Misplaced Pages

#2997

68-639: A mirage is an optical phenomenon. Mirage ( s ) or The Mirage may also refer to: Mirage A mirage is a naturally-occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky. The word comes to English via the French (se) mirer , from the Latin mirari , meaning "to look at, to wonder at". Mirages can be categorized as "inferior" (meaning lower), "superior" (meaning higher) and " Fata Morgana ", one kind of superior mirage consisting of

136-464: A , y b ) ] ⋅ rect ⁡ ( x M ⋅ c , y N ⋅ d ) {\displaystyle \mathbf {S} (x,y)=\left[\operatorname {comb} \left({\frac {x}{c}},{\frac {y}{d}}\right)*\operatorname {rect} \left({\frac {x}{a}},{\frac {y}{b}}\right)\right]\cdot \operatorname {rect} \left({\frac {x}{M\cdot c}},{\frac {y}{N\cdot d}}\right)} where

204-441: A ⋅ ξ , b ⋅ η ) {\displaystyle {\begin{aligned}\mathbf {MTF_{sensor}} (\xi ,\eta )&={\mathcal {FF}}(\mathbf {S} (x,y))\\&=[\operatorname {sinc} ((M\cdot c)\cdot \xi ,(N\cdot d)\cdot \eta )*\operatorname {comb} (c\cdot \xi ,d\cdot \eta )]\cdot \operatorname {sinc} (a\cdot \xi ,b\cdot \eta )\end{aligned}}} An imaging system running at 24 frames per second

272-517: A t m o s p h e r e ( ξ , η ) ⋅ M T F l e n s ( ξ , η ) ⋅ M T F s e n s o r ( ξ , η ) ⋅ M T F t r a n s m i s s i o n ( ξ , η ) ⋅ M T F d i s p l

340-453: A t m o s p h e r e ( x , y ) ∗ P S F l e n s ( x , y ) ∗ P S F s e n s o r ( x , y ) ∗ P S F t r a n s m i s s i o n ( x , y ) ∗ P S F d i s p l

408-425: A y ( ξ , η ) {\displaystyle {\begin{aligned}\mathbf {MTF_{sys}(\xi ,\eta )} ={}&\mathbf {MTF_{atmosphere}(\xi ,\eta )\cdot MTF_{lens}(\xi ,\eta )\cdot } \\&\mathbf {MTF_{sensor}(\xi ,\eta )\cdot MTF_{transmission}(\xi ,\eta )\cdot } \\&\mathbf {MTF_{display}(\xi ,\eta )} \end{aligned}}} The human eye is a limiting feature of many systems, when

476-421: A y ( x , y ) {\displaystyle {\begin{aligned}\mathbf {Image(x,y)} ={}&\mathbf {Object(x,y)*PSF_{atmosphere}(x,y)*} \\&\mathbf {PSF_{lens}(x,y)*PSF_{sensor}(x,y)*} \\&\mathbf {PSF_{transmission}(x,y)*PSF_{display}(x,y)} \end{aligned}}} The other method is to transform each of the components of the system into the spatial frequency domain, and then to multiply

544-590: A point source in the object diffracts through the lens aperture such that it forms a diffraction pattern in the image, which has a central spot and surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern , and the central bright lobe as an Airy disk . The angular radius of the Airy disk (measured from the center to the first null) is given by: θ = 1.22 λ D {\displaystyle \theta =1.22{\frac {\lambda }{D}}} where Two adjacent points in

612-678: A condenser is used to illuminate the sample, the shape of the pencil of light emanating from the condenser must also be included. r = 1.22 λ N A obj + N A cond {\displaystyle r={\frac {1.22\lambda }{\mathrm {NA} _{\text{obj}}+\mathrm {NA} _{\text{cond}}}}} In a properly configured microscope, N A obj + N A cond = 2 N A obj {\displaystyle \mathrm {NA} _{\text{obj}}+\mathrm {NA} _{\text{cond}}=2\mathrm {NA} _{\text{obj}}} . The above estimates of resolution are specific to

680-651: A degree high (roughly the angular diameter of the Sun and Moon) and are from objects between dozens of meters and a few kilometers away. Heat haze , also called heat shimmer , refers to the inferior mirage observed when viewing objects through a mass of heated air. Common instances when heat haze occurs include images of objects viewed across asphalt concrete (also known as tarmac ), roads and over masonry rooftops on hot days, above and behind fire (as in burning candles , patio heaters , and campfires ), and through exhaust gases from jet engines . When appearing on roads due to

748-486: A detector to resolve those differences depends mostly on the size of the detecting elements. Spatial resolution is typically expressed in line pairs per millimeter (lppmm), lines (of resolution, mostly for analog video), contrast vs. cycles/mm, or MTF (the modulus of OTF). The MTF may be found by taking the two-dimensional Fourier transform of the spatial sampling function. Smaller pixels result in wider MTF curves and thus better detection of higher frequency energy. This

SECTION 10

#1732844630003

816-505: A direct impact on spatial resolution. The spatial resolution of digital systems (e.g. HDTV and VGA ) are fixed independently of the analog bandwidth because each pixel is digitized, transmitted, and stored as a discrete value. Digital cameras, recorders, and displays must be selected so that the resolution is identical from camera to display. However, in analog systems, the resolution of the camera, recorder, cabling, amplifiers, transmitters, receivers, and display may all be independent and

884-523: A distant shoreline may appear to tower and look higher (and, thus, perhaps closer) than it really is. Because of the turbulence, there appear to be dancing spikes and towers. This type of mirage is also called the Fata Morgana , or hafgerðingar in the Icelandic language . A superior mirage can be right-side up or upside-down, depending on the distance of the true object and the temperature gradient. Often

952-466: A fixed time (outlined below), so more pixels per line becomes a requirement for more voltage changes per unit time, i.e. higher frequency. Since such signals are typically band-limited by cables, amplifiers, recorders, transmitters, and receivers, the band-limitation on the analog signal acts as an effective low-pass filter on the spatial resolution. The difference in resolutions between VHS (240 discernible lines per scanline), Betamax (280 lines), and

1020-429: A mechanical system to advance it through the exposure mechanism, or a moving optical system to expose it. These limit the speed at which successive frames may be exposed. CCD and CMOS are the modern preferences for video sensors. CCD is speed-limited by the rate at which the charge can be moved from one site to another. CMOS has the advantage of having individually addressable cells, and this has led to its advantage in

1088-472: A series of unusually elaborate, vertically stacked images, which form one rapidly-changing mirage. In contrast to a hallucination , a mirage is a real optical phenomenon that can be captured on camera, since light rays are actually refracted to form the false image at the observer's location. What the image appears to represent, however, is determined by the interpretive faculties of the human mind. For example, inferior images on land are very easily mistaken for

1156-483: A spherical, convex "horizon". In some situations, distant objects can be elevated or lowered, stretched or shortened with no mirage involved. A Fata Morgana (the name comes from the Italian translation of Morgan le Fay , the fairy, shapeshifting half-sister of King Arthur) is a very complex superior mirage. It appears with alternations of compressed and stretched areas, erect images, and inverted images. A Fata Morgana

1224-400: A static scene will not be detected, so they require choppers . They also have a decay time, so the pyroelectric system temporal response will be a bandpass, while the other detectors discussed will be a lowpass. If objects within the scene are in motion relative to the imaging system, the resulting motion blur will result in lower spatial resolution. Short integration times will minimize

1292-426: A system is based on the minimum distance r {\displaystyle r} at which the points can be distinguished as individuals. Several standards are used to determine, quantitatively, whether or not the points can be distinguished. One of the methods specifies that, on the line between the center of one point and the next, the contrast between the maximum and minimum intensity be at least 26% lower than

1360-399: Is refracted by the index gradient, making it appear as if the sky is reflected by the road's surface. This might appear as a pool of liquid (usually water, but possibly others, such as oil) on the road, as some types of liquid also reflect the sky. The illusion moves into the distance as the observer approaches the miraged object giving one the same effect as approaching a rainbow. Heat haze

1428-407: Is 50%. To find a theoretical MTF curve for a sensor, it is necessary to know three characteristics of the sensor: the active sensing area, the area comprising the sensing area and the interconnection and support structures ("real estate"), and the total number of those areas (the pixel count). The total pixel count is almost always given. Sometimes the overall sensor dimensions are given, from which

SECTION 20

#1732844630003

1496-575: Is a naturally occurring optical phenomenon in which light rays are bent to produce distorted or multiple images of an astronomical object . Mirages can be observed for such astronomical objects as the Sun , the Moon , the planets , bright stars , and very bright comets . The most commonly observed are sunset and sunrise mirages. Optical resolution Resolution depends on the distance between two distinguishable radiating points. The sections below describe

1564-453: Is also a fast-changing mirage. Fata Morgana mirages are most common in polar regions , especially over large sheets of ice with a uniform low temperature, but they can be observed almost anywhere. In polar regions, a Fata Morgana may be observed on cold days; in desert areas and over oceans and lakes, a Fata Morgana may be observed on hot days. For a Fata Morgana, temperature inversion has to be strong enough that light rays' curvatures within

1632-452: Is analogous to taking the Fourier transform of a signal sampling function; as in that case, the dominant factor is the sampling period, which is analogous to the size of the picture element ( pixel ). Other factors include pixel noise, pixel cross-talk, substrate penetration, and fill factor. A common problem among non-technicians is the use of the number of pixels on the detector to describe

1700-453: Is derived experimentally. Solid state sensor and camera manufacturers normally publish specifications from which the user may derive a theoretical MTF according to the procedure outlined below. A few may also publish MTF curves, while others (especially intensifier manufacturers) will publish the response (%) at the Nyquist frequency , or, alternatively, publish the frequency at which the response

1768-401: Is equal to the Airy disk radius to first null can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the greater the resolution. Astronomical telescopes have increasingly large lenses so they can 'see' ever finer detail in the stars. Only the very highest quality lenses have diffraction-limited resolution, however, and normally the quality of

1836-446: Is essentially a discrete sampling system that samples a 2D area. The same limitations described by Nyquist apply to this system as to any signal sampling system. All sensors have a characteristic time response. Film is limited at both the short resolution and the long resolution extremes by reciprocity breakdown . These are typically held to be anything longer than 1 second and shorter than 1/10,000 second. Furthermore, film requires

1904-421: Is not related to the atmospheric phenomenon of haze . A superior mirage is one in which the mirage image appears to be located above the real object. A superior mirage occurs when the air below the line of sight is colder than the air above it. This unusual arrangement is called a temperature inversion . During daytime, the normal temperature gradient of the atmosphere is cold air above warm air. Passing through

1972-620: Is suitable for confocal microscopy, but is also used in traditional microscopy. In confocal laser-scanned microscopes , the full-width half-maximum (FWHM) of the point spread function is often used to avoid the difficulty of measuring the Airy disc. This, combined with the rastered illumination pattern, results in better resolution, but it is still proportional to the Rayleigh-based formula given above. r = 0.4 λ N A {\displaystyle r={\frac {0.4\lambda }{\mathrm {NA} }}} Also common in

2040-521: Is to perform a series of two-dimensional convolutions , first with the image and the lens, and then, with that procedure's result and a sensor (and so on through all of the components of the system). Not only is this computationally expensive, but normally it also requires repetition of the process, for each additional object that is to be imaged. I m a g e ( x , y ) = O b j e c t ( x , y ) ∗ P S F

2108-463: The Arctic Circle . The Sun appeared to rise two weeks earlier than expected; the real Sun had still been below the horizon, but its light rays followed the curvature of Earth. This effect is often called a Novaya Zemlya mirage . For every 111.12 kilometres (69.05 mi) that light rays travel parallel to Earth's surface, the Sun will appear 1° higher on the horizon. The inversion layer must have just

Mirage (disambiguation) - Misplaced Pages Continue

2176-661: The high speed photography industry. Vidicons, Plumbicons, and image intensifiers have specific applications. The speed at which they can be sampled depends upon the decay rate of the phosphor used. For example, the P46 phosphor has a decay time of less than 2 microseconds, while the P43 decay time is on the order of 2-3 milliseconds. The P43 is therefore unusable at frame rates above 1000 frames per second (frame/s). See § External links for links to phosphor information. Pyroelectric detectors respond to changes in temperature. Therefore,

2244-647: The "Bismarck" , Ludovic Kennedy describes an incident that allegedly took place below the Denmark Strait during 1941, following the sinking of the Hood . The Bismarck , while pursued by the British cruisers Norfolk and Suffolk , passed out of sight into a sea mist. Within a matter of seconds, the ship re-appeared steaming toward the British ships at high speed. In alarm the cruisers separated, anticipating an imminent attack, and observers from both ships watched in astonishment as

2312-401: The "inner" and "outer" scale turbulence; short is considered to be much less than 10 ms for visible imaging (typically, anything less than 2 ms). Inner scale turbulence arises due to the eddies in the turbulent flow, while outer scale turbulence arises from large air mass flow. These masses typically move slowly, and so are reduced by decreasing the integration period. A system limited only by

2380-476: The 2-D results. A system response may be determined without reference to an object. Although this method is considerably more difficult to comprehend conceptually, it becomes easier to use computationally, especially when different design iterations or imaged objects are to be tested. The transformation to be used is the Fourier transform. M T F s y s ( ξ , η ) = M T F

2448-552: The German battleship fluttered, grew indistinct and faded away. Radar watch during these events indicated that the Bismarck had in fact made no change to her course. The conditions for producing a mirage can occur at night as well as during the day. Under some circumstances mirages of astronomical objects and mirages of lights from moving vehicles, aircraft, ships, buildings, etc. can be observed at night. A mirage of an astronomical object

2516-447: The active area. That last function serves as an overall envelope to the MTF function; so long as the number of pixels is much greater than one, then the active area size dominates the MTF. Sampling function: S ( x , y ) = [ comb ⁡ ( x c , y d ) ∗ rect ⁡ ( x

2584-405: The air to vary, and the variation between the hot air at the surface of the road and the denser cool air above it causes a gradient in the refractive index of the air. This produces a blurred shimmering effect , which hinders the ability to resolve the image and increases when the image is magnified through a telescope or telephoto lens . Light from the sky at a shallow angle to the road

2652-447: The blur, but integration times are limited by sensor sensitivity. Furthermore, motion between frames in motion pictures will impact digital movie compression schemes (e.g. MPEG-1, MPEG-2). Finally, there are sampling schemes that require real or apparent motion inside the camera (scanning mirrors, rolling shutters) that may result in incorrect rendering of image motion. Therefore, sensor sensitivity and other time-related factors will have

2720-416: The case in which two identical very small samples that radiate incoherently in all directions. Other considerations must be taken into account if the sources radiate at different levels of intensity, are coherent, large, or radiate in non-uniform patterns. The ability of a lens to resolve detail is usually determined by the quality of the lens, but is ultimately limited by diffraction . Light coming from

2788-406: The distance between pixels, convolved with a sinc ⁡ ( ξ , η ) {\displaystyle \operatorname {sinc} (\xi ,\eta )} function governed by the number of pixels, and multiplied by the sinc ⁡ ( ξ , η ) {\displaystyle \operatorname {sinc} (\xi ,\eta )} function corresponding to

Mirage (disambiguation) - Misplaced Pages Continue

2856-406: The frame contains more lines and is wider, so bandwidth requirements are similar. Note that a "discernible line" forms one half of a cycle (a cycle requires a dark and a light line), so "228 cycles" and "456 lines" are equivalent measures. There are two methods by which to determine "system resolution" (in the sense that omits the eye, or other final reception of the optical information). The first

2924-439: The goal of the system is to present data to humans for processing. For example, in a security or air traffic control function, the display and work station must be constructed so that average humans can detect problems and direct corrective measures. Other examples are when a human is using eyes to carry out a critical task such as flying (piloting by visual reference), driving a vehicle, and so forth. The best visual acuity of

2992-400: The hot asphalt, it is often referred to as a "highway mirage". It also occurs in deserts; in that case, it is referred to as a "desert mirage". Both tarmac and sand can become very hot when exposed to the sun, easily being more than 10 °C (18 °F) higher than the air a meter (3.3 feet) above, enough to make conditions suitable to cause the mirage. Convection causes the temperature of

3060-459: The human eye at its optical centre (the fovea) is less than 1 arc minute per line pair, reducing rapidly away from the fovea. The human brain requires more than just a line pair to understand what the eye is imaging. Johnson's criteria defines the number of line pairs of ocular resolution, or sensor resolution, needed to recognize or identify an item. Systems looking through long atmospheric paths may be limited by turbulence . A key measure of

3128-451: The image appears as a distorted mixture of up and down parts. Since the earth is round, if the downward bending curvature of light rays is about the same as the curvature of Earth , light rays can travel large distances, including from beyond the horizon. This was observed and documented in 1596, when a ship in search of the Northeast passage became stuck in the ice at Novaya Zemlya , above

3196-551: The inferior mirage is stable unlike the fata morgana which can change within seconds. Since warmer air rises while cooler air (being denser ) sinks, the layers will mix, causing turbulence . The image will be distorted accordingly; it may vibrate or be stretched vertically ( towering ) or compressed vertically ( stooping ). A combination of vibration and extension are also possible. If several temperature layers are present, several mirages may mix, perhaps causing double images. In any case, mirages are usually not larger than about half

3264-485: The inversion are stronger than the curvature of Earth . The rays will bend and form arcs . An observer needs to be within an atmospheric duct to be able to see a Fata Morgana. Fata Morgana mirages may be observed from any altitude within Earth's atmosphere , including from mountaintops or airplanes. Distortions of image and bending of light can produce spectacular effects. In his book Pursuit: The Chase and Sinking of

3332-493: The lens alone, angular frequency is preferred. OTF may be broken down into the magnitude and phase components as follows: O T F ( ξ , η ) = M T F ( ξ , η ) ⋅ P T F ( ξ , η ) {\displaystyle \mathbf {OTF(\xi ,\eta )} =\mathbf {MTF(\xi ,\eta )} \cdot \mathbf {PTF(\xi ,\eta )} } where The OTF accounts for aberration , which

3400-466: The lens limits its ability to resolve detail. This ability is expressed by the Optical Transfer Function which describes the spatial (angular) variation of the light signal as a function of spatial (angular) frequency. When the image is projected onto a flat plane, such as photographic film or a solid state detector, spatial frequency is the preferred domain, but when the image is referred to

3468-999: The limiting frequency expression above does not. The magnitude is known as the Modulation Transfer Function (MTF) and the phase portion is known as the Phase Transfer Function (PTF) . In imaging systems, the phase component is typically not captured by the sensor. Thus, the important measure with respect to imaging systems is the MTF. Phase is critically important to adaptive optics and holographic systems. Some optical sensors are designed to detect spatial differences in electromagnetic energy . These include photographic film , solid-state devices ( CCD , CMOS sensors , and infrared detectors like PtSi and InSb ), tube detectors ( vidicon , plumbicon , and photomultiplier tubes used in night-vision devices), scanning detectors (mainly used for IR), pyroelectric detectors, and microbolometer detectors. The ability of such

SECTION 50

#1732844630003

3536-561: The maximum. This corresponds to the overlap of one Airy disk on the first dark ring in the other. This standard for separation is also known as the Rayleigh criterion . In symbols, the distance is defined as follows: r = 1.22 λ 2 n sin ⁡ θ = 0.61 λ N A {\displaystyle r={\frac {1.22\lambda }{2n\sin {\theta }}}={\frac {0.61\lambda }{\mathrm {NA} }}} where This formula

3604-546: The microscopy literature is a formula for resolution that treats the above-mentioned concerns about contrast differently. The resolution predicted by this formula is proportional to the Rayleigh-based formula, differing by about 20%. For estimating theoretical resolution, it may be adequate. r = λ 2 n sin ⁡ θ = λ 2 N A {\displaystyle r={\frac {\lambda }{2n\sin {\theta }}}={\frac {\lambda }{2\mathrm {NA} }}} When

3672-454: The newer ED Beta format (500 lines) is explained primarily by the difference in the recording bandwidth. In the NTSC transmission standard, each field contains 262.5 lines, and 59.94 fields are transmitted every second. Each line must therefore take 63 microseconds, 10.7 of which are for reset to the next line. Thus, the retrace rate is 15.734 kHz. For the picture to appear to have approximately

3740-450: The object give rise to two diffraction patterns. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. Rayleigh defined the somewhat arbitrary " Rayleigh criterion " that two points whose angular separation

3808-419: The overall system resolution is governed by the bandwidth of the lowest performing component. In analog systems, each horizontal line is transmitted as a high-frequency analog signal. Each picture element (pixel) is therefore converted to an analog electrical value (voltage), and changes in values between pixels therefore become changes in voltage. The transmission standards require that the sampling be done in

3876-512: The quality of atmospheric turbulence is the seeing diameter , also known as Fried's seeing diameter . A path which is temporally coherent is known as an isoplanatic patch. Large apertures may suffer from aperture averaging , the result of several paths being integrated into one image. Turbulence scales with wavelength at approximately a 6/5 power. Thus, seeing is better at infrared wavelengths than at visible wavelengths. Short exposures suffer from turbulence less than longer exposures due to

3944-474: The real estate area can be calculated. Whether the real estate area is given or derived, if the active pixel area is not given, it may be derived from the real estate area and the fill factor , where fill factor is the ratio of the active area to the dedicated real estate area. F F = a ⋅ b c ⋅ d {\displaystyle \mathrm {FF} ={\frac {a\cdot b}{c\cdot d}}} where In Gaskill's notation,

4012-399: The reflections from a small body of water. In an inferior mirage, the mirage image appears below the real object. The real object in an inferior mirage is the (blue) sky or any distant (therefore bluish) object in that same direction. The mirage causes the observer to see a bright and bluish patch on the ground. Light rays coming from a particular distant object all travel through nearly

4080-465: The resolution. If all sensors were the same size, this would be acceptable. Since they are not, the use of the number of pixels can be misleading. For example, a 2- megapixel camera of 20-micrometre-square pixels will have worse resolution than a 1-megapixel camera with 8-micrometre pixels, all else being equal. For resolution measurement, film manufacturers typically publish a plot of Response (%) vs. Spatial Frequency (cycles per millimeter). The plot

4148-496: The right temperature gradient over the whole distance to make this possible. In the same way, ships that are so far away that they should not be visible above the geometric horizon may appear on or even above the horizon as superior mirages. This may explain some stories about flying ships or coastal cities in the sky, as described by some polar explorers. These are examples of so-called Arctic mirages, or hillingar in Icelandic. If

SECTION 60

#1732844630003

4216-406: The same horizontal and vertical resolution (see Kell factor ), it should be able to display 228 cycles per line, requiring a bandwidth of 4.28 MHz. If the line (sensor) width is known, this may be converted directly into cycles per millimeter, the unit of spatial resolution. B/G/I/K television system signals (usually used with PAL colour encoding) transmit frames less often (50 Hz), but

4284-404: The same layers of air, and all are refracted at about the same angle . Therefore, rays coming from the top of the object will arrive lower than those from the bottom. The image is usually upside-down, enhancing the illusion that the sky image seen in the distance is a specular reflection on a puddle of water or oil acting as a mirror . While the aero-dynamics are highly active, the image of

4352-436: The sensing area is a 2D comb( x , y ) function of the distance between pixels (the pitch ), convolved with a 2D rect( x , y ) function of the active area of the pixel, bounded by a 2D rect( x , y ) function of the overall sensor dimension. The Fourier transform of this is a comb ⁡ ( ξ , η ) {\displaystyle \operatorname {comb} (\xi ,\eta )} function governed by

4420-550: The sensor has M × N pixels M T F s e n s o r ( ξ , η ) = F F ( S ( x , y ) ) = [ sinc ⁡ ( ( M ⋅ c ) ⋅ ξ , ( N ⋅ d ) ⋅ η ) ∗ comb ⁡ ( c ⋅ ξ , d ⋅ η ) ] ⋅ sinc ⁡ (

4488-410: The temperature inversion, the light rays are bent down, and so the image appears above the true object, hence the name superior . Superior mirages are quite common in polar regions , especially over large sheets of ice that have a uniform low temperature. Superior mirages also occur at more moderate latitudes, although in those cases they are weaker and tend to be less smooth and stable. For example,

4556-439: The theoretical estimates of resolution, but the real values may differ. The results below are based on mathematical models of Airy discs , which assumes an adequate level of contrast. In low-contrast systems, the resolution may be much lower than predicted by the theory outlined below. Real optical systems are complex, and practical difficulties often increase the distance between distinguishable point sources. The resolution of

4624-403: The vertical temperature gradient is +12.9 °C (23.2 °F) per 100 meters/330 feet (where the positive sign means the temperature increases at higher altitudes) then horizontal light rays will just follow the curvature of Earth, and the horizon will appear flat. If the gradient is less (as it almost always is) the rays are not bent enough and get lost in space, which is the normal situation of

#2997