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By understanding and addressing these challenges, photographers can take better control of their depth of field, ultimately creating more captivating and appealing images6.

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I would have been glad to finally remove a serious mistake, but I believe my equations are correct. They agree with those in various textbooks and e.g. also in Wikipedia. Your argument concerning energy swapping back and forth between electric and magnetic fields looks somewhat plausible but is not accurate.

As explained above, a waveplate or other birefringent optical element may rotate the direction of linear polarization, but more generally one will obtain an elliptical polarization state after such an element. True polarization rotation, where a linear polarization state is always maintained (just with variable direction), can occur in the form of optical activity. Some optically active substances such as ordinary sugar (saccharose) can produce substantial rotation angles already within e.g. a few millimeters of propagation length. Optical activity can be accurately measured with polarimeters.

If the oscillations of the horizontal and vertical electric field vector do not have the same strengths, one has the case of an elliptical polarization, where the electric field vector, projected to a plane perpendicular to the propagation direction, moves along an ellipse.

Creating a deep depth of field requires using a small aperture (higher f-number), which allows less light to enter the camera lens. This results in a greater area of focus, keeping more subjects in sharp focus. Using a shorter focal length and increasing the distance between the camera and the subject will also contribute to a deeper depth of field. Reference this B&H Explora article to understand the basics.

The polarization state of monochromatic light is often described with a Jones vector, having complex electric field amplitudes for <$x$> and <$y$> direction, if propagation occurs in <$z$> direction. That Jones vector may be constant over some area across the beam, or it may vary, for example for a radially polarized beam (see above). The effect of optical elements such as waveplates, polarizers and Faraday rotators can be described with Jones matrices, with which the Jones vectors can be transformed by multiplication. (One assumes a linear relationship between input and output amplitudes.) A whole sequence of such optical elements can be described with a single Jones matrix, which is obtained as the product of the matrices corresponding to the components.

To sum up, mastering depth of field requires a combination of aperture settings, focusing techniques, and making appropriate camera and lens choices. By understanding these elements and their relationships, we can produce stunning images with desired focus and blur effects.

One distinguishes left and right circular polarization (see Figure 2). For example, left circular polarization means that the electric (and magnetic) field vector rotates in the left direction, seen in the direction of propagation. For an observer looking against the beam, the rotation of course has the opposite direction.

The polarization state of light often matters when light hits an optical surface under some angle. A linear polarization state is then denoted as p polarization when the polarization direction lies in the plane spanned by the incoming beam and the reflected beam. The polarization with a direction perpendicular to that is called s polarization. These indications have a German origin: s = senkrecht = perpendicular, p = parallel.

Elliptical polarization

There are also azimuthally polarized beams, where the electric field direction at any point is tangential, i.e., perpendicular to a line through the point and the beam axis.

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Note that radial or azimuthal polarization state requires a zero electric field strength and thus also a vanishing optical intensity on the beam axis; it is not compatible with a Gaussian beam, for example. Radially polarized beams frequently exhibit a kind of donut profile.

A radially polarized laser beam may be generated from a linearly polarized beam with some optical element, but it is also possible to obtain radially polarized emission directly from a laser. The advantage of this approach, applied in a solid-state bulk laser, is that depolarization loss may be avoided [4]. Furthermore, there are applications benefiting from radially polarized light.

The decision to use a shallow or deep depth of field depends on the desired outcome and mood you want to convey in a photograph. For instance, a shallow depth of field is often used in portrait photography, highlighting the subject while blurring the background. Alternatively, deep depth of field works well in landscape photography, where the primary goal is to capture everything in sharp focus from foreground to background.

Using the depth of field (DoF) preview button on your camera allows you to see what areas of the image will be in focus. This helps you make adjustments to your aperture or focus distance to achieve the desired effect. When using live view, you can also zoom in on specific areas to check focus, making it even easier to visualize the depth of field.

In photography, controlling the depth of field (DOF) is essential to achieve desired levels of blur and detail in an image. Shallow DOF can be achieved with larger aperture lenses, but in macro or close-up photography, maintaining the right balance can be challenging 1. One solution to maintain an ideal DOF is to use bracketing2. Bracketing involves taking multiple shots of the same subject, with gradually changing aperture settings, to later select the best image with the intended blur and detail.

Accurate focusing plays a crucial role in controlling depth of field. When focusing on a subject, consider using techniques such as manual focus, autofocus points, or focus peaking to ensure the desired area of the image is sharp. Additionally, the distance between you and your subject affects the depth of field: objects closer to the camera will have a more shallow depth of field than those farther away.

In the previous cases, the direction of the electric field vector was assumed to be constant over the full beam profile. However, there are light beams where that is not the case. For example, there are beams with radial polarization, where the polarization at any point on the beam profile is oriented in the radial direction, i.e., away from the beam axis.

To achieve a shallow depth of field, use a large aperture (lower f-number), which allows more light to enter the camera lens. This will create a smaller area of focus in your image, resulting in a blurred background. Using a longer focal length and getting closer to your subject will also help achieve a shallow depth of field. This Shotkit guide offers examples and a depth of field calculator to help.

A circular polarization state can mathematically be obtained as a superposition of electric field oscillations in the vertical and horizontal direction, both with equal strength but a relative phase change of 90°. Effectively, this leads to a rapid rotation of the electric field vector – once per optical cycle – which maintains a constant magnitude.

Your first plot shows the magnetic and electric field in phase – which is wrong. The magnetic field is made from the changing electric field. The two fields swap energy back and forth. Hence the magnetic field is at a maximum when the electric field has the largest rate of change, that is, at zero E field. The magnetic field zeros in strength when the electric field rate of change is zero, at it's peak. These are a simple consequence of Maxwell's Equations and is covered in most any text on E&M. The worst error I have found in years of use of your marvelous resource!

Of course, the polarization can have any other direction perpendicular to the beam axis. Note that a rotation of the polarization by 180° does not lead to a physically distinct state.

Polarization oflight

Another challenge when it comes to DOF is managing the trade-off between aperture size and diffraction. Larger aperture sizes generally create a shallower DOF, while smaller apertures increase DOF and lead to a more detailed image3. However, increasing aperture size beyond a certain point might introduce diffraction, causing a loss of sharpness and reduced image quality4. One way to overcome this is by staying within the sweet spot range of the lens, which is typically between f/5.6 and f/11, where diffraction is minimal.

There are three main factors that affect depth of field in photography: aperture, focal length, and distance to the subject. Changing any one of these factors will alter the appearance of the depth of field in your images. This TechRadar article provides an in-depth explanation of each factor's impact.

In addition to the aperture, the depth of field is influenced by the focal length of the lens and the distance between the camera and the subject. A lens with a longer focal length tends to produce a shallower depth of field, while a lens with a shorter focal length generally results in a greater area of focus. Additionally, the closer the camera is to the subject, the shallower the depth of field will be.

Jones vectors can be used only for fully defined polarization states, not for unpolarized or partially polarized beams (see below) having a stochastic nature.

On the other hand, the polarization state of the laser output can be disturbed e.g. by random (and temperature-dependent) birefringence, such as occurs e.g. in optical fibers (if they are not polarization-maintaining or single-polarization fibers) and also in laser crystals or glasses as a result of thermal effects (→ depolarization loss). If the laser gain is not polarization-dependent, small drifts of the birefringence may lead to large changes of the polarization state, and also a significant variation in the polarization state across the beam profile.

There are cases where polychromatic light can be described with a single Jones vector, since all its frequency components have essentially the same polarization state. However, the polarization state is substantially frequency-dependent in other cases.

To better understand the relationship between aperture and depth of field, you can experiment with various f-stop settings on your camera and observe the resulting changes in focus and blur. Keep in mind that a wider aperture also allows more light into the camera, which can affect other settings like ISO and shutter speed.

Various camera settings and lens choices can also impact depth of field. For instance, focal length of the lens influences the depth of field: a wide-angle lens typically results in a deeper depth of field, while a telephoto lens creates a shallower depth of field. Sensor size also plays a role in controlling depth of field, with larger sensors (such as those found in full-frame cameras) producing a shallower depth of field compared to smaller sensors (e.g., APS-C or Micro Four Thirds).

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Mastering depth of field requires the ability to manipulate various factors such as aperture, focal length, and distance from the subject. By adjusting these elements, photographers can create images with a shallow DOF, where only the subject is in focus and the background is blurred, or a deep DOF, where both the subject and background appear sharp. Experimenting with different settings and techniques can help you achieve the desired effect for your photography style, whether it's portraits, landscapes, or anything in between.

Focal length has a significant impact on depth of field. Longer focal lengths result in a shallower depth of field, while shorter focal lengths produce a deeper depth of field. This means that using a telephoto lens will create more background blur, while a wide-angle lens will keep more of the scene in focus. Shotkit provides examples of the difference in depth of field based on focal length.

While optical activity usually results from the presence of chiral molecules, with a concentration difference between the two possible enantiometers, it can also be induced by a magnetic field in a substance which is not naturally optically active. That is called the Faraday effect, and is exploited in Faraday rotators and Faraday isolators.

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Polarization

When it comes to landscape photography, we generally want a wide depth of field to showcase the sharpness, texture, and details across the entire scene. This often involves using a narrow aperture, such as f/8 or f/11, to maintain focus from foreground to background. It's crucial to carefully choose a focal point and balance depth of field with other factors like angle of view, field of view, and camera settings. A more expansive depth of field helps tell a story of the landscape, emphasizing the natural beauty and bringing it to life for the viewer.

A final consideration is the size of the image sensor. Larger sensors typically produce a shallower DOF when compared to smaller sensors, given the same aperture and focal length settings5. Understanding the impact of sensor sizes on DOF can help photographers make better choices when choosing a camera and settings[^;width:400px;height;border;padding:3^6^px;text-align

polarization中文

One technique that photographers use to maximize sharpness across an image is calculating the hyperfocal distance. This is the point at which everything from half the distance to the hyperfocal point to infinity is in focus. It's especially useful in landscape photography, where you want to achieve maximum depth of field.

When discussing depth of field in photography, it is important to distinguish between shallow depth of field and deep depth of field. A shallow depth of field results in only a small range of the image appearing sharp and in focus, while the rest of the scene is blurred. Conversely, a deep depth of field achieves a broader range of focus, where more of the scene appears sharp and clear. This distinction plays a crucial role in the overall aesthetic and composition of a photograph.

In portrait photography, depth of field plays a vital role in highlighting the subject, often by creating an aesthetically pleasing background blur, called bokeh. By using a shallow depth of field, we can isolate the subject and capture sharp, focused portraits with smooth, out-of-focus backgrounds. This separation directs the viewer's attention to the subject's features; while a wider aperture, longer focal length, and closer camera-to-subject distance work together to create a more dramatic effect.

Linearly polarized light can be depolarized (made unpolarized) with a polarization scrambler, which applies the mentioned random polarization changes, or at least quasi-random changes.

There are also partially polarized states of light. These can be described with Stokes vectors (but not with Jones vectors). Further, one can define a degree of polarization which can be calculated from the Stokes vector and can vary between 0 (unpolarized) and 1 (fully polarized).

In many respects, light can be described as a wave phenomenon (→ wave optics). More specifically, light waves are recognized as electromagnetic transverse waves, i.e., with transverse oscillations of the electric and magnetic field.

Another technique for controlling depth of field is focus stacking. This involves taking multiple images at different focus distances, then combining them in an editing program like Photoshop. The result is a single, sharp image with an extended depth of field. A tripod is essential for this technique, ensuring that the camera remains steady between shots.

A light beam is called unpolarized when the analysis with a polarizer results in 50% of the power to be in each polarization state, regardless of the rotational orientation. Microscopically, this usually means that the polarization state is randomly fluctuating, so that on average no polarization is detected. Note that such fluctuations are not possible for strictly monochromatic light.

Fully polarized states can be associated with points on the so-called Poincaré sphere. Partially polarized states correspond to points inside that sphere; unpolarized light is represented by the point at its center.

Circularlypolarized light

The distance between the camera and the subject is another factor that affects depth of field. The closer you are to your subject, the shallower the depth of field, resulting in a blurred background. Conversely, moving farther away from your subject will increase the depth of field, keeping more of the scene in focus. This TechRadar article further explains how distance and focus control sharpness in photos.

In the simplest case, a light beam is linearly polarized, which means that the electric field oscillates in a certain linear direction perpendicular to the beam axis, and the magnetic field oscillates in a direction which is perpendicular both to the propagation axis and the electric field direction. The direction of polarization is taken to be the direction of the electric field oscillations (i.e., not the magnetic ones). For example, a laser beam propagating in <$z$> direction may have the electric field oscillations in the vertical (<$y$>) direction and the magnetic field oscillations in the horizontal (<$x$>) direction (see Figure 1); it can be called vertically polarized or <$y$>-polarized. In a different perspective, this is also shown in the second part of Figure 2.

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Understanding the factors affecting depth of field — including the relationship between aperture, f-stop, focal length, and distance — allows us to create images with the desired focus and blur. By considering these elements, we can effectively control the aesthetic and composition of our photos.

Similarly, in wildlife photography, a shallow depth of field is helpful to isolate an animal against its surroundings and make it stand out. However, when photographing animals within their habitat or interacting with each other, a wider depth of field allows the viewer to appreciate the context, the landscape, and the circle of life in which these animals live. Each unique situation and desired outcome will dictate the depth of field necessary to achieve the photographer's vision.

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One of the primary ways to control the depth of field is by adjusting the aperture setting of your camera. A wide aperture (represented by a small f-stop number, such as f/2.8) will create a shallow depth of field, resulting in a blurred background. On the other hand, a narrow aperture (larger f-stop number, like f/16) will produce a deeper depth of field, keeping more of the image in focus.

Electric polarization

Depth of field (DOF) in photography is a critical aspect of capturing visually stunning images by controlling focus and blur in your shots. Essentially, it refers to the area within a photograph that appears acceptably sharp and in focus. A strong understanding of DOF allows photographers to purposely guide their viewers' attention to specific elements within an image, making it a powerful tool for storytelling and creating compelling compositions.

DoF calculators are valuable tools for determining depth of field. These can be standalone devices, apps on your smartphone, or online resources. By inputting information such as focal length, aperture, and camera sensor size, these calculators can estimate the depth of field for your specific scenario. This can help guide your decisions when adjusting camera settings to achieve an ideal depth of field.

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To calculate hyperfocal distance, we need to know the focal length, aperture, and circle of confusion. Alternatively, you can use a DoF calculator or app, which makes the process much easier.

To achieve a shallow depth of field, use a larger aperture (lower f-stop number) to create a narrow area of focus within your image. In contrast, using a smaller aperture (higher f-stop number) will result in a larger zone of focus, leading to a deeper depth of field.

The degree of linear polarization is often quantified with the polarization extinction ratio (PER), defined as the ratio of optical powers in the two polarization directions. It is often specified in decibels, and measured by recording the orientation-dependent power transmission of a polarizer. Of course, the extinction ratio of the polarizer itself must be higher than that of the laser beam.

The aperture, which is an adjustable opening in the camera lens, plays a significant role in determining depth of field. A wider aperture allows more light to enter the camera, and a smaller aperture permits less light. The size of the aperture is measured by the f-stop number, with lower f-stop numbers corresponding to a wider aperture and higher f-stop numbers indicating a smaller aperture.

In street and wildlife photography, depth of field varies across different images and styles. For more candid moments, street photographers often use a shallow depth of field to draw emphasis to a single subject, with a background blur that helps evoke a sense of intimacy and emotion. On the other hand, when photographing scenes that feature multiple subjects or convey a broader context, a deeper depth of field may be used to keep everything in focus.

Aperture is one of the main factors affecting depth of field. A larger aperture (lower f-number) results in a shallower depth of field, while a smaller aperture (higher f-number) creates a deeper depth of field. Adjusting the aperture allows you to control the amount of focus and blur in your image. This Digital Camera World cheat sheet demonstrates how to affect depth of field using aperture.

Note that a very small gain or loss difference for the two polarization directions can be sufficient for obtaining a stable linear polarization, provided that there is no significant coupling of polarization modes within the laser resonator.