Sensor formats: does size matter?

For the last couple of decades before the rise of digital photography, for the overwhelming majority of photographers, the choice of which format to use was easy: 35mm film. The larger formats were a niche market for the wealthy or especially demanding photographers, and on the other side of the spectrum, APS never gained much traction among enthusiasts, due to its lower image quality and the lack of serious photographic tools.

In today's digital market, two major changes have given the concept of sensor size a prominent place in considerations about photography equipment. First, the appearance of many different sensor sizes in the affordable segment of the market means that many photography enthousiasts will have the choice between models with differently sized sensors, and will often even own two or more of them. Second, the two largest DSLR manufacturers, Canon and Nikon, now offer their users the option of two or more sensor sizes within the same system, which can greatly complicate lens buying decisions. Many photography enthusiasts are confused about the implications a larger or smaller sensor may or may not have for their photography, and to make things worse, the manufacturers' marketing departments seem to be feeding confusion, if and when it suits their needs.

This essay is my view on the pros and cons of different sensor sizes, from the perspective of a DSLR user. Below, I will attempt to deduce a number of generic statements about sensor sizes, starting from the physics of sensors and optics, and taking into account major technological hurdles. The text deals with the generic properties of sensors within the current technological paradigm, so they indicate the trends for the industry as a whole. At any given time, it is of course possible for company A to have a slight technological advantage compared to company B, but this may not be related to a sensor size per se. Whenever I think that a technological breakthrough may change a given competitive advantage/disadvantage, I will indicate this in the text.

Advantages of larger/smaller sensors (summary)

For reference, and for the concentration-deficient internet audience, we will start by listing the advantages of both larger and smaller sensors. These claims will be substantiated in the remainder of the text, and will reappear at the end, with a few additional comments.

Advantages of larger sensors

  • Higher maximum resolution with current state of the art sensor technology
  • The ability to increase subject isolation with limited depth of field, using large-aperture lenses
  • The ability to get lower noise with equal shutter speeds, at the cost of decreasing the depth of field
  • Better noise performance at the base ISO value
  • Lenses may be cheaper to produce, because of the lower resolution requirements (in lp/mm, assuming equal MP count)
  • For DSLR focusing screens, easier manual focusing at equivalent depth of field

Advantages of smaller sensors

  • Shorter telephoto lenses
  • The ability to construct smaller lenses for smaller apertures (often in the f/4-5.6 range)
  • Lower cost sensors

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The effect of sensor size on photography

In the following sections we will put some meat onto the bare statements above. We start out by dicussing the way the sensor's interaction with light affects the image quality. Later, we'll take the optics into account as well.

Sensor: image quality and noise

This section discusses the sensor and its impact on the quality of the photo. I will focus on the aspect of sensor noise, as this is the only aspect that is directly related to the size of the sensor. There are generally three types of noise that affect the quality of the image (see also this page.)

  • readout/amplifier noise
  • pattern/dark current noise
  • shot noise

The pattern/dark current noise generally appears on long exposures. This type of noise has the convenient property that is is predicable in nature. Therefore it can be taken care of by calibration or dark frame subtraction (at the cost of an 1.4x increase in the random noise factors).

The readout/amplifier noise is noise that gets added to the signal in the digitization process. This noise is (supposedly) purely random, so it cannot be compensated for without loss of signal integrity. I will assume that this source of noise can be approximated by a constant value plus a contribution proportional to the strength of the signal (the number of electrons to be counted). This seems justified, based on the information on clarkvision.com, which is an excellent reference for more detailed information on these matters. Furthermore, the dependence on the number of electrons seems to be fairly similar among cameras of the same generation. As sensor technology improves, the read noise will decrease overall. The limit of vanishing read noise is especially interesting, because it allows for 'free' downsampling of an image, i.e. downsampling a 100MP image to 10MP gives an image of the same noise performance as a native 10MP image.

The third and final source of noise is the most counterintuitive: shot noise. This type of noise has nothing
to do with the sensor per se, but it's inherent to the light itself, and is caused by the fact that light consists of individual photons. For a given luminous flux F (photons per second), the photons do not arrive in neatly spaced time intervals. Instead, they arrive with random intervals (according to a Poissionian process), with an average luminous flux F. Therefore, if you count the number of photons that arrive within a short time interval, you'll get a slightly different number each time. For very low numbers of photons, the relative noise will be very high, whereas this will decrease for increasing photon counts. Quantitatively, the shot shot noise strength (expected deviation from the average) is equal to the square root of the average number of photons that is being counted.

In addition to these sources of noise, we should take into account one other aspect: the total conversion efficiency. A sensor counts photons by creating a free electron for every detected photon. However, not every photon that passes through the lens will be detected. There are a number of factors contributing to the loss of photons, like the fill factor (partially offset by microlenses), color filters (different for exotic technologies like Foveon) and the quantum efficiency of the sensor itself. In combination, these factors cause the total conversion efficiency to be significantly less than one (the only quantitative information I've been able to find places these numbers in the 10-20% range; see this link). However, it is unlikely that these total conversion efficiencies differ a lot among cameras from the same generation. Having said that, it is to be expected that technological innovations like multi-layer sensors, once adopted, will drastically improve these numbers across the board.

Looking at the above sources of noise, we conclude that pattern/dark current noise is not an issue in day-to-day use, that the per-pixel read noise is, for a given sensor generation, only dependent on the counted number of electrons, and shot noise is only dependent on the number of electrons. Furthermore, we assume that the total conversion efficiency is comparable among cameras of the same generation for the same target market. In this case, we see that the amount of noise is purely dependent on the number of incoming photons and the number of pixels they are divided into. It is important to realize that any existing differences in conversion efficiencies and read noise are likely to only decrease as sensor technology improves, approaching the theoretical maximum (100% conversion efficiency and the absence of read noise). Summarizing, we find the following:

At a given level of technological sophistication, the noise performance is mostly determined by the total amount of light (the number of photons) that reaches the sensor.

Optics: focal length, light gathering and depth of field

A photographic lens has two important properties: the focal length (or, for a zoom, a range of focal lengths) and the aperture. The focal length is listed in millimeters, but the size of the aperture is usually indicated in an indirect manner by the f-number, defined as the focal length divided by the diameter of the aperture.

The focal length, in conjunction with the sensor size, determines the field of view. To maintain the field of view across sensor sizes, the focal length should simply be scaled along with the sensor size. It has become customary to denote lenses by their '35mm-equivalent' focal length numbers, indicating the focal length one would need to get the same field of view on a 35mm film camera.

The f-number is a useful quantity, because it determines the relative intensity at the focal plane. It relates the intensity of the scene to the intensity at the sensor plane (measured in lux), by relative intensity = 1 / (4 f-number²) (assuming non-macro shooting; follow this link for more details). Multiplying the intensity at the sensor plane by the exposure time, we obtain the exposure: the total amount of light that the sensor receives per unit area (measured in lux seconds). For a properly exposed photograph (assuming medium gray is what you want) this needs to be adapted to the ISO speed value.

It is important to note that the conventional unit system using ISO value, shutter speed and f-number is built around the intensity of the light arriving at the sensor (photons per unit time per unit area). This makes sense for two reasons. First, it allows one to decouple the lens characteristics from those of the recording medium. Secondly, it has been very convenient for film, which comes in sheets that can be cut to any size. However, this may not be the most convenient system for comparing performance across different formats, especially when these formats are 'hard', as is the case with digital sensors. We have seen in the previous section that the image quality is primarily determined by the total amount of light arriving at the sensor. The total amount of light that is collected for a given intensity (f-number), scales linearly with the area of the sensor.

As a technical aside, the ISO/f-number system is based on luminous energy densities (measured in lux seconds), whereas the quantity that defines the maximum attainable image quality it the total luminous energy (measured in lumen seconds). The two are related through the sensor size. Also, this explains why it is possible for compact cameras to have fast f/2 zooms: they optimize the luminous energy density, but because of the smaller sensor the amount of luminous energy (the determinant of image quality) is often rather mundane.

Besides controlling the relative intensity of the light reaching the sensor, the f-number also affects the depth of field, with larger f-numbers (smaller apertures) increasing the depth of field. To maintain the same depth of field across formats, after first scaling the focal length, one has to preserve the (real) aperture size (this can be seen from the depth of field formulas, as seen for example on the Wikipedia page on depth of field). In the idealized image of a photographic lens consisting of a single element, this means that the size of the size of this element has to remain constant. In the more familiar photographic units, this implies that the f-number (focal length/aperture size) must also scale with the format size. Interestingly this is the same scaling that exactly maintains the total luminous flux onto the sensor! Note that we did not start out by demanding that the depth of field remain the same, but rather it's a consequence of our previous arguments.

Summarizing this section, we can state the following.

Scaling the focal length and f-number along with the sensor size conserves the field of view, the depth of field and the luminous flux.

Photographic equivalence

Now that we have introduced the various aspects that play a role in photographic imaging and how these relate to sensor size, we can start to address the initial question: what are the advantages and disadvantages of the different sensor sizes? We will answer this question in the inverse way. First, we determine under which circumstances two camera systems with differing sensor sizes can take images that cannot be distinguished from one another. In this case we say that the two systems are photographically equivalent. As a next step, we determine when this photographic equivalence breaks down, which leads us to a list of advantages for both larger and smaller formats.

Let us start by defining the concept of photographic equivalence. We consider to systems to be equivalent if they are equal in terms of:

  • resolution
  • noise
  • field of view
  • depth of field
  • motion blur (shutter speed)

At the end of the previous section, we have seen that scaling both the focal length and the f-number along with the sensor size conserves the field of view, depth of field and the luminous flux. If we also keep the shutter speed constant, we then conserve the total amount of light that is gathered by the lens and sensor, and therefore we also maintain a constant noise level. Note that this implies changing the luminous energy density, so the ISO value must be compensated to reflect this adjustment. For a similar take on equivalence, see also this page.

Suppose we have two systems, A and B. The sensors have the same resolution and sensor technology, but A's sensor is a factor s times larger than B's sensor. The images created by both systems are photographically equivalent if

  • focal length(A) = s * focal length(B)
  • f-number(A) = s * f-number(B)
  • ISO(A) = s² * ISO(B)

Note that this also implies that it is not very illuminating to compare the results produced by inequivalent setups. You simply can't expect a camera with a smaller sensor to perform like a larger sensor at the same ISO and f-number (surprise: you'll get more noise and more depth of field). Instead, it is more useful to compare cameras to the baseline that is set by photographic equivalence. For example, test a full frame sensor camera at ISO1600 and f/4 against a 4/3 sensor (2 time smaller) camera at ISO400 and f/2. The results should be very similar. If they are not, this indicates a difference that was not to be expected, and is therefore a competitive advantage/disadvantage of a specific camera model, instead of the sensor size.

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The limits of equivalence

The concept of photographic equivalence seems to indicate that any photograph can in principle be produced using a sensor of any size. At the same time, we know from experience that this is not the case in practice. For example, there is something about the look of large format portraits that simply cannot be reproduced in APS-C DSLRs. We will now delve further into the practical or fundamental limits of photographic equivalence. For each of the listed limitations, we will indicate how it affects cameras of various sensor sizes.

f-number

The f-numbers that appear in regular photographic lenses tend to lie within a fairly narrow range. On the low end of the scale, the f-number is constrained by complexity of lens designs and the thickness of the necessary optical elements. For this reason, one rarely sees zoom lenses that are faster than f/2.8, or fixed focal lenses that are faster than f/1.4. Faster lenses tend to be exotic specimens for specialized use, and are usually extraordinarily expensive, large and heavy. In practice, this means that f/2.8 zooms and f/1.4 primes for a certain format tend to have no equivalent on smaller formats.

At the other end of the scale, it is a rare sight to see lenses that are slower than f/5.6 wide open. Besides other practical purposes, this limit is strictly enforced by most modern AF systems, which need a brightness of f/5.6 or higher to operate. This f-number limit means that popular entry-level f/4-5.6 zoom lenses for a certain format only have an equivalent lens on larger formats by stopping down a lens that has more light gathering ability. Obviously, those lenses for the larger format will tend be larger, giving the smaller sensor system a size advantage.

A final interesting observation is that most DSLR lens manufacturers seem to divide the accessible f-number range into two parts, regardless of sensor size. Professional and enthousiast lenses are in the f/1.4-f/4 range, entry level amateur lenses in the f/3.5-5.6 range. Besides the differences in f-number, there are usually also differences in mechanical and optical quality. Coupled with the availability of a multitude of sensor sizes, this leads to interesting differences between systems. Take, for example, the Olympus 14-54mm f/2.8-3.5 lens for the 4/3 format. In terms of light gathering power, it is equivalent to Nikon's 18-70mm f/3.5-4.5 lens for the DX format, but, being in the sub-f/4 range, it is built to a higher standard, at a correspondingly higher price. This adds an extra dimension to the choice of a particular sensor size.

Diffraction limit

It is often being said that smaller sensors "have more depth of field." We have seen above that using the brightest lenses available for each system (say f/2) at wide open apertures, the system with a smaller sensor indeed has more depth of field. However, this begs the question whether the same difference also holds at the other end of the scale, for maximal depth of field (in landscape photography, for example). In practice, the maximum depth of field is determined by the diffraction limit, which relates the maximally attainable resolution to the f-number of the lens. It implies that there is an f-number, depending on thee sensor size and resolution, beyond which stopping down further will lead to a loss of resolution. This site has a very detailed discussion of the diffraction limit, complete with an online calculator.

For any given resolution, the diffraction-limited f-stop scales linearly with the sensor size, analogous to the scaling to maintain depth of field. The implication is that all systems are equally constrained (or unconstrained, if you wish) by the diffraction limit. The only exception are small sensors with very high resolution, so that an exceptionally bright < f/2 lens is necessary to avoid being limited by diffraction. This limit comes in sight for the new breed of 12MP compact cameras, that are diffraction limited already at f/4.

DSLR focusing screens

Within digital SLRs, the image is focused onto the focusing screen. These days, focusing screens are optimized for brightness more than manual focus ability. This means that most screens are not capable of profiting from the extra brightness an f/1.4 lens delivers over an f/2.0 lens. In practice, it will therefore be easier to focus an f/2.8 lens on a full format digital camera than an equivalent f/1.4 lens on a 4/3 camera, even though both have the same depth of field properties. For more information on this subject, see this page.

Electron well capacity

The sensor converts photons into free electrons. Within today's sensors, these electrons accumulate within the sensor until they are read out at the end of the exposure. It follows that the sensor must have enough capacity to store these electrons, to avoid the dreaded digital clipping. The storage capacity of silicon has remained fairly constant over the years, which means that most sensors can store a similar number of electrons per unit of area, and the full well capacity scales with the pixel area. This is reflected by the fact that most sensor have a base ISO value around ISO 100. The implication of this limit is that larger sensors can accumulate more electrons during an exposure. For an equal number of megapixels, at the base ISO setting this leads to a cleaner signal with a higher dynamic range.

This limit may be overcome by new technologies that count electrons as they are generated or, more likely, measure the time until a well has been filled. An implementation of such technology has recently been introduced in Toshiba's Dynastron-WD sensor for camera phones (see the white paper here; registration required), but it is likely only a matter of time until similar technologies reach other market segments. In practice this would open up additional low ISO settings, leading to cleaner images - at proportionally longer exposures, of course.

Manufacturing precision

Smaller sensors place higher resolution demands on lenses. As the required resolution approaches the limits of regular manufacturing precision, this can start to have a large effect on the lens production costs. As manufacturing technology progresses, this factor is likely to become less important over time, at any given resolution. However, this may be offset by rising resolution requirements due to increased pixel counts.

Sensor cost

Production costs for digital sensors rise very steeply with sensor size. Currently (early 2008), the cheapest 'full-frame' (24x36mm) digital camera costs around $2000, and the cheapest 'medium format' (36x48mm) digital back comes in at around $7000. To a large extent, these high prices seem to be caused by the sensor. Citing the rapid increase of processing power in ICs, many people seem to expect the prices for large sensors to fall rapidly in the coming years. However, I think it is being overlooked that most of the progress in that field has been driven by the miniaturization of circuits. Today's top-of-the-bill CPUs have still have a surface area of 200-300 mm², not too far from the 100 mm² of the old Intel 386. Full frame sensors are quite a bit larger still, and will probably remain very expensive for some time to come. See also this analysis.

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Advantages of larger/smaller sensors (expanded)

At this point, all the cards are on the table, and we can revisit the list of advantages of larger and smaller formats that was given at the start. Many of these follow straightforwardly from the information that has been presented, but I have added a few notes wherever confusion may still arise.

Advantages of larger sensors

  • Higher maximum resolution with current state of the art sensor technology As technology progresses, an increasing number of megapixels can be packed onto a chip of a certain size. However, at any given time, larger sensors tend to have higher pixel counts. Therefore, very high resolution requirements will often dictate a minimum sensor size (even though this minimum size may decrease over time). Also, we are approaching the point where the diffraction limit starts to impose limits on the pixel counts at the smaller sensor sizes.
  • The ability to increase subject isolation with limited depth of field, using large-aperture lenses Lenses with very low f-numbers will have no equivalent for smaller sensor sizes. 
  • The ability to get lower noise with equal shutter speeds, at the cost of decreasing the depth of field Lenses with very low f-numbers deliver a luminous flux that is unattainable on smaller sensors. However, it is important to note that this cannot be decoupled from its effect on depth of field. The luminous flux is only larger than for a system with a smaller sensor when the depth of field is shallower, and vice versa.
  • Better noise performance at the base ISO value Assuming an equal megapixel count (or downsampling), larger sensors can accumulate more electrons per pixel. This leads to increased dynamic range at the base ISO value.
  • Lenses may be cheaper to produce, because of the lower resolution requirements (in lp/mm, assuming equal MP count)
  • For DSLR focusing screens, easier manual focusing at equivalent depth of field DSLRs may have difficulties in accurately showing the effect of f/1.4-f/2 lenses in the viewfinder. For lenses in this range on smaller formats, its larger format equivalent is more likely to fall outside of this range.

Advantages of smaller sensors

  • Shorter telephoto lenses For telephoto lenses, the physical length of the lens is often closely related to the focal length in millimeters. The use of a smaller sensor therefore enables the use of telephoto lenses that are shorter than their equivalents for larger formats. Note, however, that the diameter of the lenses (roughly based on the physical aperture) is unlikely to change very much.
  • The ability to construct smaller lenses for smaller apertures (often in the f/4-5.6 range) The empirical fact that most lenses seem to be constrained to the < f/5.6 range creates an interesting opportunity for systems that are based around smaller sensors. Lenses in the f/4-5.6 range (or sometimes from f/2.8 upwards when a large gap in sensor sizes exists) tend to have no equivalents for larger formats. Therefore, these lenses can often be made much smaller. One can get a feeling for this by looking at the absolute aperture size. For this class of lenses these apertures are smaller than those available for larger lenses (with a similar field of view), so the front elements can be smaller as well.
  • Lower cost sensors

Conclusions

In the text, I have discussed the relative advantages of larger sensors compared to smaller ones, and vice versa. However, the most important take-home message may be the large number of photographic situations in which there is no appreciable difference in the performance of systems with different sensor sizes. For a very large number of photographs, you wouldn't be able to tell whether it was taken using a flagship DSLR or a compact camera (provided the lens is good enough).

This also shows that some of the 'common knowledge' pertaining sensor sizes is incorrect in the strict sense. Statements like "larger sensors are less noisy" and "smaller sensors have more depth of field" only apply to particular types of photography, and are certainly not true in general.

When deciding on a camera system, ask yourself what your requirements and wishes really are, and look at the type of photography you are doing. Then, compare this with the list of requirements above to see whether your needs are better matched by one of the larger or smaller formats. Don't be surprised if there is a range of formats that is suitable for your photography and budget. The final choice will most likely depend on numerous other factors, such as the availability of lenses, ergonomics and build quality.