Optics studies light, its propagation, and instruments for forming images and measuring optical spectra.
Light is electromagnetic radiation in the visible range; optics also studies neighboring infrared and ultraviolet radiation.
An optical spectrum describes the distribution of optical radiation over wavelength or frequency. A spectrograph records it by separating wavelengths, while a photometric passband integrates a chosen part.
A wavefront is a surface of constant phase function. A plane wave has planar wavefronts; variations in refractive index distort them.
The optical path length along a ray is the integral of its refractive index over geometric length. A difference in optical path length produces a phase difference , where is the vacuum wavelength.
A wavefront error is the difference in optical path length from a reference wavefront, often an ideal plane or sphere. Its root mean square should specify the illuminated pupil and which modes, such as constant phase or image displacement, have been removed.
Wave interference occurs when amplitudes add coherently. Equal phases give constructive interference; opposite phases can cancel.
A diffraction grating is a periodic optical structure that directs different wavelengths into different angles through wave interference.
A diffraction order labels a constructive interference maximum by the integer number of wavelengths in the path difference between adjacent grating elements.
For a reflection diffraction grating with both ray directions measured on the same side of its normal, adjacent grooves have path difference . Constructive interference requires this to be an integer multiple . Signed-angle conventions can turn the sum into a difference; the physical path difference is unchanged.
At fixed incidence angle, differentiating the grating equation gives . A camera with focal length therefore has local focal-plane dispersion near its optical axis. With coordinate , the full derivative is .
At fixed wavelength, the grating equation gives . Thus an incident angular width is magnified by in the dispersion direction. Including the ratio of camera and collimator focal lengths gives the projected slit width. The ESO B&C operating manual, Appendix A explicitly includes this anamorphic factor.
A slit of width at the focus of a collimator subtends . Its projected width is . Dividing this width by the grating dispersion gives . Thus the spectral resolving power is . Omitting the anamorphic factor gives a denominator instead; these agree in the Littrow configuration.
In the Littrow configuration the selected diffracted ray retraces the incident ray, so and the grating equation becomes .
An echelle grating works in high diffraction orders. A separate cross-disperser separates their overlapping optical spectra on a two-dimensional detector.
The free spectral range is the wavelength or frequency spacing between adjacent orders or resonances of an optical instrument. It identifies when different orders can overlap.
At fixed incident and central outgoing angles, the grating equation gives . Adjacent central wavelengths are separated byThis is the usual adjacent-order free spectral range. A detector width of approximately , where is the grating dispersion, covers one such interval.
The point spread function is the image of an unresolved point source. It describes blurring from diffraction, optical aberrations, and astronomical seeing.
A diffraction-limited system has imaging performance set primarily by diffraction rather than by optical aberrations.
For a circular illuminated aperture of diameter , the characteristic angular diffraction scale is . The first zero of the ideal intensity pattern lies at approximately .
The Strehl ratio compares the peak of an observed point spread function with the ideal diffraction-limited system peak for the same pupil and total flux. It measures how strongly wavefront errors redistribute light away from the central peak.
For small residual phase errors, , where . The variance is taken after removing irrelevant constant phase. This approximation to the Strehl ratio is most useful near the diffraction limit of a telescope.
A speckle pattern is a granular intensity pattern from coherent wave interference. In stellar imaging, residual wavefront errors produce speckles around the central point spread function.
For a small sinusoidal optical path length error , expand its phase factor to first order. The two exponential harmonics each have field amplitude relative to the unperturbed field, so each speckle has contrast . Its angular displacement is . Here is optical path error, not physical mirror displacement; a reflecting mirror introduces twice its surface displacement in the near-normal limit.
Geometrical optics describes propagation by rays and Snell's law, neglecting diffraction on scales much larger than the wavelength.
An optical axis is the reference line through the centres of rotational symmetry of an optical system. A folded system can have successive axis segments related by reflection.
The incident ray, reflected ray and surface normal lie in one plane; incidence and reflection angles measured from the normal are equal. For a unit incident direction and unit normal , reflection gives .
In a stationary reciprocal optical medium, reversing the direction of a ray produces a ray along the same path. Snell's law is unchanged when its two media and ray directions are interchanged.
The focal length measures the focusing power of an optical lens or mirror. In a thin converging lens, parallel paraxial rays meet a distance beyond the lens.
A thin lens is modeled with negligible thickness relative to its object and image distances. For real conjugate distances , it obeys , with focal length .
For fixed object-screen separation , a converging thin lens focuses at two positions separated by . Thus . The method finds focal length without needing to locate a thin lens's optical center precisely.
For a thin optical lens in air, surface radii and refractive index give . The radii carry the usual signed curvature convention.
The five Seidel aberrations of a rotationally symmetric optical system are spherical aberration, coma, astigmatism, field curvature, and optical distortion.
Spherical aberration makes rays at different pupil radii focus at different axial positions. Its primary pupil dependence is quartic; the balanced Zernike spherical mode also contains quadratic and constant terms to remove defocus and piston.
Chromatic aberration is wavelength-dependent imaging caused by optical dispersion. Axial chromatic aberration changes focal length with wavelength; lateral chromatic aberration changes image scale.
An achromatic lens combines elements with different Abbe numbers to make two specified wavelengths share a focal length. Other wavelengths can retain secondary chromatic error.
For two thin lenses in contact, achromatism requires , where are their Abbe numbers. With total power , the component powers are and . A positive doublet using a larger- crown glass element and smaller- flint glass element therefore uses a converging crown and a diverging flint.
Optical dispersion is the dependence of refractive index or phase velocity on frequency. It gives an optical prism wavelength-dependent deviation and causes chromatic aberration.
The Abbe number compares refractive strength with visible optical dispersion. The traditional reference lines are near nm, respectively. A large means weak relative dispersion.
An Abbe diagram plots refractive index against Abbe number to show available optical glass families. Many diagrams put increasing to the left. Ordinary crown glasses have larger than ordinary flint glasses, while modern compositions occupy a broader region.
For a homogeneous optical prism in air, with apex angle and refractive index , minimum deviation occurs at the symmetric ray path. Then both internal angles are and both external angles are , so Snell's law givesMeasuring the deviation therefore determines the refractive index at the chosen wavelength.
Atmospheric extinction attenuates starlight through absorption and scattering. It depends on wavelength and path length, and is described by an optical depth or an extinction coefficient in astronomical magnitudes per airmass.
An atmospheric window is a wavelength interval of relatively high atmospheric transmission. Infrared photometric bands are largely chosen to lie in such windows.
Atmospheric refraction bends a ray through the vertical refractive index gradient, shifting its apparent direction. Because of optical dispersion, the shift varies with wavelength.
Atmospheric dispersion is the wavelength dependence of atmospheric refraction. It spreads a broadband stellar image along the vertical direction toward the zenith.
Atmospheric turbulence produces changing refractive index fluctuations. These alter optical path lengths, distorting wavefronts and causing astronomical seeing and atmospheric scintillation.
Astronomical seeing is the atmospheric blurring of a stellar image, conventionally expressed as the angular full width at half maximum of its long-exposure point spread function, usually in arcseconds. For a large aperture in the ideal Kolmogorov model, it is approximately radians, with Fried parameter .
The Fried parameter is the atmospheric coherence length for optical phase. In the standard inertial-range model, the phase structure function is . For unchanged atmospheric turbulence, . The NACO manual, section 3.1 describes this scaling and its role in adaptive correction.
Anisoplanatism is the loss of correlation between wavefront errors along different viewing directions. Correcting a guide star therefore leaves a larger residual for a sufficiently separated target.
The isoplanatic angle is the characteristic angular separation over which a single-direction atmospheric correction remains useful. It depends on the altitude distribution of atmospheric turbulence as well as on wavelength.
Atmospheric scintillation is the fluctuation of received stellar intensity produced by propagation through atmospheric turbulence. A phase-only deformable mirror does not generally remove these amplitude fluctuations.
A focal plane is a plane in which an optical system forms images of distant directions. Aberrations can make the best-focus surface curved; a flat detector may then require a field-flattening optical element.
High-contrast imaging seeks faint objects near a bright source. Residual point spread functions and speckle patterns can dominate photon shot noise; angular differential imaging and simultaneous spectral differential imaging use source motion or spectral diversity to distinguish them.
A companion or extended source contributes to the stellar reference used in differential imaging. Subtracting that reference removes part of the desired signal and distorts its shape, photometry or astrometry. Artificial-source injection and forward modelling can estimate the throughput loss.
Simultaneous spectral differential imaging compares images in nearby bands, rescaled so stellar speckle patterns approximately coincide. A companion has a different positional or spectral response. Simultaneity reduces temporal variation but does not remove chromatic and non-common-path errors.
Angular differential imaging keeps the instrument pupil fixed while the sky rotates. A stellar reference point spread function is subtracted, then the residuals are derotated and combined. Insufficient rotation and imperfect reference selection cause differential-imaging self-subtraction.
A Fabry–Pérot interferometer uses multiple reflections between two nearly parallel surfaces. Its transmission peaks select narrow wavelength intervals; scanning the spacing or incidence angle can build an imaging spectral cube.
A lenslet array is a set of small lenses that divides a field or a pupil into many optical samples. In an integral field spectrograph each field sample generates a microspectrum or feeds an optical fiber.
The field of view is the angular region imaged or otherwise sampled by an instrument in one pointing.
The Giant Magellan Telescope design combines seven 8.4-metre primary mirrors, including off-axis segments. It was a planned extremely large telescope in the 2018 examination context.
The Thirty Meter Telescope design uses a thirty-metre primary with 492 hexagonal segments. It was among the planned extremely large telescopes in the 2018 examination context.
The Large Binocular Telescope has two 8.4-metre primary mirrors with lightweight honeycomb structures.
A segmented mirror assembles smaller mirrors into a large aperture. Sensors and actuators maintain position and figure; coherent imaging additionally requires mirror segment phasing.
Phasing adjusts relative piston and tilt so adjacent segments form a continuous optical wavefront. Near normal reflection a surface piston changes optical path length by twice that displacement.
A lightweight mirror uses a thin optical face backed by ribs or a honeycomb structure. The deep backing provides rigidity with less mass than a solid disk and facilitates thermal equilibration.
Active optics uses controlled support forces and alignment to correct slow changes in telescope figure, particularly gravity and thermal deformation. It permits thin large primary mirrors. Adaptive optics instead corrects rapid atmospheric turbulence.
A Schmidt camera combines a spherical primary mirror with a thin aspheric corrector at the mirror’s centre of curvature. The corrector compensates spherical aberration; the symmetric stop location gives a wide useful field. The native focal surface is curved and lies inside the instrument.
A reflecting telescope forms an image using curved mirrors. Its primary and secondary shapes, spacing and aperture stop determine its optical aberrations, access to the focus, and obstruction.
A Gregorian telescope has a concave parabolic primary and a concave ellipsoidal secondary beyond the primary focus. Light crosses the intermediate focus, reaches the secondary, and returns through the primary to the final focus. The ellipsoid’s two foci are the intermediate and final focus.
A Cassegrain arrangement places a secondary before the primary focus and returns light through a hole in the primary to a focus behind it. In the classical design the primary is parabolic and the secondary convex hyperbolic. The compact arrangement has a long effective focal length; its classical implementation retains off-axis coma.
A Ritchey–Chrétien telescope has hyperbolic primary and secondary mirrors chosen to cancel third-order spherical aberration and coma. It retains astigmatism and field curvature; wide-field instruments may require additional correction.
A classical Cassegrain reflector uses a concave parabolic primary and a convex hyperbolic secondary before the prime focus. The secondary returns the converging beam through a hole in the primary. It corrects on-axis spherical aberration but retains off-axis coma.
A Newtonian telescope uses a concave parabolic primary and a flat diagonal secondary to send the converging beam to a side focus. The primary avoids on-axis spherical aberration, but has off-axis coma.
The angular diffraction-limited resolution of a telescope scales as , with wavelength and illuminated diameter . Larger diameter resolves smaller angular structure, while longer wavelength makes atmospheric phase correction easier.
A collimator turns light from a source near its focus into a nearly parallel beam. A slit of width produces an angular width approximately , where is the focal length.
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Optics is the branch of physics that focuses on the study of light and its interactions with matter. It encompasses the behavior of light in various mediums, including reflection, refraction, diffraction, and polarization. There are two main branches of optics: 1. **Geometric Optics**: This branch deals with the approximation of light as rays. It studies how light travels in straight lines, how it interacts with lenses and mirrors, and how images are formed by optical systems.
