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Sep 7, 2015 — The numbers before the mm relate to the focal length of the lens. Essentially, focal length means what you are going to be able to see when ...

The diffraction pattern resulting from a uniformly illuminated circular aperture has a bright region in the center, known as the Airy disc which together with a ...

Homogeneous 中文 醫學

The con­stant angle of view of a prime lens forces this type of experimentation—“zooming with your feet”—because the oth­er options are either bad pic­tures or no pic­tures. Fur­ther­more, restrict­ing your­self to a sin­gle focal length for an extend­ed peri­od of time acquaints you to its angle of view and allows you to visu­al­ize a com­po­si­tion before rais­ing the cam­era to your face.

The focal length of a lens deter­mines its mag­ni­fy­ing pow­er, which is the appar­ent size of your sub­ject as pro­ject­ed onto the focal plane where your image sen­sor resides. A longer focal length cor­re­sponds to greater mag­ni­fy­ing pow­er and a larg­er ren­di­tion of your sub­ject, and vice ver­sa.

Sub­ject size is direct­ly pro­por­tion­al to the focal length of the lens. For exam­ple, if you pho­to­graph a soc­cer play­er kick­ing a ball, then switch to a lens that is twice the focal length of the first, the ren­dered size of every ele­ment in your image, from the per­son to the ball, will be dou­bled in size along the lin­ear dimen­sions.

heterogeneity中文

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homogeneity of variance中文

There are two types of wide-angle lens­es, rec­ti­lin­ear and fish­eye (some­times termed curvi­lin­ear). The vast major­i­ty of wide-angle lens—and oth­er focal lengths, too—are rec­ti­lin­ear. These types of lens­es are designed to ren­der the straight ele­ments found in a scene as straight lines on the pro­ject­ed image. Despite this, wide-angle rec­ti­lin­ear lens­es cause ren­dered objects to pro­gres­sive­ly stretch and enlarge as they approach the edges of the frame. In pho­tog­ra­phy, all fish­eye lens­es are ultra wide-angle lens­es that pro­duce images fea­tur­ing strong con­vex cur­va­ture. Fish­eye lens­es ren­der the straight ele­ments of a scene with a strong cur­va­ture about the cen­tre of the frame (the lens axis). The effect is sim­i­lar to look­ing through a door’s peep­hole, or the con­vex safe­ty mir­rors com­mon­ly placed at the blind cor­ners of indoor park­ing lots and hos­pi­tal cor­ri­dors. Only straight lines that inter­sect with the lens axis will be ren­dered as straight in images cap­tured by fish­eye lens­es.

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The rela­tion­ship between the angle of view and a lens’s focal length is rough­ly inverse­ly pro­por­tion­al from 50mm and up on a full-frame cam­era. How­ev­er, as the focal length grows increas­ing­ly short­er than 50mm, that rough pro­por­tion­al­i­ty breaks down, and the rate of change in the angle of view slows. For exam­ple, the change in angle of view from 100mm to 50mm is more pro­nounced than the change from 28mm to 14mm.

Due to their abil­i­ty to mag­ni­fy dis­tance objects, long-focus lens­es present pho­tog­ra­phers with many uses. They are almost uni­ver­sal­ly laud­ed for por­trai­ture because their nar­row angle of view allows for a high­er mag­ni­fi­ca­tion of the sub­ject from con­ven­tion­al­ly more pleas­ing per­spec­tives. As a rule of thumb, a desir­able focal length for a por­trait lens starts at twice the nor­mal focal length for the cam­era sys­tem (about 85 mm for full-frame and 56 mm for APS‑C).

Homogeneity

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A true zoom lens, known as a par­fo­cal lens, main­tains a set focus dis­tance across its entire focal length range. In the days before dig­i­tal photography—before elec­tron­ic aut­o­fo­cus, even—it was com­mon prac­tice to focus a zoom lens at its longest focal length before tak­ing the pic­ture at the desired (if dif­fer­ent) focal length. This tech­nique is no longer pos­si­ble because con­tem­po­rary vari­able focal length lens­es designed for pho­tog­ra­phy are almost exclu­sive­ly var­i­fo­cal lens­es, which do not main­tain set focus across their zoom range. In prac­tice, most pho­tog­ra­phers do not know the dif­fer­ence because the aut­o­fo­cus algo­rithms in their cam­eras com­pen­sate for the slight vari­a­tions.

If you’re into math—and who isn’t?—the gen­er­al for­mu­la for cal­cu­lat­ing the angle of view when you know the focal length and the sen­sor size is:

As you have learned in the sec­tion on aper­tures and f‑numbers, “an increase in focal length decreas­es the inten­si­ty of light reach­ing the image sen­sor.” This rela­tion­ship is most obvi­ous in zoom lens­es. A “vari­able” aper­ture zoom lens is a lens whose max­i­mum aper­ture becomes small­er with increased focal length. These types of zoom lens­es are sim­ple to spot because they list a max­i­mum aper­ture range instead of a sin­gle num­ber. The range spec­i­fies the max­i­mum aper­ture for the short­est and longest focal lengths of the zoom range. Vari­able aper­ture lens­es are the most com­mon type of zoom lens. A con­stant aper­ture or “fixed” aper­ture zoom lens is one whose max­i­mum aper­ture remains con­stant across the entire zoom range. Fixed aper­ture lens­es are typ­i­cal­ly more mas­sive and more expen­sive than their vari­able aper­ture coun­ter­parts. They are also more straight­for­ward to work with when prac­tic­ing man­u­al expo­sure at the max­i­mum aper­ture since no com­pen­sa­tion for lost light is required dur­ing zoom­ing.

A zoom lens allows pho­tog­ra­phers to vary its effec­tive focal length through a spec­i­fied range, which alters the angle of view and mag­ni­fi­ca­tion of the image. Zoom lens­es are described by stat­ing their focal length range from the short­est to longest, such as 24–70 mm and 70–200 mm. The focal length range of a zoom lens direct­ly cor­re­lates to its zoom ratio, which is derived by divid­ing the longest focal length by the short­est. Both of the lens­es above have a zoom ratio of approx­i­mate­ly 2.9x, or 2.9:1. The zoom ratio also describes the amount of sub­ject mag­ni­fi­ca­tion a sin­gle lens can achieve across its avail­able focal length range.

heterogeneous中文

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Homogeneity of variance

In pho­tog­ra­phy, the most essen­tial char­ac­ter­is­tic of a lens is its focal length, which is a mea­sure­ment that describes how much of the scene in front of you can be cap­tured by the cam­era. Tech­ni­cal­ly, the focal length is the dis­tance between the sec­ondary prin­ci­pal point (com­mon­ly and incor­rect­ly called the opti­cal cen­tre) and the rear focal point, where sub­jects at infin­i­ty come into focus. The focal length of a lens deter­mines two inter­re­lat­ed char­ac­ter­is­tics: mag­ni­fi­ca­tion and angle of view.

A prime or fixed focal length lens has a set focal length that can­not be changed. There are sev­er­al crit­i­cal dif­fer­ences between prime and zoom lens­es that you should know. Prime lens­es are gen­er­al­ly small­er, faster, and have bet­ter opti­cal char­ac­ter­is­tics than zoom lens­es. Despite this, pho­tog­ra­phers fre­quent­ly opt to shoot with zoom lens­es because of their con­ve­nience: a sin­gle lens can replace sev­er­al of the most pop­u­lar focal length prime lens­es. This is espe­cial­ly impor­tant when you’d pre­fer to pack light, such as dur­ing a trip or a hike.

For any giv­en cam­era sys­tem, nor­mal lens­es are gen­er­al­ly the “fastest” avail­able. Adjec­tives such as “fast” and “slow” always describe lens speed, which refers to a lens’ max­i­mum aper­ture open­ing. For instance, a lens with a ƒ/2 or larg­er aper­ture is gen­er­al­ly con­sid­ered fast; a lens with a ƒ/5.6 or small­er aper­ture is deemed to be slow. How is speed rel­e­vant to aper­ture? Recall the reci­procity law: larg­er aper­tures per­mit more light into the cam­era, there­by allow­ing you to use faster shut­ter speeds, and vice ver­sa.

2015710 — The focal length of a lens, expressed in millimeters, is the distance from the lens's optical center (or nodal point) to the image plane in the camera.

A: Working distance refers to the distance from the objective's front lens to the focused object. For applications requiring object placement within a chamber ...

The angle of view describes the breadth, or how much, of a scene is cap­tured by the lens and pro­ject­ed onto your camera’s image sen­sor. It’s expressed in degrees of arc and mea­sured diag­o­nal­ly along the image sen­sor. Thus, the angle of view of any lens of a giv­en focal length will change depend­ing on the size of the cam­er­a’s image sen­sor. For exam­ple, a 50 mm lens has a wide angle of view on a medi­um for­mat cam­era, a nor­mal angle of view on a full-frame cam­era, a nar­row­er angle of view on an APS‑C cam­era, and a nar­row angle of view on a Micro Four-Thirds cam­era.

For instance, on full-frame cam­eras, whose image sen­sors mea­sure 36×24 mm, the diag­o­nal length is approx­i­mate­ly 43 mm, and yet, the 50 mm lens is con­ven­tion­al­ly con­sid­ered nor­mal. On APS‑C cam­eras (24 × 16 mm), whose diag­o­nal spans about 28 mm, a 35 mm focal length is regard­ed as nor­mal pri­mar­i­ly because its angle of view is sim­i­lar to the 50 mm lens on the full-frame for­mat. There­fore, nor­mal focal lengths will dif­fer as a func­tion of the camera’s image sen­sor size. In fact, as you con­tin­ue read­ing, keep in mind that descrip­tive terms such as “ultra-wide,” “short,” “long,” et cetera, implic­it­ly refer to the angle of view of a lens.

Beyond por­trai­ture, long-focus lens­es are use­ful for iso­lat­ing sub­jects in busy and crowd­ed envi­ron­ments. Pho­to­jour­nal­ists, wed­ding, and sports pho­tog­ra­phers exploit this abil­i­ty reg­u­lar­ly. Due to their mag­ni­fy­ing pow­er, super tele­pho­to lens­es are a main­stay for wildlife and nature pho­tog­ra­phers. Last­ly, long-focus lens­es are fre­quent­ly used by land­scape pho­tog­ra­phers to cap­ture dis­tant vis­tas or to iso­late a fea­ture from its sur­round­ings.

Wide-angle lens­es rep­re­sent the only prac­ti­cal method of cap­tur­ing a scene whose essen­tial ele­ments would oth­er­wise fall out­side the angle of view of a nor­mal lens. Con­ven­tion­al sub­jects of ultra wide-angle lens­es include archi­tec­ture (espe­cial­ly inte­ri­ors), land­scapes, seascapes, cityscapes, astropho­tog­ra­phy, and the entire domain of under­wa­ter pho­tog­ra­phy. Wide-angle lens­es are often used for pho­to­jour­nal­ism, street pho­tog­ra­phy, auto­mo­tive, some sports, and niche por­trai­ture.

It’s impor­tant to under­stand that the degree to which the focal length mag­ni­fies an object does not depend on your cam­era or the size of its image sen­sor. Assum­ing a fixed sub­ject and sub­ject dis­tance, every lens of the same focal length will project an image of your sub­ject at the same scale. For exam­ple, if a 35 mm lens casts a 1.2 cm image of a per­son, that image will remain 1.2 cm high regard­less of your camera’s sen­sor for­mat. How­ev­er, on a Micro Four Thirds for­mat cam­era, the image of that per­son will fill the height of the frame, where­as it will occu­py half the height of a full-frame image sen­sor, and about one-third the height of a medi­um for­mat image sen­sor. As you progress from a small­er sen­sor to a larg­er one, the 1.2 cm high pro­jec­tion of the per­son remains unchanged, but it occu­pies a small­er part of the total frame. There­fore, although the absolute size of the image will stay con­stant across vary­ing image sen­sor for­mats, its size in pro­por­tion to each image sen­sor for­mat will be dif­fer­ent.

homogeneity數學

homogeneity統計

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Lens­es with an angle of view of 35° or nar­row­er are con­sid­ered long-focus lens­es. This trans­lates to a focal length of about 70 mm and greater on full-frame cam­eras, and about 45 mm and longer on APS‑C cam­eras. It’s com­mon for pho­tog­ra­phers to (incor­rect­ly) refer to long-focus lens­es as “tele­pho­to” lens­es. A true tele­pho­to lens is one whose indi­cat­ed focal length is longer than the phys­i­cal length of its body. Due to this ubiq­ui­tous mis­use of the word, there exists a fur­ther clas­si­fi­ca­tion of long-focus lens­es whose angle of view is 10° or nar­row­er called “super tele­pho­to” lens­es (equal to or greater than 250 mm on full-frame cam­eras and 165 mm on APS‑C cam­eras). For­tu­nate­ly, super tele­pho­to lens­es are more often than not actu­al tele­pho­to designs. A great exam­ple is the Canon EF 800 mm f/5.6L IS USM Lens, which is only 461 mm long.

A “nor­mal” lens is defined as one whose focal length is equal to the approx­i­mate diag­o­nal length of a camera’s image sen­sor. In prac­tice, such lens­es tend to fall into a range of slight­ly longer focal lengths that are claimed to pos­sess an angle of view com­pa­ra­ble to that of the human eye’s cone of visu­al atten­tion, which is about 55°.

It’s impor­tant to rec­og­nize that the con­ve­nience and flex­i­bil­i­ty of zoom lens­es can inspire lazy pho­tog­ra­phy. The ease of chang­ing the angle of view encour­ages pho­tog­ra­phers to set­tle on com­po­si­tions that are good-enough, instead of seek­ing out bet­ter per­spec­tives and gain­ing a deep­er under­stand­ing of their sub­jects. What­ev­er lens you have, be it zoom or prime, it’s vital for the devel­op­ment of good pho­tog­ra­phy to con­sid­er your sub­ject from sev­er­al per­spec­tives by walk­ing towards, step­ping away, and cir­cling around them.

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In gen­er­al, a short focal length—or short focus, or “wide-angle”—lens is one whose angle of view is 65° or greater. Recall from above that angle of view is deter­mined by both focal length and image sen­sor size, which means that what qual­i­fies as “short” is pred­i­cat­ed upon a camera’s image sen­sor for­mat. There­fore, on full-frame cam­eras, the thresh­old for wide-angle lens­es is 35 mm or less, and on APS‑C cam­eras, it’s 23 mm or less. Lens­es with an angle of view of 85° or greater are called “ultra wide-angle,” which is about 24 mm or less on full-frame and 16mm or less on APS‑C cam­eras.

In pho­tog­ra­phy, the term macro refers to extreme close-ups. Macro lens­es are nor­mal to long-focus lens­es capa­ble of focus­ing on extreme­ly close sub­jects, there­by ren­der­ing large repro­duc­tions. The mag­ni­fi­ca­tion ratio or mag­ni­fi­ca­tion fac­tor is the size of the sub­ject pro­ject­ed onto the image sen­sor in com­par­i­son to its actu­al size. A macro lens’ mag­ni­fi­ca­tion ratio is cal­cu­lat­ed at its clos­est focus­ing dis­tance. A true macro lens is capa­ble of achiev­ing a mag­ni­fi­ca­tion ratio of 1:1 or high­er. Lens­es with mag­ni­fi­ca­tion ratios from 2:1 to 10:1 are called super macro. Ratios over 10:1 cross over into the field of microscopy. When shop­ping for a macro lens, keep in mind that in the con­text of kit lens­es and point-and-shoot cam­eras, some man­u­fac­tur­ers use the macro moniker as mar­ket­ing short­hand for “close-up pho­tog­ra­phy.” These prod­ucts do not achieve 1:1 mag­ni­fi­ca­tion ratios. When in doubt, check the tech­ni­cal spec­i­fi­ca­tions.