Digital Photography For What It's Worth: User-to-user help for digital photographers in general and Oly Camedia users in particular. Click to go to home page.

 

 

Digital Photography For What It's Worth

Vertical band of maximum scatter polarization at top right, late afternoon looking NW over the Berkeley Hills from Vollmer Peak, Orinda, California. Click to see 600x800. [C-2000Z with polarizer]

Marks major topics. Click to see Limited Warranty section on the home page. Using a polarizer effectively without TTL control

How to set camera angle and rotating ring without seeing what the camera sees

On this page—

Last updated July 27, 2004


Unwanted Light—Scatter and Glare

Polarizing filters (AKA polarizers) are far and away the most important and frequently used filters in the outdoor photographer's arsenal and can be indispensable indoors as well. Polarizers add richness and clarity to photographs by suppressing two all too common forms of unwanted light—atmospheric scatter and specular reflections, including glare off water, glass and even foliage. The samples below illustrate the polarizer's effect.

Marks the paydirt Unwanted Light To Be Suppressed »

Scatter

Glare

No polarizer: Note the muted hillside colors, the indistinct clouds and the desaturated light blue sky at left. Bright glare off the water and pool deck washes out deck tiles and lane markings. Berkeley Hills looking NNE--no polarizer. Click here to see original 1600x1200. [C-2000Z] Pool glare--no polarizer. Click here to see original 1600x1200. [C-2000Z]
Polarizer 45° off proper setting: This does little for scatter, but it cuts some foliage and water glare. Note the somewhat richer hillside colors at left. Berkeley Hills looking NNE--polarizer 90 degrees off proper setting. Click here to see original 1600x1200. [C-2000Z] Pool glare--polarizer 90 degrees to proper setting. Click here to see original 1200x1600. [C-2000Z]
Polarizer set properly: The sky is a much darker, richer blue, the clouds are distinct and white, and the hills are alive with the sound of music natural color. The blue deck tiles at left are richer, too. Berkeley Hills looking NNE--polarizer at proper setting. Click here to see original 1600x1200. [C-2000Z] Pool glare--polarizer at proper setting. Click here to see original 1200x1600. [C-2000Z]
Table Notes: Camera angles chosen for maximum polarization of unwanted light in all samples; automatic exposures; no post-processing other than resizing.

To my mind, there are no polarizer advantages unique to digital cameras, but digital cameras with limited dynamic range benefit greatly from the selective suppression of excess contrast. Due to the limited UV sensitivity found in most digital cameras, polarizers also provide a welcome and effective alternative for haze control at favorable camera-sun angles.


What, No TTL Control?

The direct through-the-lens (TTL) view of a single lens reflex (SLR) camera simplifies polarizer use considerably: Adjust your aim and the rotating ring of your polarizer for the desired effect under direct visual control and shoot. The same goes for cameras with well-shaded electronic viewfinders (EVFs). But these cameras are still vastly outnumbered by the digital rangefinders, which provide real-time TTL control only via their main rear LCDs. 

Here's the rub: In practice, you can't always see these rear LCDs well enough to fine-tune your polarizer technique. That's all too often the case with my Oly C-2020Z in bright sunlight—just when I might need a polarizer the most. To guarantee workable TTL control with a rangefinder in all conditions, you'd have to carry an LCD shade. I have one, but frankly, I hate to futz with it.

So how do you use a polarizer on a rangefinder camera without TTL control? Well, there are several possibilities:

  • If the direction of maximum polarization is within ~45° of the horizontal, and you happen to be wearing polarized sunglasses, pan and tilt your head until you get maximum effect, then match the pan with your camera angle and align your polarizer's blocking direction with the right-left axis of the glasses. If the polarization direction is steeper than ~45°, take off the glasses and do the same.

  • Remove the polarizer from the camera and do the same, or carry a spare polarizer for just this purpose.

  • Gauge polarizer effect via the light loss reported by your camera's TTL metering system.

Or your could keep things quick and simple with the "blind" polarizer technique described next.


Well, You Needn't

Marks the paydirt Fortunately, there's a much faster and easier way to get the most from a polarizer without relying on anything other than your own eyeballs and an understanding of how ambient light gets polarized. You'll have to learn to think like the enemy (unwanted scatter and reflections, or more specifically, the polarized components of these phenomena), but once armed with a certain practical understanding of polarization, you'll be able to determine accurately and reliably the only 2 things you need to know to use your polarizer to maximum effect:

  • Target direction(s)—the direction(s) from which the most strongly polarized scatter or reflections will come, and

  • Target polarization—the orientation of the polarization the unwanted light will bear.

With that information in hand, the strategy for maximum scatter or reflection control becomes straightforward:

There's nothing wrong with a direct look through the LCD or dismounted polarizer to

  • remind yourself how the incoming light is polarized

  • dial in a partial polarizer effect

  • fine-tune target direction and polarizer orientation

  • confirm a mission-critical shot

You can also confirm polarizer effect with your camera's TTL metering system. But now that I've become one with polarization, I seldom feel a need to peek. The blind method works very well in nearly all cases.


It's Just A Tool

Before going any further, let me emphasize that the polarizer, like any other accessory, is simply a means to an end, with benefits and costs that must be balanced against many others in the shot at hand.

Marks the gotchas Whatever you do, don't leave a polarizer mounted on your camera in perpetuity.

In low-light situations, the exposure hit (at least 2 stops with most polarizers) may well be untenable. Even in decent light, the 2+ stops of potential shutter speed lost to the polarizer will make camera shake that much more likely in handheld shots, especially telephotos.

You'll often find it inconvenient, impossible or undesirable to shoot in or even near a target direction. And there will be many times when the polarizer will predictably have no beneficial effect whatsoever. In such circumstances, removing the polarizer will reclaim at least 2 stops of light, clean up your optics and reduce the chance of flare.

Marks the paydirt Bottom line: Whatever the constraints, the ability to predict target direction and polarization and likely polarizer effect will save you time and help you make the most of the photographic choices at hand—whether or not you have TTL control, and whether or not you end up actually using a polarizer.


The Really Short Answer

To use a polarizer effectively without TTL control, you must first find and if necessary mark your polarizer's blocking axis, which may or may not align with a white dot or other symbol on the polarizer's outer rotating ring. Figuring out where the most strongly polarized light's coming from and the direction of its polarization is the next step. For the filter to have maximum effect, the blocking axis of the polarizer must align closely with the polarization of the unwanted light.


Blocking Scatter

To block atmospheric scatter

  • Shoot in any direction 75-105° from the sun (because that's the direction the most strongly polarized scatter comes from).

  • Turn the polarizer's blocking axis 90° to the line between you and the sun (because that's the way the scatter will be polarized).

So, if the sun is 30° above the horizon in the west, you should be aiming north or south with the top of the blocking axis 30° east of vertical.


Blocking Reflections

To block reflections off water or glass, 

  • Arrange your shot so that the reflections reach you along a line making a ~35° angle with the reflecting surface

  • Align your polarizer's blocking axis parallel to the reflecting surface at the point of reflection.

For water reflections, for example, put the blocking axis at 3 or 9 o'clock. For reflections off vertical glass windows, put the blocking axis at 12 or 6 o'clock.


Coverage Limitations

At 30° and wider angles (i.e., at 35 mm equivalent focal lengths under 85-100 mm), polarizer coverage becomes limited by deviations from the target direction across the camera's field of view. This predictable fall-off in polarizer efficacy most strongly affects peripheral scene elements more than 15° off the target direction—e.g., sky well off the arc of maximally polarized skylight or specular reflections well off Brewster's angle. A prime example of the former is the sky banding seen in wide-angle big-sky shots early and late in the day.Uneven suppression of reflections can be seen to some extent in the glare examples shown above.


Other Uses for Polarizers

Besides minimizing scatter and glare, you can use your polarizer:

  • At intermediate settings, to dial in wanted reflections.

  • As a 1- to 2-stop neutral density filter—e.g., to get a longer exposure speed in aperture-priority mode.

  • To suppress skylight around rainbows and quarter moons.

  • To cool the colors in a scene. (Many polarizers impart a slight bluish color bias, but it's probably easier to do this in post-processing or with an incandescent white balance preset.)

The neutral density application requires the polarizer to be set for minimum effect, which is also easily be done without TTL control. The remaining techniques typically require full TTL control for best results, but they are beyond the scope of this article.

Marks opportunities to bypass long-winded discussions and cut to the action line. Click to review Limited Warranty section on the home page. At this point, you can skip directly to the non-TTL scatter control technique or read on for more background on polarization.
   

When Not to Bother with a Polarizer

In the absence of polarized light, a polarizer is nothing more than a 1- to 2-stop neutral density (ND) filter. If an ND effect isn't what you're after, a polarizer won't do you any good in unpolarized light.


Poorly Polarized Scatter

If you find yourself shooting within ~30° of the line between you and the sun, either toward or away, a polarizer won't help you much with atmospheric scatter. Skylight coming from those directions acquires very little polarization in the scattering process. 

But Glare off Foliage May Still Benefit

That said, note that many leaves and grasses turn out to be surprisingly good specular reflectors. Even if the sky is hopeless, a polarizer can often cut a rewarding amount of color-sapping white glare off foliage under these circumstances, especially when shooting close to the sun.


Poorly Polarized Glare

Reflections off very dull or metallic surfaces are almost always lost causes—there just won't be enough polarization to work with. 

When controlling glare off a non-metallic specular reflector like water or glass, the farther you are off Brewster's angle (generally ~55°) from the normal to the offending surface, the less effective your polarizer will be. At 90° to Brewster's angle, reflections will be completely unpolarized—and thus immune to your polarizer. This is often the case when shooting opposite the sun, with either water or foliage glare, as illustrated in the scatter samples below.

But Foliage and Water May Still Benefit

When shooting near the sun, however,  glare off foliage or water with waves may well be coming at you from a wide range of angles, some of which may still be profitably blocked. 


Bottom Line

When in doubt, try it out, particularly if you're shooting toward the sun. Even if you can't see the effect in your LCD or electronic TTL viewfinder, if there's a profit to be made, your meter will register a light loss as you rotate the polarizer. If the polarizer's already off the camera, look through it, rotate it, and see for yourself if there's anything to be gained. You'll often be pleasantly surprised. 


Polarization Primer

Scattered light, glare and other strong reflections can degrade photographs in many ways—e.g., by diluting colors, by obscuring or distracting the viewer from important image details, or by forcing suboptimal exposure compromises. Luckily, nature tends to tag such "bad light" with varying degrees of polarization, and that marker provides an easy way to suppress the "bad light" while capturing the good.

Most of the primary light sources encountered in photography—the sun, moon, indoor lighting, flash lamps—are unpolarized, meaning that the electric field fluctuations accompanying the light are oriented equally and randomly in all directions perpendicular to the light's direction of travel. If all the light's electric fields were oriented in the same direction, we'd say it's linearly or plane polarized. Other types of polarization—e.g., circular and elliptical—are seldom encountered by photographers outside their cameras.

Unpolarized light typically acquires polarization through absorption, scattering or reflection. We'd better examine these processes one at a time.


Polarization By Absorption—How Polarizers Work

Linear polarizing filters use optical materials with crystalline structures aligned in such a way that they readily pass incident light linearly polarized in one direction (we'll call it the passing axis) while strongly absorbing light polarized along the perpendicular direction, or blocking axis. These 2 optical axes always lie 90° apart. 

Marks the paydirt When unpolarized light falls on a linear polarizer, those polarizations closest to the passing axis get through with the least attenuation.

Other polarizations are variably filtered out of the mix by absorption. Those closest to the blocking axis are attenuated the most.

For a beautifully illustrated and animated explanation of polarization, see this Polarization of Light tutorial.


Polarizing Filters

Polarizing filters are not all created equally. For starters, there are 2 basic types, linear and circular, differing only with regard to camera compatibility and price. Linear and circular polarizers block polarized light equally well, but some cameras (SLRs in particular) don't work properly with linears, as detailed below. Circular polarizers are compatible all cameras but usually cost more than linears of comparable quality. 

Polarizing materials also vary in their effectiveness and spectral properties. Construction quality enters the equation as well. My Tiffen circular polarizer is noticeably more effective at blocking polarized reflections than my Tiffen linear polarizer, but the performance difference reflects the quality of the materials in these two particular filters, not the circular vs. linear design. Polarizers normally impart a very subtle blue tint, but some are bluer than others.

Marks the paydirt Polarizer on an Oly C-2000Z Rangefinder

A bold white dot on the rotating ring of this Tiffen circular polarizer marks the blocking axis, while the the final "r" in "Polarizer" marks the passing axis. Conveniently, these markings are visible through the optical viewfinder in the set up shown.  Oly C-2000Z with 49 mm Tiffen circular polarizer mounted. Click to see 1280x960 original. [D-340L]

Once you've established that your camera does or doesn't require a circular polarizer, blocking efficiency becomes the most important selection criterion. If you have the opportunity to compare several polarizers in person, test them all against a strongly polarized reflection like the one set up in the reflection calibration method outlined below and favor the polarizer that blocks the best. A multicoated polarizer will reduce the risk of flare, but when the situation calls for a polarizer, an uncoated polarizer will usually be far better than none at all. 

Marks opportunities to bypass long-winded discussions and cut to the action line. Click to review Limited Warranty section on the home page. To skip over polarizer calibration and adjustment, and what happens at intermediate polarizer positions, cut to Polarization by Scattering now.
   

Calibrating and Adjusting Your Polarizer

The non-TTL techniques espoused in this article assume a polarizer with its blocking axis clearly marked as shown above, but some polarizers come with their passing axis marked instead, and many come with no dedicated markings at all—presumably on the assumption that they'll always be used with TTL control. At the other extreme, Heliopan's thin circular polarizer has a finely graduated rotating ring for precision work. My inexpensive Tiffen circular polarizer came with a single white dot sitting on its blocking axis, but I had to mark an even cheaper Tiffen linear polarizer myself. 

Marks the gotchas If your polarizer is unmarked, or you're unsure of the meaning of the markings present, calibrate it before relying on any of the non-TTL polarizer techniques offered in this article.

Two simple calibration methods are discussed next.


The Reflection Method

This method uses a strongly polarized reflection as a reference.

  • Find a flat, shiny tabletop, countertop or water surface with bright reflections. Don't use a curved surface like a car fender here.

  • View the reflections obliquely through your polarizer at an angle near 35° above the reflecting surface. This special angle  (Brewster's angle) will insure that the reflections are maximally polarized by the bounce. (If yours is a circular polarizer, be sure to hold it with the male threads toward you.)

  • Keeping this aim, rotate your polarizer until the reflections are maximally suppressed. The polarizer's blocking axis will now run parallel to the reflecting surface and perpendicular to the reflected light's direction of travel to the camera.


The Sunglass Method

Polarized sunglasses are always constructed such that the blocking axes of both lenses run right to left as the glasses are meant to be worn. You can use this fact to calibrate your polarizing filter:

  • Don the sunglasses. If necessary, confirm that the sunglasses really are polarized by tilting your head side to side while viewing a bright reflection from a non-metallic surface or a patch of sky ~90° to the sun. The tilting should make an obvious brightness difference.

  • View an incandescent lamp or any other safe unpolarized light source through the filter while wearing the sunglasses. (If yours is a circular polarizer, be sure to hold it with the male threads toward you.)

  • Rotate the polarizer until the light source is maximally suppressed. The polarizer's blocking axis will now parallel the right-left axis of the sunglasses.


Making and Using the Markings

Once you've determined your polarizer's blocking axis, mark either end of it on the outer rotating ring for future reference. (Ring positions 180° apart are functionally equivalent.) Some recommend a dot of nail polish for this purpose, but I've also had good luck with a sliver of white electrical tape. If your polarizer has writing on the outer ring, note any characters that happen to line up with the blocking axis.

In the field, I find it much simpler to work with a mark on blocking axis. Once I've discerned the polarization of the unwanted scatter or reflection to be suppressed, I can simply turn the outer rotating ring to align my mark with that target polarization.

Effective polarizer use involves careful attention to camera angle as well, but polarizer ring adjustment depends only on the orientation of the target polarization.


Polarizer Theory 101—Intermediate Settings

Light linearly polarized in a direction between the polarizer's passing and blocking axes is partially blocked. The passed intensity of such light varies with the square of the cosine of the angle ø between the polarizer's passing axis and the incident light's direction of polarization:

Ipassed = I0 · k · cos2(ø)

where I0 is the incident intensity and k is a constant between 0 and 1 representing the intensity fraction passed when ø = 0. (The better quality the polarizer, the more closely k approaches 1.)

Conversely, the percentage of linearly polarized incident light blocked by the polarizer is

Blocking efficiency (%) = 100% · [1 - k · sin2(ø')]

where ø' is the angle between the polarizer's blocking axis and the incident light's direction of polarization. Note that ø and ø' are always complementary angles.

Marks the paydirt Intensity Passed As A Function of Polarizer Angle

Passing angle ø (°) 1 0 15 30 45 60 75 90
Intensity passed (%) 100 93 75 50 25 7 0
Blocking angle ø' (°) 2 90 75 60 45 30 15 0
Intensity blocked (%) 3

0

7

25

50

75

93

100

Table Notes:
  1. Angle between the polarizer's passing axis and the incident light's plane of polarization.
  2. Angle between the polarizer's blocking axis (white dot) and the incident plane of polarization.
  3. For an ideal polarizer with k = 1.

Polarization By Scattering—Targeting Atmospheric Scatter

Atmospheric scattering occurs when gas molecules, water droplets and other airborne particles absorb and reradiate light, usually sunlight, in a process know as Rayleigh scattering. Scattering efficiency depends on particle size and the altitude (angular height) of the light source above the horizon, and varies inversely with the 4th power of the incident light's wavelength (color). Sunlight suffers the least scattering at local noon in clean, dry air, but the preferential scattering of shorter wavelengths slightly reddens the light reaching ground level even then.

As a process, scattering isn't all bad. After all, we owe our gorgeous blue skies and cherished red-yellow sunsets to it. Clean, dry air scatters blue light (~400 nm) about 7 times more efficiently than red (~650 nm) and about 3 times more efficiently than green (~520 nm). Violet (~350 nm) is actually the most strongly scattered color, but the human eye responds very poorly to violet, so blue sky is what we see. Late sunlight skimming the horizon loses much of its blue-green content to scatter over its long path through the lower atmosphere before ever reaching admiring eyes.

Adding moisture or particulates to the air substantially increases scattering efficiency at longer (redder) wavelengths. With more colors represented in their scattered light, clouds look white, and hazy (damp or smoggy) skies take on a grayish to whitish cast.

Marks the gotchas Bright white scatter flooding into a camera effectively mutes or desaturates all the colors in the scene, especially the blue of the sky, while bright blue scatter effectively desaturates all other colors.

Polarization Due to Scattering

Luckily for photographers, details of the molecular-level reradiation process at the heart of scattering ensure that at all wavelengths, 

Marks the paydirt Scattered light is strongly polarized perpendicular to its direction of travel from the primary source

whether it be sun, moon or searchlight. The polarization differentiates scatter from the desirable and largely unpolarized light reflected from our photographic subjects, and is thus our point of attack.


Non-TTL Scatter Control

We're now ready to apply what we know about scatter to defeat it.

Marks the paydirt Filtering Out Atmospheric Scatter Without TTL Monitoring

1. First, locate the arc of target directions.
  • Point an index finger at the light source and hold the attached thumb at 90° to the finger.

  • Now rotate the thumb around the index finger to sweep out the arc of maximum scatter polarization. These are all target directions.

2. Arrange to shoot your subject with your camera pointed in a target direction as best you can.

3. With your camera aimed, turn the polarizer dot (or blocking axis) 90° to the direction of the light source to block the target polarization.

Note that at high noon, the arc of target directions will fall near or even below the horizon, depending on latitude, time of year and local topography.

Of course, you won't always be able to shoot in a target direction, but to the extent that you can, this polarizer technique will give you bluer skies, more conspicuous clouds and more vibrant colors throughout your scene, as you can see in the samples below.

Marks the paydirt Camera Angle Relative To the Sun's Direction »

90° (on target) 150°
No polarizer: On the left, same observations as in the introductory scatter samples above. On the right, the polarizer or lack thereof makes little difference with the camera angle well off any available target direction. As my shadow at left shows, the sun is at my back. Berkeley Hills looking N--no polarizer. Click here to see raw original 1600x1200. [C-2000Z] Berkeley Hills looking W--no polarizer. Click here to see raw original 1200x1600. [C-2000Z]
Polarizer ring 90° off target polarization: On the left, hillside colors are little better than with no polarizer at all. On the right, there's no discernable difference—because there's no suitably polarized light coming from the hillside or sky in this direction. Berkeley Hills looking N--polarizer dot 90 degrees off target polarization. Click here to see raw original 1600x1200. [C-2000Z] Berkeley Hills looking W--polarizer dot 90 degrees off target polarization. Click here to see raw original 1200x1600. [C-2000Z]
Polarizer on target polarization: On the left, same observations as in the introductory scatter samples above. Note the fairly distinct dark blue arc of maximum polarization in the sky at top center. On the right, no polarized light and no visible difference once again. Berkeley Hills looking N--polarizer dot on target polarization, 90 degrees to sun. Click here to see raw original 1600x1200. [C-2000Z] Berkeley Hills looking W--polarizer dot set on target polarization, 90 degrees to sun. Click here to see raw original 1200x1600. [C-2000Z]
Table Note: Automatic exposures; no post-processing, looking NW in late afternoon sun.

Sky Banding

The vertically banded sky in the bottom left sample directly above nicely illustrates

  • the near-vertical arc of target directions found whenever the sun is low in the sky,

  • how quickly polarization falls off from the target direction, and

  • the challenge of using a polarizer with a wide angle lens.

To mitigate sky banding in wide angle shots,

  • Purposely set your polarizer for less than full effect

  • Zoom in or otherwise exclude as much sky as possible

  • Shoot near noon, when the maximally polarized arc of sky hugs the horizon and tends not to exceed the camera's field of view

  • Try feathering out the band in post-processing

BTW, bright sky suppression can also be had with graduated neutral density filters—sometimes with better results in wide angle situations near the ends of the day. But proper GND technique demands a nearly flat horizon and reliable TTL control—i.e., a clearly visible LCD image—and generally involves more setup and effort than polarizer technique. In my experience, GNDs make polarizers look easy, but they can be very rewarding at times.


See what the camera sees

Marks the paydirt Take your polarizer off the camera and observe the sky as your rotate it to confirm this technique with your own eyes. With a circular polarizer, you'll only see the effect if the male threads face you. With a linear polarizer, you'll see the effect either way, but if you align the rotating ring for a particular effect with the threads away and then flip the polarizer around to mount it, you might lose your hard-earned alignment.

Marks opportunities to bypass long-winded discussions and cut to the action line. Click to review Limited Warranty section on the home page. To see how to control reflections without further ado, cut to the non-TTL reflection control technique now. Otherwise, read on.
   

Polarization By Reflection—Targeting Glare

Reflecting surfaces generally come in 3 textures: smooth, rough and in between. Reflections off smooth, mirror-like surfaces are termed specular reflections. By happy coincidence, specular reflections are the kind best controlled by polarizers and also the kind photographers most often need to suppress.

Smooth metallic surfaces generally preserve the polarization (or lack thereof) of the incident light on reflection. (Actually, such surfaces reverse the incident polarization, but with linearly polarized light, the reversal's not readily observable.) Since sunlight is unpolarized, sunlight reflected off a metallic surface will remain unpolarized. 

By constrast, most smooth non-metallic surfaces—most notably water and glass—tend to impart polarization on the light they reflect by absorbing or transmitting certain electric field orientations and reflecting (more accurately, reradiating) others.

A photographer armed with a polarizer can profitably exploit this fact:

Marks the paydirt Unpolarized light reflected from smooth non-metallic surfaces (e.g., water, glass and leaves) tends to become at least partially polarized in the process, while light reflected from rough surfaces (rocks, trees, animals, dirt, etc.) or metallic surfaces tends to remain unpolarized.

Reflections from uniformly rough surfaces are termed diffuse. The even omnidirectional reflection off coming off baking soda neatly leveled in a bowl is diffuse. In between specular and diffuse reflections are spread reflections, which exhibit some directionality and may acquire some polarization.

For a beautifully illustrated and animated explanation of reflection, click here.

Marks opportunities to bypass long-winded discussions and cut to the action line. Click to review Limited Warranty section on the home page. Cut to the non-TTL reflection control technique below without further ado, or read on to see how it works first.
   

Polarizer Theory 102—Brewster's Angle

Just how much polarization specular reflections acquire in the reflection process depends on

  • the degree and orientation of polarization of the incident light (usually unpolarized),

  • the angle of incidence, and

  • the optical properties of the substances on either side of the reflecting interface.

Reflection Optics—A Few Important Basics

By definition, the angle of incidence is the angle between the path of the incident light and the normal (perpendicular) to the reflecting surface at the point of reflection. Analogously, the angle of reflection is the angle between the normal to the reflecting surface and the path of the reflected light, again at the point of reflection.

These definitions power the Law of Reflection: The angle of incidence always equals the angle of reflection. (Were we to measure angles of incidence and reflection from the reflecting surface, the law would cease to hold for most irregular and curved surfaces.)

The plane of incidence—defined as the plane containing both incident and reflected lightpaths—is always normal (perpendicular) to the reflecting surface, at least at the point of reflection.

Unpolarized light, the kind photographers usually encounter, can be thought of as a mix of components polarized parallel and perpendicular to the plane of incidence. A non-metallic specular reflector will reflect the incoming component polarized perpendicular to the plane of incidence (i.e., parallel or tangential to the reflecting surface) in toto, without change in either polarization or intensity. Meanwhile, a variable portion of the incoming component polarized parallel to the plane of incidence will refract (bend) into the reflecting surface, to be transmitted or absorbed as dictated by the optical properties of the reflector.

In other words, partial refraction effectively filters from the reflection some of the light polarized parallel to the plane of incidence, while the component perpendicular to the plane of incidence reflects unscathed.


Brewster's Angle

At a certain angle of incidence known as Brewster's angle, the reflection ends up 100% polarized perpendicular to the plane of incidence—i.e., parallel or tangential to the reflecting surface—because the component parallel to the plane of incidence has been completely refracted into the reflecting material.

Brewster's angle = arctan(n' / n)

where

n'= refractive index of the reflecting material—e.g., water or glass

n = refractive index of the material through which the light travels before and after reflection.

For reflections in air (n = 1), the expression reduces to

Brewster's angle = arctan(n')


Brewster's Angle in Photography

The table below shows the Brewster's angles of most interest to photographers.

Brewster's Angles For Water and Glass Reflections in Air

Medium Refractive index (n') Brewster's angle
Air 1 [no reflection]
Water 1.333 53°
Glass 1.5 (depends on the glass) 56°

Marks the paydirt In fact, all the reflecting surfaces you're likely to need to control photographically turn out to have Brewster's angles near 55° in air. 

At other angles of incidence, the reflected light becomes only partially polarized, but the net polarization remains tangential to the reflecting surface. At 30° and wider angles (i.e., at 35 mm equivalent focal lengths under 85-100 mm), polarizer efficacy falls off progressively as peripheral reflections deviate more and more from Brewster's angle. Uneven suppression of reflections can be seen to some extent in the glare examples shown above.

Acknowledgement: Thanks to Chris Andreev for alerting me to polarizer coverage limitations as they relate to reflections.

Non-TTL Reflection Control

Now we're ready to put all this reflection theory into practice.

Marks the paydirt Filtering Out Specular Reflections Without TTL Control

The target direction for reflections is 55° from the normal or 35° from the tangent to the reflecting surface. The target polarization is tangential to the reflecting surface.
Whether you need to shoot
  • Through a window without burying the subject in unwanted light reflected off the glass, or

  • A submerged subject without interference from reflections off the water's surface, or

  • Toward an unpolarized light source (sun, moon, streetlight, etc.) without glare or other annoying bright reflections off intervening smooth non-metallic surfaces (water, glass, foliage, car paint, shiny bald heads, etc.),

just follow these 2 simple steps:

  • Arrange your shot for a camera angle ~55° off the normal to the reflecting surface (or ~35° off the tangent to the reflecting surface) as best you can.

  • Set your polarizer's blocking axis parallel or tangential to the reflecting surface at the point of reflection.

Polarized sunglasses use this strategy. Having observed that

  • sunglass users are usually upright when their eyes are open, and

  • glare-producing surfaces (water, snow, polished floors, leaves, car hoods) tend to be horizontal or nearly so,

their designers set the blocking axis of the polarizing coating horizontally across the frames. As you might have guessed, this arrangement does little to reduce atmospheric scatter, except along the horizon near local noon, but then scatter's not a major cause of squinting. 

Of course, you won't always have the freedom to base camera angle solely on polarization, but knowing the ideal arrangement will allow you to exercise the freedom you do have to get the most out of your polarizer.

The table below illustrates the non-TTL reflection control technique in use.

Marks the paydirt Camera Angle Relative To Reflecting Surface Normal

55° (on  target direction) 10° (off target direction))
No polarizer: Note the strong glare off the red apple and the countertop from the overhead fluorescent lights in both samples. Kitchen counter at Brewster's angle--no polarizer. Click here to see raw original 1600x1200. [C-2000Z] Kitchen counter at 10 degrees off normal--no polarizer. Click here to see raw original 1600x1200. [C-2000Z]
Blocking axis 90° off target polarization: At left, a little less glare than with no polarizer at all. At right, no visible difference. Kitchen counter at Brewster's angle--polarizer dot 90 degrees to target polarization. Click here to see raw original 1600x1200. [C-2000Z] Kitchen counter at 10 degrees off normal--polarizer dot 90 degrees off target polarization. Click here to see raw original 1600x1200. [C-2000Z]
Blocking axis on target polarization: At left, glare is strongly suppressed, but no visible difference at right because the light coming from this direction has little polarization. Kitchen counter at Brewster's angle--polarizer dot on target polarization. Click here to see raw original 1600x1200. [C-2000Z] Kitchen counter at 10 degrees off normal--polarizer dot on target polarization. Click here to see raw original 1600x1200. [C-2000Z]
Table Note: Automatic exposures; no post-processing.

Marks the paydirt Reflection control tips:

  • Get to know polarization: Now that you know that your polarized sunglasses block horizontally, use them as a polarization probe in day-to-day settings. The sooner you become one with polarization, the sooner you'll be able to set your polarizer properly without even thinking about it.

  • Learn to estimate a 55° angle from the normal (or, equivalently, a 35° angle from the tangent) to the reflecting surface. My index and long fingers just happen to make a 35° angle when signing "V" for victory over reflections.

  • See what your camera sees: Play around with your polarizer off the camera. Use it to observe reflections off your kitchen counter (or any other handy non-metallic reflecting surface) to confirm the above technique with your own eyes.

Regarding the last item, you'll only see the effect with a circular polarizer if the male threads face you. With a linear polarizer, you'll see the effect either way, but if you align the rotating ring for a particular effect with the threads away and then flip the polarizer around to mount it, you risk losing your alignment.


Correcting Exposure For Your Polarizer

Marks the paydirt In completely unpolarized light like sunlight or incandescent light, an ideal polarizer acts like a 1-stop (50%, 0.3 density) neutral density filter in any position. That said, real polarizers require more like 1-2 stops of exposure correction in unpolarized light, and even more in scenes with polarization. The exact amount will vary from one polarizer and one scene to another.

In unpolarized light on my C-2020Z, for instance, my Tiffen linear polarizer requires a 1 2/3-stop exposure correction (a filter factor of 3.0), while my Tiffen circular polarizer requires exactly 2 stops, or a filter factor of 4.0. I rather doubt that this slight difference in density can be generalized to other LP-CP pairs, even those from the same manufacturer.

Luckily, digital cameras with automatic exposure via TTL metering afford a number of ways to compensate for polarizer losses. Which one to use depends largely on which camera settings you need to control manually.

  • Fully automatic mode—the camera will take care of it all for you, probably with decent results.

  • Aperture- or shutter-priority modes: Manual adjustment of one causes TTL-based adjustment of the other by the camera.

  • Fully manual mode: Manual adjustment of aperture and shutter speed.

  • Manual adjustment of exposure compensation.

Many higher-end digital cameras now offer all these features.

Marks opportunities to bypass long-winded discussions and cut to the action line. Click to review Limited Warranty section on the home page. To skip over gory calibration details, cut to Circular vs. Linear Polarizers now. Otherwise, read on.

Marks the paydirt Calibrating Your Polarizer For Manual Exposures

With a digital camera, it's fairly easy to calibrate a polarizer for manual exposure by analyzing a series of test images with PIE (Picture Information Extractor), a worth-its-weight-in-memory-cards image management utility that lists the exposure (EXIF header) data most digital cameras store within their image files.

  • Plan out a series of test shots—e.g., first with the polarizer aimed in a target direction (for maximum effect) and rotated in varying orientations 0-90° to the target polarization and finally with the polarizer removed.

  • Record the pertinent polarizer details for each test shot in temporal order for later correlation with the exposure data being recorded by the camera. Include the fluffed test shots, too.

  • Set up PIE to rename your images with their date-time stamp and to create a text listing (picinfo.txt) of all images and their exposure data.

  • Use PIE to upload the test shots to a separate folder to limit picinfo.txt to the test sequence.

  • Match up the exposure data in picinfo.txt with the polarizer data in your test record. The temporal order will make the correlation a snap.

If you prefer fully manual exposure control and use a polarizer a lot, you'll probably find this procedure worthwhile.


Circular vs. Linear Polarizers

Circular polarizers (CPs) are 2-layer affairs—a linear polarizer (LP) backed with a special birefringent optical layer known as a quarter-wave plate (QWP). The QWP is bonded to the LP with its fast optical axis oriented 45° to the LP's passing axis. In this configuration, the QWP transforms the linearly polarized light emerging from the outer LP layer into circularly polarized light, which to the polarization-sensitive metering and auto-focus components found in many modern SLR cameras is indistinguishable from unpolarized light.

The QWP layer in CPs insures accurate TTL auto-focus and metering in all cameras but adds cost and another potential source of image degradation, as illustrated in the Fun with a Reversed Circular Polarizer section below.

Technical Note: For a beautifully illustrated interactive explanation of birefringence, click here.

So Which to Use, LP or CP?

You can usually go either way—CP or LP—with popular digital rangefinder cameras like the Oly C-20x0Z, C-30x0Z and C-4040Z lines, the Nikon CoolPix series and the Canon PowerShot G1 and G2. The straight-through designs found in such cameras usually don't involve polarization-sensitive internals like folded lightpaths and beam-splitters. However, digital SLRs like the Oly E-10 and E-20 and the Nikon D1 generally do, and they'll likely require a CP for proper metering and auto-focus. (The D1 definitely does, at least for metering.)

Marks the paydirt The bottom line:

  • CPs work well with any camera, including your future cameras.

  • LPs will work well with most digital rangefinder cameras.

  • SLR cameras, film or digital, will almost certainly need a CP.

Generally speaking, LPs and CPs are equally effective at blocking polarized light. Oft-repeated claims that one typically outperforms the other have no basis in optics but have a lot to do with the variable quality of commercially available polarizers. Such myths also apparently feed off a widespread lack of appreciation for the optical complexity of the CP—particularly when reversed

Marks the paydirt LPs are simpler, less expensive and theoretically optically cleaner than their circular counterparts. If you know for a fact that your camera meters and auto-focuses properly with an LP, feel free to go linear. Otherwise, play it safe with a CP.

Quality Counts

Of course, things are never quite that simple. My particular Tiffen CP (~$25) blocks polarized reflections noticeably better than my Tiffen LP (~$15), presumably due to quality differences peculiar to the Tiffen line. (Near Brewster's angle, the LP passes a clearly visible reflection at maximum effect while the CP passes none.) For an extra $10, the Tiffen CP offers better performance and universal compatibility, too. Guess which one I carry?

I seriously doubt that the quality difference here has anything to do the CP vs. LP design. When LP compatibility isn't an issue, I'd choose a polarizer based on a balance of blocking performance and cost and let the LP vs. CP chip fall where it may. 


Testing for Linear Polarizer Compatibility

It's easy to test your camera's LP compatibility, at least with regard to metering: 

  • Mount the LP and fill the viewfinder with a large dull light-colored surface like an indoor wall.

  • Make sure no specular reflections, atmospheric scatter or other polarized light sources reach the camera during the test.

  • Under constant lighting, turn on the LCD and watch the exposure settings as you rotate the polarizer.

Marks the paydirt If the exposure settings change significantly over any 180° rotation of the polarizer ring, your camera requires a CP.

If your camera passes the LP metering test, an LP will in all likelihood be OK, but an LP-related auto-focus malfunction is still theoretically possible. I suppose you could test the camera's ability to auto-focus at several different polarizer positions over a 180° arc, but I have no reliable information here. 

Conclusively establishing that a specific digital camera works properly with an LP under all circumstances can be challenging, as chronicled in The Great C-20x0Z Circular vs. Linear Polarizer Debate elsewhere on dpFWIW .


How to Tell a CP from an LP—the Mirror Test

Polarizers aren't always clearly marked, but thanks to an RPD tip from Dennis Duke, it's easy to tell whether a polarizer in hand is circular or linear. All you need is a mirror:

Marks the paydirt Look in a mirror through the polarizer—once with the male threads toward you and then with the threads flipped toward the mirror. If the flip makes no difference, the polarizer's an LP. If the flip causes the polarizer to turn black or nearly so, it's a CP.

How black the CP turns is probably an indication of its quality, particularly with regard to the spectral tuning of its QWP layer.

Dennis also notes that most polarizers not marked as circular are linear. That jibes with my limited experience with a CP and LP from Tiffen.


Fascinating, Captain, But How Does It Work?

Ready for a nice yawn? 

In the table below, L represents the linear polarizing layer found in both LPs and CPs, Q represents the quarter-wave plate (QWP) layer added inboard to an LP to make a CP, and M represents the mirror. Thanks to physicist Joe Miller of RPD for helping me work this out.

Mirror Test to Distinguish Linear and Circular Polarizers

Polarizer Type  Thread Direction Result Active Lightpath  Explanation 1
LP either way 75% darkening LML Looking in the mirror through an LP causes the usual 2-stop darkening of the image but has no other effect since the L layer is unavoidably aligned with itself. The reflection at M has no significant effect on the linear polarization involved here. By symmetry, thread orientation makes no difference. 
CP away from mirror  75% darkening QLMLQ Looking in the mirror through a CP with its threads away from the mirror is equivalent to the LML case. The first Q layer pass has no relevant downstream effect on unpolarized light 1, and the final Q layer pass has no practical effect on what your eye sees. 2
CP toward mirrror 100% blackening LQMQL Flipping the CP threads toward the mirror finally brings the mirror and Q layer into play. Recall that in a CP, the birefringent 3 Q layer's fast axis is always 45° off the L layer's optic axis. The 1st Q layer pass converts the linearly polarized light emerging from the 1st L layer pass into circularly polarized light with a certain handedness (direction of rotation) depending on how the Q layer was mounted. The M reflection reverses that handedness but has no other effect on polarization at the normal incidence involved in this test. The subsequent 2nd Q layer pass converts the circularly polarized light coming off the mirror back into linearly polarized light, but this time, thanks to the reversal of handedness, the resulting plane of polarization falls 45° to the other side to the Q layer's fast axis. The linearly polarized light emerging from the LQMQ segment thus ends up with a plane of polarization 90° off the axis of the L layer, which blocks the light completely on the final L layer pass—hence a black-looking CP.
Technical notes:  1. The explanations above reasonably assume unpolarized ambient light.  2. Some vision physiology sources claim that the human eye can detect and the brain can perceive polarization, but the effect is at best extremely subtle.  3. Birefringent materials like cellophane transmit light faster in some directions than in others due to anisotropies in their molecular structures. The directions of maximum and minimum light velocity (or equivalently, of minimum and maximum refractive index) are known respectively as the fast and slow axes of the material and are generally 90° apart. The difference in light velocity (or refractive index) between the fast and slow axes determines how thick a given birefringent material must be to function as a quarter-wave or half-wave plate at a given wavelength.

Fun with a Reversed Circular Polarizer—An Instructive Diversion

Look at a polarized light source through your CP with the male threads pointing away from you, and you'll see some very interesting color shifts that nicely illustrate several important polarization concepts, thanks to the surprisingly complex optical properties of a typical QWP. Henceforth I'll refer to a CP held male threads away as a reversed CP.

Marks the paydirt In a nutshell, a reversed CP acts like a ~2-stop (75%) neutral density filter with an adjustable warming or cooling effect, depending on its orientation. Maximum bluing comes with the polarizer turned to block the incoming polarized light. Maximum reddening occurs at 90° to the bluest setting and neutrality at any 45° setting in between. 

It might just be possible to mount a reversed Cokin-style CP to put this effect to use, but that's pure speculation on my part.


The Experimental Setup

To explore reversed CP behavior, I created a simple desktop scene containing a highly polarized reflection provided by a cup of still water positioned to reflect the bulb of a desk lamp near Brewster's angle, ~55° off the normal to the water's surface. (An uncoated filter would have made an equally good reflector, and the optimum angle would have been about the same.)

The reflection coming off the water was highly polarized in a direction both tangential to the water's surface and perpendicular to the eye-water line. Light coming from the scene around the water was largely unpolarized, including light coming directly from the bulb.


The Observations

Viewing this scene (water + surroundings) through a rotating reversed circular polarizer (CP), I consistently observed orientation-dependent color shifts, but only in the water reflection—i.e., only in incident light bearing a net linear polarization. No color shifts ever appeared in the unpolarized light coming from the scene around the cup.

The white dot on my Tiffen CP sits on the LP layer's blocking axis. As expected, the unreversed CP maximally blocked the water reflection with white dots at 3:00 and 9:00 (i.e., parallel to the surface of the water) with no color shifting whatsoever.

With the CP reversed, however, I saw just the opposite—mild but noticeable color shifting limited to the water reflection but little if any overall reflection blocking. White dots at 3:00 and 9:00 always yielded the bluest color shift, while white dots at 12:00 and 6:00 (90° to the water's surface) always gave the reddest. White dots ~45° between these cardinal positions seemed to yield a neutral tone.


What's It All Mean, Mr. Natural?

After digging through The Feynman Lectures on Physics, I think I understand what's going on here, at least in part. The key to the puzzle is the CP's quarter-wave plate (QWP).

QWP Details

As noted briefly above, a CP consists of 2 layers: A simple LP on the outside and a birefringent QWP on the male-threaded side. The QWP has a molecular structure that transmits light at different speeds in different directions. The directions of greatest and least speed are known respectively as the QWP's fast and slow optic axes. In QWPs, as in most birefringent materials, these optic axes are 90° apart. 

On exiting an ideal QWP, the phase of incident light linearly polarized along the QWP's slow optic axis is retarded by exactly one quarter wavelength relative to incident light polarized along its fast optic axis. When the QWP is oriented with its optic axes offset 45° from the pass direction of the LP layer in a CP, this phase shift "remixes" the linearly polarized light emerging from the LP into circularly polarized light. To polarization-sensitive camera internals, circularly polarized light is indistinguishable from unpolarized light. All CPs are constructed with this 45° LP-QWP offset.

Real-world QWPs can achieve perfect linear-to-circular polarization conversions only for a relatively narrow band of wavelengths. All other wavelengths in the incident linearly polarized light exit the QWP with an elliptical polarization that acts like a residual linear polarization. (Linear and circular polarizations are in fact opposite extreme cases of elliptical polarization.) To spread the misery across the visible spectrum with minimal impact, the QWPs used in CPs are usually tuned to green light (~520 nm) at the peak of the solar power spectrum. 

The green wavelengths in the incident polarized light thus emerge from the CP with perfect circular polarization, while the blue and red components come out with elliptical polarizations. The long axis of the red polarization ellipse remains roughly aligned with the incident plane of polarization, but the long axis of the blue polarization ellipse deviates by nearly 90°, as we'll see below

QWP In Action

With the CP reversed, light from the scene first hits the QWP, which does no filtering itself. Aside from minor reflections off its incident face, the QWP passes all the light it receives, polarized or not.

The QWP has no effect whatsoever on the unpolarized light coming off the scene. Nor does it have any effect on light polarized along its fast or slow optic axes, as occurs in the setup above with the CP's white dot at 1:30, 4:30, 7:30 or 10:30—hence the neutral coloration observed at those positions.

Interesting things happen, however, when the reflection is polarized at 45° to the QWP's fast axis, as occurs in the setup above with the CP's white dot at 12:00, 3:00, 6:00 or 9:00. In these cases, the QWP does its usual thing—it converts the linearly polarized reflection into a circularly polarized green component and elliptically polarized red and blue components of varying orientations.

The subsequent LP layer indiscriminately blocks exactly half the unpolarized light and exactly half the circularly polarized green light coming through the QWP. However, it blocks more or less than half the elliptically polarized red and blue light, as we'll see next. 

The reversed CP color shifts observed at 12:00, 3:00, 6:00 or 9:00 arise here, but why maximum bluing at 3:00 and 9:00 and maximum reddening at 12:00 and 6:00 white dot positions? To understand that, we'll need to take an even closer look at the spectral properties of the green-tuned QWP.


The Colors, Man, the Colors!

At short blue (~450 nm) and violet (~400 nm) wavelengths, a QWP tuned for green light (~520 nm) begins to look and act more like a half-wave plate (HWP) than an ideal QWP. The HWP is another curious birefringent optical device with the ability to flip the polarization of incident linearly polarized light by exactly twice the angle between the HWP's fast axis and the incident plane of polarization. 

Now, at 3:00 or 9:00 white dot positions, the reflection's incident polarization is squarely aligned with the LP layer's blocking axis but 45° off the fast QWP axis. The resulting blue-violet polarization flip of 2 x 45° = 90° swings the long axis of the reflection's blue-violet polarization ellipse into rough alignment with the LP layer's passing axis instead. This allows some of the blue-violet light to sneak through the LP layer.

The longer red (~650-700 nm) wavelengths don't fare as well, however. A green-tuned QWP has relatively little effect on the polarization of red light within the water reflection. At 3:00 or 9:00 white dot positions, the elliptically polarized red component emerging from the QWP, still roughly aligned with the LP layer's blocking axis, suffers heavy attenuation. Thus red gets filtered out disproportionately.

On balance, the LP layer ends up being more transparent to blue-violet than to red light at the 3:00 and 9:00 white dot positions, thanks to the spectral properties of the reversed CP's imperfect QWP layer. The result is maximum bluing at 3:00 and 9:00, just as I had observed.

The same mechanism nicely accounts for the observed maximum reddening at 12:00 and 6:00. I'll leave it to the interested reader to work through the details for those positions.

Anyone still awake? Didn't think so.


Geez, Why Not Just Post-Process?

Why fool with polarizers at all when you can clean up digital pictures in post-processing?

Well, for one thing, you'll have a mighty hard time editing out interfering reflections in shots taken through or around glass or water. You'll also have a heck of a time editing out white-out reflections from foliage in bright sunlight.

You might have more luck with atmospheric scatter. For example, you could shoot the exact same bright-sky scene twice, once with spot-metering in the foreground and again with spot-metering on the sky. Or you could just crank down 3 stops on the sky shot. You could then cut and paste the two together in post-processing and airbrush, blur or otherwise obscure the seam. Just pray there aren't any trees, buildings or other pesky objects (subjects?) around to bugger up your skyline.

At bottom, you have to ask yourself, just how good are you and your software at post-processing, and how much time do you have to spend on it?

Personally, I'd rather rely on a polarizer.


Editor's Note

Sorry for this long-winded "more than you ever wanted to know about polarizers" exposition. I just couldn't resist. Something about polarization physics tickles me, strange as that may be.


References and Links

(See also the home page links.)

Hunter, Fil and Fuqua, Paul, Light — Science & Magic, Focal Press,  1997. 

Rowell, Galen, Mountain Light, 2nd ed., Yolla Bolly Press, Sierra Club Books, San Francisco, 1995.

Filters for Outdoor Photography—an excellent introduction to polarizing, GND and other filters by accomplished photographer Darwin Wiggett.

Feynman, RP, Leighton, RB, Sands, M, The Feynman Lectures on Physics, Vol. 1, Addison-Wesley Publishing Company, Reading, MA 1963.

Encarta 99 Reference Suite, Microsoft, 1998.

Philip Greenspun's filter article—comprehensive and well-illustrated, on photo.net, of course.

Jens Roesner's polarizer article—still under development but already with brimming graphs and demonstration photos on polarization. Jens also discusses the limited blocking of near IR by crossed linear polarizers.

UV and Polarizing Filter FAQs—a well-written and informative FAQ section within a site that otherwise appears to be largely under construction.

"Tiffen Filter Facts"—a well-illustrated "infomercial" pamphlet packaged with Tiffen filters. See also the Tiffen filter web page has filter specifications and many color illustrations of filter effects.

Paul Saunders, Wilderness Wales.


Unless explicitly attributed to another contributor, all content on this site © Jeremy McCreary

Comments and corrections to Jeremy McCreary at dpFWIW@cliffshade.com, but please see here first.

URL: http://www.cliffshade.com/dpfwiw/polarizer.htm