You note that using a macro adapter affects field of view. In fact, they also increase the focal length, although since macro extension tubes remove the ability to actually focus at infinity, we leave practical reality and get into the realm of theory.

fov是什么

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The very good reason for cameras is that field of view also strongly depends on the sensor size. A small sensor captures a more narrow view than a larger sensor can.

From the physics POV of it all, what determines the effective FOV for a given sensor is the effective focal length of the lens and the distance between the back principal plane of the lens to the sensor, which is determined unambiguously by the distance between the principal plane and the flange of the lens plus the distance between the flange of the camera and the sensor.

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The lens focal length does provide some field of view, which the sensor size crops to capture possibly a lesser amount of it. Cameras with tiny sensors only capture a small field, so they have to use a much shorter focal length lens to compare to an expected "regular picture" view seen by other cameras with larger sensors. Crop Factor compares that sensor size view to the historical 35 mm film frame size view that so many of us are very familiar with.

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fov和焦距的关系

Focal length is NOT at all about the mounting flange distance. The internal focus node can be moved by design. A "telephoto" lens means that node is slightly in front of the front lens element (lens is shorter than the focal length). A retro-focus (wide angle) lens places that focus node behind the rear element, to create space behind the lens. But focal length is to that focal node.

Focal length

To further clarify by an example: you can have a 50mm and a 40mm lenses both with the same distance between the principal plane and the flange of the lens. In this case, if you place the 40mm lens sufficiently further from the sensor (compared to the 50mm lens) you will have the same effective FOV.

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field ofview中文

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Please try to answer my original question instead of trying to educate me about optics - that part of the conversation I got down pretty good :)

Focaldistance vsfocal length

Polarizers are used to filter the input polarization, increase its purity, or separate orthogonal components of a linearly polarized beam. However, a polarizer cannot convert the polarization state of the input light into a different polarization state. For this type of modification, an optical component known as a waveplate or retarder is required. To understand its operation, it is important to know that any polarization state (not just linear) can be decomposed into orthogonal components. The difference between the polarization states then results from the phase difference between the orthogonal components. Linear polarization possesses components that are in-phase, i.e., no phase difference, but have different amplitudes depending on their angle. Circular and elliptical polarization components possess a phase difference of π/2 or a quarter of a wavelength (circular polarization has the same amplitudes for the different components while elliptical has different amplitudes). Consequently, in order to convert one polarization to another, the phase difference between the two components must be controlled. This can be accomplished by sending a polarized beam into a birefringent crystal such that the o-wave or e-wave each experience a different phase delay. The operation of a waveplate and a summary of how quarter and half waveplates convert one polarization state to another are shown in Figure 4. An important case of polarization conversion is shown on the right side of Figure 4. A half waveplate can rotate the angle of a linearly polarized beam to any other angle, which can be used for rotating a vertically polarized laser beam to obtain horizontal polarization. Furthermore, proper combinations of waveplates and polarizers can be used to form optical systems that allow for variable attenuation of a laser beam or for isolating a laser cavity from spurious reflections.

FOV tofocal lengthcalculator

The way in which polarized light interacts with an optical material can enable selective filtering of the polarization or conversion of the incident polarization state to a different one. This polarization control relies on a material's optical properties to respond differently depending on the polarization of the incident light. A material that exhibits birefringence, or different refractive indices for different input polarizations, is said to be anisotropic. This anisotropy affects the transmission and absorption properties of light and is the primary mechanism used in polarizers and waveplates as discussed below. However, even isotropic materials (same index for different polarizations) can enable polarization selection via reflection. The Fresnel equations describe the change in reflectivity as a function of angle of incidence. For a linearly polarized beam, both S- and P-polarizations exhibit different changes in reflectivity versus incident angle. There is an incident angle known as Brewster's angle (θB) at which P-polarized light is transmitted without loss, or exhibits zero reflectance, while S-polarized light is partially reflected. This angle can be determined from Snell's law to be θB = arctan(n2/n1). Figure 2 shows this response when light is incident from air onto a dielectric material where θB ≈ 56°. This polarization-selective reflectivity is exploited in laser cavities to produce strongly polarized light and for fine tuning of the output laser wavelength.

Field of view

In photography, it's the accepted norm to say that if you know the sensor size of your camera and the focal length of your lens, then you know the field of view of your system.

When focused closer than infinity, the lens is extended forward (the frontal elements are, or possibly only internal elements) so that the internal focus node in the lens is further from the sensor plane. If we instead assume focal length is the distance from this internal node to the sensor plane, then of course the focal length is a bit longer when focused closer. That longer focal length changes things, like f-number, which can affect exposure, so regular lenses don't allow distances shorter than some nominal close distance, typically at around 0.1x magnification.

Focal length and lens FOV are inherently the same thing. The variable is how much of the lens' FOV is utilized (i.e. extension tubes/TC's/crop sensor/etc). Why would you specify a lens' characteristic by something that may be variable?

1/F = 1/S1 + 1/S2, Where F is the focal length of the lens, ans S1 and S2 are the subject and image distance respectively. https://en.wikipedia.org/wiki/Angle_of_view

My question was: given that both parameters affect the FOV, why is it then that we attribute only the focal length to the FOV of the lens?

Incoherent light sources such as lamps, LEDs, or the sun typically emit unpolarized light, which is a random superposition of all possible polarization states. On the other hand, the output light from a laser is typically highly polarized, that is, it consists almost entirely of one linear polarization. Analyzing laser polarization is easier if it is decomposed into two linear components in orthogonal directions. In this way, depicting the polarization can be done using the standard symbols shown in Figure 1. The upper part of the table lists the symbols generally used for unpolarized, vertically polarized, and horizontally polarized light. For the graphic shown in the figure, the vertical direction would be along the y-axis while the horizontal direction would lie along the x-axis. When a plane of incidence is specified (see lower part of table in Figure 1), the polarization components acquire specific designations. S-polarization refers to the component perpendicular to the plane while P-polarization refers to the component in the plane. Examples of the depictions of linearly polarized light are illustrated in the remaining figures of the section.

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This question is predicated on a misconception. The flange distance is included in the focal length in lens labels — it is the distance from the optical center of the lens focused at infinity to the imaging medium. This includes the flange distance. (See What is the reference point that the focal length of a lens is calculated from?, and What exactly is focal length when there is also flange focal distance?)

The focal length marked on the lens is when focused at infinity. Some imagine that is the definition of focal length, but it is merely one setting for it. Zoom lenses also vary focal length.

A polarizer is an optical component whose transmission depends strongly on the incident polarization of the light. Polarizers typically filter linear polarization, so an ideal polarizer would transmit 100% of one polarization component while rejecting all of the orthogonal component (see Figure 3). In practice, a portion of the undesired polarization will be transmitted. The transmittances of the target polarization and the undesired polarization through the polarizer are measured (by simply rotating the polarizer by 90 degrees) and the extinction ratio is defined as the ratio of these transmittances. The difference between a polarizer and a Brewster plate is that the former results in strong polarization-dependent transmission while the latter does not (only the reflection is highly polarized).

In the link above it can be seen that the angle of view depends on S2. If S1 is large, F and S2 are approximately the same, and one can say that the field of view is related to the focal length. In macro photography the subject distance S2 is not very large, therefore it has a significant influence, and the field of view is no longer related to the focal length of the lens. Because we are used to relating the field of view to the focal length, we define the effective focal length f, as the image distance. In that case the field of view is related to the effective focal length, which depends on the subject distance.

However, in optics, it's well known that for a fixed sensor size, the distance from the lens to the image plane (which we can equate with the flange distance) also affects your field of view. Everyone who mounted his\her lens on a macro adapter had seen that increasing the flange distance will narrow down your field of view, and they will end up with a macro lens.

Unlike the angle of coverage, the field of view, or angle of view are not lens properties. They depend on the focal length of the lens, the size of the sensor and the distance between the rear focal point and the sensor. When a lens is focused at infinity, the distance between the rear focal point and the sensor is zero. When the lens is focused on something closer, the sensor is placed behind the focal point. The location can be determined with the thin lens formula:

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Polarizers rely on birefringent materials and, since the index of refraction is complex, these materials can exhibit a polarization-dependent absorption and refraction. The first polarizers were based on selective absorption of incident light and are usually denoted as dichroic polarizers. Typical materials used for this anisotropic absorption are stretched polymers or elongated silver crystals; their operation is shown in Figure 3. The strongly absorbing axis of the material is placed perpendicular to the desired output polarization such that the undesired polarization is strongly absorbed. A different type of polarizer is based on the anisotropic refractive indices of a birefringent crystal such as calcite. A birefringent crystal will produce an o-wave or e-wave depending on the axis of the crystal to which the polarization component is aligned. These waves experience different refractive indices and will possess different critical angles for TIR, resulting in one polarization component being reflected while the other is transmitted (see Figure 3). By placing two calcite prisms back-to-back to form a rectangular optic, the transmitted beam will follow the same direction as the incident beam. The gap between these prisms can either be air or an optically transparent cement, depending on whether a high damage threshold or large acceptance angle, respectively, is desired.

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I realize that it could be the case that it was just an arbitrary historical decision, but I'm curious whether there's justification for that which I'm missing.

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The electric field of a light wave vibrates perpendicularly to the direction of propagation as shown in Figure 1. Since the electric field is a vector quantity, it can be represented by an arrow that has both a magnitude (or length) and a direction of orientation. This orientation direction is the polarization of the light. There are basically three polarization states: linear, circular, and elliptical. These terms describe the path traced out by the tip of the electric field vector as it propagates in space. Figure 1 shows a snapshot in time of a linearly polarized wave. Although the electric field alternates direction (or sign), it stays confined to a single plane. Therefore, sitting at a fixed point in z as time passes, the arrow tip would oscillate up and down along a line. The angle (θ) of this line with respect to some reference set of axes completely specifies this linear polarization state. For circular polarization, the electric field vector tip forms a helix or corkscrew shape. For a fixed point in z, the vector would rotate in time, like the second hand on a watch. Circularly polarized light can be either left-handed or right-handed, depending on the clockwise or counterclockwise nature of the rotation. Elliptical polarization is the most general case of polarization. It is the same as circular polarization but with unequal major and minor axes (for circular polarization, these are equal).

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Lenses are characterized by their optical and physical properties. Field of view is not an optical property, but a consequence of the camera system to which the lens is attached. The same 50mm lens has different fields of view when paired with differently sized sensors, such as crop frame vs full frame.

These two properties are completely independent of each other, but changing either of them will change the effective FOV - this is a fact of geometrical optics.

FOV tofocal length

Precise control of polarization behavior is necessary to obtain optimal performance from optical components and systems. Characteristics such as reflectivity, insertion loss, and beamsplitter ratios will be different for different polarizations. Polarization is also important because it can be used to transmit signals and make sensitive measurements. Even though the light intensity may be constant, valuable information can be conveyed in the polarization state of an optical beam. Deciphering its polarization can reveal how the beam has been modified by numerous material interactions (magnetic, chemical, mechanical, etc.). Sensors and measurement equipment can be designed to operate on such polarization changes. For these reasons, optical components capable of filtering, modifying, and characterizing a light source's polarization are valuable. Such polarization control can be accomplished by exploiting the reflection, absorption, and transmission properties of materials used in these components. The physical phenomena that enable polarization control, as well as the key components that exploit them, are discussed below.

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This means that for a given sensor size, lenses made for different mounts are still comparable — a 24mm lens gives (approximately) the same field of view regardless of the mount distance of any given system. So, focal length does correspond to field of view.