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.
Fourier transform spectroscopy measures an interferogram as a function of optical path length difference. Its Fourier transform recovers the spectrum. An imaging implementation obtains an interferogram at every detector pixel, but a scanned cube is not simultaneous at all wavelengths.
A spectrograph records the optical spectrum dispersed by an instrument. Its spectral resolving power describes which nearby wavelengths it separates.
An integral field spectrograph records a spectrum for each of many spatial elements across a two-dimensional field, producing a spectral data cube. Field reformatters include lenslet arrays, optical fibers and image slicers.
An image slicer divides a two-dimensional image into narrow strips and optically rearranges them into a long pseudo-slit. A spectrograph then disperses each strip while preserving its position along the slit.
A spectral data cube stores intensity with two spatial coordinates and one spectral coordinate. The third coordinate is wavelength, not an additional spatial dimension.
Spectral resolving power is , where is the wavelength separation just resolved under the specified instrumental and source conditions.
A cross-dispersed echelle spectrograph uses an echelle grating for strong dispersion and a cross-disperser in the perpendicular direction to separate overlapping diffraction orders. It records many orders simultaneously in an echellogram.
A cross-disperser is a second dispersing element, often an optical prism or diffraction grating, oriented to separate optical spectra perpendicular to their principal dispersion direction.
An echellogram is the two-dimensional detector pattern of separated diffraction orders from a cross-dispersed echelle spectrograph.
A multi-object spectrograph records optical spectra of many selected objects simultaneously. The main designs are multi-slit spectrographs and fiber-fed spectrographs. The ESO instrumentation overview describes both arrangements.
A multi-slit spectrograph puts separate slits at target positions in the focal plane. Each slit transmits the target plus nearby sky; dispersion places its spatially resolved optical spectrum on the detector.
A fiber-fed spectrograph places optical fibers on selected targets and reformats their output into a common entrance slit. Dedicated sky fibers sample sky brightness. Fiber coupling, transmission, and output beam spreading affect throughput and resolution.
Focal-ratio degradation is the broadening of the output angular cone of an optical fiber relative to its input cone. It can make a spectrograph collimator lose transmitted light or require larger optics. Stress, bends, and mode mixing in the fiber can contribute.
Adaptive optics measures changing wavefront errors and corrects them using a deformable mirror. A wavefront sensor supplies measurements to a fast feedback controller; a guide star provides the reference. It improves astronomical seeing toward diffraction-limited resolution.
A deformable mirror changes its optical surface using an array of actuators. For reflection near normal incidence, surface displacement changes optical path length by twice that displacement.
With actuators across diameter , the projected pitch is approximately . The Nyquist spatial frequency is , so the largest correctable angular speckle displacement along an actuator row is . A square actuator array gives a square ideal spatial-frequency region. See the Bordé–Traub wavefront-control derivation.
A wavefront sensor measures information from which a wavefront error can be reconstructed. For example, a Shack–Hartmann wavefront sensor measures local wavefront slopes using lenslets.
A guide star provides photons for a wavefront sensor. Its brightness and angular separation from the target limit adaptive optics sky coverage.
A laser guide star is an artificial atmospheric beacon for adaptive optics. It improves sky coverage but samples a finite-distance cone rather than the full incoming stellar beam. Conventional systems still require a natural reference for absolute image motion.
Adaptive-optics sky coverage is the fraction of targets for which a sufficiently bright nearby guide star allows useful correction. Anisoplanatism limits the offset, and photon statistics limit the sensing speed. A laser guide star improves coverage but does not remove all low-order and finite-distance limitations.
A photodiode is a semiconductor diode that converts absorbed photons into electrical carriers. A reverse-biased detector separates the carriers and collects charge; its quantum efficiency and dark current determine sensitivity.
Dark current is charge produced in a detector without illumination, often by thermally excited carriers. Cooling reduces it, although cooling requirements also depend on the wavelength range and thermal background.
A hybrid infrared detector bonds a photosensitive semiconductor array to a separate silicon readout circuit. Each pixel has its own electrical connection; charge need not be transferred across the array as in a charge-coupled device.
A detector reference pixel has no illuminated photosensitive connection and samples readout offsets. Reference-pixel subtraction can suppress common electronic drifts but does not measure the sky background or all pixel-dependent errors.
A nondestructive read samples a pixel’s accumulated signal without resetting it. Repeated samples permit Fowler sampling and up-the-ramp sampling, and can help identify saturation and cosmic-ray charge steps.
Up-the-ramp sampling measures accumulated charge repeatedly through an exposure and estimates flux from its slope. Cosmic-ray steps, saturation and nonlinearity must be identified or modelled.
Fowler sampling averages several nondestructive reads near the start and end of an integration and differences the two averages. For independent equal read noise, averaging lowers the read-noise variance; correlated noise limits the improvement.
The HAWAII-2RG architecture has a grid with an 18-micrometre pitch. For infrared work its readout circuit is normally bonded to a mercury cadmium telluride absorber. Reference pixels track electronic offsets and an independently addressed guide window can be read alongside the science array.
Background subtraction estimates a source contribution by removing a sky or detector-background measurement. An independent background estimate adds photon shot noise; a mismatched background adds bias of an estimator.
Let and be independent. Then has source-estimation bias and variance . Its accuracy ratio tends to when , and grows. This uses mean squared error, not variance alone, and assumes a fixed uncorrected mismatch.
Read noise is uncertainty added by measuring detector charge or voltage. It is often expressed as an equivalent number of input electrons per pixel per read.
Independent photon arrivals have a Poisson distribution: a mean count has variance and standard deviation . Subtraction of independent counting measurements adds their variances.
Quantum efficiency is the mean fraction of incident photons producing collected signal carriers. Noise-equivalent quantum efficiency can be lower when amplification adds fluctuations; this does not imply a corresponding loss of actual photon absorption.
A charge-coupled device stores photoelectrons in potential wells and transfers the charge through clocked stages to an output amplifier. The transfer differs from independently addressed pixels in a hybrid infrared detector.
An electron-multiplying CCD adds a high-field multiplication register before the output amplifier. Impact ionization generates a large mean gain, reducing input-referred read noise but adding multiplication excess noise.
Random multiplication increases the noise relative to deterministic gain. If the output from one input electron has mean and variance , a Poisson distribution of input electrons with mean produces output variance , by the law of total variance. The high-gain analog-mode excess-noise factor is .
An energetic charge carrier creates an additional electron–hole pair. In a multiplication register this is stochastic, so the output charge fluctuates even when the input electron number is fixed.
For source counts and independent background counts with Poisson distributions, the ideal counting standard deviation is , so the signal-to-noise ratio is . Detector noise and uncertainty in the estimated background add further variance. A larger sky aperture raises , while better throughput raises ; both affect the faintness limit of a spectrograph.
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