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Isaiah Kelly
Isaiah Kelly

How Óptica básica by Daniel Malacara Covers the Fundamentals and Applications of Optics



Introduction




Optics is one of the oldest branches of physics that studies the nature and behavior of light and its interaction with matter. It has many applications in science, engineering, medicine, art, and everyday life. Optics can be divided into several subfields depending on the aspects of light that are considered: geometric optics deals with light rays and their reflection and refraction by lenses and mirrors; wave optics deals with light waves and their interference, diffraction, polarization, and coherence; photon and quantum optics deals with light particles (photons) and their emission, absorption, scattering, amplification (lasers), quantum states, and entanglement.




Daniel Malacara Optica Basica.pdf


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One of the most comprehensive books on optics is Óptica básica by Daniel Malacara. This book is written in Spanish and was first published in 1988 by Fondo de Cultura Económica. It has been revised and updated several times since then. The latest edition was published in 2015 and contains 532 pages. The book is intended for students of physics, engineering, optometry or any other career related to optics. It covers both the fundamentals of optical engineering and the design and operation of various optical instruments. The book also reviews some recent advances in optics such as automatic lens design, thin-film interference coatings, holograms, spatial filters or linear optics.


In this article, we will summarize the main topics covered by Óptica básica by Daniel Malacara. We will also provide some examples and illustrations to help you understand the concepts better. We hope that this article will inspire you to read the book or learn more about optics.


Fundamentals of optical engineering




Basic ray optics




Ray optics is the simplest way to describe the propagation of light. It assumes that light travels in straight lines called rays. When a ray encounters a surface, it can be reflected or refracted according to some laws. Reflection is the bouncing of light from a surface. The angle of reflection is equal to the angle of incidence. Refraction is the bending of light when it passes from one medium to another with a different refractive index. The refractive index is a measure of how much a medium slows down light. The angle of refraction is related to the angle of incidence and the refractive indices of the two media by Snell's law.


Lenses and mirrors are optical components that use reflection and refraction to change the direction and shape of light rays. A lens is a transparent object with curved surfaces that refracts light rays. A mirror is an opaque object with a smooth surface that reflects light rays. Lenses and mirrors can be classified as converging or diverging depending on whether they bring parallel rays closer together or farther apart. Converging lenses and mirrors have positive focal lengths, while diverging lenses and mirrors have negative focal lengths. The focal length is the distance from the lens or mirror to the point where parallel rays converge or diverge.


The formation of images by lenses and mirrors can be analyzed using ray tracing, which is the drawing of representative rays through an optical system. There are some rules for ray tracing that depend on the type and position of the lens or mirror. For example, for a thin lens, we can use three principal rays: one that passes through the center of the lens without bending, one that is parallel to the optical axis before the lens and passes through the focal point after the lens, and one that passes through the focal point before the lens and becomes parallel to the optical axis after the lens. The intersection of these rays gives the position and size of the image.


Basic wave optics




Wave optics is a more accurate way to describe the propagation of light. It considers light as a wave that has a wavelength, a frequency, and an amplitude. The wavelength is the distance between two consecutive peaks or troughs of the wave. The frequency is the number of peaks or troughs that pass a point per unit time. The amplitude is the height of the peak or depth of the trough from the equilibrium position. The speed of light in vacuum is constant and equal to c = 299,792 km/s. The speed of light in a medium is lower than c and depends on its refractive index. The relationship between speed, wavelength, and frequency is given by v = λf, where v is speed, λ is wavelength, and f is frequency.


One of the most important phenomena in wave optics is interference, which is the superposition of two or more waves that results in a new wave with a different amplitude and phase. Interference can be constructive or destructive depending on whether the waves add up or cancel out each other. Interference can be observed when light waves pass through narrow slits, thin films, or gratings. These devices create multiple coherent sources of light that interfere with each other to produce characteristic patterns of bright and dark fringes.


Another important phenomenon in wave optics is diffraction, which is the bending of light waves around obstacles or apertures. Diffraction occurs because light waves behave like waves and not like particles. Diffraction can be observed when light waves pass through small holes, edges, or slits that are comparable in size to their wavelength. Diffraction can also be observed when light waves pass through gratings, which are periodic arrays of slits that diffract light into different directions according to their wavelength.


A third important phenomenon in wave optics is polarization, which is the orientation of the electric field vector of a light wave. Polarization can be linear, circular, or elliptical depending on how the electric field vector changes over time and space. Polarization can be measured and manipulated using polarizers, which are devices that transmit only one component of polarization and block others. Polarization can also be affected by birefringence, which is the property of some materials to have different refractive indices for different polarizations; optical activity, which is the property of some materials to rotate the plane of polarization of linearly polarized light; and Kerr effect, which is the property of some materials to change their refractive index in response to an applied electric field.


A fourth important phenomenon in wave optics is coherence, which is the degree of correlation between two or more waves in terms of their phase difference and relative intensity. Coherence can be temporal or spatial depending on whether it refers to waves at different times or at different points in space. Coherence can be measured using interferometers, which are devices that split a beam of light into two paths and then recombine them to produce interference patterns that depend on their coherence properties.


Basic photon and quantum optics




Photon and quantum optics is an advanced way to describe the propagation of light. It considers light as a stream of particles called photons that have both wave and particle properties. Photons have energy and momentum that depend on their frequency and wavelength according to the Planck-Einstein relation E = hf = hc/λ, where h is Planck's constant. Photons also have spin angular momentum that depends on their polarization state.


One of the most remarkable phenomena in photon and quantum optics is the emission and absorption of photons by atoms and molecules. When an atom or molecule absorbs a photon, it jumps from a lower energy level to a higher energy level. When an atom or molecule emits a photon, it jumps from a higher energy level to a lower energy level. The energy difference between the levels determines the frequency and wavelength of the photon. The emission and absorption of photons can be spontaneous or stimulated depending on whether they occur randomly or in response to an external field.


Another remarkable phenomenon in photon and quantum optics is the amplification and generation of coherent light by lasers. A laser is a device that uses stimulated emission to produce a beam of light that has high intensity, low divergence, and high coherence. A laser consists of three main components: an active medium that provides the atoms or molecules that emit photons; a pumping source that provides the energy to excite the atoms or molecules; and an optical cavity that provides feedback and resonance for the photons. The optical cavity usually has two mirrors, one of which is partially transparent to allow some photons to escape as the laser output.


A third remarkable phenomenon in photon and quantum optics is the manipulation and measurement of quantum states of light. Quantum states of light are superpositions of different numbers of photons with different frequencies, wavelengths, polarizations, phases, and directions. Quantum states of light can be prepared, transformed, and detected using various optical devices such as beam splitters, phase shifters, filters, detectors, etc. Quantum states of light can exhibit non-classical features such as entanglement, squeezing, superposition, interference, complementarity, uncertainty, and no-cloning.


Optical design and instrumentation




Ray tracing and aberrations




Ray tracing is a technique for designing and analyzing optical systems by tracing rays through them using geometric optics principles. Ray tracing can be used to determine the position, size, orientation, and quality of images formed by optical systems. Ray tracing can also be used to optimize the parameters of optical systems such as focal lengths, apertures, distances, etc.


Aberrations are deviations from ideal image formation caused by imperfections in optical systems. Aberrations can be classified into two types: monochromatic aberrations and chromatic aberrations. Monochromatic aberrations are caused by the shape and alignment of optical components and affect all wavelengths of light equally. Chromatic aberrations are caused by the dispersion of light in refractive components and affect different wavelengths of light differently.


Monochromatic aberrations can be further classified into five types: spherical aberration, coma, astigmatism, field curvature, and distortion. Spherical aberration is caused by the difference in focal lengths for rays passing through different parts of a spherical lens or mirror. Coma is caused by the difference in magnification for rays passing through different parts of an off-axis lens or mirror. Astigmatism is caused by the difference in focal lengths for rays passing through different meridians of a lens or mirror. Field curvature is caused by the curvature of the image plane for rays passing through an on-axis lens or mirror. Distortion is caused by the difference in magnification for rays passing through different parts of an image plane.


Chromatic aberrations can be further classified into two types: longitudinal chromatic aberration and lateral chromatic aberration. Longitudinal chromatic aberration is caused by the difference in focal lengths for different wavelengths of light passing through a lens or mirror. Lateral chromatic aberration is caused by the difference in magnification for different wavelengths of light passing through an image plane.


Aberrations can be corrected or minimized by using various methods such as choosing appropriate shapes and materials for optical components; using combinations of lenses or mirrors with opposite signs of aberrations; using aspheric surfaces instead of spherical surfaces; using apertures or stops to limit the range of rays; using coatings or filters to reduce dispersion; etc.


Prisms and refractive optical components




Prisms are transparent objects with flat surfaces that refract light rays. Prisms can be used for various purposes such as dispersion, deviation, inversion, rotation, and splitting of light beams. Prisms can be classified into different types according to their shape and function.


Dispersion prisms are used to separate white light into its constituent colors by exploiting the dependence of refractive index on wavelength. Dispersion prisms have triangular or rectangular shapes and are usually made of glass or plastic. Examples of dispersion prisms are equilateral prisms, which produce a symmetrical spectrum; right-angle prisms, which produce an asymmetrical spectrum; and Littrow prisms, which produce a minimum deviation spectrum.


Deviation prisms are used to change the direction of light rays by a fixed angle without changing their color. Deviation prisms have triangular or trapezoidal shapes and are usually made of glass or plastic. Examples of deviation prisms are wedge prisms, which produce a small deviation; roof prisms, which produce a 90-degree deviation; and Porro prisms, which produce a 180-degree deviation.


Inversion and rotation prisms are used to invert or rotate the orientation of images or polarization states of light rays. Inversion and rotation prisms have pentagonal or hexagonal shapes and are usually made of glass or plastic. Examples of inversion and rotation prisms are Dove prisms, which invert images; Pechan prisms, which rotate images by 180 degrees; and Fresnel rhombs, which rotate the plane of polarization by 90 degrees.


Splitting prisms are used to divide a beam of light into two or more beams with different directions, intensities, or polarizations. Splitting prisms have rectangular or cubic shapes and are usually made of glass or plastic. Examples of splitting prisms are beam splitter cubes, which split a beam into two beams with equal intensities; polarizing beam splitter cubes, which split a beam into two beams with orthogonal polarizations; and Wollaston prisms, which split a beam into two beams with different directions and polarizations.


Refractive optical components are transparent objects that have curved surfaces that refract light rays. Refractive optical components can be used for various purposes such as focusing, collimating, magnifying, imaging, and correcting vision. Refractive optical components can be classified into different types according to their shape and function.


Lenses are refractive optical components that have spherical or aspherical surfaces that converge or diverge light rays. Lenses can be classified into different types according to their shape and function. Examples of lenses are convex lenses, which converge parallel rays to a focal point; concave lenses, which diverge parallel rays from a focal point; cylindrical lenses, which focus or defocus light rays in one direction only; Fresnel lenses, which have thin concentric rings that act as small lenses; gradient-index lenses, which have a variable refractive index that bends light rays continuously; etc.


Prisms are refractive optical components that have flat surfaces that deviate light rays by a fixed angle. Prisms can be classified into different types according to their shape and function. Examples of prisms are dispersion prisms, deviation prisms, inversion and rotation prisms, and splitting prisms.


Reflective optical components




Reflective optical components are opaque objects that have smooth surfaces that reflect light rays. Reflective optical components can be used for various purposes such as reflection, focusing, collimation, scanning, and modulation of light beams. Reflective optical components can be classified into different types according to their shape and function.


Mirrors are reflective optical components that have flat or curved surfaces that reflect light rays. Mirrors can be classified into different types according to their shape and function. Examples of mirrors are plane mirrors, which reflect light rays without changing their direction; spherical mirrors, which reflect light rays to or from a focal point; parabolic mirrors, which reflect parallel rays to a common focus; ellipsoidal mirrors, which reflect rays from one focus to another focus; etc.


Gratings are reflective optical components that have periodic grooves or slits that diffract light rays into different directions according to their wavelength. Gratings can be classified into different types according to their shape and function. Examples of gratings are transmission gratings, which transmit diffracted light rays through the grooves or slits; reflection gratings, which reflect diffracted light rays from the grooves or slits; blazed gratings, which have asymmetric grooves that enhance the efficiency of a particular diffraction order; holographic gratings, which are recorded by interference patterns of coherent light beams; etc.


Examples of scanners are rotating mirrors, which rotate around an axis to scan a beam in a circular or linear motion; galvanometer mirrors, which oscillate around an axis to scan a beam in a sinusoidal or triangular motion; polygon mirrors, which have multiple facets that rotate around an axis to scan a beam in a stepwise motion; etc.


Modulators are reflective optical components that have variable surfaces that change the amplitude, phase, or polarization of light rays by applying external stimuli. Modulators can be classified into different types according to their shape and function. Examples of modulators are acousto-optic modulators, which use sound waves to create periodic variations in the refractive index of a medium that reflect light rays with different frequencies; electro-optic modulators, which use electric fields to create periodic variations in the refractive index of a medium that reflect light rays with different phases; magneto-optic modulators, which use magnetic fields to create periodic variations in the refractive index of a medium that reflect light rays with different polarizations; etc.


Diffractive elements




Diffractive elements are optical components that have microstructures that diffract light rays into different directions according to their wavelength and angle of incidence. Diffractive elements can be used for various purposes such as diffraction, modulation, filtering, and reconstruction of light waves. Diffractive elements can be classified into different types according to their shape and function.


Gratings are diffractive elements that have periodic grooves or slits that diffract light rays into different directions according to their wavelength and angle of incidence. Gratings can be classified into different types according to their shape and function. Examples of gratings are transmission gratings, reflection gratings, blazed gratings, holographic gratings, etc.


Holograms are diffractive elements that are recorded by interference patterns of coherent light beams and can reconstruct the original light beams when illuminated by a reference beam. Holograms can be classified into different types according to their shape and function. Examples of holograms are amplitude holograms, which modulate the amplitude of the reconstructed beam; phase holograms, which modulate the phase of the reconstructed beam; volume holograms, which are recorded in thick media and have high diffraction efficiency; surface holograms, which are recorded in thin media and have low diffraction efficiency; etc.


Zone plates are diffractive elements that have concentric rings that act as small lenses and focus light rays to a common point. Zone plates can be classified into different types according to their shape and function. Examples of zone plates are Fresnel zone plates, which have equal-width rings and focus light rays with alternating phases; phase zone plates, which have variable-width rings and focus light rays with constant phase; binary zone plates, which have two-level rings and approximate phase zone plat


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