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Distortion (optics)

Radial distortion [ edit ]

Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a photographic lens. These radial distortions can usually be classified as either barrel distortions or pincushion distortions. [1]

In barrel distortion, image magnification decreases with distance from the optical axis. The apparent effect is that of an image which has been mapped around a sphere (or barrel). Fisheye lenses, which take hemispherical views, utilize this type of distortion as a way to map an infinitely wide object plane into a finite image area. In a zoom lens, barrel distortion appears in the middle of the lens’s focal length range and is worst at the wide-angle end of the range. [2]

In pincushion distortion, image magnification increases with the distance from the optical axis. The visible effect is that lines that do not go through the centre of the image are bowed inwards, towards the centre of the image, like a pincushion.

A mixture of both types, sometimes referred to as mustache distortion (moustache distortion) or complex distortion, is less common but not rare. It starts out as barrel distortion close to the image center and gradually turns into pincushion distortion towards the image periphery, making horizontal lines in the top half of the frame look like a handlebar mustache.

Mathematically, barrel and pincushion distortion are quadratic, meaning they increase as the square of distance from the center. In mustache distortion the quartic (degree 4) term is significant: in the center, the degree 2 barrel distortion is dominant, while at the edge the degree 4 distortion in the pincushion direction dominates. Other distortions are in principle possible – pincushion in center and barrel at the edge, or higher order distortions (degree 6, degree 8) – but do not generally occur in practical lenses, and higher order distortions are small relative to the main barrel and pincushion effects.

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Occurrence [ edit ]

In photography, distortion is particularly associated with zoom lenses, particularly large-range zooms, but may also be found in prime lenses, and depends on focal distance – for example, the Canon EF 50mm f /1.4 exhibits barrel distortion at extremely short focal distances. Barrel distortion may be found in wide-angle lenses, and is often seen at the wide-angle end of zoom lenses, while pincushion distortion is often seen in older or low-end telephoto lenses. Mustache distortion is observed particularly on the wide end of zooms, with certain retrofocus lenses, and more recently on large-range zooms such as the Nikon 18–200 mm.

A certain amount of pincushion distortion is often found with visual optical instruments, e.g., binoculars, where it serves to eliminate the globe effect.

In order to understand these distortions, it should be remembered that these are radial defects; the optical systems in question have rotational symmetry (omitting non-radial defects), so the didactically correct test image would be a set of concentric circles having even separation—like a shooter’s target. It will then be observed that these common distortions actually imply a nonlinear radius mapping from the object to the image: What is seemingly pincushion distortion, is actually simply an exaggerated radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be steeper in the upper (rightmost) end. Conversely, barrel distortion is actually a diminished radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be less steep in the upper (rightmost) end.

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Chromatic aberration [ edit ]

Radial distortion that depends on wavelength is called «lateral chromatic aberration» – «lateral» because radial, «chromatic» because dependent on color (wavelength). This can cause colored fringes in high-contrast areas in the outer parts of the image. This should not be confused with axial (longitudinal) chromatic aberration, which causes aberrations throughout the field, particularly purple fringing.

Origin of terms [ edit ]

The names for these distortions come from familiar objects which are visually similar.

In barrel distortion, straight lines bulge outwards at the center, as in a barrel.

In pincushion distortion, corners of squares form elongated points, as in a cushion.

In mustache distortion, horizontal lines bulge up in the center, then bend the other way as they approach the edge of the frame (if in the top of the frame), as in curly handlebar mustaches.

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New Zealand spinner Mitchell Santner conceded Namibia would be "dangerous" on a tricky Sharjah wicket during their clash later on Friday, following their gritty display in a losing cause against Pakistan and a four-wicket win against Scotland in their opening 'Super 12' game at the ICC T20 World Cup here.

Despite being the underdogs, Namibia have had fruitful outings at the T20 World Cup and the Black Caps wouldn't want to take any risks with the side by underestimating their potential, given that the Kane Williamson-led side has one foot in the semifinals.

"They are (dangerous> for sure. Especially in T20 cricket. There's an upset just around the corner. We've got to be ready. We've seen the wicket at Sharjah can be tricky, and it brings both teams back into it, said Santner ahead of the afternoon game on Friday.

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"Namibia have played some good cricket. And so we've just got to be ready for that, ready for what the pitch is going to bring, (and ready for) a day game is obviously something new again in Sharjah."

After two wins in three games, New Zealand are third on the 'Super 12' Group 2 table. If they win their final two matches, they will jump ahead of Afghanistan to claim the second position, which will confirm a spot in the semifinals. Pakistan have already secured a last-4 berth with four-of-four wins in 'Super 12'.

The first of those two must-win matches is against Namibia in Sharjah. Scotland gave New Zealand a good fight in their previous game, so the Black Caps will be wary of underestimating the threat posed by the Associate Nation.

New Zealand have been clinical in their performances so far, keeping it simple and doing well to win the crunch moments against India and Scotland. Against Pakistan, they were in the game for long periods of time until Asif Ali's late six-hitting took the game away.

Their biggest challenge is the quick turnaround and the change in conditions to Sharjah. "It's pretty full on. All day games as well. So it takes a lot of out of you," said Santner, New Zealand's left-arm spinner, adding that the team was focused on rest and recovery when they could.

"The biggest adjustment (we need to make) — obviously there's a bit of difference playing in Sharjah versus outside the other two grounds. In New Zealand you're looking for a bit of bounce, trying to bowl hard length into the wicket, get a bit of bounce, and you don't really get that at Sharjah, where it actually sits up," he told icc-cricket.com.

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"The guys that have done well at Sharjah are the guys that are skiddier out in the front and keeping it low. That's probably the biggest adjustment for me and Ish [Sodhi] where in the past you look for that over-spin and bounce, it's a little less effective in Sharjah."

Namibia, too, mathematically still have a chance to qualify for the semifinal, but they will be taking one match at a time, keen to first put in performances that ensure they are constantly competing with the higher-ranked sides.

New Zealand have worked like a swell-oiled machine, with several players doing their bit in defined roles. Martin Guptill's 93 against Scotland was perhaps the first big example of individual brilliance from them.

Namibia could bring back Bernard Scholtz, the left-arm spinner, especially if the Sharjah surface has something for spin. They have tweaked their opening combination for a few games, but might stick to the Stephan Baard-Michael van Lingen one for another game. There are injury concerns over their captain Gerhard Erasmus, who has been managing a long-standing finger injury with injections.

"We know New Zealand are a tough opposition. They've got world-class players there. And we're again being seen as the underdogs in the game, but we've played the games at Sharjah before, we've had a bit of success at Sharjah, and we think it's a wicket that could suit our type of bowling. So we've done our prep," said Namibia all-rounder David Wiese.

Probable XI: Martin Guptill, Daryl Mitchell, Kane Williamson (capt), Devon Conway (wk), Glenn Phillips, Jimmy Neesham, Mitchell Santner, Adam Milne, Tim Southee, Trent Boult, Ish Sodhi.

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Probable XI: Stephan Baard, Michael van Lingen, Craig Williams, Gerhard Erasmus (capt), David Wiese, JJ Smit, Nicol Loftie-Eaton, Zane Green (wk), Jan Frylinck, Ruben Trumpelmann, Bernard Scholtz.

(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)

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