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75-472: Typical shutter speeds for a star trail range from 15 minutes to several hours, requiring a " Bulb " setting on the camera to open the shutter for a period longer than usual. However, a more practiced technique is to blend a number of frames together to create the final star trail image. Star trails have been used by professional astronomers to measure the quality of observing locations for major telescopes . Star trail photographs are captured by placing

150-449: A ( ρ ) {\displaystyle D_{\phi _{a}}\left({\mathbf {\rho } }\right)} is the atmospherically induced variance between the phase at two parts of the wavefront separated by a distance ρ {\displaystyle {\boldsymbol {\rho }}} in the aperture plane, and ⟨ ⋅ ⟩ {\displaystyle \langle \cdot \rangle } represents

225-550: A ( r ) {\displaystyle \phi _{a}\left(\mathbf {r} \right)} describe the effect of the Earth's atmosphere, and the timescales for any changes in these functions will be set by the speed of refractive index fluctuations in the atmosphere. A description of the nature of the wavefront perturbations introduced by the atmosphere is provided by the Kolmogorov model developed by Tatarski, based partly on

300-413: A ( r ) {\displaystyle \phi _{a}\left(\mathbf {r} \right)} , but any amplitude fluctuations are only brought about as a second-order effect while the perturbed wavefronts propagate from the perturbing atmospheric layer to the telescope. For all reasonable models of the Earth's atmosphere at optical and infrared wavelengths the instantaneous imaging performance is dominated by

375-480: A ( r ) e i ϕ a ( r ) ) ψ 0 ( r ) {\displaystyle \psi _{p}\left(\mathbf {r} \right)=\left(\chi _{a}\left(\mathbf {r} \right)e^{i\phi _{a}\left(\mathbf {r} \right)}\right)\psi _{0}\left(\mathbf {r} \right)} where χ a ( r ) {\displaystyle \chi _{a}\left(\mathbf {r} \right)} represents

450-469: A ( r ) {\displaystyle \phi _{a}(\mathbf {r} )} is the optical phase error introduced by atmospheric turbulence, R (k) is a two-dimensional square array of independent random complex numbers which have a Gaussian distribution about zero and white noise spectrum, K (k) is the (real) Fourier amplitude expected from the Kolmogorov (or Von Karman) spectrum, Re[] represents taking

525-419: A ( r ) = Re ⁡ [ FT [ ( R ( k ) ⊗ I ( k ) ) K ( k ) ] ] {\displaystyle \phi _{a}(\mathbf {r} )=\operatorname {Re} [{\mbox{FT}}[(R(\mathbf {k} )\otimes I(\mathbf {k} ))K(\mathbf {k} )]]} where I ( k ) is a two-dimensional array which represents the spectrum of intermittency, with

600-505: A 35 mm camera with a 50 mm normal lens , the closest shutter speed is 1 ⁄ 60  s (closest to "50"), while for a 200 mm lens it is recommended not to choose shutter speeds below 1 ⁄ 200  s. This rule can be augmented with knowledge of the intended application for the photograph, an image intended for significant enlargement and closeup viewing would require faster shutter speeds to avoid obvious blur. Through practice and special techniques such as bracing

675-555: A battery to open and close the shutter have an advantage over more modern film and digital cameras that rely on battery power. On these cameras, the Bulb , or B, exposure setting keeps the shutter open. Another problem that digital cameras encounter is an increase in electronic noise with increasing exposure time. However, this can be avoided through the use of shorter exposure times that are then stacked in post production software. This avoids possible heat build up or digital noise caused from

750-405: A camera on a tripod , pointing the lens toward the night sky , and allowing the shutter to stay open for a long period of time. Star trails are considered relatively easy for amateur astrophotographers to create. Photographers generally make these images by using a DSLR or Mirrorless camera with its lens focus set to infinity. A cable release or intervalometer allows the photographer to hold

825-769: A commonly used definition for r 0 {\displaystyle r_{0}} , a parameter frequently used to describe the atmospheric conditions at astronomical observatories. r 0 {\displaystyle r_{0}} can be determined from a measured C N profile (described below) as follows: r 0 = ( 16.7 λ − 2 ( cos ⁡ γ ) − 1 ∫ 0 ∞ C N 2 ( h ) d h ) − 3 / 5 {\displaystyle r_{0}=\left(16.7\lambda ^{-2}(\cos \gamma )^{-1}\int _{0}^{\infty }C_{N}^{2}(h)dh\right)^{-3/5}} where

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900-407: A filled disc called the "seeing disc". The diameter of the seeing disk, most often defined as the full width at half maximum (FWHM), is a measure of the astronomical seeing conditions. It follows from this definition that seeing is always a variable quantity, different from place to place, from night to night, and even variable on a scale of minutes. Astronomers often talk about "good" nights with

975-475: A low average seeing disc diameter, and "bad" nights where the seeing diameter was so high that all observations were worthless. The FWHM of the seeing disc (or just "seeing") is usually measured in arcseconds , abbreviated with the symbol (″). A 1.0″ seeing is a good one for average astronomical sites. The seeing of an urban environment is usually much worse. Good seeing nights tend to be clear, cold nights without wind gusts. Warm air rises ( convection ), degrading

1050-623: A mechanical rotating shutter . The shutter rotation is synchronized with film being pulled through the gate, hence shutter speed is a function of the frame rate and shutter angle . Where E = shutter speed (reciprocal of exposure time in seconds), F = frames per second, and S = shutter angle: With a traditional shutter angle of 180°, film is exposed for 1 ⁄ 48 second at 24 frame/s. To avoid effect of light interference when shooting under artificial lights or when shooting television screens and computer monitors, 1 ⁄ 50  s (172.8°) or 1 ⁄ 60  s (144°) shutter

1125-640: A moving subject for effect. Short exposure times are sometimes called "fast", and long exposure times "slow". Adjustments to the aperture need to be compensated by changes of the shutter speed to keep the same (right) exposure. In early days of photography, available shutter speeds were not standardized, though a typical sequence might have been 1 ⁄ 10  s, 1 ⁄ 25  s, 1 ⁄ 50  s, 1 ⁄ 100  s, 1 ⁄ 200  s and 1 ⁄ 500  s; neither were apertures or film sensitivity (at least 3 different national standards existed). Soon this problem resulted in

1200-434: A shooting mode used in cameras. It allows the photographer to choose a shutter speed setting and allow the camera to decide the correct aperture. This is sometimes referred to as Shutter Speed Priority Auto Exposure , or TV (time value on Canon cameras) mode, S mode on Nikons and most other brands. Shutter speed is one of several methods used to control the amount of light recorded by the camera's digital sensor or film. It

1275-539: A single long exposure. American astronaut Don Pettit recorded star trails with a digital camera from the International Space Station in Earth orbit between April and June, 2012. Pettit described his technique as follows: "My star trail images are made by taking a time exposure of about 10 to 15 minutes. However, with modern digital cameras, 30 seconds is about the longest exposure possible, due to electronic detector noise effectively snowing out

1350-412: A solution consisting in the adoption of a standardized way of choosing aperture so that each major step exactly doubled or halved the amount of light entering the camera ( f /2.8 , f /4 , f /5.6 , f /8 , f /11 , f /16 , etc.), a standardized 2:1 scale was adopted for shutter speed so that opening one aperture stop and reducing the amount of time of the shutter speed by one step resulted in

1425-409: A telescope. The perturbed wavefront ψ p {\displaystyle \psi _{p}} may be related at any given instant to the original planar wavefront ψ 0 ( r ) {\displaystyle \psi _{0}\left(\mathbf {r} \right)} in the following way: ψ p ( r ) = ( χ

1500-410: Is 10–20 cm at visible wavelengths under the best conditions) and this limits the resolution of telescopes to be about the same as given by a space-based 10–20 cm telescope. The distortion changes at a high rate, typically more frequently than 100 times a second. In a typical astronomical image of a star with an exposure time of seconds or even minutes, the different distortions average out as

1575-413: Is a commonly used measurement of the astronomical seeing at observatories. At visible wavelengths, r 0 {\displaystyle r_{0}} varies from 20 cm at the best locations to 5 cm at typical sea-level sites. In reality, the pattern of blobs ( speckles ) in the images changes very rapidly, so that long-exposure photographs would just show a single large blurred blob in

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1650-419: Is also used to manipulate the visual effects of the final image. Slower shutter speeds are often selected to suggest the movement of an object in a still photograph. Excessively fast shutter speeds can cause a moving subject to appear unnaturally frozen. For instance, a running person may be caught with both feet in the air with all indication of movement lost in the frozen moment. When a slower shutter speed

1725-549: Is assumed to occur on slow timescales, then the timescale t 0 is simply proportional to r 0 divided by the mean wind speed. The refractive index fluctuations caused by Gaussian random turbulence can be simulated using the following algorithm: ϕ a ( r ) = Re [ FT [ R ( k ) K ( k ) ] ] {\displaystyle \phi _{a}(\mathbf {r} )={\mbox{Re}}[{\mbox{FT}}[R(\mathbf {k} )K(\mathbf {k} )]]} where ϕ

1800-455: Is often used. Electronic video cameras do not have mechanical shutters and allow setting shutter speed directly in time units. Professional video cameras often allow selecting shutter speed in terms of shutter angle instead of time units, especially those that are capable of overcranking or undercranking . Astronomical seeing In astronomy , seeing is the degradation of the image of an astronomical object due to turbulence in

1875-410: Is selected, a longer time passes from the moment the shutter opens till the moment it closes. More time is available for movement in the subject to be recorded by the camera as a blur. A slightly slower shutter speed will allow the photographer to introduce an element of blur, either in the subject, where, in our example, the feet, which are the fastest moving element in the frame, might be blurred while

1950-462: Is the Dirac delta function . A more thorough description of the astronomical seeing at an observatory is given by producing a profile of the turbulence strength as a function of altitude, called a C n 2 {\displaystyle C_{n}^{2}} profile. C n 2 {\displaystyle C_{n}^{2}} profiles are generally performed when deciding on

2025-401: Is the complex field at position r {\displaystyle \mathbf {r} } and time t {\displaystyle t} , with real and imaginary parts corresponding to the electric and magnetic field components, ϕ u {\displaystyle \phi _{u}} represents a phase offset, ν {\displaystyle \nu } is

2100-421: Is the length of time that the film or digital sensor inside the camera is exposed to light (that is, when the camera 's shutter is open) when taking a photograph. The amount of light that reaches the film or image sensor is proportional to the exposure time. 1 ⁄ 500 of a second will let half as much light in as 1 ⁄ 250 . The camera's shutter speed, the lens's aperture or f-stop , and

2175-693: Is treated as an oscillation in a field ψ {\displaystyle \psi } . For monochromatic plane waves arriving from a distant point source with wave-vector k {\displaystyle \mathbf {k} } : ψ 0 ( r , t ) = A u e i ( ϕ u + 2 π ν t + k ⋅ r ) {\displaystyle \psi _{0}\left(\mathbf {r} ,t\right)=A_{u}e^{i\left(\phi _{u}+2\pi \nu t+\mathbf {k} \cdot \mathbf {r} \right)}} where ψ 0 {\displaystyle \psi _{0}}

2250-553: The C n 2 {\displaystyle C_{n}^{2}} profile. Some are empirical fits from measured data and others attempt to incorporate elements of theory. One common model for continental land masses is known as Hufnagel-Valley after two workers in this subject. The first answer to this problem was speckle imaging , which allowed bright objects with simple morphology to be observed with diffraction-limited angular resolution. Later came space telescopes , such as NASA 's Hubble Space Telescope , working outside

2325-408: The atmosphere of Earth that may become visible as blurring, twinkling or variable distortion . The origin of this effect is rapidly changing variations of the optical refractive index along the light path from the object to the detector. Seeing is a major limitation to the angular resolution in astronomical observations with telescopes that would otherwise be limited through diffraction by

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2400-438: The strength of the phase fluctuations as it corresponds to the diameter of a circular telescope aperture at which atmospheric phase perturbations begin to seriously limit the image resolution. Typical r 0 {\displaystyle r_{0}} values for I band (900 nm wavelength) observations at good sites are 20–40 cm. r 0 {\displaystyle r_{0}} also corresponds to

2475-576: The 1990s, many telescopes have developed adaptive optics systems that partially solve the seeing problem. The best systems so far built, such as SPHERE on the ESO VLT and GPI on the Gemini telescope, achieve a Strehl ratio of 90% at a wavelength of 2.2 micrometers, but only within a very small region of the sky at a time. A wider field of view can be obtained by using multiple deformable mirrors conjugated to several atmospheric heights and measuring

2550-436: The aperture diameter for which the variance σ 2 {\displaystyle \sigma ^{2}} of the wavefront phase averaged over the aperture comes approximately to unity: σ 2 = 1.0299 ( d r 0 ) 5 / 3 {\displaystyle \sigma ^{2}=1.0299\left({\frac {d}{r_{0}}}\right)^{5/3}} This equation represents

2625-638: The atmosphere and thus not having any seeing problems and allowing observations of faint targets for the first time (although with poorer resolution than speckle observations of bright sources from ground-based telescopes because of Hubble's smaller telescope diameter). The highest resolution visible and infrared images currently come from imaging optical interferometers such as the Navy Prototype Optical Interferometer or Cambridge Optical Aperture Synthesis Telescope , but those can only be used on very bright stars. Starting in

2700-586: The atmosphere. The parameters r 0 and t 0 vary with the wavelength used for the astronomical imaging, allowing slightly higher resolution imaging at longer wavelengths using large telescopes. The seeing parameter r 0 is often known as the Fried parameter , named after David L. Fried . The atmospheric time constant t 0 is often referred to as the Greenwood time constant , after Darryl Greenwood . Mathematical models can give an accurate model of

2775-416: The belief that there were canals on Mars . In viewing a bright object such as Mars, occasionally a still patch of air will come in front of the planet, resulting in a brief moment of clarity. Before the use of charge-coupled devices , there was no way of recording the image of the planet in the brief moment other than having the observer remember the image and draw it later. This had the effect of having

2850-440: The camera southward. In this case, the arc streaks are centered on the south celestial pole (near Sigma Octantis ). Aiming the camera eastward or westward shows straight streaks on the celestial equator , which is tilted at angle with respect to the horizon . The angular measure of this tilt depends on the photographer's latitude ( L ), and is equal to 90° − L . Star trail photographs can be used by astronomers to determine

2925-404: The camera, arms, or body to minimize camera movement, using a monopod or a tripod, slower shutter speeds can be used without blur. If a shutter speed is too slow for hand holding, a camera support, usually a tripod , must be used. Image stabilization on digital cameras or lenses can often permit the use of shutter speeds 3–4 stops slower (exposures 8–16 times longer). Shutter priority refers to

3000-404: The center for each telescope diameter. The diameter (FWHM) of the large blurred blob in long-exposure images is called the seeing disc diameter, and is independent of the telescope diameter used (as long as adaptive optics correction is not applied). It is first useful to give a brief overview of the basic theory of optical propagation through the atmosphere. In the standard classical theory, light

3075-400: The changes in the dancing speckle patterns is substantially lower. There are three common descriptions of the astronomical seeing conditions at an observatory: These are described in the sub-sections below: Without an atmosphere, a small star would have an apparent size, an " Airy disk ", in a telescope image determined by diffraction and would be inversely proportional to the diameter of

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3150-544: The effects of astronomical seeing on images taken through ground-based telescopes. Three simulated short-exposure images are shown at the right through three different telescope diameters (as negative images to highlight the fainter features more clearly—a common astronomical convention). The telescope diameters are quoted in terms of the Fried parameter r 0 {\displaystyle r_{0}} (defined below). r 0 {\displaystyle r_{0}}

3225-525: The effects of the atmosphere will be negligible, and hence by recording large numbers of images in real-time, a 'lucky' excellent image can be picked out. This happens more often when the number of r0-size patches over the telescope pupil is not too large, and the technique consequently breaks down for very large telescopes. It can nonetheless outperform adaptive optics in some cases and is accessible to amateurs. It does require very much longer observation times than adaptive optics for imaging faint targets, and

3300-682: The ensemble average. For the Gaussian random approximation, the structure function of Tatarski (1961) can be described in terms of a single parameter r 0 {\displaystyle r_{0}} : D ϕ a ( ρ ) = 6.88 ( | ρ | r 0 ) 5 / 3 {\displaystyle D_{\phi _{a}}\left({\mathbf {\rho } }\right)=6.88\left({\frac {\left|\mathbf {\rho } \right|}{r_{0}}}\right)^{5/3}} r 0 {\displaystyle r_{0}} indicates

3375-492: The exposure time doubles the amount of light (subtracts 1 EV). Reducing the aperture size at multiples of one over the square root of two lets half as much light into the camera, usually at a predefined scale of f /1 , f /1.4 , f /2 , f /2.8 , f /4 , f /5.6 , f /8 , f /11 , f /16 , f /22 , and so on. For example, f /8 lets four times more light into the camera as f /16 does. A shutter speed of 1 ⁄ 50  s with an f /4 aperture gives

3450-453: The film or sensor sensitivity to light. This will achieve a good exposure when all the details of the scene are legible on the photograph. Too much light let into the camera results in an overly pale image (or "over-exposure") while too little light will result in an overly dark image (or "under-exposure"). Multiple combinations of shutter speed and f-number can give the same exposure value (E.V.). According to exposure value formula, doubling

3525-417: The fractional change in wavefront amplitude and ϕ a ( r ) {\displaystyle \phi _{a}\left(\mathbf {r} \right)} is the change in wavefront phase introduced by the atmosphere. It is important to emphasise that χ a ( r ) {\displaystyle \chi _{a}\left(\mathbf {r} \right)} and ϕ

3600-442: The frequency of the light determined by ν = 1 π c | k | {\textstyle \nu ={\frac {1}{\pi }}c\left|\mathbf {k} \right|} , and A u {\displaystyle A_{u}} is the amplitude of the light. The photon flux in this case is proportional to the square of the amplitude A u {\displaystyle A_{u}} , and

3675-565: The identical exposure. The agreed standards for shutter speeds are: 1 ⁄ 1000  s; 1 ⁄ 500  s; 1 ⁄ 250  s; 1 ⁄ 125  s; 1 ⁄ 60  s; 1 ⁄ 30  s; 1 ⁄ 15  s; 1 ⁄ 8  s; 1 ⁄ 4  s; 1 ⁄ 2  s; and 1 s. With this scale, each increment roughly doubles the amount of light (longer time) or halves it (shorter time). Camera shutters often include one or two other settings for making very long exposures: The ability of

3750-400: The image of the planet be dependent on the observer's memory and preconceptions which led the belief that Mars had linear features. The effects of atmospheric seeing are qualitatively similar throughout the visible and near infrared wavebands. At large telescopes the long exposure image resolution is generally slightly higher at longer wavelengths, and the timescale ( t 0 - see below) for

3825-445: The image. To achieve the longer exposures I do what many amateur astronomers do. I take multiple 30-second exposures, then 'stack' them using imaging software , thus producing the longer exposure." Star trail images have also been taken on Mars. The Spirit rover produced them while looking for meteors. Since the camera was limited to 60 second exposures the trails appear as dashed lines. Star trail photographs are possible because of

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3900-403: The length-scale over which the turbulence becomes significant (10–20 cm at visible wavelengths at good observatories), and t 0 corresponds to the time-scale over which the changes in the turbulence become significant. r 0 determines the spacing of the actuators needed in an adaptive optics system, and t 0 determines the correction speed required to compensate for the effects of

3975-407: The optical phase corresponds to the complex argument of ψ 0 {\displaystyle \psi _{0}} . As wavefronts pass through the Earth's atmosphere they may be perturbed by refractive index variations in the atmosphere. The diagram at the top-right of this page shows schematically a turbulent layer in the Earth's atmosphere perturbing planar wavefronts before they enter

4050-421: The phase fluctuations ϕ a ( r ) {\displaystyle \phi _{a}\left(\mathbf {r} \right)} . The amplitude fluctuations described by χ a ( r ) {\displaystyle \chi _{a}\left(\mathbf {r} \right)} have negligible effect on the structure of the images seen in the focus of a large telescope. For simplicity,

4125-759: The phase fluctuations in Tatarski's model are often assumed to have a Gaussian random distribution with the following second-order structure function: D ϕ a ( ρ ) = ⟨ | ϕ a ( r ) − ϕ a ( r + ρ ) | 2 ⟩ r {\displaystyle D_{\phi _{a}}\left(\mathbf {\rho } \right)=\left\langle \left|\phi _{a}\left(\mathbf {r} \right)-\phi _{a}\left(\mathbf {r} +\mathbf {\rho } \right)\right|^{2}\right\rangle _{\mathbf {r} }} where D ϕ

4200-426: The photographer to take images without noticeable blurring by camera movement is an important parameter in the choice of the slowest possible shutter speed for a handheld camera. The rough guide used by most 35 mm photographers is that the slowest shutter speed that can be used easily without much blur due to camera shake is the shutter speed numerically closest to the lens focal length. For example, for handheld use of

4275-408: The quality of a location for telescope observations. Star trail observations of Polaris have been used to measure the quality of seeing in the atmosphere, and the vibrations in telescope mounting systems. The first recorded suggestion of this technique is from E.S. Skinner's 1931 book A Manual of Celestial Photography . Shutter speed In photography , shutter speed or exposure time

4350-419: The real part, and FT[] represents a discrete Fourier transform of the resulting two-dimensional square array (typically an FFT). The assumption that the phase fluctuations in Tatarski's model have a Gaussian random distribution is usually unrealistic. In reality, turbulence exhibits intermittency. These fluctuations in the turbulence strength can be straightforwardly simulated as follows: ϕ

4425-495: The resolution of long-exposure images is determined primarily by diffraction and the size of the Airy pattern and thus is inversely proportional to the telescope diameter. For telescopes with diameters larger than r 0 , the image resolution is determined primarily by the atmosphere and is independent of telescope diameter, remaining constant at the value given by a telescope of diameter equal to r 0 . r 0 also corresponds to

4500-420: The rest remains sharp; or if the camera is panned to follow a moving subject, the background is blurred while the subject remains relatively sharp. The exact point at which the background or subject will start to blur depends on the speed at which the object is moving, the angle that the object is moving in relation to the camera, the distance it is from the camera and the focal length of the lens in relation to

4575-541: The rotation of Earth about its axis. The apparent motion of the stars is recorded as mostly curved streaks on the film or detector. For observers in the Northern Hemisphere , aiming the camera northward creates an image with concentric circular arcs centered on the north celestial pole (very near Polaris ). For those in the Southern Hemisphere , this same effect is achieved by aiming

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4650-606: The same dimensions as R ( k ) , and where ⊗ {\displaystyle \otimes } represents convolution . The intermittency is described in terms of fluctuations in the turbulence strength C n 2 {\displaystyle C_{n}^{2}} . It can be seen that the equation for the Gaussian random case above is just the special case from this equation with: I ( k ) = δ ( | k | ) {\displaystyle I(k)=\delta (|k|)} where δ ( ) {\displaystyle \delta ()}

4725-512: The same exposure value as a 1 ⁄ 100  s shutter speed with an f /2.8 aperture, and also the same exposure value as a 1 ⁄ 200  s shutter speed with an f /2 aperture, or 1 ⁄ 25  s at f /5.6 . In addition to its effect on exposure, the shutter speed changes the way movement appears in photographs. Very short shutter speeds can be used to freeze fast-moving subjects, for example at sporting events. Very long shutter speeds are used to intentionally blur

4800-452: The scene's luminance together determine the amount of light that reaches the film or sensor (the exposure ). Exposure value (EV) is a quantity that accounts for the shutter speed and the f-number. Once the sensitivity to light of the recording surface (either film or sensor) is set in numbers expressed in " ISOs " (e.g. 200 ISO, 400 ISO), the light emitted by the scene photographed can be controlled through aperture and shutter-speed to match

4875-402: The seeing, as do wind and clouds. At the best high-altitude mountaintop observatories , the wind brings in stable air which has not previously been in contact with the ground, sometimes providing seeing as good as 0.4". The astronomical seeing conditions at an observatory can be conveniently described by the parameters r 0 and t 0 . For telescopes with diameters smaller than r 0 ,

4950-449: The shutter is opened, the lens is zoomed in, changing the focal length during the exposure. The center of the image remains sharp, while the details away from the center form a radial blur, which causes a strong visual effect, forcing the eye into the center of the image. The following list provides an overview of common photographic uses for standard shutter speeds. Motion picture cameras used in traditional film cinematography employ

5025-557: The shutter open for the desired amount of time. Typical exposure times range from 15 minutes to many hours long, depending on the desired length of the star trail arcs for the image. Even though star trail pictures are created under low-light conditions, long exposure times allow fast films , such as ISO 200 and ISO 400. Wide-apertures, such as f/5.6 and f/4, are recommended for star trails. Because exposure times for star trail photographs can be several hours long, camera batteries can be easily depleted. Mechanical cameras that do not require

5100-660: The size of an imaginary telescope aperture for which the diffraction limited angular resolution is equal to the resolution limited by seeing. Both the size of the seeing disc and the Fried parameter depend on the optical wavelength, but it is common to specify them for 500 nanometers. A seeing disk smaller than 0.4 arcseconds or a Fried parameter larger than 30 centimeters can be considered excellent seeing. The best conditions are typically found at high-altitude observatories on small islands, such as those at Mauna Kea or La Palma . Astronomical seeing has several effects: The effects of atmospheric seeing were indirectly responsible for

5175-402: The size of the digital sensor or film. When slower shutter-speeds, in excess of about half a second, are used on running water, the water in the photo will have a ghostly white appearance reminiscent of fog . This effect can be used in landscape photography . Zoom burst is a technique which entails the variation of the focal length of a zoom lens during a longer exposure. In the moment that

5250-524: The size of the telescope aperture . Today, many large scientific ground-based optical telescopes include adaptive optics to overcome seeing. The strength of seeing is often characterized by the angular diameter of the long-exposure image of a star ( seeing disk ) or by the Fried parameter r 0 . The diameter of the seeing disk is the full width at half maximum of its optical intensity. An exposure time of several tens of milliseconds can be considered long in this context. The Fried parameter describes

5325-491: The studies of turbulence by the Russian mathematician Andrey Kolmogorov . This model is supported by a variety of experimental measurements and is widely used in simulations of astronomical imaging. The model assumes that the wavefront perturbations are brought about by variations in the refractive index of the atmosphere. These refractive index variations lead directly to phase fluctuations described by ϕ

5400-469: The telescope. However, when light enters the Earth's atmosphere , the different temperature layers and different wind speeds distort the light waves, leading to distortions in the image of a star. The effects of the atmosphere can be modeled as rotating cells of air moving turbulently. At most observatories, the turbulence is only significant on scales larger than r 0 (see below—the seeing parameter r 0

5475-401: The turbulence strength C N 2 ( h ) {\displaystyle C_{N}^{2}(h)} varies as a function of height h {\displaystyle h} above the telescope, and γ {\displaystyle \gamma } is the angular distance of the astronomical source from the zenith (from directly overhead). If turbulent evolution

5550-466: The type of adaptive optics system which will be needed at a particular telescope, or in deciding whether or not a particular location would be a good site for setting up a new astronomical observatory. Typically, several methods are used simultaneously for measuring the C n 2 {\displaystyle C_{n}^{2}} profile and then compared. Some of the most common methods include: There are also mathematical functions describing

5625-408: The vertical structure of the turbulence, in a technique known as Multiconjugate Adaptive Optics. Another cheaper technique, lucky imaging , has had good results on smaller telescopes. This idea dates back to pre-war naked-eye observations of moments of good seeing, which were followed by observations of the planets on cine film after World War II . The technique relies on the fact that every so often

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