Light passing through a narrow opening on the lens, a smaller aperture, is passing through the lens much closer to the optical axis and is not refracted as much as light entering at the extreme edges of the lens. This reduction in refraction means that the defocused light rays are closer together when they intersect before or after the image plane—forming a smaller blurry spot at the image plane. Even though the light rays are intersecting before or after the image plane, the smaller angle creates a smaller blurry spot and this gives you a longer DOF.

If you want comparatively shallower DOF, use a lens with a longer focal length. A wider-angle lens will give you longer DOF.

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

Enlargement: The larger the image is reproduced, the shallower the DOF. The smaller the reproduction, the longer the DOF. This factor is similar to the viewing distance described above. Reproduce a blurry spot on a giant highway billboard and it’s a huge, blurry spot. Reproduce it on a tiny wallet-sized print and it might look like a single point of light.

The COC is defined as the size of the largest blur spot that still appears as a single point (in focus) in an image. What COC brings to the DOF equation is a standard criterion for sharpness. You may have seen other definitions of DOF that refer to the term: “acceptable sharpness” or “acceptable focus.” By itself, “acceptable” is a subjective term. What might be acceptably sharp or in focus to one viewer might be horribly blurry to another. So, for optics and camera engineers, we need to make this a definitive measurement and not subjective. The term “acceptable” will reappear in this article, but know that, when calculating DOF, “acceptable” is a mathematically defined quantity when discussing sharpness or focus.

Confusingly known as the disk of confusion, blur circle, blur spot, and circle of indistinctness, the circle of confusion (COC) is the most complex and difficult DOF concept to grasp.

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

It was interesting and timely for me, because I just recently scanned a large group of 35mm images I made in Okinawa and southest asia in 1958-1959.  The slides and negatives have been preseved fairly well, but the constant I kept seeing was that scanned at high resolutions, when you got down to the nitty gritty, thay weren't all that sharp.  Most of the imges were made with a Contax lllA, with a 1.5 Sonar or one of a couple of Nikon lenses I used. Most always my 35mm Nikor lens gave sharper results (expected from a wide angle lens).  I had concluded that the reason for the unsharp images was due to my almost complete reliance on using the depth of field scales.  And your article leads me to believe that is a correct conclusion. This problem wasn't so much noticed before, since the viewing methods for such images then were generally eyballing the slide, or projecting it on a screen.  But the new high resolution scans revealed what I had never realized.  There were some that were pretty sharp, and I concluded these were ones that were focused on the primary subject.

There are a great many articles on DOF online. I sometimes find mistakes in the articles, or conflicting information. What you have read above has been carefully researched and is the best information I feel that I can present. However, if you have a question, comment, or see something that you feel is inaccurate, please bring it to my attention in the Comments section, below. Thanks for reading!

Depthof focus

As I told Larry, see if your web browser has a "Save as .PDF" or "Export as .PDF" option. It sometimes isn't perfect, but its a quick and easy way to save the article and print it out. Or, you can manually cut-and-paste the images and text.

If you review my article about focus, you will see simplified diagrams showing rays of light reflecting from a subject, passing through a lens with a moving focus element, and then being focused, ideally, onto the sensor/film or image plane. The rays of light that converge before or after that image plane, when the focus lens is moved toward or away from the subject, are rendered out of focus at the plane. Now, let us imagine fixing the focus lens element at a constant distance from the subject. Assuming the subject is three-dimensional, only those light rays that are at the focus distance are converging correctly onto the image plane. Any light rays reflecting from the subject at different distances from the lens are going to either converge before or after the image plane. This creates a blurry spot at the image plane. However, many of those convergences are happening just prior to or just after the plane; close enough that the blurry spots are tiny and we do not notice that those reflected areas of the subject or scene are not in true focus.

At a greater distance from the subject, light rays will have a narrowed path through the lens and, when the out-of-focus rays intersect before or after the image plane, they will produce a smaller blurry spot and create longer DOF.

DOF is not specific to a certain camera or lens. It is a combination of these four things that creates the DOF we get to observe in a projected image. The first factor is somewhat confusing and intricate. The final three factors are easily controlled by the photographer.

In regards to bokeh, while related, has the potential to derail the DOF discussion as its mention might create questions that could only be answered by a discussion of a lens' optical and aperture design. Gotta keep on topic! We should probably have a separate bokeh article. I'll look into it!

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

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

Illustration of light from finite subjects passing through lenses of different focal lengths shows the relative distance of the image points.

Let’s set up a visual aid to help you “see” the phenomenon. Instead of visualizing arbitrary light rays being reflected from a subject, for the purposes of this article, we can imagine we are taking photographs of a single tiny point of light. If that glowing point of light is in focus, it looks like the single point of light that it is. If it is out of focus, it looks like a larger, blurrier point of light. Right?

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

Lensfocus

If you care to dive into the proverbial weeds of DOF, click on Part II to see how mathematics is at the heart of the way DOF is calculated. If you don't give a hoot about the math, and are more into the mythology, proceed directly to Part III.

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

Depthof field

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

Thanks for the comments! You are certainly correct. Having said that, I have found, especially when writing these pieces, is that the world of photographic terminology is very fluid and not always consistent from book to book or website to website. It is immensely frustrating! I purposely chose terms that, I felt, were the least confusing.

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

Shallowfocus

The focal length of the lens, the distance from the rear nodal point of the lens to the image plane when the lens is focused at infinity, has an effect on both your field of view and your DOF.

The depth of the DOF region is described in several ways. A DOF that does not encompass a great distance is called shallow, small, narrow, or short. A DOF that covers a great distance is known as deep, large, wide, or long. These terms are synonymous and can be used interchangeably. No term is more correct than another, but I have found that, for simplicity, describing DOF as “long” or "shallow" works the best and helps to reduce misunderstanding.

Illustration of light from finite subjects at different distances passing through lenses shows the relative distance of the image points and the difference in the size of the infinite blur spots.

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

depthoffield中文

Thanks for your comments and sharing the insights on the camera obscura. That method of photography is still very viable and fun!

First, an admittedly picky quibble: In the usual terminology, the "focal plane" is behind the lens (on the film or image sensor). What's labeled the "focal plane" in the diagrams here is more usually called the "field plane." On the other hand, one could quite reasonably argue that the clearest, most self-defining term for the field plane might actually be the "in-focus plane." Still, it might help to mention in passing the usual terms to help avoid confusion for people reading other articles or textbooks on optics.

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Another reason that "slow" lenses are less expensive is that they contain smaller amounts of glass. Glass is the expensive part of the lens, not the metal and plastic!

Many thanks fro the clear and informative article. Requires a couple of reading, but that is the way it should be. Thanks again. John

Having the focal plane at a short distance from the image plane renders shallow DOF. Conversely, the farther the image plane is from the focal plane, the longer the DOF.

Conversely, place the camera close to your subject and the light rays must be bent more to intersect at or near the image plane. Again, just as with focal length, the change of distance produces a larger blurry circle and, therefore shallower DOF.

If you want to have a shallow DOF effect on your image, get closer to your subject. Conversely, move farther away from your subject if you want longer DOF where more of the background will appear in focus.

One simple way to see the influence of the apperture of the lens in the DOF is through the concept of The Camara Obscura, used for some painters  more than a centuy ago. Then they didn't used lenses, but only a pinhole in a window or wall in a dark room or space. They saw inverted images as with any simple lens, and didin't need a way of focusing because de size of the COC was the same of the pinhole at every distance of it, being always "in focus". The more you close de diafragm, the smaller the COC that defines the image on the negative, sensor or wall, and the better the image quality. The ninth illustration shows it clearly.

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

Why is that? A shorter focal length lens has to bend the light entering the lens at a sharper angle to meet the image plane, because the lens and image plane are closer together. Because of the greater angle of refraction, the out of focus intersections happen closer to the image plane. This shorter distance causes a smaller blurry spot to be created, resulting in longer DOF.

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

If you want to take an image with a softer focused background, a shallower DOF, you may use a larger aperture, a longer focal length lens, or get closer to your subject with a given lens. To get an image where the background appears more in focus, a longer DOF, you should narrow your lens’s aperture, use a shorter focal length lens, or get further away from your subject.

The true variable for DOF equations is: focus distance, assuming you have focused on a finite subject. This is the distance from the lens where the focal plane exists. Older lenses had markings on the barrel that told you exactly how far the lens was focused, but many modern lenses have eliminated those markings.

Great article!  Besides being a working professional, I teach a photography class at a local unicersity.  May I reference your illustrations to help my students?

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

Quick addendum: One advantage to the term "field plane" is that it's consistent with the term "depth of field." (There's also "depth of focus" in on both sides of the focal plane behind the lens, but that's mainly of intererst with respect to pro cameras with interchangeable lenses and adjustable backfocus (and of course to designers of cameras, lenses, and imaging systems).

This is most easily visualized when you think about some photographs you have likely seen. A close-up portrait features a background that is not in focus, while a landscape photograph taken across an expansive view will show the foreground river and trees to be in focus, as well as the mountains dozens of miles beyond it.

If your curiosity is heightened and you want to know more about how and why this happens, please keep reading! Then, if you want to know the math behind it, we have you covered in Part II.

Now that we have COC out of the way, the DOF discussion gets much easier to understand moving forward. We are also about to discuss the elements of DOF that we can control directly with our camera and lens.

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

Today, with mirrorless interchangeable-lens cameras and point-and-shoot digital cameras, as well as DSLR cameras with live view, the image you see on your LCD monitor or in the electronic viewfinder will show you the live DOF without having to press a dedicated DOF preview button.

From our friends at Nikon: "The term depth of focus, which refers to image space, is often used interchangeably with depth of field, which refers to object space."

Way, way back, when you connected a lens to a camera, the image you saw on the ground glass or viewfinder showed you the light that was making its way through the camera through whatever aperture opening you had dialed in, or at which the lens was fixed. Auto-diaphragm changed this on SLR and other types of cameras. Auto-diaphragm means that when you attached a lens, the camera automatically opened the aperture on the lens to its maximum setting. Why do we want this? If the lens aperture is open fully, you will get the brightest possible image in the viewfinder from which to compose your image.

Viewing distance: The blurry spot above looks like a blurry spot when viewed from a normal distance from your computeror tablet screen. However, if you view this same spot from across a room, it will look like a crisp, clean, green dot.

Here is an illustration of how objects at different distances, although identical in size,will create spots of different sizes (and blur) at the image plane.

In another explaination, I found this: depth of field is the area in front of the lens that is in focus—what this and the two follow-on articles discuss—and depth of focus is the area aft of the lens where the film plane is placed to allow a focused image.

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

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

Reference away! Feel free to credit the source, however. Our graphics folks work hard on these products and I want them to get the credit when they can.

Enlargement: An identical image is reproduced at different sizes.Note how, in the smaller image, the golf ball’s texture is more consistent where, in the larger image,the image shows short depth of field in which only a portion of the dimples are in focus.

Depthof fieldcalculator

Using our advertising package, you can display your logo, further below your product description, and these will been seen by many photonics professionals.

The bottom line is that, if you know that you can change your DOF by changing aperture, changing your distance from the subject (or focus distance), or by changing the focal length of your lens, and you know how those three things affect your DOF, then you are all set and you can go out and start manipulating DOF while you take photos!

Unfortunately, we don't have .pdf files available for download, but your web browser might have the ability to save the page(s) as a .pdf or another type of file. You can also cut-and-paste the images and text into a word processor if you have the time.

The possibilities of creative DOF are endless, and it all comes down to how you want your image to look, and what DOF your lens is capable of producing on your camera.

The bottom two illustrations illustrate what happens when light emitted aft orbefore the focus plane intersects the image plane. A blurry spot is created. If the intersection of light is closeto the image plane, the blurry spot is small and the light appears in focus.

If your eye is closer to the reproduced image, the DOF is shallower. Points of light must be points to not look blurry. If you are farther from the image, the DOF is longer. Blurry points might look not-so-blurry from a distance.

I have the same question as Larry. I often get asked to explain DOP to new photographers, and struggle. People just starting out, have trouble getting their head around apertures, shutter speeds, exposures, focal lenghts etc. I know I could refer them to this page, but I would love a pdf print out that I could put in front of them and explain it that way. Hope this request doesn't come across as rude, because of all your hard work. Thanks

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

Adjusting your DOF changes the way your image looks. Shallow DOF is sometimes used to enhance portraits or close-up macro images, aesthetically. Long DOF is used often by landscape photographers to make sure that both the foreground and the background appear to be in focus.

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

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

Aperture, the relative size of the opening of the lens, not only controls how much light enters a lens, it has an effect on DOF.

Now, here is the cool part: there are physical variables in photography that allow us to adjust the depth of the region of what looks to be sharp before and after the plane of focus—the DOF.

Without auto-diaphragm, what you saw on the ground glass or through the viewfinder showed your depth of field (and sometimes a very dark image). The invention of the “depth of field preview” button allowed photographers with SLR cameras to depress a button and close down the diaphragm to whatever F-stop they had selected. The image would get darker (if you chose an aperture smaller than maximum) and then you could pre-visualize the depth of field for that scene. Release the button and the auto-diaphragm feature would open the lens to its maximum aperture again.

Visual acuity: We apologize to those with less-than-perfect eyesight. If that point of light looks blurry to you because your eyes are not focusing correctly, your DOF is longer than those who can see the point of light more clearly. The better your vision, the shallower the DOF.

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

All you explanation about the DOF theme, also serves to explain why "slow" lenses are cheaper than "fast" ones. The more DOF you get at wide open, the less de defects in the lens are shown, for the same Focal length, and the leeser influence of field curvature in the periferical quality of the images in some lenses al higher f number. At least some kind of them.

DOF simulator

Shallow depthof field

If you feel a wave of confusion bearing down on you and you do not want to reference diagrams, talk about blurry spots, or look at formulas, the following is for you:

Also, with respect to the circle of confusion, it might help to point out the connection with bokeh, since most people are at least somewhat familiar with that concept.

Thanks so much for your comments and perspective. I guarantee that if we all looked at our old film prints or slides with the same kind of eye for sharpness that we have today (not to even mention the ability to zoom in on a digital image on a computer screen), we would be horrified at the "sharpness" of some of our "sharp" images.

With aperture, we noted that the more refracting of light rays meant a larger blurry spot at the image plane and, therefore a shallower DOF. Here, we have the greater refraction due to the focal length, but, because the lens is a different physical size, we are also changing the distance at which those points are reproduced before and after the focal plane. This change of distance is having an effect on DOF.

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

So, to give your photographs longer depth of field, dial in a smaller aperture (larger F-stop number). If you want shallow depth of field, open the aperture (smaller F-stop number).

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

The farther you move the lens from the image plane—a longer focal length—the less the light needs to bend to intersect at the image plane. This means the out-of-focus intersections will happen at a greater distance from the image plane, meaning a larger blurry spot, thereby causing a shallow DOF.

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These explain quite comprehensively a wide range of aspects, not only physical principles of operation, but also various practical issues.

Viewing distance: Let’s get back to that point of light in an image. If you put your nose to the computer screen, or up to the print or poster, that point of light might look like a blurry spot at very close range. However, if you stand across the room and look at that same spot, it will now look like a single point.

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

One of the most common questions asked at the photo counter at B&H is, “How can I take portraits with a blurry background?” Utilizing your knowledge of DOF to open up your aperture and close the distance between you and your subject will help you achieve this.

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

Light entering a lens with a diaphragm that has been opened to its maximum aperture will have to be bent more to meet at a single point at the sensor. Many light rays are passing through the aperture, far from the optical axis of the lens. Because they are bent more, they intersect the image plane at a greater angle than light passing nearer the optical axis. When the light rays converge before or after the image plane—out of focus—the greater angle causes a larger blurry spot to be produced at the image plane and, therefore, produces shallower DOF.

Depth of field (DOF) is defined as the area in a projected image, forward and aft of the focal plane, which also appears to be in focus in the image. When you pass light through a lens and focus that light to form an image on a piece of film, digital sensor, projection screen, etc., the area of the image that is in true focus is razor thin—the focal plane. Everything else is out of focus, to some degree. However, because of the subtlety of the out-of focus regions, we do not notice the softness of the image until, as objects are located farther away from that plane of focus, the blur reaches a certain level; our eyes, and cameras, see a region of depth in an image where everything appears to be in focus.

Depth of field can be kept really simple, or, it can get deep! I tried to give the readers options on how deep they wanted to get.

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

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