We can see that the tip of E traces out a circle as we follow the wave along the z axis at a fixed time. Similarly, if we sit at a fixed position, the tip of E appears to trace out a circle as time evolves. Hence this type of polarization is called circular polarization.

Jun 21, 2019 — Visible or white light is made up of a range of colours each with a different wavelength. One way to see the different colours is to use a ...

Does that mean you should always shoot at the fastest aperture you have? Is f-stop ƒ/1.4 always going to be king? Is more defocusing always going to be preferrable?

Observe how the shallow aperture in this image lends to an overall dreamy effect; this is a direct result of the low aperture creating larger circles of confusion, a high amount of defocusing, and large fokeh (front bokeh).To contrast this, below we demonstrate an image shot at a high aperture which has created too strong a contrast between the 'prismed' part of the image and the non prismed part. We quickly notice there's an object in front of the lens, which removes some artistic integrity. The abstractity and nuance is lost. Aaand it wasn't a good image to begin with, but we're just trying to illustrate a point. You can clearly make out which part of the image is encompassed by the prism:

A polarizer transmits only a single orientation of linear polarization, and blocks the rest of the light. For example, a polarizer oriented along x passes x and blocks Ey.

Other materials are nominally isotropic, but when they are bent or deformed in some way, they become anisotropic and therefore exhibit birefringence. This effect is widely used to study the mechanical properties of materials with optics.

The subject might strike you as too complex, esoteric, granular.. Name your favorite adjective, but I will argue that understanding these minutae actually will help you create better images. You will forever understand your equipment better, be able to make better photographic small talk, and wrapping your head around this subject will only take you a minute. Sounds like a pretty sweet deal, right? Knowledge is power; let's get into it.

There's actually nothing spooky about it, and it's more intuitive than we may have guessed. The first important thing to understand is that apertures are just fractional numbers. Specifically speaking, they are a fraction of the focal length of your lens. The math is easy:

F-stops

When light is incident on an interface between two different media with different indexes of refraction, some of the light is reflected and some is transmitted. When the angle of incidence is not normal, different polarizations are reflected (and transmitted) by different amounts. This dependence was first properly described by Fresnel, and hence it is often called “Fresnel Reflection.” It is simplest to describe the polarization of the incident, reflected, and transmitted (refracted) light in terms of a vector component perpendicular to the plane of incidence, called the “s” component, and a component parallel to the plane of incidence, called the “p” component. The “plane of incidence” is the plane which contains the incident ray and the transmitted and reflected rays (i.e., all of these rays lie on one plane). In the example in the diagram below, the plane of incidence is the plane containing the x and z axes. That is, Es || y, while Ep lies in the x-z plane.

No! Prism photography is slightly more nuanced than that, and it is possible to create so much defocusing that it crowds out the subjects in our images. This becomes increasingly true as our focal lengths increase.

To understand the polarization of light, we must first recognize that light can be described as a classical wave. The most basic parameters that describe any wave are the amplitude and the wavelength. For example, the amplitude of a wave represents the longitudinal displacement of air molecules for a sound wave traveling through the air, or the transverse displacement of a string or water molecules for a wave on a guitar string or on the surface of a pond, respectively. We will refer to the amplitude of a light wave with the letter “E.” The amplitude of a light wave represents the potential for a charged particle (such as an electron) to feel a force – formally it may represent the “electric field” of an electromagnetic wave. Because this potential vibrates along the directions transverse to the direction the wave is traveling, light is a “transverse wave,” just like the waves on a string or water surface.Because light is a transverse wave, and because there are two transverse dimensions, there are fundamentally two distinct directions in which the light wave may oscillate. Let’s call these the x and y directions for a light wave traveling along the z direction. We’ll call the two distinct waves Ex and Ey, where we denote these by vectors to remind us that they point in (or oscillate along) a certain direction (the x and y directions, respectively).The amplitude of the light wave describes how the wave propagates in position and time. Mathematically, we can write it as a “sine wave” where the angle of the sine function is a linear combination of both position and time terms:

Objectives are also called object lenses, object glasses, or objective glasses. Several objective lenses on a microscope. Objective lenses of binoculars ...

Ok, before we get into the deep end.. let's back up a bit. What is a stop? Well, it's essentially a relative measure of light. By relative, I mean that a stop can only be judged in relation to an absolute exposure. For example, you can't look at a photo and describe it as having been shot at 12 stops.

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You can however, look at a photo, and say that it could be a stop brighter, or a stop darker. This brings us to an important golden rule...

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If your intuition is like mine, you'll probably do some naive math; like some very naive multiplication, and come up with the wrong answer. Sorry, nope! That's not how f-numbers work at all. If you got that right, then well, you probably already know everything, you may as well just be done here. Thanks for reading! Joking, you're not getting off that easily.

So, the rules that we discussed earlier will apply to your effetive focal length. At an effective focal length of 50mm, try starting out at around ƒ/1.4. For an effective focal length of 85mm, try starting around ƒ/4. Again, your mileage may vary, and you'll want to play with your aperture a lot as you shoot to produce a result that's desirable for your scene/subject combo.

Aperture

Years ago, I ran into an issue during a wedding in which the electronic displays on my camera stopped working. Like, completely dark. Everything else functioned fine—the camera would still fire and capture shots perfectly, but, I had no idea what my shots looked like or if they were exposed correctly!

We've demonstrated that you'll create larger circles of confusion and more defocusing (fokeh 🤭), when your aperture is shallower; in layman's terms:

We can see that in general the light emerges in a different state of elliptic polarization. In fact, for the example illustrated above, the particular choice of L for a given difference between nx and ny causes the linearly polarized light at the input end to be converted to circularly polarized light at the other end of the birefringent material. How did this happen? Let’s look at the math. Consider the phases accumulated by the two component waves as they travel through the birefringent material. The waves can be described by

Multilayer thin-film coatings have a large number of interfaces, since they are generally comprised of alternating layers of a high- and low-index layer materials. The fraction of incident light intensity Iin that is reflected (IR) and transmitted (IT) through a thin-film coating can be calculated from the indexes of refraction and the precise thicknesses of each layer. These intensity reflection and transmission functions R(l) and T(l), respectively, generally depend strongly on the wavelength of the light, because the total amount of light reflected from and transmitted through the coating comes from the interference of many individual waves that arise from the partial reflection and transmission at each interface. That is why optical filters based on thin-film coatings are called “interference filters.”

In the above example, when we decrease the depth of field by a factor of two, our circles of confusion become twice as large for rays that pass through the prism. The prism therefore becomes twice as defocused, and starts to blend in quite nicely with the surrounding scene:

f-number

Polarization is a fundamental property of light. While many optical applications are based on systems that are “blind” to polarization, a very large number are not. Some applications rely directly on polarization as a key measurement variable, such as those based on how much an object depolarizes or rotates a polarized probe beam. For other applications, variations due to polarization are a source of noise, and thus throughout the system light must maintain a fixed state of polarization – or remain completely depolarized – to eliminate these variations. And for applications based on interference of non-parallel light beams, polarization greatly impacts contrast. As a result, for a large number of applications control of polarization is just as critical as control of ray propagation, diffraction, or the spectrum of the light. Yet despite its importance, polarization is often considered a more esoteric property of light that is not so well understood. In this article our aim is to answer some basic questions about the polarization of light, including: what polarization is and how it is described, how it is controlled by optical components, and when it matters in optical systems.

Because the polarization response of a tilted multilayer thin-film coating can be very strong, optical filters can make excellent polarizers. For example, a basic edge filter at a high angle of incidence exhibits “edge splitting” – the edge wavelength for light at normal incidence shifts to a different wavelength for p-polarized light than it does for s-polarized light. As a result, there is a range of wavelengths for which p-polarized light is highly transmitted while s-polarized light ishighly reflected, as shown below.

where A is called the “amplitude factor,” the variable l (“lambda”) is the “wavelength” (units of nm), and the variable v (“nu”) is the “frequency” (units of Hz, or sec–1). If a snapshot of the wave could be taken at a fixed time, l would be the distance from one wave peak to the next. If one sits at a fixed point in space and counts the wave peaks as they pass by, v gives the frequency of these counts, or 1/v gives the time between peaks. The sign between the position and time terms determines the direction the wave travels: when the two terms have the opposite sign (i.e., the “–” sign is chosen), the wave travels in the positive z direction. For convenience we often use two new variables called the “wavenumber” k = 2p/l and the “angular frequency” 2pv (“omega”), which absorb the factor of 2p, so that the wave amplitude can now be written more compactly as

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aperture中文

Ok, but how exactly does changing the aperture modify the intensity of light? Well, it's actually as intuitive as you'd guess it would be. An increase of one stop (i.e. ƒ/2.8 -> ƒ/4) halves the area (as in, the geometrical formula for obtaining the area of a circle, area = πr²) of the aperture. Inversely, a decrease of one stop (i.e. ƒ/2.8 -> ƒ/2) doubles the area of the aperture. Doubling the area, quite literally doubles the amount of light hitting the sensor, making the light twice as intense. Just like eating a cookie twice as big as another cookie, will make you twice as fat 😨.

It is also possible to take advantage of an appreciable difference in reflected or transmitted phase for p- and s-polarized light over a region of the spectrum where the reflected and transmitted intensities are essentially equal, thus forming a waveplate.

What if the two components Ex and Ey have unequal amplitude factors? We can see that the light wave is still linearly polarized.

f-stop是什么

Some materials have a different index of refraction for light polarized along different directions. This phenomenon is called birefringence. For example, suppose light polarized along the x direction sees an index of nx, while light polarized along the y direction sees an index ny. Now suppose linearly polarized light passes through a piece of such a material of length L, where the linear polarization axis is oriented at 45° with respect to the x and y axes. The fixed time picture thus looks like:

This was achieved through the use of a narrower aperture, which, again, reduced the amount of defocus that the prism's reflection could create. Had he shot with the lens wide open, the haze would produced by the prsim would be overwhelming. Kyun's choice was artistically appropriate given the context:

We can observe that this is true with the simple proof. If we're using a 100mm lens at ƒ/2, the diameter of our aperture is 50mm, as per the equation:

The amplitude E, or the potential for a charged particle to feel a force, is vibrating along both the x and y directions. An actual charged particle would feel both of these fields simultaneously, or it would feel

This is why equivalent exposures are so easy to calculate. Equivalent exposures are two different exposure settings that allow the exact same amount of light to reach the sensor, resulting in the exact same (equivalent) exposure. For example, the setting f/2.8 @ 1/500 a second would expose a photo exactly the same as ƒ/2 @ 1/1000 a second. Why? ƒ/2.8 -> f/2 is a doubling of the area (πr²) of your aperture, letting in twice as much light, so you need to double your shutter speed, from 1/500 to 1/1000 to maintain the same exposure.

A question arose from reader John Harvey Perez—for non-full frame (crop) sensors, what focal length and aperture combination is best? Many of us use cameras that are not full frame, and therefore use specialty lenses which are designed for non-full frame cameras, or use full-frame lenses and fail to appreciate the full viewing angle of the elements in the lens.

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That is, E appears to oscillate along a line oriented at 45° with respect to the x axis. Hence this situation is called linear polarization.Notice that equivalently we could view the wave at a particular location (“fixed position”) and watch its amplitude evolve with time. Suppose we sit at the position z = 0. Then we see that

Bam! This fact matters a lot. Why? Well, most people think ƒ/2.8 is fast enough. But... if we're being prudent, we can dispel this with some math.

And I started really really obsessing over this concept. How did they do it? What did they know? Having joined the photography movement during the digital era, there was so much about the internal mechanics of exposure that I was not aware of.

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Most polarizing beamsplitters are very efficient polarizers for the transmitted light (i.e., the ratio of desired to undesired polarization is very high); however, the reflected light generally contains some of both polarization components.How does a polarizer work? There are different ways of making a polarizer, and they are not described in detail here (see [1] for more examples). However, as an example consider one of the most popular absorbing polarizers: the well-known Polaroid “H-Sheet.” This polarizer, invented by E. H. Land in 1938, is a plastic, Poly-Vinyl Alcohol (PVA) sheet that has been heated and then stretched in one direction, forming long, nearly parallel hydrocarbon molecule chains. After dipping the sheet into an iodine-rich ink, long iodine chains form along the hydrocarbon molecules. Electrons freely move along the iodine chains, but do not easily move perpendicular to the chains. This ability for electrons to move freely in one direction but not the perpendicular direction is the key principle upon which most absorbing polarizers are based.

You can think of circles of confusion as the amount of 'defocusing', or blurring, that occurs. Larger circles of confusion allow light to defocus more dramatically as it hits the sensor; which give you your bokeh—like effects. Larger circles of confusion = larger bokeh. Except, this is not really bokeh because it's happening in front of the lens. It's more like front-bokeh. Fokeh, anyone?

When the electric field of a light wave encounters the sheet, the component parallel to the chains causes electrons to oscillate along the direction of that component (Ey in the above example), thus absorbing energy and inhibiting the component from passing through the sheet. Because electrons can not respond to the other component (Ex), it is readily transmitted.

Suppose the two components have equal amplitudes again, but now consider the case where these two components are not in phase, such that the angles of the sine functions are different. In particular, suppose there is a constant phase difference of p/2 between them, which corresponds to a distance of l/4 in the “fixed time” picture. The x component is

OK, this headline is purposely clickbaity. Of course ISO and shutter speed are important—otherwise they wouldn't have been introduced to begin with. Aperture though, is uniquely king over these two other settings—and its importance is generally overlooked by most photographers. Our reluctance to recognize the powerhouse that we can unleash by truly understanding our aperture is making our images worse!

and where, as before, E = Ex< + Ey. The three special cases described in sections a, b, and c above thus correspond to: (a) Ax = Ay and  = 0 (linear polarization; equal amplitudes); (b) 

To contrast this, below we demonstrate an image shot at a high aperture which has created too strong a contrast between the 'prismed' part of the image and the non prismed part. We quickly notice there's an object in front of the lens, which removes some artistic integrity. The abstractity and nuance is lost. Aaand it wasn't a good image to begin with, but we're just trying to illustrate a point. You can clearly make out which part of the image is encompassed by the prism:

Notice from the graph above on the right that for the case of reflection from a higher-index region to a lower-index region (in this case glass-to-air, or ni = 1.5 and nt = 1.0), the reflectivity becomes 100% for all angles greater than the “critical angle” θc = arcsin(nt/ni) and for both polarizations. This phenomenon is known as “Total Internal Reflection” (TIR).For angles of incidence below the critical angle only the amplitudes of the different polarization components are affected by reflection or transmission at an interface. Except for discrete changes of p (or 180°), the phase of the light is unchanged. Thus, the state of polarization can change in only limited ways. For example, linearly polarized light remains linearly polarized, although its orientation (angle ) may rotate. However, for angles greater than θc, different polarizations experience different phase changes, and thus TIR can affect the state of polarization of a light wave in the same way birefringence does. Thus linearly polarized light may become elliptical, or vice versa, in addition to changes in the orientation.

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Polarization is a critical property of light for many optical systems and applications. This brief tutorial summarizes some of the most basic aspects of polarization, including how it is described, the impact of polarizing and birefringent elements on light, and how optical interfaces and filters can change the polarization of light.

Most of us probably feel as though we know enough about aperture to get by. Under critique, though, how well do these beliefs hold up? Well, let's start off with a little quiz. Here's a seemingly straightforward question that many will find to be remarkably counterintuitive:

We highly suggest reading each of the following posts in order to learn how to better fractalize your images. Don't expect to shoot at your best without first understanding this information! Some of the facts you'll learn might surprise you (they sure surprised us 😲).

It embodies the study of light, its behaviors, and how it interacts with matter. There are many applications of optics, including telescopes and microscopes, ...

I scrambled my way home, plugged the images into the computer, aaaaaand *drumroll*... most of the images were... salvageable. The modern era has stressed the importance of shooting RAW over JPEGs, a law I luckily abided by, so I had 3 stops in either direction to pull my exposure up and down. Yes, 3 stops, this was in the early 2010's; none of that crazy, 20 stop exposure compensation stuff that's available today.

Aperture confuses people, especially the f-stop scale—it doesn't seem to make any sense. Why is ƒ/2.8 a stop, and why does a stop of ƒ/2.8 signify a bigger diameter than an f-stop of ƒ/4?

We observe that the area 981mm² is roughly half the area 1,963mm², which allows half the amount of light to enter the lens, exactly as we were expecting.

If the difference between the two phase values is p/2, then the wave emerging from the material (say into air) will be circularly polarized. This occurs when

This blog post is the first in a three part series explaining how photographers can use prisms like Fractals to capture creative images.

Pupilaperture

Ok, but numbers like f/2.8 or f/5.6 are still weird. Why not just f/1, f/2, f/3...? Does math exist purely to make life confusing?

The polarization of light reflected and transmitted at an interface between two media or at a thin-film multilayer coating can be altered dramatically. These two cases are considered below.

We must strictly control our aperture. I've worked with prism photographers for many years now, and many of them pay little attention to their aperture, or fail to shoot aperture priority entirely. In prism photography, this won't work! We must be mindful of our aperture, and we'll often need to dial it up or down a stop to get the results that we're looking for. But we absolutely must make sure that we shoot as wide as possible, and wide focal lengths often prefer apertures like ƒ/1.4 or shallower.

Lens choice: the fixed-range 50mm lens (aka the "nifty fifty") might be the only lens you need for prisming. Here's why.

Total area decreases by half every time we increase our aperture by one stop. That's why we can deterministically state that exposure will decrease by a factor of .5 everytime we increase our aperture, and increase by a factor of two everytime we decrease our aperture.

Worried that will break your bank? Check out our writeup on why the nifty-fifty is the best and most inexpensive way to prism. The nifty fifty will allow you to shoot at ƒ/1.4 for a mere few hundred bucks—it's a prismer's dream!

However, if the optical system is in any way sensitive to polarization, even when the incident light is unpolarized, it is important to recognize that the beamsplitter can transmit and reflect different amounts of the “s” and “p” polarization states, as shown below.

All of the states of polarization described above are actually special cases of the most general state of polarization, called elliptical polarization, in which the tip of the electric field vector E traces out an ellipse in the x-y plane. The two components might have unequal amplitudes Ax  Ay , and also might contain a different relative phase, often denoted  That is, we may write generally

The answer is that effective focal length should be the factor which you pay attention to. That is to say, if you have a 25mm lens, and a crop factor of two, the effective focal length of your lens is:

The depth of field with a subject 10ft from the camera, at ƒ/2.8, is 1.29 ft. What will happen to our depth of field if we decrease it by two stops, from ƒ/2.8 to -> ƒ/1.4? Let's take a look:

F-stop

Subsequent apertures (i.e. ƒ/2 -> ƒ/2.8 or ƒ/2 -> ƒ/1.4) decrease or increase the diameter of the aperture's pupil by a factor of √2 to halve or double the total area of the aperture's pupil.

Because of this relationship, a material with birefringence Dn of the appropriate thickness L to convert linear polarization to circular polarization is called a quarter-wave plate.What causes materials to be birefringent? Some materials, especially crystals, are naturally anisotropic at microscopic (sub-wavelength) size scales. For example, Calcite (CaCO3) is shown in the drawing below. The structure, and hence the response to polarized light, along the c direction is markedly different than that along the a and b directions, thus leading to a different index of refraction for light polarized along this direction.

f-stop vsaperture

Unpolarized light can be polarized using a “polarizer” or “polarizing beamsplitter,” and the state of already polarized light can be altered using a polarizer and/or optical components that are “birefringent.” In this section we explore some examples of these types of components.

Being on the scene is more important than worrying about technical details. This may be true in many a case, but when we're dealing with art as delicate and as intricate as prisming, we have to be a bit more mindful.

In other words, if we look down the propagation axis in the positive x direction, the vector E at various locations (and at t = 0) now looks like:

It's therefore important to note that longer focal lenghts require narrower apertures when prisming. In these scenarios, increasing your aperture will allow you to create smaller circles of confusion and create more attractive front bokeh.

Early lens manufacturers decided that sequential stops should double or halve the amount of light that enters the lens. As we discussed before, this is done by doubling or halving the area of the aperture. So how do we double or halve the area of the aperture? It's actually quite easy: it can be done by increasing or decreasing the aperture's diameter by a factor of square root of two!

Manual shooting mode will be OK too, but might require extra work. In either case, the goal is absolute control and comfortability when setting your camera's aperture. Don't be afraid to experiment and shift your aperture up and down a stop, even in a live shoot.

The angle of the reflected ray,θr, is always equal to the angle of the incident ray, θi, this result is called the “law of reflection.” The angle of the transmitted (or refracted) ray, θT, is related to the angle of incidence by the well-known “Snell’s Law” relationship: ni sin θinbsp;= nt sin θT. It turns out that s-polarized light is always more highly reflected than p-polarized light. In fact, at a special angle called “Brewster’s Angle,” denoted θB, the p-polarized component sees no reflection, or is completely transmitted. Brewster’s angle is given by θB = arctan(nt/ni). The power or intensity reflection coefficients for a light wave (i.e., the squares of the amplitude reflection coefficients) for air-to-glass (left) and glass-to-air (right) look like:

Lux is an absolute measure of brightness. Imagine that the measurable amount of brightness on a sunny day measures in at 100,000 lux, and we have our camera set as to allow all 100,000 lux to pass through to the camera's sensor at an aperture of ƒ/1.

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Using this description of a single transverse orientation of a light wave, we can now consider multiple orientations to describe different states of polarization.

We have about half the depth of field at ƒ/1.4 .645 ft than we do at ƒ/2.8. This is a big deal. Without getting too esoteric, we must understand that the circle of confusion for light rays passing through the prism continue to grow larger, the more out of focus the prism becomes.

An interesting tidbit, the fastest lens in film history was the ASA/Zeiss 50mm f/0.7. We then know that wide open, the diameter of the aperture was:

This blog post is an overview for our four part series explaining how photographers can use prisms like Fractals to capture creative images.

So what aperture should you shoot? There is no strict answer to this question; but generally speaking, to emulate the prism effect that you get at f-stop ƒ/1.4 at 50mm, you may want to try an f-stop of around ƒ/4 if you're shooting at 85mm or f-stop ƒ/5.6 if you're shooting at 135mm. Your mileage may vary, and you want to be sure that you're moving your aperture up and down a lot to achieve an effect that's desirable for your scene, as these things tend to be highly context depending. The correct setting is in there—you just have to find it!

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Here we present a shot by Kyun Se Yawn, which demonstrates proper use of a narrower aperture at an extended focal length. Notice that the defocus from the prism around the couple in the image is relatively in focus; allowing the perfect amount of haze to be produced by the prism.

This continues in a linear fashion as we continue increasing our aperture, leading to only 3,125 lux reaching our camera's sensor at ƒ/5.6, a dramatic decrease!

If Ax  Ay , the total wave E is linearly polarized, but it is no longer oriented at 45° with respect to the x axis. In fact we can see that it is oriented at an angle  where

After my fear began to settle, I started to think. Before the era of digital photography, the phenomenon I had just weathered through would have been completely normal to the average photographer. Before digital metering, there was no automatic way to know how to expose your images!

By this measure, if we were to increase our aperture by one stop, from ƒ/1 -> ƒ/1.4, we'd decrease the amount of brightness that reaches our camera's sensor by half: 50,000 = 100,000 / 2

When an optical filter is used at a non-normal angle of incidence, as is common with so-called “plate beamsplitters,” the filter can impact the polarization of the light. If the incident light is incoherent and unpolarized, and the optical system is “blind” to polarization, the standard intensity reflection and transmission functions R(l) and T(l) may be determined for the new angle of incidence, and they are sufficient to characterize the two emerging beams.

Okay great, but why does any of this matter? Especially for prisming? Well, it's a little known fact that your depth of field amount also sequentially increases and decreases by a factor of √2 for each stop changed. (!!!)

Why halves, or doubles? Well, that's purely a matter of convention. Early lens designers decided that doubling or halving the current aperture, stop by stop, would be an easy way to move between different apertures. There's no law of nature that requires stops to be defined in this way—but it was defined that way, and it's a convention that we've all agreed on, it's here to stay.

The only way I can recount the experience was that it was like reading while blind... or, like, driving while asleep... while texting.. you get the idea. There would be an important event, say, the bride performing the bouquet toss. I'd snap images furiously, as if I had a clue what I was doing, and then a wedding guest would walk up to me:

The amount of light output in each polarization state can be determined by simply breaking up the incident light into its two polarization components (s and p), and then calculating how much of each intensity is transmitted and reflected. For systems based on incoherent light, this level of detail is usually sufficient to keep track of the impacts of components like optical filters on polarization.For some optical systems – particularly those based on coherent light and that utilize or are sensitive to interference effects, for example – the complete state of polarization should be tracked at every point through the system. In that case, it is important to understand that optical filters based on multilayer thin-film coatings not only reflect and transmit different amounts of intensity for the s and p polarization states, but also impart different phases to the two different states. And both the amplitude and phase contributions can depend strongly on the wavelength of light. Thus, in general, an optical filter can act like the combination of a partial polarizer and a birefringent waveplate, for both reflected and transmitted light.To determine the effect of an optical filter on the light in such a system, the incident light should first be broken up into the two fundamental components associated with the plane of incidence of the filter (s and p components). Then, the amplitude and phase responses of the filter for the s and p components should be applied separately to each of the incident light components to determine the amplitudes and phases of the reflected and transmitted light components. Finally, the reflected s and p components can be recombined to determine the total reflected light and its state of polarization, and likewise for the transmitted light. These steps are illustrated in the diagram below.

Some polarizers eliminate the non-passed polarization component (Ey in the above example) by absorbing it, while others reflect this component. Absorbing polarizers are convenient when it is desirable to completely eliminate one polarization component from the system. A disadvantage  of absorbing polarizers is that they are not very durable and may be damaged by high intensity light (as found in many laser applications).When a reflective polarizer is operated in such a way that the blocked (i.e., reflected) polarization component is deflected into a convenient direction, such as 90° relative to the transmitted polarization component, then the polarizer acts like a polarizing beamsplitter, as shown below.

The circles of confusion —i.e. amount of defocusing increases as your focal length increases. Why? Because your focal plane is typically further away from your lens at longer focal lengths, but your prism is still just a few cm from the front element of your lens! The increased delta between the prism and the plane of focus (where your subject lie) causes your prism to become more defocused as your camera's sensor sees it, which can make your subject just too blurry: