a low frequency (compared to other EM radiation.) In the case of EM radiation, the velocity is the speed of light, denoted by c. the speed of light is as mentioned before, approximately 3x108 meters per second. Using algebra, one can solve for any one of the variables. c Where c is the speed of light (3 x 108m/s) Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

E = h Photons Photons are little “packets” of energy.
Each photon’s energy is proportional to its frequency. A photon’s energy is represented by “h” E = h Now the particle nature of EM radiation. These little packets of light is known as photons. These photons carry a certain energy which is related to its frequency. This energy is equal to Planck’s constant (h) multiplied by the frequency of the photon. By substituting “nu” with the equation in the previous slide, we can get the equivalent equation in terms of wavelength. Planck’s constant is x joule second Energy = (Planck’s constant) x (frequency of photon) Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Light Wave Transverse Wave
Travels perpendicular to change of amplitude. E B Direction of Travel The case of light: Light waves are called electromagnetic waves because they contain two types of energy that change amplitudes. Both electrical and magnetic energy vary perpendicular to each other. Light is a transverse wave because the direction of travel is perpendicular to the amplitude change of BOTH electrical and magnetic fields. Transverse waves of light are composed of an electric field (E) and a magnetic field (B). Each field is perpendicular to the other and the amplitude change of both fields is perpendicular to the direction of travel. Light is also called electromagnetic waves or radiation because of the two fields of energy that compose it. Transverse waves also don’t require a medium by which to pass the energy through, thus they can travel through a vacuum. Longitudinal waves are also called compression waves. They compress and expand energy through a medium. They cannot travel with a medium by which to pass, thus they cannot travel through a vacuum. In this course, the light wave has been the focus of attention: an electromagnetic transverse wave. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Light Intensity Intensity of a monochromatic light relates to the brightness of that light. The intensity of an electromagnetic wave is proportional to the amplitude squared. Higher Intensity Lower Intensity Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Wave Phase Phase: The phase of light refers to the timing and position of two or more waves. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Waves ‘In Phase’ In Phase:
Two waves that are “in phase” move together with the same motions. They are at the same cyclic position at the same time. Example The turn signal on the car in front of you blinks at the same time as your signal. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Waves ‘Out of Phase’ Out of Phase:
Two waves that are “out of phase” do NOT move together with the same motions. At the same time they are at different cyclic positions. Example The turn signal inside your car alternates with the signal of the car in front of you. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference Two waves of the same type and frequency can interfere when they meet at the same place. Types of waves: Transverse waves propagate perpendicular to the change of amplitude. Longitudinal waves propagate parallel to the change of amplitude. Transverse waves can only interfere with transverse waves - longitudinal waves can only interfere with longitudinal waves. Light is a transverse wave. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference Superposition occurs when waves combine to form a new wave. Constructive Interference Waves in phase always superpose to add amplitudes. = TV and radio signals are interfering when the reception is not clear; there is static or multiple transmissions in what you watch or listen to. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference Superposition occurs when waves combine to form a new wave. Destructive Interference Waves out of phase superpose to subtract amplitudes. = TV and radio signals are interfering when the reception is not clear; there is static or multiple transmissions in what you watch or listen to. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference Coherent waves are continuously in phase with each other.
Example: Laser Light Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference The phases of incoherent waves vary randomly. Example:
Light bulb Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference To observe interference:
Use light that that has the same frequency, and is coherent; e.g. LASER light. Split a light beam into two paths. amplitude splitting Allow the two beams to meet (recombine) at the same location on a viewing screen or detector. Beam-splitter Mirror Laser Mirror Viewing Screen Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference To observe interference:
When the two beams recombine at the viewing plane they produce interference patterns of dark and bright fringes because the distances traveled by the beams determine their phases relative to each other. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Thin Films Thin films, such as gasoline, oil, or soap bubbles, also cause interference by amplitude splitting. One light source (sun), is used to create two virtual light sources, splitting the amplitude of the original. The first source is the reflection off the first surface of the film. The second source is the reflection off the second surface of the film. s1 s2 Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Thin Films Thickness The distance between the two surfaces is half the distance between the virtual sources -- this path difference determines the wavelength(s) of the reflected light. Oil or gasoline on wet pavement is seen as different colors as the thickness of the film changes. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

waves from two slits combine in phase
Interference Fringes When two or more beams of coherent light interfere, patterns appear in the form of fringes (dark and bright bands of light). Constructive interference: waves from two slits combine in phase Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

waves from two slits combine out of phase
Interference Fringes The bright spots are caused by constructive interference, and the dark spots by destructive interference Destructive interference: waves from two slits combine out of phase Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Diffraction Diffraction will cause interference fringes to form when a single beam interacts with an object nearly the same size as the wavelength of the light. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Diffraction A circular hole or just a tiny circular shaped particle could create the diffraction pattern below: Alternating fringes of concentric circular rings Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Diffraction Many tiny dust particles can decrease the resolving power of a lens by overlapping many diffraction patterns. Loss of resolving power = difficult to distinguish fine details High Low Resolving Power: Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Diffraction Gratings What is a diffraction grating?
A transmission grating is an opaque plate that has numerous equally spaced parallel slits that serve to break up light into its component wavelengths. A reflection grating is to similarly space numerous reflective surfaces. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Diffraction Gratings The slits cause light to diffract
Shorter wavelengths (e.g. blue) interfere constructively at a smaller angle than longer wavelengths As a result, a grating spreads incident white light out into a spectrum of colors. Grating Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Interference Applications
Diffraction Gratings Iridescent colors: When the diffracted color changes with the angle an object is looked at. Many birds, insects, and fish have iridescent colorings via diffraction (feathers make excellent gratings!). Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science

Summary Physical optics is the study of light traveling as a wave.
Coherent light of the same frequency can interfere both constructively and destructively, sometimes forming fringe patterns. Diffraction of light due to tiny objects causes diffraction patterns to form. Diffraction gratings are used to diffract light into its component wavelengths. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science