2 MegaPixel Fixed Focal Length Lenses - fixed focal length

 2024-09-06 19:21:05

source of width δ Light waves emitted from the two edges of the source have a some definite phase difference right in the center between the two points at some time t. A ray traveling from the left edge of δ to point P2 must travel a distance ~d(sinθ)/2 farther then a ray traveling to the center. The path of a ray traveling from the right edge of δ to point P2 travel is ~d(sinθ)/2 shorter then the path to the center. The path difference for the two rays therefore is dsinθ, which introduces a phase difference Δφ' = 2πdsinθ/λ. For the distance from P1 to P2 along the wave front we therefore get a phase difference Δφ = 2Δφ' = 4πdsinθ/λ. Wavelets emitted from the two edges of the source are that are in phase at P1 at time t are are out of phase by 4πdsinθ/λ at P2 at the same time t. We have sinθ ~ δ/(2L), so Δφ = 2πdδ/(Lλ). When Δφ = 1 or Δφ ~ 60o, the light is no longer considered coherent. Δφ = 1 --> d = Lλ/(2πδ) = 0.16 Lλ/δ.]

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.

Uncertainty principle for wave packets: ΔfΔt ~ 1. The frequency bandwidth is of the same order as the reciprocal of the temporal extend of the pulse.

Focal length of lensformula

[At time t look at a source of width δ a perpendicular distance L from a screen. Look at two points (P1 and P2) on the screen separated by a distance d. The electric field at P1 and P2 is a superposition of the electric fields of the waves emitted by all source points, whose emissions are not correlated. In order for EM waves leaving P1 and P2 to produce a recognizable interference pattern, the superpositions at P1 and P2 must stay in phase. screen source of width δ Light waves emitted from the two edges of the source have a some definite phase difference right in the center between the two points at some time t. A ray traveling from the left edge of δ to point P2 must travel a distance ~d(sinθ)/2 farther then a ray traveling to the center. The path of a ray traveling from the right edge of δ to point P2 travel is ~d(sinθ)/2 shorter then the path to the center. The path difference for the two rays therefore is dsinθ, which introduces a phase difference Δφ' = 2πdsinθ/λ. For the distance from P1 to P2 along the wave front we therefore get a phase difference Δφ = 2Δφ' = 4πdsinθ/λ. Wavelets emitted from the two edges of the source are that are in phase at P1 at time t are are out of phase by 4πdsinθ/λ at P2 at the same time t. We have sinθ ~ δ/(2L), so Δφ = 2πdδ/(Lλ). When Δφ = 1 or Δφ ~ 60o, the light is no longer considered coherent. Δφ = 1 --> d = Lλ/(2πδ) = 0.16 Lλ/δ.]

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:

A distance L from a thermal monochromatic (line) source whose linear dimensions are on the order of δ, two slits separated by a distance greater than dc = 0.16λL/δ will no longer produce a recognizable interference pattern. We call πdc2/4 the coherence area of the source.[At time t look at a source of width δ a perpendicular distance L from a screen. Look at two points (P1 and P2) on the screen separated by a distance d. The electric field at P1 and P2 is a superposition of the electric fields of the waves emitted by all source points, whose emissions are not correlated. In order for EM waves leaving P1 and P2 to produce a recognizable interference pattern, the superpositions at P1 and P2 must stay in phase. screen source of width δ Light waves emitted from the two edges of the source have a some definite phase difference right in the center between the two points at some time t. A ray traveling from the left edge of δ to point P2 must travel a distance ~d(sinθ)/2 farther then a ray traveling to the center. The path of a ray traveling from the right edge of δ to point P2 travel is ~d(sinθ)/2 shorter then the path to the center. The path difference for the two rays therefore is dsinθ, which introduces a phase difference Δφ' = 2πdsinθ/λ. For the distance from P1 to P2 along the wave front we therefore get a phase difference Δφ = 2Δφ' = 4πdsinθ/λ. Wavelets emitted from the two edges of the source are that are in phase at P1 at time t are are out of phase by 4πdsinθ/λ at P2 at the same time t. We have sinθ ~ δ/(2L), so Δφ = 2πdδ/(Lλ). When Δφ = 1 or Δφ ~ 60o, the light is no longer considered coherent. Δφ = 1 --> d = Lλ/(2πδ) = 0.16 Lλ/δ.]

FOV tofocal length

Consider a wave propagating through space. Coherence is a measure of the correlation that exists between the phases of the wave measured at different points. The coherence of a wave depends on the characteristics of its source.

We can produce coherent light from an incoherent source if we are willing to throw away a lot of the light. We do this by first spatially filtering the light from the incoherent source to increase the spatial coherence, and then spectrally filtering the light to increase the temporal coherence.

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.

If we know the wavelength or frequency spread of a light source, we can calculate lc and tc. We cannot observe interference patterns produced by division of amplitude, such as thin-film interference, if the optical path difference greatly exceeds lc.

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 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.

Fourier's theorem states that any periodic function with period T (or spatial period or wavelength L) can be synthesized by a sum of harmonic functions whose periods (wavelengths) are integral submultiples of T (or L), such as T/2, T/3, ..., (or L/2, L/3, ...).

A sinusoidal plane wave extends to infinity in space and time. It is perfectly coherent in space and time, its coherence length, coherence time, and coherence area are all infinite. All real waves are wave pulses, they last for a finite time interval and have finite extend perpendicular to their direction of propagation. They are mathematically described by non-periodic functions. We therefore have to learn how to analyze non-periodic functions to find the frequencies present in wave pulses to determine Δω and the coherence length.

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.

Focal length

f(ω) is a representation of the wave train in frequency space. It gives the amplitudes and phases of the harmonic waves of all possible frequencies needed to synthesize the wave train.

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.

focallength是什么

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.

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.

Camerafocal lengthchart

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°.

Any set of sinusoidal waves whose frequencies do not belong to a harmonic series will combine to produce a complex wave that is not periodic. Any non-periodic waveform may be built from a set of sinusoidal waves. Each component must have just the right amplitude and relative phase to produce the desired waveform.

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.

Assume our source emits waves with wavelength λ ± Δλ. Waves with wavelength λ and λ + Δλ, which at some point in space constructively interfere, will no longer constructively interfere after some optical path length lc = λ2/(2πΔλ); lc is called the coherence length.

focallength中文

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.

Shortfocal length

Any piece-wise regular periodic function (finite # of discontinuities, finite # of extreme values) can be written as a series of imaginary exponentials. Assume f(t) is a periodic function of t with fundamental period T = 1/f.

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.

screen source of width δ Light waves emitted from the two edges of the source have a some definite phase difference right in the center between the two points at some time t. A ray traveling from the left edge of δ to point P2 must travel a distance ~d(sinθ)/2 farther then a ray traveling to the center. The path of a ray traveling from the right edge of δ to point P2 travel is ~d(sinθ)/2 shorter then the path to the center. The path difference for the two rays therefore is dsinθ, which introduces a phase difference Δφ' = 2πdsinθ/λ. For the distance from P1 to P2 along the wave front we therefore get a phase difference Δφ = 2Δφ' = 4πdsinθ/λ. Wavelets emitted from the two edges of the source are that are in phase at P1 at time t are are out of phase by 4πdsinθ/λ at P2 at the same time t. We have sinθ ~ δ/(2L), so Δφ = 2πdδ/(Lλ). When Δφ = 1 or Δφ ~ 60o, the light is no longer considered coherent. Δφ = 1 --> d = Lλ/(2πδ) = 0.16 Lλ/δ.]

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.

[The phase of a wave propagating into the x-direction is given by φ = kx - ωt. Look at the wave pattern in space at some time t. At some distance l the phase difference between two waves with wave vectors k1 and k2 which are in phase at x = 0 becomes Δφ = (k1 - k2)l. When Δφ = 1, or Δφ ~ 60o, the light is no longer considered coherent. Interference and diffraction patterns severely loose contrast. We therefore have 1 = (k1 - k2)lc = (2π/λ - 2π/(λ + Δλ))lc. (λ + Δλ - λ)lc/(λ(λ + Δλ)) ~ Δλlc/λ2 = 1/2π. lc = λ2/(2πΔλ).]

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).

According to Fourier analysis, an arbitrary periodical waveform can be regarded as a superposition of sinusoidal waves. Fourier synthesis means superimposing many sinusoidal waves to obtain the arbitrary periodic waveform.

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.

Light waves emitted from the two edges of the source have a some definite phase difference right in the center between the two points at some time t. A ray traveling from the left edge of δ to point P2 must travel a distance ~d(sinθ)/2 farther then a ray traveling to the center. The path of a ray traveling from the right edge of δ to point P2 travel is ~d(sinθ)/2 shorter then the path to the center. The path difference for the two rays therefore is dsinθ, which introduces a phase difference Δφ' = 2πdsinθ/λ. For the distance from P1 to P2 along the wave front we therefore get a phase difference Δφ = 2Δφ' = 4πdsinθ/λ. Wavelets emitted from the two edges of the source are that are in phase at P1 at time t are are out of phase by 4πdsinθ/λ at P2 at the same time t. We have sinθ ~ δ/(2L), so Δφ = 2πdδ/(Lλ). When Δφ = 1 or Δφ ~ 60o, the light is no longer considered coherent. Δφ = 1 --> d = Lλ/(2πδ) = 0.16 Lλ/δ.]

Let us look at a simple example. Imagine two corks bobbing up and down on a wavy water surface. Suppose the source of the water waves is a single stick moved harmonically in and out of the water, breaking the otherwise smooth water surface. There exists a perfect correlation between the motions of the two corks. They may not bop up and down exactly in phase, one may go up while the other one goes down, but the phase difference between the positions of the two corks is constant in time. We say that the source is perfectly coherent. A harmonically oscillating point source produces a perfectly coherent wave.

f(ω) = (A/((2π)1/2i(ω-ω0)))[exp(i(ω+ω0)(T1/2)) - exp(-i(ω-ω0)(T1/2))] = (AT1/(2π)1/2)sin[(ω-ω0)(T1/2)]/(ω-ω0)(T1/2) = (AT1/(2π)1/2)sin(u)/u with u = (ω-ω0)(T1/2).

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.

Focaldistance vsfocal length

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.

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.

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.

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.

The light pulse in the figure above contains many frequencies. To determine the coherence length, we need to know its frequency content.

Any set of sinusoidal waves whose frequencies belong to a harmonic series will combine to produce a periodic complex wave, whose repetition frequency is that of the series fundamental. The individual components may have any amplitudes and any relative phases. These amplitudes and phases determine the shape of the complex waveform.

While it is not zero for |x| > some number, we find that it has a dominant peak between x = -π and x = π with smaller fringes on the sides. The major contributions to f(ω) sinc[(ω-ω0)(T1/2)] therefore come from the region -π < (ω - ω0)(T1/2) < π, or -2π < (ω - ω0)T1 < 2π. If we define Δω = (ω-ω0) as the width of the wave train in frequency space and Δt = T1/2 as its width in time, then ΔωΔt = 2π, ΔfΔt = 1.

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.

The wave pattern travels through space with speed c. The coherence time tc is tc = lc/c. Since λf = c, we have Δf/f = Δω/ω = Δλ/λ. We can write

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.