You might also encounter rectangular polarizing filters. The original purpose of rectangular filters was for filter holder use. Such filters are becoming less common since many filter manufacturers have been able to modify their filter holders to accommodate larger, circular filters instead.

lim t → ∞ y ( t ) = lim s ↘ 0 ( s × k c s ( s + 1 ) + k c × Δ R s ) = Δ R = y ( t ) | t = ∞ {\displaystyle \lim _{t\to \infty }y(t)=\lim _{s\,\searrow \,0}\left(s\times {\frac {k_{c}}{s(s+1)+k_{c}}}\times {\frac {\Delta R}{s}}\right)=\Delta R=y(t)|_{t=\infty }}

Proportional control dictates g c = k c {\displaystyle {\mathit {g_{c}=k_{c}}}} . From the block diagram shown, assume that r, the setpoint, is the flowrate into a tank and e is error, which is the difference between setpoint and measured process output. g p , {\displaystyle {\mathit {g_{p}}},} is process transfer function; the input into the block is flow rate and output is tank level.

Introducing a step change to the system gives the output response of y ( s ) = g C L × Δ R s {\displaystyle y(s)=g_{CL}\times {\frac {\Delta R}{s}}} .

Tom. Nasim wrote that it is the linear version that messes up light meters and auto focus while the circular versions are safe this way. Chances are you have some other issue at play. Also if it happens only in low light situations, the focus sensors may simply not be getting enough light once the CPL exacts its toll.

A polarizing filter is one of the most essential tools in a photographer’s bag. It is typically the first filter landscape photographers buy to instantly improve their pictures by adding vividness and contrast to them. Putting a polarizing filter on your lens is like wearing a pair of polarized sunglasses over your eyes – the polarized glass blocks random light waves from passing through, creating a clearer image. In this article, we will go through detailed information on polarizing filters, what they do, why they are important, and why you should consider using them for your photography needs.

PDcontroller

So if K p {\displaystyle K_{p}} , the proportional gain, is very high, the proportional band is very small, which means that the band of controller output over which the final control element will go from minimum to maximum (or vice versa) is very small. This is the case with on–off controllers, where K p {\displaystyle K_{p}} is very high and hence, for even a small error, the controller output is driven from one extreme to another.

Both linear and circular polarizers come in different shapes and forms. The most common shape of a polarizing filter is circular, which is designed to be screwed onto a filter thread of lenses that have them. Circular filters can be used on filter holders, as well as lenses with drop-in filter holders. A circular polarizer is very easy to use. Once it is attached to the front of the lens, it can be rotated either clockwise or counter-clockwise to increase or decrease the effect of polarization.

Unfortunately, polarizing filters do come with a set of disadvantages and problems. Here are a few other things you be aware of:

meaning there is no offset in this system. This is the only process that will not have any offset when using a proportional controller.[1]

Due to the popularity of DSLR cameras, the demand for linear polarizers plummeted over time, causing filter manufacturers to concentrate on primarily making circular polarizers – from cheap, poorly-coated filters, to high-quality multi-coated circular polarizers with superb light transmission qualities. Although linear polarizers are still available today and work just fine on modern mirrorless cameras, they are not recommended for use due to the unavailability of high-quality options.

The maximum degree of polarization occurs in a circular band 90° from the sun, so it is relatively easy to pinpoint exactly where the sky will appear at its darkest in your photographs. A simple trick is to form a pistol with your index and thumb fingers, then point your index finger straight at the sun. Now rotate your thumb clockwise or counter-clockwise (while keeping your index finger directed at the sun). The parts of the sky where your thumb points towards are going to have the maximum degree of polarization, as they are at the right angle from the sun. This means that when the sun is directly overhead close to the zenith, the sky will be polarized horizontally, making the sky appear more or less even in all directions. Take a look at the below photograph taken at high noon:

Qualifications: It is preferable to express K p {\displaystyle K_{p}} as a unitless number. To do this, we can express e ( t ) {\displaystyle e(t)} as a ratio with the span of the instrument. This span is in the same units as error (e.g. C degrees) so the ratio has no units.

A polarizing filter, also known as a “polarizer”, is a photographic filter that is typically used in front of a camera lens in order to reduce reflections, reduce atmospheric haze and increase color saturation in images. It is a popular filter among landscape, cityscape and architecture photographers, although it is commonly used for other types of photography as well.

As you can see, Hagia Sophia is relatively close, but the distant hills in the back are quite far, so they looked quite hazy. By using a polarizing filter, I was able to cut down the haze and improve the contrast of the background.

I captured this image from the Dubai Frame. It was tough to shoot through the thick glass with all kinds of reflections (they use all kinds of LED lights inside), so a polarizing filter was basically a necessity. Once I rotated the filter and cut down most of the reflections, I was able to walk away with another usable image.

As you can see from this article, a polarizer is not just something that can help enhance the color of the sky – it is a much more versatile tool that can reduce reflections and haze, and effectively boost both colors and contrast in your images. A polarizing filter is not something you want to leave on your lenses at all times though since it reduces light transmission and it can potentially make the sky look unevenly gradient when using wide-angle lenses. High-quality circular polarizing filters can also be rather expensive to buy and can take some time to get used to. However, those are small disadvantages compared to the benefits they bring.

Once again, a polarizing filter was necessary to reduce internal reflections and improve the overall contrast of the scene.

One of the main reasons why photographers use polarizing filters is to reduce reflections in a scene. Reflections are everywhere around us and they are very common in nature. Aside from common water reflections originating from ponds and lakes, we might be dealing with window reflections or perhaps even tiny reflections of light bouncing off vegetation or rocks surrounding waterfalls. In such situations, using a polarizing filter can help dramatically reduce reflections, even potentially adding contrast and saturation to the image. Take a look at the image below:

A drawback of proportional control is that it cannot eliminate the residual SP − PV error in processes with compensation e.g. temperature control, as it requires an error to generate a proportional output. To overcome this the PI controller was devised, which uses a proportional term (P) to remove the gross error, and an integral term (I) to eliminate the residual offset error by integrating the error over time to produce an "I" component for the controller output.

Gradient skies can be very difficult to deal with in post-processing, so one must be very careful when using polarizing filters close to sunrise and sunset times, especially when using wide-angle lenses. In many cases, reducing the amount of sky captured in a scene and rotating the polarizing filter to lighten its effect can be effective, as seen below. However, in some cases where re-framing is not desired, it might be better to remove the polarizing filter completely to avoid capturing gradient skies.

Nasim Mansurov is the author and founder of Photography Life, based out of Denver, Colorado. He is recognized as one of the leading educators in the photography industry, conducting workshops, producing educational videos and frequently writing content for Photography Life. You can follow him on Instagram and Facebook. Read more about Nasim here.

The clear advantage of proportional over on–off control can be demonstrated by car speed control. An analogy to on–off control is driving a car by applying either full power or no power and varying the duty cycle, to control speed. The power would be on until the target speed is reached, and then the power would be removed, so the car reduces speed. When the speed falls below the target, with a certain hysteresis, full power would again be applied. It can be seen that this would obviously result in poor control and large variations in speed. The more powerful the engine, the greater the instability; the heavier the car, the greater the stability. Stability may be expressed as correlating to the power-to-weight ratio of the vehicle.

One of the easiest ways to substantially improve the image quality of your daytime cityscapes is to use a circular polarizing filter. Using a polarizing filter is critical when photographing subjects that are one or more miles away. The longer the distance, the more critical it is to polarize the light you are capturing. For example, this image of Dubai skyline was captured from a vantage point that was over a mile away:

One of the main reasons why I personally take a polarizing filter everywhere I go is because I often rely on it to reduce haze in my images. Haze is something we landscape photographers have to deal with very often, so being able to use a polarizing filter in such situations helps quite a bit during post-processing since we can take it one step further and reduce haze even more through various “dehaze” and contrast adjustment tools in the software. Some haze is relatively easy to deal with in post, but when there is a lot of it, a circular polarizing filter can definitely help. Take a look at the below image comparison:

When photographing waterfalls, you deal with highly reflective rocks, since they have water and other wet vegetation on them, all of which send nasty reflections right into your camera. A polarizing filter makes a huge difference in such situations, not only significantly cutting down on those reflections, but also increasing the overall saturation and contrast of the image.

Chris, just put your mouse pointer inside the circle, then left-click-and-hold, then drag the central vertical line – as if it were a curtain – to the left or to the right. Dragging to the left will uncover the left half of the [after] image, while dragging to the right will uncover the right half of the [before] image.

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When using a camera with an EVF, I lock the exposure before adjusting the polarizer, else I make sure the EVF auto gain feature is turned off. This allows me to more easily evaluate the polarizing effect. Otherwise, the auto gain feature can make it seem the polarizer is not having any effect.

Overall, a polarizing filter is a must-have tool in every photographer’s bag. One of the challenges of being a photographer is making the best of the light you have available to you. Polarizers give you the ability to control the light that comes through your lens, creating vibrant images that might otherwise look dull.

Active vs passiveoutput

As you can see, the pond was reflecting the sky and the trees in the background into my camera. By using a polarizing filter, I was not just able to cut down most of the reflections from the pond, but also reduce the micro reflections coming from the surrounding grass the scene, which changed the appearance and the color of the glass in the resulting photograph. Such effects can never be replicated in post-processing software.

Offset error is the difference between the desired value and the actual value, SP − PV error. Over a range of operating conditions, proportional control alone is unable to eliminate offset error, as it requires an error to generate an output adjustment.[1] While a proportional controller may be tuned (via p0 adjustment, if possible) to eliminate offset error for expected conditions, when a disturbance (deviation from existing state or setpoint adjustment) occurs in the process, corrective control action, based purely on proportional control, will result in an offset error.

There are two types of polarizing filters available on the market today: linear and circular. These types do not refer to the shape of the polarizing filter, but rather to the way lightwaves are modified as they pass through the filter. Linear polarizers have a single polarizing layer and are known to cause mirrors to cross-polarize on SLR and DSLR cameras, resulting in metering and autofocus issues. Circular polarizers (also known as “CPL”), on the other hand, have a second quarter-wave layer that repolarizes the light, which makes it safe to use on any classic or modern digital camera. The only downside of a circular polarizer is reduced light transmission when compared to a linear polarizer.

PIDcontrollerPython

It is very clear that there is a dramatic difference between the two images. Both are “as is, straight out of the camera”, meaning, I did not apply any post-processing to them. The “Before” image is the one I captured before mounting a circular polarizing filter and the “After” image was captured with a polarizing filter attached and rotated to reduce the reflections in the scene.

The only thing you have to watch out when photographing cityscapes is flare, especially if you are using a poor-quality polarizing filter, or if the filter is not very clean. When capturing the below image of Burj Khalifa, I noticed that I had some flare when using my polarizer.

The proportional band is the band of controller output over which the final control element (a control valve, for instance) will move from one extreme to another. Mathematically, it can be expressed as:

With the sun rising from the left of the frame, it is very clear that the right side of the sky in the image above is where the maximum degree of polarization is, making that particular part of the sky much darker compared to the left. Such situations are commonly encountered when photographing landscapes at the golden hour, so one must be careful when using a polarizing filter, especially when shooting with a wide-angle lens. In some cases, it might be helpful to switch to a telephoto lens and concentrate on a much smaller area of the scene, effectively concealing the uneven sky.

I didn’t find the ‘Photography Life’ website as early as some other sites, but have been very impressed by both the reviews and articles. However, this and some other articles include “Before” and “After” images. I use Firefox on Windows. If I put the mouse pointer in the central circle, I see one version of the image, with left and right arrows within the circle. If I move the pointer outside the central circle, the image changes to the other version, a [Before] label appears on the left, and an [After] label on the right, in addition to the central left and right arrows. The view is divided down the centre, but consistent each side, and moving the pointer from one half to the other, moving it over the [Before] or [After] labels, or clicking the mouse anywhere, has no effect. I have to rely on the context to decide which is the “Before” image and which the “After”, and sometimes I struggle to decide which is which. Is there an explanation of how to operate ‘Before and After’ images somewhere on the website?

I personally use and highly recommend the B+W 77mm High-Transmission MRC-Nano filter, because of its top-notch optics, small footprint, and very minimal light loss of 1-1.5 stops. Although I linked to the 77mm size, make sure to get one that matches your lens.

Due to the fact that sunlight gets bounced all over the atmosphere and objects present in a landscape, eventually making its way into your camera at specific angles, your landscape photographs might end up looking rather dull and lifeless. Once attached to the front of a lens and rotated to a particular angle, a polarizing filter is capable of cutting out most of the reflected light in a scene, instantly enhancing your photographs by increasing their color saturation and contrast.

Nassim has a good photo taken with a polarising filter from a helicopter, but I have had colour bands on photos taken from aircraft windows with a polariser. Apparently this is due to “birefringence”.

On the other hand, when the sun is closer to the horizon at sunrise and sunset times, the sky will be polarized mostly vertically. This can present problems when photographing landscapes with a wide-angle lens, since the more polarized areas of the sky will be visible in the frame, as shown below:

When your camera is pointed towards the part of the sky that has the maximum degree of polarization and the circular polarizing filter is at its strongest point, the sky might appear unnaturally dark in images, making it look very fake. In such situations, rotating the filter further and thus reducing the effect of the polarizing filter can take care of the problem, creating not only a brighter sky but also addressing the potential of having a gradient sky in the photograph. Take a look at the two images below:

The proportional control concept is more complex than an on–off control system such as a bi-metallic domestic thermostat, but simpler than a proportional–integral–derivative (PID) control system used in something like an automobile cruise control. On–off control will work where the overall system has a relatively long response time, but can result in instability if the system being controlled has a rapid response time. Proportional control overcomes this by modulating the output to the controlling device, such as a control valve at a level which avoids instability, but applies correction as fast as practicable by applying the optimum quantity of proportional gain.

As you can see, there are huge differences throughout the image. First, the image with the polarizing filter has significantly less haze in the distant mountains. Second, take a look at the colorful areas of the image: the reds and the yellows appear much more saturated. Note how the evergreens appear completely different, looking greener and lighter in comparison. This is all the result of reduced reflections in the atmosphere and reduced reflections originating from objects in the scene. Without a polarizing filter, the greens appear “dirty”, giving evergreens a much darker and uglier tone.

Could one use two polarizing filters (first would have to be linear) to have an “adjustable” ND filter? I know a lot of reflections would be lost too so it’s a backup plan if more ND is needed.

PIDcontrollertransfer function

Due to my proximity to the Morning Glory hot spring in Yellowstone National Park and lack of an ultra wide-angle lens, I had to shoot a panorama at 24mm focal length, composed of several vertical frames. Once the panorama was stitched in Lightroom, the problem with the polarization in the sky became very apparent. Here, one can clearly see that the center of the sky is where the maximum degree of polarization is – both left and right sides of the frame look much brighter in comparison. This is because the sun was setting on the right side of the frame, which means that the darkest part of the sky would have been vertical, as seen here.

In proportional control, the power output is always proportional to the (actual versus target speed) error. If the car is at target speed and the speed increases slightly due to a falling gradient, the power is reduced slightly, or in proportion to the change in error, so that the car reduces speed gradually and reaches the new target point with very little, if any, "overshoot", which is much smoother control than on–off control. In practice, PID controllers are used for this and the large number of other control processes that require more responsive control than using proportional alone.

Lastly, some manufacturers might even sell drop-in polarizing filters that are specifically made to fit a particular type of filter holder. The one pictured above allows photographers to easily rotate the polarizing filter using the dial on its top.

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Introducing a step change to the system gives the output response of y ( s ) = g C L × Δ R s {\displaystyle y(s)=g_{CL}\times {\frac {\Delta R}{s}}} .

Constraints: In a real plant, actuators have physical limitations that can be expressed as constraints on P o u t {\displaystyle P_{\mathrm {out} }} . For example, P o u t {\displaystyle P_{\mathrm {out} }} may be bounded between −1 and +1 if those are the maximum output limits.

pd controller是什么

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In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the setpoint and the process variable. In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain.

Even if you have buildings that are fairly close, a polarizing filter can help reduce haze and improve the clarity of distant buildings and subjects. Take a look at the below image of Hagia Sophia:

Lastly, note the difference in the sky – the clouds appear to pop out much more and the sky looks a bit more saturated and darker. This is something you could never replicate in post! The image went from “bland and lifeless”, to “colorful and natural” by simply using a polarizing filter.

This article proves you can always learn something new. Thanks! I used a CPL filter for a long time until I discovered that it interferes with auto focus. You mentioned it briefly here but do you have any other suggestions for dealing with that problem?

Just to correct the understanding on how they work. The atmospheric water vapour, water surfaces like ponds etc and reflective surfaces are not ‘scattering’ the light, they are partially polarizing it. Sunlight, and most other light sources are not polarized. They emit light in all directions and angles to the horizontal and vertical. And a ‘normal’ matt surface will scatter light in a random manner leading to just the emittance of the objects detail, whereas, a watery or reflective surface will reflect some of the light in this normal way (so you can see that it’s water), but will also allow some of the light through it and reflect just a portion of light that hit it at a certain angle to the horizontal/vertical plane, hence revealing a reflection of sky / trees etc. The polarizing filter eliminates such ‘plane-polarized’ reflected light, which will be oscillating only in one plane by being able to be aligned in that plane, whilst allowing through most of the light that is ‘normally’ scattered and hence not aligned in just one plane. So it is a bit incorrect to say the problem is ‘randomized’ light, as that is actually what normal light is with regards to polarization, the problem is the polarized light.

I captured the first image with the polarizing filter rotated to yield the maximum polarizing effect, which unnaturally darkened the sky and made it appear uneven. To take care of the problem, all I had to do was rotate the filter until the sky returned to a much brighter state. As you can see, the photograph on the right looks much better in comparison, and with just a single turn, I was able to address the issue without having to remove the filter.

For a first-order process, a general transfer function is g p = k p τ p s + 1 {\displaystyle g_{p}={\frac {k_{p}}{\tau _{p}s+1}}} . Combining this with the closed-loop transfer function above returns g C L = k p k c τ p s + 1 1 + k p k c τ p s + 1 {\displaystyle g_{CL}={\frac {\frac {k_{p}k_{c}}{\tau _{p}s+1}}{1+{\frac {k_{p}k_{c}}{\tau _{p}s+1}}}}} . Simplifying this equation results in g C L = k C L τ C L s + 1 {\displaystyle g_{CL}={\frac {k_{CL}}{\tau _{CL}s+1}}} where k C L = k p k c 1 + k p k c {\displaystyle k_{CL}={\frac {k_{p}k_{c}}{1+k_{p}k_{c}}}} and τ C L = τ p 1 + k p k c {\displaystyle \tau _{CL}={\frac {\tau _{p}}{1+k_{p}k_{c}}}} . For stability in this system, τ C L > 0 {\displaystyle \tau _{CL}>0} ; therefore, τ p {\displaystyle \tau _{p}} must be a positive number, and k p k c > − 1 {\displaystyle k_{p}k_{c}>-1} (standard practice is to make sure that k p k c > 0 {\displaystyle k_{p}k_{c}>0} ).

Many newer lenses have 82mm front threads. Now I wish I had bought the excellent 77mm B&W polarizer Nasim recommends in this size, but when I made the decision 8 years ago, 77mm was about the maximum size needed.

Aside from B+W, there are many polarizing filters on the market today. Most of them are cheaper, but please buy with caution and look at trusted reviews ahead of time. You don’t want to put a cheap piece of glass in front of your expensive lens, only to be later disappointed by the poor image quality and unwanted ghosting and flare. Bad quality filters are not worth wasting your money and time on! It’s better to go without any polarizing filter than to use a bad one.

Just like atmospheric particles randomize light, so do reflective surfaces. Using a polarizing filter can increase color saturation in your images by reducing reflections from water, glass, leaves, and other non-metal surfaces. Additionally, using a polarizing filter helps you create deep blue skies in your images. Blue light waves are shorter than red and green waves, causing them to scatter more easily. Polarizing your view of the sky will prevent randomized blue light from coming into your lens, leaving you with the purest blue light possible.

The vast majority of our planet’s atmosphere is composed of gases that are invisible to the human eye. However, a small portion of the atmosphere is made up of water vapor, pollutants, and other particulate matter. These elements vary in quantity depending on the weather, time of day, and location. Water vapor and pollutants contribute to haze, which decreases visibility over long distances, especially close to bodies of water. The haze we see is a result of light waves hitting particles in the air, causing randomization. Even on a clear, sunny day, distant subjects can be obscured by haze. The best way to cut through that haze is to use a polarizing filter.

The same goes for photographing waterfalls and foliage – a polarizing filter in such cases can be invaluable. The below image would have looked vastly different without a polarizing filter:

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Polarization can vary greatly depending on the celestial position of the sun, so it is important to understand that both times of the day and the time of the year can impact the amount of polarization one can obtain from a polarizing filter.

The output as a function of the setpoint, r, is known as the closed-loop transfer function. g c l = g p g c 1 + g p g c , {\displaystyle {\mathit {g_{cl}}}={\frac {\mathit {g_{p}g_{c}}}{1+g_{p}g_{c}}},} If the poles of g c l , {\displaystyle {\mathit {g_{cl}}},} are stable, then the closed-loop system is stable.

If I had not used a circular polarizing filter, it would have taken me a significant amount of time to try to replicate these changes in Photoshop and I am fairly confident that the result would not even come close in comparison.

For an integrating process, a general transfer function is g p = 1 s ( s + 1 ) {\displaystyle g_{p}={\frac {1}{s(s+1)}}} , which, when combined with the closed-loop transfer function, becomes g C L = k c s ( s + 1 ) + k c {\displaystyle g_{CL}={\frac {k_{c}}{s(s+1)+k_{c}}}} .

lim t → ∞ y ( t ) = lim s ↘ 0 ( s × k C L τ C L s + 1 × Δ R s ) = k C L × Δ R = y ( t ) | t = ∞ {\displaystyle \lim _{t\to \infty }y(t)=\lim _{s\,\searrow \,0}\left(s\times {\frac {k_{CL}}{\tau _{CL}s+1}}\times {\frac {\Delta R}{s}}\right)=k_{CL}\times \Delta R=y(t)|_{t=\infty }}

Proportional control, in engineering and process control, is a type of linear feedback control system in which a correction is applied to the controlled variable, and the size of the correction is proportional to the difference between the desired value (setpoint, SP) and the measured value (process variable, PV). Two classic mechanical examples are the toilet bowl float proportioning valve and the fly-ball governor.

Consider an object suspended by a spring as a simple proportional control. The spring will attempt to maintain the object in a certain location despite disturbances that may temporarily displace it. Hooke's law tells us that the spring applies a corrective force that is proportional to the object's displacement. While this will tend to hold the object in a particular location, the absolute resting location of the object will vary if its mass is changed. This difference in resting location is the offset error.

Another potential use of a polarizing filter is when you shoot through the glass of a building or a helicopter. Take a look at the below image:

I used the pro “thin” B+W filter you recommend, and it worked very well. I pretty much left it on my lens. However, over time it became very hard to rotate, and the bezel is very thin so getting a good grip could be tricky. A few weeks ago, my lens cap broke the glass somehow, I think because the filter thread area is also extremely thin, making the lens cap more easily push into the filter glass under pressure.

When photographing distant subjects such as mountains, a polarizing filter can also help in reducing atmospheric haze, as explained further down below. So if you are wondering how some photographers manage to get rich colors in their photographs, particularly when it comes to the sky, foliage, and distant subjects, you will find that they often heavily rely on polarizing filters. Although color can certainly be added to photographs in post-processing, the effect of a polarizing filter cannot be fully replicated in software, especially when it comes to reducing reflections and haze in a scene, making the filter indispensable for landscape photography.

Although there is still some haze and softness visible in the image (especially when looking at distant buildings), it would have been an unusable image without a polarizer. I was able to cut down most of the fog and haze in this image.

When I removed it from the lens and looked at it, the filter was quite dirty. After cleaning up the filter and mounting it back on the lens, the flare issues went away.

Not suggested (unless I missed it), is the use of a tripod! Of course, with landscape work a tripod might be a given! Fiddling with a polarizing filter or any filter can be a disaster without a tripod. BTW: Don’t try to photograph Victoria Falls without a polarizing filter or a tripod!

Controller outputdefinition

During the mid-day hours, especially during the time of year when the sun is directly overhead, a polarizer works equally well when pointed at the horizon in any direction, with an even polarizing effect. This makes it easy to get dramatic, dark blue skies against puffy clouds. Also, when converted to B&W, they appear almost black. It can make shooting in otherwise harsh mid-day light more interesting.

The only downside here is the gradient sky introduced by the polarizer (you could tell it was early in the morning), but with a couple of simple techniques in software, I can address such problems very easily. Just by using a graduated filter tool in Lightroom, along with a couple of small tweaks, I was able to make my image look even better: