Modulation Transfer Function (MTF) or Spatial Frequency Response (SFR): The relative amplitude response of an imaging system as a function of input spatial frequency. ISO 12233:2017 specifies methods for measuring the resolution and the SFR of electronic still-picture cameras. Line pairs per millimeter (lp/mm) was the most common spatial frequency unit for film, but cycles/pixel (C/P) and line widths/picture height (LW/PH) are more convenient for digital sensors.

For example, to support a final-image resolution equivalent to 5 lp/mm for a 25 cm viewing distance when the anticipated viewing distance is 50 cm and the anticipated enlargement is 8:

Check out this article "Staging Foregrounds" by R.J. Kern on foreground blur, which includes many photos with background and foreground blur.

If we ignore print size and film, for a given digital sensor with a specific pixel density, DoF is a function of focal length, relative aperture, and subject distance. From that, one could make the argument that DoF is purely a function of the lens, as "subject distance" refers to the distance at which the lens is focused, which would also be a function of the lens.

In the larger trucks equipped with heavy duty U-joints, we did not experience this issue. Because this is an electrical unit, the speed at which it becomes fully engaged is extremely fast-there is no lag time, and braking torque is also very high. This is a very important point for intercity operation or any congested stop-and go-operation for ERVs. All brake retarders, not just the electromagnetic induction retarders, have some type of on/off switch on the dash so the driver can turn them off. This is because there is the possibility of rear-wheel lockup in slippery conditions. The switch also gives the driver the option to turn it off when not needed. The modern electromagnetic induction retarders interface with antilock brake systems (ABS) to prevent wheel lockup in slippery conditions, which is good because even if the driver forgets to disengage the unit, it still won’t come on in an ABS event.

These retarders can be configured to apply in several ways. They can be applied at different percentages of application output-either from closing the throttle, brake pedal application, or a combination of the two. For example, you can have it apply or come on at 50 percent when the throttle closes and the remaining 50 percent when the brake is applied. It can also be configured to progressively apply in three steps when the air brakes are applied: Two-psi switch equals 30 percent, seven-psi switch equals 33 percent, and 10-psi switch equals 100 percent retarder engagement. These were only examples as there are more options available. With this type of retarder, the speed to fully apply maximum retardation is related to how fast the retarder cavity is filled with oil and is proportional to driveline or vehicle speed.

Depth of fieldphotography settings

Ok for a change I'm going to dispense with the formulas, photos of rulers and definitions of "magnification" and go with what you actually experience in practice. The major factors that actually matter to shooting are:

RMS stands for Root Mean Square and is used to measure the surface roughness of irregular surfaces. It is calculated by taking the square root of the sum of the ...

This is an excellent question, and one that has different answers depending on context. You mentioned several specific questions each of which might warrant their own answers. I'll try to address them more as a unified whole here.

As with everything, one should always prove the concept by actually running the math. Here are some intriguing results when running the formulas above with F# code in the F# Interactive command line utility (easy for anyone to download and double check):

Specifically, a photographic aperture (nowadays) is universally measured as a fraction of the focal length -- it's written like a fraction (f/number) because that's what it is.

Is it just a property of the lens? Can lenses be designed to give more depth of field for the same aperture and focal length? Does it change with camera sensor size? Does it change with print size? How do those last two relate?

The hyperfocal distance is variable and a function of the aperture, focal length, and aforementioned COC. The smaller you make the lens aperture, the closer to the lens the hyperfocal distance becomes. Hyperfocal distance is used in the calculations used to compute DOF.

As an aside, I think it's worth considering what an incredible stroke of brilliance it was to start measuring the diameters of lenses as a fraction of the focal length. In a single stroke of genius it makes two separate (and seemingly unrelated) issues: exposure and depth of field controllable and predictable. Trying to predict (much less control) exposure or depth of field (not to mention both) before that innovation must have been tremendously difficult by comparison...

The term circle of confusion is applied more generally, to the size of the out-of-focus spot to which a lens images an object point. It relates to 1. visual acuity, 2. viewing conditions, and 3. enlargement from the original image to the final image. In photography, the circle of confusion (CoC) is used to mathematically determine the depth of field, the part of an image that is acceptably sharp.

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First, to define DoF meaningfully, you need to specify the amount of "blur" you're willing to accept as sufficiently sharp. Depth of field is basically just measuring when something that started as a point in the original will be blurred enough to become larger than whatever size you've picked out.

It's probably also worth pointing out that this (I believe, anyway) why catadioptric lenses are noted for their lack of depth of field. In a normal lens, even when you're using a large aperture some of the light still enters through the central part of the lens, so a small percentage of the light is focused as if you were shooting at a smaller aperture. With a catadioptric lens, however, you have a central obstruction, which blocks light from entering toward the center, so all of the light enters from the outer parts of the lens. This means all of the light has to be focused at a relatively shallow angle, so as the image goes out of focus, essentially all of it goes out of focus together (or a much higher percentage anyway) instead of having at least a little that's still in focus.

The Jacobs Brake, known as the Jake brake, was also developed by an engineer because he saw the need to reduce or eliminate brake fade. Its inventor, Clessie L. Cummins, inventor of the Cummins diesel engine, got the idea for it in 1931 when he was driving a truck through a mountainous region of California and lost the brakes because of brake fade in a steep downhill grade. Miraculously, he and the two others that were with him were not hurt. They missed hitting a train that crossed the road in front of them by inches. That was also lucky for the industry because if Cummins had been killed, who knows how long it would have taken someone to invent this ingenious device-if ever.

Depth of field: The distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. Although a lens can precisely focus at only one distance at a time, the decrease in sharpness is gradual on each side of the focused distance, so that within the DOF, the unsharpness is imperceptible under normal viewing conditions.

$$ \begin{align} D_\text{n} &= \frac{Hs}{H + s} \\ D_\text{f} &= \frac{Hs}{H - s} && \text{for }s

All the other factors (sensor size and focal length being the two more obvious) only affect depth of field to the extent that they affect the reproduction ratio or the aperture.

My first experience with these units goes back almost 30 years. We had a number of apparatus and rescue trucks (aka ambulances) that had severe brake failure problems because of excessive weight. All of the units we retrofitted with the electromagnetic induction retarders were driveline-mounted units with the exception of one pumper that received a focal-mount unit. All of the modified units showed improvement in reducing stopping distances and increasing brake life. However, the most dramatic improvements I saw were in a group of 1987 Ford E-350 Type III rescue trucks equipped with 6.9-liter diesel engines that were 2,000 pounds greater than GVWR. As most probably know, brake life also has a lot to do with how the drivers use and treat their brakes. The worst one of these ambulances, prior to the installation of the Telma, was only getting to be averaging about 3,000 miles out of the front brakes and about 7,000 out of the rear brakes. This is not acceptable when it comes to brake life. After the retrofit, the average brake life on this fleet of ambulances went to 12,000 to 15,000 miles on the front axle and 17,000 to 40,000 miles on the rear axle. Thankfully, we never had a serious accident with those units, and we all breathed a sigh of relief when we finally retired those units.

Aperture. Wide aperture lenses give you a shallower depth of field. This is probably the least controversial factor! This is important as some lenses have much larger apertures e.g. 18-55 f/3.5-5.6 vs. 50 f/1.8

There are several mathematical formulas that can be used to calculate the depth of field. Sadly, there does not seem to be a single formula that accurately produces a depth of field at any distance to subject. Hyperfocal Distance, or the distance where you effectively get maximum DoF, can be calculated as so:

Q. Is it just a property of the lens? A. Simply put, no, although if you ignore CoC, one could (given the math) make the argument that it is. Depth of field is a "fuzzy" thing, and depends a lot on viewing context. By that, I mean it depends on how large the final image being viewed is in relation to the native resolution of the sensor; the visual acuity of the viewer; the aperture used when taking the shot; the distance to subject when taking the shot.

There are several different types and makes of retarders on the market today, and they differ in operation; efficiency; cost; installation; and, most importantly, to me as far as the fire service goes, how much they can really slow the vehicle down in brake horsepower (BHP) at low-speed operation or intercity service and how quickly they achieve maximum retardation. They run the gamut-ranging from hydraulic transmission output retarders to electromagnetic driveline retarders and engine retarders.

If memory serves me correctly, the first Allison transmission hydraulic output retarders we used were on pumpers in the early 1990s with the Allison heavy-duty electronic transmission. The retarder housing is mounted at the rear of the transmission and essentially oil (transmission fluid) is directed at a vaned rotating wheel very similar to a transmission torque converter. Only in this case, it works for the opposing reason. As the fluid fills the retarder cavity and hits the vanes, it serves to slow the vehicle down via the driveshaft. The energy absorbed by the oil as it hits the vanes in slowing the vehicle down has to be cooled via a coolant-to-oil cooler, generally mounted near or below the radiator.

They are very effective and can generally produce up to a maximum of 70 percent of the engine’s maximum BHP in certain applications and are most efficient at highway speeds. These units, along with the Jake brakes, have been associated with engine overheating issues. But, the ones we have tested and used never exhibited these problems. I would venture to say that units which have had overheating issues may have had marginal cooling systems or systems that had not been maintained properly. The exhaust piping and exhaust manifold must not have any leaks for this system to operate properly. These units have been around for almost as long as the Jake brake and are also used in conjunction with the Jake in modern over-the-road trucks to help quiet and muffle the Jake. Maintenance involves servicing the butterfly or knife-type valve on a schedule.

The circle of confusion is a quirky value here, so we'll discuss that later. A useful average CoC for digital sensors can be assumed at 0.021mm. This formula gives you the hyperfocal distance, which isn't exactly telling you what your depth of field is, rather it tells you the subject distance you should focus at to get maximum depth of field. To calculate the actual Depth of Field, you need an additional calculation. The formula below will provide DoF for moderate to large subject distances, which more specifically means when the distance to subject is larger than the focal length (i.e. non-macro shots):

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Assuming we pick one number for that and stick to it, depth of field only depends on two factors: the aperture and the reproduction ratio. The larger the reproduction ratio (i.e., the larger an item appears on the sensor/film compared to its size in real life) the less depth of field you get. Likewise, the larger the aperture (larger diameter opening -- smaller f/stop number) the less depth of field you get.

Using the same focal length lens on an APS-C and full frame camera at the same subject-to-camera distance produces two different image framings and causes the DOF distance and thickness (depth, of the field) to differ.

They all serve the same basic purpose: to assist the foundation brakes in stopping heavy ERVs and commercial over-the-road rigs. However, there are several different makes and types on the market, and how they are mounted and operate all differ. Impact to the rest of the vehicles’ systems and reliability also differs as well as how much retardation output they can produce. In this article, I will briefly cover the history behind some of the different types of retarders we have used in my department and some of my experiences dealing with repairs and maintenance.

Switching lenses or changing subject-to-camera in accordance with the crop factor when switching between an APS-C and full frame camera to maintain identical framing results in a similar DOF. Moving your position to maintain identical framing slightly favors the full frame sensor (for a greater DOF), it's only when changing lenses to match the crop factor and maintain framing that the larger sensor gains a narrower DOF (and not by much).

Every amateur magazine (and ezine now) loves to say 'switch to a wide angle lens for more depth of field'... but if you keep the subject the same size in the frame (by moving in closer) then the sharp bits have the same limits. Walking backwards with the lens you've got on will give more DOF too, but maybe you like the shot the way it is already set up?

The above formulas only apply when the distance \$s\$ appreciably is larger than the focal length of the lens. As such, it breaks down for macro photography. When it comes to macro photography, it is much easier to express DoF in terms of focal length, relative aperture, and subject magnification (i.e. 1.0x):

Recognizing that real lenses do not focus all rays perfectly under even the best conditions, the term circle of least confusion is often used for the smallest blur spot a lens can make (Ray 2002, 89), for example by picking a best focus position that makes a good compromise between the varying effective focal lengths of different lens zones due to spherical or other aberrations.

Unlike DoF for moderate to large subject distances, with 1:1 (or better) macro photography, you are ALWAYS enlarging for print, even if you print at 2x3". At common print sizes such as 8x10, 13x19, etc., the factor of enlargement can be considerable. One should assume CoC is at the minimum resolvable for your imaging medium, which is still likely not small enough to compensate for apparent DoF shrink due to enlargement.

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Hyperfocal distance is defined as the distance, when the lens is focused at infinity, where objects from half of this distance to infinity will be in focus for a particular lens. Alternatively, hyperfocal distance may refer to the closest distance that a lens can be focused for a given aperture while objects at a distance (infinity) will remain sharp.

Because retarders provide added stopping power, they will also reduce the possibility of brake fade, which I am sure all will agree is huge when it comes to safety. Reducing or eliminating brake fade is the main reason they were invented. Keep in mind that they do a lot more than this because they not only improve or reduce stopping distances but also extend brake life. Extending brake life means cost savings and less time at the shop. Fewer changeouts (crews transferring their gear from a frontline ERV to a spare) is a good thing for the overall operation, the crews, and the communities they serve. These are two extremely important subjects, particularly in today’s highly litigious environment not to mention tighter budgets. To reiterate and make sure I get my point across, retarders not only improve the safe operation of any ERV equipped with these devices, they will also reduce brake maintenance and replacement costs over the life of the ERV while reducing equipment downtime simultaneously.

Mathematically, it is clear why DoF is not simply a function of the lens, and involves either the imaging medium or print size from a CoS perspective. To clearly specify the factors of DoF:

To provide a background on how it works, let’s first look at how a gasoline engine helps to slow a car or truck down when the throttle is closed. The throttle plate in a gas engine closes off incoming air and the cylinders, as the pistons go up and down against the closed throttle plate, create a vacuum pumping action that helps slow the vehicle down. During deceleration in a diesel engine, the opposite actually occurs because there is no throttle plate. The air that is going directly into the cylinders is being compressed, and as it pushes back on the pistons, it actually helps to propel the truck forward and will not slow it down. The Jake brake basically converts the diesel engine into an energy-absorbing air compressor of sorts by opening the exhaust valves at a precise time and letting this air escape out the exhaust before it can direct pressure back down on the piston. Cummins’s invention holds open the engine’s exhaust valves using precise timing through hydraulic (engine oil) actuation that is controlled electrically. I am sure most have heard 18-wheelers making a loud machine-gun like clattering noise from the exhaust when slowing down on the interstates. The noise can be quite loud, and in some municipal areas and cities, their use is not allowed. They can be so loud they have been known to trigger avalanches and are also restricted in certain areas during the winter.

Criteria relating CoC to the lens focal length have also been used. Kodak (1972), 5) recommended 2 minutes of arc (the Snellen criterion of 30 cycles/degree for normal vision) for critical viewing, giving CoC ≈ f /1720, where f is the lens focal length. For a 50 mm lens on full-frame 35 mm format, this gave CoC ≈ 0.0291 mm. This criterion evidently assumed that a final image would be viewed at “perspective-correct” distance (i.e., the angle of view would be the same as that of the original image):

Focal length. This does affect depth of field, but only in certain ranges, when maintaining subject size. Wide lenses have very deep depth of field at most subject distances. Once you get past a certain point, DoF changes very little with focal length. This is important again because if you want to increase / decrease DoF you can use focal length to do this whilst still filling the frame with your subject.

Cummins and Detroit diesels were the first engines that were easily adaptable to this technology because they had a separate lobe on the camshaft to actuate the fuel injector. By modifying this camshaft lobe and designing a hydraulic mechanism that would open the exhaust valve at the right time, Cummins created an engine brake that is relatively light and goes virtually unnoticed in the engine with up to 90 percent or more retardation of the engine’s maximum BHP. We installed several of these Jake brakes in some very heavy rigs equipped with 8V92 Detroit engines with Allison automatic transmissions in the mid to late 1980s with limited success in intercity service. Had they been on-highway rigs, I’m sure the results would have been much better. These units proved to be trouble-free with some minor issues with the governor buffer switch adjustments. There are many types available for a wide range of makes and models, and all have different modes of operation available to the driver.

\$H\$ is the hyperfocal distance; \$f\$ is the lens's focal length; \$N\$ is the f-number (relative aperture) of the lens; and \$c\$ is the circle of confusion (CoC) diameter.

Since the final-image size is not usually known at the time of taking a photograph, it is common to assume a standard size such as 25 cm width, along with a conventional final-image CoC of 0.2 mm, which is 1/1250 of the image width. Conventions in terms of the diagonal measure are also commonly used. The DoF computed using these conventions will need to be adjusted if the original image is cropped before enlarging to the final image size, or if the size and viewing assumptions are altered.

Depth of Field is a function of Focal Length, Effective Aperture, Distance to Subject and Minimum Circle of Confusion. Minimum Circle of Confusion is where things get fuzzy, as that can either be viewed as a function of the imaging medium, or a function of print size.

Subject: The object that you intend to capture an image of, not necessarily everything that appears in frame, certainly not Photo Bombers, and often not objects appearing in the extreme fore and backgrounds; thus the use of bokeh or DOF to defocus objects which are not the subject.

This brings me to the exhaust type of engine brake, which consists of a butterfly valve or knife-type valve located downstream of the exhaust or at the outlet of the exhaust after the turbo. It closes on deceleration and restricts the gases leaving the engine from combusting. When this happens, the pressure buildup inside the cylinders resists the pistons from going up and basically slows down the vehicle, acting like a brake. There are limits to the pressure allowed to build inside the engine, dictated by the engine manufacturers. If these limits are exceeded, engine damage can result from exhaust valves being lifted off their seats and hitting pistons. However, the units are carefully designed to operate within the engine manufacturers’ specifications. They are available from various manufacturers and for a wide range of engines-from light duty to heavy duty-and modern ones interface with the engine electronic control unit (ECU) for precise operation and with automatic transmissions to downshift into specific gears to add more braking power.

However, if you really do hold the reproduction ratio constant, the depth of field really is constant. For example, if you have a 20mm lens and a 200 mm lens and take a picture with each at (say) f/4, but take the picture with the 200 mm from 10 times as far away so the subject really is the same size, the two theoretically have the same depth of field. That happens so rarely, however, that it's mostly theoretical.

The following answer was originally published (by me) as an answer about background bokeh but it necessarily explains depth of field, with a bias to explaining fore and background blur.

Q. Can lenses be designed to give more depth of field for the same aperture and focal length? A. Given the math, I would have to say no. I am not an optical engineer, so take what I say here with the necessary grain of salt. I tend to follow the math, though, which is pretty clear about depth of field.

What does depth of field meanin photography

Subject distance. This is a really important consideration. Depth of field gets drastically shallower when you start to get really close. This is important as at macro focussing distances DoF is a major problem. It also means you can get shallow DoF regardless of aperture if you get close enough, and that if you want deep DoF in low light compose to focus further away.

At a narrower aperture, the diaphragm DOES block some light from the periphery of the light cone, while light from the center is allowed through. The maximum angle of light rays reaching the sensor is low (less oblique). This causes the maximum CoC to be smaller, and progression from a focused point of light to maximum CoC is slower. (In an effort to keep the diagram as simple as possible, the effect of spherical aberration was ignored, so the diagram is not 100% accurate, but should still demonstrate the point):

In the average case, one can assume that CoC is always the minimum achievable with a digital sensor, which these days rolls in at an average of 0.021mm, although a realistic range covering APS-C, APS-H, and Full Frame sensors covers anywhere from 0.015mm – 0.029mm. For most common print sizes, around 13x19" or lower, an acceptable CoC is about 0.05mm, or about twice the average for digital sensors. If you are the type who likes to print at very large sizes, CoC could be a factor (requiring less than 0.01mm), and your apparent DoF in a big enlargement will be smaller than you calculate mathematically.

The original (longer) answer is here - this is the abridged version. Simply making a one sentence answer with a link causes the answer to be converted to a comment to the above question, with a risk of deletion because it's a comment.

DOF simply tells the photographer at what distances before and aft of the focus distance that blurriness will occur. It does not specify how blurry or what “quality” those areas will be. The design of the lens, the design of the diaphragm, and your background define the characteristics of the blur—its intensity, texture, and quality.

It's because of the crop factor and the resulting focal length along with the necessary aperture for the light gathering ability of the sensor that gives the greatest affect upon your calculations.

CHRISTIAN P. KOOP is the fleet manager for the Miami-Dade (FL) Fire Department. He has been involved in the repair and maintenance of autos, heavy equipment, and emergency response vehicles for the past 35 years. He has an associate degree from Central Texas College and a bachelor’s degree in public administration from Barry University and has taken course work in basic and digital electronics. He is an ASE-certified master auto/heavy truck technician and master EVT apparatus and ambulance technician. He is a member of the board of directors of EVTCC and FAEVT and a technical committee member for NFPA 1071, Standard for Emergency Vehicle Technician Professional Qualifications.

It's the aperture advantage that makes the full frame sensor a better and more expensive choice both for camera and lenses and often for features (FPS not being one of them, nor size and weight).

If we used the compact camera at the same 1:2 reproduction ratio as the 8x10, we'd get the same depth of field -- but instead of head and shoulders, we'd be taking a picture of part of one eyeball.

This COC value represents the maximum blur spot diameter, measured at the image plane, which looks to be in focus. A spot with a diameter smaller than this COC value will appear as a point of light and, therefore, in focus in the image. Spots with a greater diameter will appear blurry to the observer.

Depth of fielddefinition microscope

Going to a medium sized sensor over a tiny sensor further advantages the larger sensor but bokeh likely isn't the best use case to justify 20x+ times price difference.

At relatively close distances, the DOF is nearly symmetrical, with about half of the focus area existing before the focus plane and half appearing after. The farther the focal plane moves from the image plane, the larger the shift in symmetry favoring the area beyond the focal plane. Eventually, the lens focuses at the infinity point and the DOF is at its maximum dissymmetry, with the vast majority of the focused area being beyond the plane of focus to infinity. This distance is known as the “hyperfocal distance” and leads us to our next section.

On the other hand, if you change the focal length but maintain the same photographic aperture (f/stop), the depth of field also remains constant because as the focal length increases the diameter increases proportionally so the rays of light are getting focused on the film/sensor from the same angles.

What you will see are more gradual cut-offs in sharpness so that the background & foreground appear sharper (not sharp as if within the DOF!) hence the lovely out of focus backgrounds with long lenses and the nearly sharp ones with wide angles.

In a nutshell, there are a set of fixed nonrotating electrical coils with two metal stators on either side that rotate with the driveline. As the electrical field generated in the coils is induced into the stator, it serves as a driveline brake and will slow and eventually almost bring the vehicle to a full stop. They generally are programmed to turn off or deactivate at a predetermined speed so they do not remain on when the vehicle is stopped. The units we had in service years back had four stages of retardation that applied progressively in direct relation to air brake application pressure or travel of the brake pedal in hydraulic brake applications.

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The first type I will cover is the electromagnetic induction retarder from Telma, which is probably the oldest, having been around for almost 70 years. It was developed by an engineer in Europe who saw the need to add a means of assisting brakes to reduce total brake failure because of brake fade. Heavy trucks would lose their brakes in mountainous regions of Europe, resulting in many lost lives and destruction of equipment and goods. These retarders can be mounted in the driveline hanging from the chassis rails or in a “focal mount,” which bolts directly to the differential input housing. This retarder is totally frictionless, and the energy absorbed by these retarders is released directly to the air surrounding them.

There are several questions here about the definition of depth of field, about focal length, and about subject distance. And of course there's the basic how does aperture affect my photographs. And plenty of how do I get super-shallow d.o.f questions. There's related questions like this one. But there's no be-all-end-all question asking:

CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25

For example, it's pretty well known that at f/1.4 you'll get less depth of field than at f/2.8. What may not immediately be so obvious is that (for example) a 50 mm f/1.4 lens and a 100 mm f/2.8 lens have the same effective diameter. It's the wider angle at which light rays enter the 50 mm lens that gives it less depth of field than the 100 mm lens, even though the two have exactly the same physical diameter.

The output of the above program is intriguing, as it indicates that depth of field is indeed directly influenced by focal length as an independent factor from relative aperture, assuming only focal length changes and everything else remains equal. The two DoF's converge at f/1.4 and f/5.6, as demonstrated by the above program:

The greater number of pixels per dot of light certainly will produce smoother bokeh but so would moving closer with a small sensor camera. You can charge proportionality more for use of more expensive equipment if you make money off of your photos or videos, otherwise a bit of footwork or additional lower cost lenses will save you a lot of money over investing in a larger format system.

Photography: In photography the sensor size is measured based upon the width of film or the active area of a digital sensor. The name 35 mm originates with the total width of the 135 film, the perforated cartridge film which was the primary medium of the format prior to the invention of the full frame DSLR. The term 135 format remains in use. In digital photography, the format has come to be known as full frame. While the actual size of the usable area of photographic 35 mm film is 24w×36h mm the 35 millimeters refers to the dimension 24 mm plus the sprocket holes (used to advance the film).

Bokeh: The quality of the blurring of the out of focus areas of the image outside of the depth of field when the lens is correctly focused on the subject.

Shallowdepth of fieldphotography

Edit2: Since I (sort of) persuaded @jrista to remove his diagram relating focal length to depth of field, I should probably try to explain why there's not a relationship between focal length and depth of field -- at least when you look at things the way they're normally measured in photography.

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Several companies manufactured the early coolers, and some had defects that have since been improved on. However, service life is still not optimal when compared with most other cooling components. Because of this, it is recommended that the coolers be changed at a specified schedule so as to not chance a cooler failure that may result in transmission failure requiring an expensive overhaul. As with all retarders, they have an on/off switch on the dash for the driver that should be turned off in slippery conditions.

Using the “Zeiss formula”, the circle of confusion is sometimes calculated as d/1730 where d is the diagonal measure of the original image (the camera format). For full-frame 35 mm format (24 mm × 36 mm, 43 mm diagonal) this comes out to be 0.025 mm. A more widely used CoC is d/1500, or 0.029 mm for full-frame 35 mm format, which corresponds to resolving 5 lines per millimeter on a print of 30 cm diagonal. Values of 0.030 mm and 0.033 mm are also common for full-frame 35 mm format. For practical purposes, d/1730, a final-image CoC of 0.2 mm, and d/1500 give very similar results.

These units were very effective at high-speed driveline operation, were not affected by engine speed or transmission gear, and could deliver more than maximum engine BHP at the higher speeds. The early versions we used had clutch packs in the retarder housing that did not enjoy a very long service life with our units. However, Allison redesigned these in their World Transmission series (WT) to correct this. Another issue we ran into was short service life of the oil coolers. Part of the reason for cooler failure, I believe, had to do with thermal shock as transmission fluid temperatures could easily go from 200°F to greater than 300°F and quickly back to 200°F during use. If the transmission oil cooler leaked internally, as they were prone to do, engine coolant would contaminate the transmission fluid, causing eventual clutch pack failure. This is because ethylene glycol can dissolve the clutch pack lining material.

A higher resolution sensor and a better quality lens will produce better bokeh but even a cellphone sized sensor and lens can produce reasonably acceptable bokeh.

Shallowdepth of field

DOF is not symmetrical. This means that the area of acceptable focus does not have the same linear distance before and after the focal plane. This is because the light from closer objects converges at a greater distance aft of the image plane than the distance that the light from farther objects converges prior to the image plane.

ERVs require brake retarders primarily for the sake of safety. I think it is important to understand the theory of how the different retarders operate to understand which type will work best for your budget, operation, traffic conditions, and fleet. Keep in mind that you can use them in a wide ranges of vehicle types-not just the heavy ones-to reap the same benefits. Over the long haul, they will easily return the investment many times over-not to mention risk reduction exposure connected to brake failure.

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How does aperture affect depth of field? It ultimately boils down to the angles of the rays of light that actually reach the image plane. At a wider aperture, all rays, including those from the outer edge of the lens, reach the image plane. The diaphragm does not block any incoming rays of light, so the maximum angle of light that can reach the sensor is high (more oblique). This allows the maximum CoC to be large, and progression from a focused point of light to maximum CoC is rapid:

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The term 'infinity' here is not used in its classical sense, rather it is more of an optical engineering term meaning a focal point beyond the hyperfocal distance. The full formula for calculating DoF directly, without first calculating hyperfocal distance, as as follows (substitute for \$H\$):

The same is true with sensor size: in theory, if the reproduction ratio is held constant, the sensor size is completely irrelevant. From a practical viewpoint, however sensor size matters for a very simple reason: regardless of the sensor size, we generally want the same framing. That means that as the sensor size increases, we nearly always use large reproduction ratios. For example, a typical head and shoulders shot of a person might cover a height of, say, 50 cm (I'll use metric, to match how sensor sizes are usually quoted). On an 8x10 view camera, that works out to about a 1:2 reproduction ratio, giving very little depth of field. On a full 35mm size sensor, the reproduction ratio works out to about 1:14, giving a lot more depth of field. On a compact camera with, say, an 6.6x8.8 mm sensor, it works out to about 1:57.

Intriguing results, if a little non-intuitive. Another convergence occurs when the distances are adjusted, which provides a more intuitive correlation:

There are only two factors that actually affect DOF - aperture and magnification - yes switching distance, sensor size, focal length, display size, and viewing distance appear to have an effect but they are all just changes in the size of the image (the subject/part-you're-looking at) as seen by the eye that views it - the magnification. Kristof Claes summarized it a few posts earlier.

Q. Does it change with camera sensor size? A. Ultimately, it depends here. More important than the size of the sensor would be the minimum Circle of Confusion (CoC) of the imaging medium. Curiously, the Circle of Confusion of an imaging medium is not necessarily an intrinsic trait, as the minimum acceptable CoC is often determined by the maximum size you intend to print at. Digital sensors do have a fixed minimum size for CoC, as the size of a single sensel is as small as any single point of light can get (in a Bayer sensor, the size of a quartet of sensels is actually the smallest resolution.)

What does depth of field meanon camera

Circle of confusion: In idealized ray optics rays are assumed to converge to a point when perfectly focused, the shape of a defocus blur spot from a lens with a circular aperture is a hard-edged circle of light. A more general blur spot has soft edges due to diffraction and aberrations (Stokseth 1969, paywall; Merklinger 1992, accessible), and may be non-circular due to the aperture shape.

For example, even a really fast (large aperture) lens that has a short focal length makes it fairly difficult to high reproduction ratio. For example, if you take a picture of a person with a 20mm f/2 lens, the lens has to practically touch them before you get a very large reproduction ratio. At the opposite extreme, longer lenses often appear to have less depth of field because they make it relatively easy to achieve a large reproduction ratio.

Most importantly, "bokeh" isn't simply "background blur" but all blur outside the DOF; even in the foreground. It's that small lights at a distance are easier to judge bokeh quality.

Q. Does it change with print size? A. Given the answer to the previous question, possibly. Scaling an image above, or even below, its "native" print size can affect what value you use for the minimum acceptable CoC. Therefor, yes, the size(es) you intend to print at do play a role, however I would say the role is generally minor unless you print at very large sizes.

Complex mathematics aside, DoF can be intuitively visualized with a basic understanding of light, how optics bend light, and what effect the aperture has on light.

\$D_\text{n}\$ = Near limit of DoF \$D_\text{f}\$ = Far limit of DoF \$H\$ = Hyperfocal distance (previous formula) \$s\$ = Subject distance (distance at which the lens is focused, may not actually be "the subject")

The formula is fairly simple, outside of the pupil magnification aspect. A true, properly built macro lens will have largely equivalent entrance and exit pupils (the size of the aperture as viewed through the front of the lens (entrance) and the size of the aperture as viewed from the back of the lens (exit)), although they may not be exactly identical. In such cases, one can assume a value of \$P = 1\$, unless you have reasonable doubt.

This semi-apochromat objective series provides flat images and high transmission up to the near-infrared region of the spectrum. Acquiring sharp, clear images ...

Depth of fieldexamples

Aperture changes the rate of CoC growth. Wider apertures increase the rate at which out of focus blur circles grow, therefor DoF is shallower. Narrower apertures reduce the rate at which out of focus blur circles grow, therefor DoF is deeper.

@Matt Grum's comment is quite good: you do have to be really careful to specify conditions, or you can end up with three people saying things that seem to conflict, but are really just talking about different conditions.

Prior to installation, we had been warned by detractors that we could have electrical system issues because of the new electrical load the Telma would be imparting during operation. However, we did not have any electrical system issues. When the brakes are applied, the coils of the electromagnetic induction retarders use current when they are being energized. However, it is a momentary surge or spike, and it did not affect the batteries or our charging systems. What I did notice was that driveline U-joint life was cut roughly in half, even though it was being greased according to schedule. This probably had a lot to do with the unit being overweight, and the driveline is not only being loaded during acceleration but also during deceleration when the driveline absorbs the braking loads from the electromagnetic induction retarder.

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This typically changes with the size at which you print a picture -- bigger pictures are normally viewed from a greater distance, so more blur is acceptable. Most lens markings, etc., are defined based on a print around 8x10 being viewed at roughly arm's length distance (a couple of feet or so). The math for this works out fairly simple: start with an estimate of visual acuity, which will be measured as an angle. Then you just figure out what size that angle works out to at a specified distance.

The vernier metric micrometer has the ability to measure to two thousandths of a millimeter (0.002-mm). 0.002 mm is equivalent to approximately 0.00008 of an ...

Depth of fieldphotography examples

Video: Sensor sizes are expressed in inches notation because at the time of the popularization of digital image sensors they were used to replace video camera tubes. The common 1" circular video camera tubes had a rectangular photo sensitive area about 16 mm diagonal, so a digital sensor with a 16 mm diagonal size was a 1" video tube equivalent. The name of a 1" digital sensor should more accurately be read as "one inch video camera tube equivalent" sensor. Current digital image sensor size descriptors are the video camera tube equivalency size, not the actual size of the sensor. For example, a 1" sensor has a diagonal measurement of 16 mm.

There is one more factor to consider though: with a shorter lens, objects in the background get smaller a lot "faster" than with a longer lens. For example, consider a person with a fence 20 feet behind them. If you take a picture from 5 feet away with a 50 mm lens, the fence is 5 times as far away as the person, so it looks comparatively small. If you use a 200 mm lens instead, you have to back away 20 feet for the person to be the same size -- but now the fence is only twice as far away instead of 5 times as far away, so it looks comparatively large, making the fence (and degree to which it's blurred) much more apparent in a picture.

Sensor size. This affects DoF when you maintain the same subject distance and field of view between sensor sizes. The bigger the sensor the shallower the depth of field. DSLRs have much bigger sensors than compacts, and so for the same FoV and f-ratio they have shallower DoF. This is important because by the same token cropping images increases DoF when maintaining the same final output size, as it's akin to using a smaller sensor.

However, images seldom are viewed at the “correct” distance; the viewer usually doesn't know the focal length of the taking lens, and the “correct” distance may be uncomfortably short or long. Consequently, criteria based on lens focal length have generally given way to criteria (such as d/1500) related to the camera format.