cicala, roger - sensor size matters

7/30/2019 Cicala, Roger - Sensor Size Matters

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Sensor size matters

By Roger Cicala

Jan 30th 2012


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We get a lot of questions about sensor sizes and crop factors. Most

people know the difference between a standard (APS-C) cropsensor and a full-frame sensor. Not many, though, know how muchsmaller a 2/3 sensor is than a 4/3 sensor, and fewer still thedifference between those and a 1/1.8 sensor. Plus Canon andNikon have thrown new sensor sizes into the mix in the last year anda lot of people arent sure exactly where those sensors fit in amongthe better known ones. Hardly a day goes by that someone doesntask if the Fuji X-10 sensor is bigger than the Nikon J1 sensor. Is theCanon GX-1 sensor as big as those or more like a point and shoot?

The problem is even more complicated now that SLR lenses arebeing used on video cameras and video lenses on SLRs cameras.People want to know things like is Super 35mm format equivalent toa crop sensor or full-frame? Other people, trying to sell their 16mmfilm lenses with adapters for 4/3 cameras fail to mention how muchsmaller 16mm film was than 4/3 sensors. Not to mention themarketers, always ready to make things as confusing as possible,

are doing things like calling a 1/1.7 sensor large (it is compared toa cell phone camera chip, I guess).

Anyway, since I havent been able to find a single source to answerall these sensor format questions, I thought Id put it all togetherhere. The table below shows the dimensions, in millimeters, of thevarious sensor (or film) sizes. Please note that the dimensions may

vary slightly from camera to camera. For example, Canons APS-Csensor is slightly smaller than Nikons, but slightly larger thanSigmas. The aspect ratio of the sensor (4:3, 3:2, 16:9) will causesome variation, too. For example, the 35mm Cinema, Super 35mm,and APS-C crop sensor formats are nearly the same size (look atthe sensor area) but of slightly different rectangular proportions.


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Format height width Diag Area Crop Examples

mm mm mm (mm2) factor

Medium Format 44.0 33.0 55.0 1452 0.7 Pentax 645Full-frame 24.0 36.0 43.4 864 1.0 FF SLRsRed Epic 14.6 27.7 31.3 404 1.3 Red Epic/Scarlet35 Cine 13.7 24.4 28 334 1.4 Red OneSuper 35mm 13.8 24.6 28.0 339 1.4 Canon C300APS-C crop** 15.0 22.0 27.3 329 1.5 crop SLRs1.5 14.0 18.7 23.4 262 1.9 Canon G1X4/3 13.5 18.0 22.4 243 2.0 Four-thirdsNikon CX 8.8 13.2 15.8 116 2.7 Nikon J1/V1Super 16 7.4 12.5 14.5 93 3.0 film only

2/3 6.6 8.8 11.0 58 4.0Fuji X-10;

camcorders

1/1.7

5.6 7.4 9.5 42 4.6 Best P&S1/1.8 5.3 7.2 8.9 38 4.8 Best P&S1/2 4.8 6.4 8.0 31 5.4 camcorders1/2.5 4.3 5.8 7.2 25 6.0 P&S1/2.7 4.0 5.4 6.7 21 6.4 P&S1/3 3.6 4.8 6.0 17 7.2 camcorders

First, About those inch () sensors

Commonly used sensor abbreviations make absolutely no sense.(Get it, sense, sensor I have to have at least one pun perarticle. Its in my contract). Larger sensors are measured in

millimeters: full-frame, Super 35mm, APS-C, etc. The 4/3 marketingpeople probably thought half as big as full frame wasnt a goodway to present things, so 4/3 it was. But its easy to find how big a4/3 sensor is in mm.

But then we get into all of these fractional-inch-type-measurementsfor the smaller sensors. That measurement system originated inancient times (the 1950s to 1980s) when vacuum tubes were usedinstead of CCD or CMOS sensors in video and televisioncameras. The image sensor was, in those days, referred to in termsof the outside diameter of the vacuum tube that contained it.


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A video camera tube (courtesy Wikepedia Commons)

Why do manufacturers keep using such an archaic measurement?Because it helps them lie to you, of course. If you do the math 1/2.7equals 0.37 inches, which equals 9.39 mm. But if you look at thechart above youll see that a 1/2.7 sensor actually has a diagonal of6.7 mm. Why? Because, of course, a thick glass tube used tosurround the sensors. So they calculate the sensor size as if theglass tube was still included. Makes perfect sense to a marketingperson who wants to make their sensor seem larger than it is. Whatsounds better: 1/2.7 or less than 10% the size of a full frame

sensor?


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Calculating the Crop Factor from the Sensor Diagonal

It surprises me how many people do not really understand what thecrop factor is, and technical explanations seem to make it worsefor newcomers. But in simplest terms if I set up several cameraswith different size sensors at point A, put the same 100mm lens oneach of them and took a picture the picture taken with the smallersensors would seem more magnified than the pictures taken withthe larger sensors. The picture taken with the APS-C size sensorwould appear magnified 1.5X compared to the full-frame picture. Or

put another way, a picture taken with a 150mm lens on the full-framecamera would frame exactly the same area as one taken with a100mm lens on the APS-C sensor camera. Hence the term 1.5 cropfactor.

OK, thats pretty easy. But what if you are shooting video with a50mm lens on an APS-C size camera, and want to frame the shotidentically on a camcorder with a 2/3 sensor? Well you could

probably convert back and forth from APS-C to full frame and thento 2/3 sensor using the handy table I made for you above. But youmight have noticed in that table that the diagonal measurement ofthe sensor size is proportional to the crop factor. For example,43.3mm (full frame sensor diagonal) / 22.4mm (4/3 sensordiagonal) = 2, etc.

So, to make that conversion from 4/3 sensor to 2/3

sensor we canjust divide the diagonal measurements of the sensors (27.3mmdiagonal for the APS-C sensor, 11mm diagonal for the 2/3 sensor).The result is about 2.5, so wed need a 20mm lens on our 2/3sensor video camera to frame the shot the same way.


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Really, really look at the sensor rea

The numbers for crop factor and diagonal measurement of thesensors minimizes the actual differences in sensor sizes. If you wantto really understand how much larger one sensor is than another,look at the column for the surface areaof the sensor. The diagonalmeasurement and crop factor of a full-frame 35mm sensor is only1.5 times longer than an APS-C camera, and twice the size of a 4/3sensor. But the area of the full frame sensor is more than doublethat of a crop sensor, and almost 4 times that of a 4/3 sensor.

If the resolution of the cameras are the same, larger sensors meanlarger pixels resulting in better ISO performance. (You can comparepixel sizes for a 12 Mp Nikon D700 and a 12 Mpix 4/3 camera by

just pretending the above sensor size diagram is pixel size nowonder theres a difference in high ISO perforamance). Or, insteadof bigger pixels on the sensor, the manufacturer may put morepixels, which gives the camera higher resolution. Or some of each.Most full frame cameras have both more pixels and bigger pixels

than most 4/3 cameras.


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There are other factors involved, of course. Newer sensors havebetter microlenses and newer cameras better computer chips, bothof which can make a big difference in high ISO performance.

Underexpose the picture two stops and ISO performance doesntmatter either you cant differentiate black from black. Put a crappylens in front of the camera and the sensors resolution doesntmatter the camera cant photograph what the lens doesntresolve. If youre just putting web-sized jpgs up none of it mattersmuch. If youre making large prints every bit of it matters a lot.

But the area of the sensors explains why so many video people areabandoning their old camcorders and picking up AG-AF100s, SonyF3s, and video capable SLR cameras in droves. As an example,consider that a few years ago a very good $15,000 camcorder camewith 2/3 sensors (58 square mm in area). Today, about the sameamount of money will get you a Sony F3 with a Super 35 sizedsensor (339 square mm in area, nearly 6 times larger), or 5 or 6 cropsensor SLRs with roughly the same size sensor.

Its also interesting to look at some new mirrorless and fixed-lenscamera systems in terms of sensor size. Nikon chose to create theCX sensor size for its new J1/V1 cameras. The reason is obvious:there was a large gap between the smallest SLR sensor (4/3) andthe largest video (2/3) and point and shoot (1/1.7) sensors. The CXsensor fills that gap nicely. The CX sensor should be better than anypoint and shoot, but not so good that it takes business away fromtheir SLR cameras. (Theres an old saying that if you dont eat your

own lunch, somebody else will. But apparently Nikon doesnt believein that.) The Fuji X10 is using the very largest non-SLR sensor, the2/3, which until now has only been used in video cameras. Canon,on the other hand, is releasing their G1X with a sensor slightly largerthan the 4/3 sensors, although still smaller than their APS-Ccameras.


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Theres a lot more to a camera than its sensor size, of course.Lenses come to mind. (Yes, Sony, Im talking to you. Othercompanies are getting rich selling decent lenses and adapters to

shoot on your mirrorless cameras.) It will be interesting, though, tosee how the choice of sensor size affects the image quality of thesenew cameras. Software algorithms, electronics, and bettermicrolenses all make a difference, but small pixels are still smallpixels.

Addendum:

Patricks comment made me consider that while I unconsciouslygroup sensors into categories, I didnt really present that in thearticle. So maybe it will help if I do it here:

Sensor Areamm2

Sensor Type Examples

1200+ MediumFormat*

Leica S2, Hasselblad, etc.

800-900 Full Frame Canon 5DII, Nikon D700, etc.300-400 Crop Frame APS-C SLRs and mirrorless, Red,

Super 35, 35 Cine200-300 4/3 type Canon G1X, 4/3 cameras

about 100 CX Nikon J1/V1, Super 16 film40-60 2/3, 1/1.7 Best camcorders and P&S, Fuji X10

under 40 P&S sensors Camcorders, P&S


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Why Sensor Size Matters

Part 1 of this series discussed what the different sensor sizesactually are and encouraged you to think in terms of the surfacearea of the sensors. It assured you the size of the sensor wasimportant, but really didnt explain how it was important (other thanthe crop-factor effect). This article will go into more detail about howsensor size, and its derivative, pixel size, affect our images. For thepurists among you, yes, I know sensel is the proper term ratherthan pixel. This stuff is confusing enough without using a term 98%

of photographers dont use, so cut me some slack.

Ive made this an overview for people who arent really into thephysics and mathematics of quantum electrodynamics. It will coversimply what happens and some very basic why it happens. Iveavoided complex mathematics, and dont mention every possibleexception to the general rule (there are plenty). Ive added an

appendix at the end of the article that will go into more detail aboutwhy it happens for each topic and some references for those whowant more depth.

Ill warn you now that this post is too long it should have been splitinto two articles. But I just couldnt find a logical place to split it. Myfirst literary agent gave me great advice for writing about complexsubjects: Tell them what youre gonna tell them. Then tell them.

And finally, tell them what you told them. So for those of you whodont want to tackle 4500 words, heres what Im going to tell youabout sensor and pixel size:

Noise and high ISO performance: Smaller pixels are worse.Sensor size doesnt matter.

Dynamic Range: Very small pixels (point and shoot size) suffer

at higher ISO, sensor size doesnt matter.


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Depth of field: Is larger for smaller size sensors for an imageframed the same way as on a larger sensor. Pixel size doesntmatter.

Diffraction effects: Occur at wider apertures for both smallersensors and for smaller pixels.

Smaller sensors do offer some advantages, though, and formany types of photography their downside isnt very important.

If you have other things to do, are in a rush, and trust me to bereasonably accurate, then theres no need to read further. But if youwant to see why those 5 statements are true (most of the time) read

on! (Plus, in old-time-gamer-programming style, Ive left an EasterEgg at the end for those who get all the way to the 42nd level.)

Calculating Pixel Size

Unlike crop factor, which we covered in the first article, some of theeffects seen with different sensor sizes are the result of smaller orlarger pixels rather than absolute sensor size. Obviously if a smallersensor has the same number of pixels as a large sensor, the pixelpitch (the distance between the center of two adjacent pixels) mustbe smaller. But the pixel pitch is less obvious when a smaller sensorhas fewer pixels. Quick, which has bigger pixels: a 21 Mpix full-frame or a 12 Mpix 4/3 camera?

Pixel pitch is easy to calculate. We know the size of the camerassensor and the size of its image in pixels. Simply dividing the lengthof the sensor by the number of pixels along that length gives us thepixel pitch. For example, the full-frame Canon 5D Mk II has animage that is 5616 x 3744 pixels in size, and a sensor that is 36mmx 24mm. 36mm / 5616 pixels (or 23mm / 3744 pixels)= 0.0064mm/pixel (or 6.4 microns/pixel). We can usually use either

length or width for our calculation since since the vast majority ofsensors have square pixels.


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To give some examples, Ive calculated the pixel pitch for a numberof popular cameras and put them in the table below.

Table 1: Pixel sizes for various cameras

Pixel size Camera

(microns)8.4 Nikon D700, D3s7.3 Nikon D46.9 Canon 1D-X6.4 Canon 5D Mk II5.9 Sony A900, Nikon D3x5.7 Canon 1D Mk IV5.5 Nikon D300s, Fuji X1004.8 Nikon D7000, D800, Sony NEX 5n, Fuji X

Pro 14.4 Panasonic AG AF100,4.3 Canon GX1, 7D; Olympus E-P33.8 Panasonic GH-2, Sony NEX-73.4 Nikon J1 / V12.2 Fuji X102.0 Canon G12

A really small pixel size, like those found in cell phone cameras andtiny point and shoots, would be around 1.4 microns (1). To put thatin perspective, if a full-frame camera had 1.4 micron pixels it wouldgive an image of 25,700 x 17,142 pixels, which would be a 440Megapixel sensor. Makes the D800 look puny, now, doesnt it?Unless youve got some really impressive computing power youprobably dont have much use for a 440 megapixel image, though.

Anyway, you dont have any lenses that would resolve it.


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Effects on Noise and ISO Performance

We all know what high ISO noise looks like in our photographs. Pixelsize (not sensor size) has a huge effect (although not the only effect)on noise. The reason is pretty simple. Lets assume every photonthat strikes the sensor is converted to an electron for the camera torecord. For a given image (same light, aperture, etc.) X number ofphotons hits each of our Canon G12s pixels (these are 2 microns oneach side, so the pixel is 4 square microns in surface area). If weexpose our Canon 5D Mk II to the same image, each pixel (6.4

micron sides, so 41 square microns in surface area) will be struck by10 times as many photons, sending 10 times the number ofelectrons to the image processor.

There are other electrons bouncing around in our camera that werenot created by photons striking the image sensor (see appendix).These random electrons create background noise the imageprocessor doesnt know if the electron came from the image on the

sensor or from random noise.

Just for an example, lets pretend in our original image one photonstrikes every square micron of our sensor, and both cameras have abackground noise equivalent to one electron per pixel. The smallerpixels of the G12 will receive 4 electrons from light rays reachingeach pixel of the sensor (4 square microns) for each pixel of noise

(4:1 signal-to-noise ratio) while the 5DII will receive 41 electronsfrom each pixel (41:1 signal-to-noise ratio). The electronic wizardrybuilt into our camera may be able to make 4:1 and 41:1 look prettysimilar.

But lets then cut the amount of light in half, so only half as manyphotons strike each sensor. Now the SNR ratios are 2:1 and 20:1.Maybe both images will look OK. Of course we can amplify the

signal (increase ISO) but that also increases the amount of noise inthe camera. And if we cut the light in half again and the SNR is now


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1:1 and 10:1. The 5DII still has a better SNR ratio at this lower lightthan the G12 had in the original image. But the G12 has no image atall: the signal (image) strength is no greater than the noise.

Thats an exaggerated example, the difference isnt actually thatdramatic. The sensor absorbs far more than 40 photons per pixeland there are several other factors that influence how well a givencamera handles high ISO and noise. If you want more detail andfacts, theres plenty in the appendix and the references. But thetakeaway message is smaller pixels have lower signal to noiseratios than larger pixels.

Newer cameras are better than older cameras, but . . . .

It is very obvious that newer cameras handle high ISO noise betterthan cameras from 3 years ago. And just as obvious is that somemanufacturers do a better job handling high ISO than others (Someof them cheat a lot to do it, with in-camera noise reduction even inRAW images that can cause loss of detail but thats another articlesomeday).

People often get carried away with this, thinking newer camerashave overcome the laws of physics and can shoot at any ISO youwould please. They are better, theres no question about it, but theimprovements are incremental and steady. DxO optics has tested alot of sensors for a pretty long time and has graphed theimprovement theyve seen in signal to noise ratio, normalized forpixel size. The improvement over the last few years is obvious, buton the order of 20% or so, not a doubling or tripling for pixels of the

same size.


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Signal to noise ratio, normalized for pixel size. (DxO optics)

Other things being equal (same manufacturer, similar time sincerelease), a camera with bigger pixels has less noise than one withsmaller pixels. DxO graphs ISO performance for all the camerasthey test. If you look at the cameras with the best ISO performance(top of the graph) they arent the newest cameras, theyre the oneswith the largest pixels. In fact, most of them were released severalyears ago.


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DxO Mark score for high ISO performance, with pixel size of thebest cameras added.

The miracle increase in high ISO performance isnt just aboutincreased technology. Its largely about decisions by designers atCanon, Nikon, and Sony in 2008 and 2009 to make cameras withlarge sensors containing large pixels. There is a simplemathematical formula for comparing the signal-to-noise ratio fordifferent pixel sizes: the signal to noise ratio is proportional to thesquare root of the pixel pitch. There is more detail about it in theappendix.

Effects on Dynamic Range

You might think the effects of pixel size on dynamic range should besimilar to that of noise, discussed above. However, dynamic rangeseems to be the area where manufacturers are making the greateststrides at least with reasonably sized pixels. When measured atideal ISO (ISO 200 for most cameras) dynamic range varies moreby how recently the camera was produced than by how large thepixels are (at least until the pixels get quite small). If you look at DxOMarks data for sensor dynamic range the cameras with the bestdynamic range are basically newer cameras, not those with thelargest pixels.


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DxO Dynamic range scores with pixel sizes added for certaincameras. Recent release date seems much more important than

pixel size.

There is no simple formula for calculating the effect of pixel size ondynamic range, but in general both large and medium size pixelsensors do well at low ISOs, but dynamic range falls moredramatically at higher ISOs for smaller pixels.


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Effects on Depth of Field

Depth of field is a complex subject and takes some complex math tocalculate. But the principles behind it are simple. To put it in words,rather than math, every lens is sharpest at the exact distance whereit is focused. It gets a bit less sharp nearer and further from thatplane. For some distance nearer and further from the plane of focus,however, our equipment and eyes cant detect the difference insharpness and for all practical purposes everything within thatrange appearsto be at sharpest focus.

The depth of field is affected by 4 factors: the circle of confusion,lens focal length, lens aperture, and distance of the subject from thecamera. Pixel size has no effect on depth of field, but sensor sizehas a direct effect on the circle of confusion, and the crop factor mayalso affect our choice of focal length and shooting distance.Depending on how you look at things, the sensor size can make thedepth of field larger, shallower, or not change it at all. Lets try to

clarify things a bit.

Circle of Confusion

The circle of confusion causes a lot of confusion. But basically it is ameasure of how large of a circle appears, to our vision, to be just apoint (rather than a circle). It is determined (with a lot of argumentabout the specifics) from its size on a print. Obviously to make aprint of a given size, you have to magnify a small sensor more thana large sensor. That means a smaller circle on the smaller sensorwould be the limits of our vision, hence the circle of confusion is

smaller for smaller sensor sizes.


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There is more depth to the discussion in the appendix (and itsactually rather interesting). But if you dont want to read all that,below is a table of the circle of confusion (CoC = d/1500) size for

various sensors.

Table 2: Circle of Confusion for Various Sensor Sizes

Sensor Size CoCFull Frame 0.029 mmAPS-C 0.018 mm1.5 0.016 mm4/3 0.015 mmNikon CX 0.011 mm1/1.7 0.006 mm

The bottom line is that the smaller the sensor size, the smaller thecircle of confusion. The smaller the circle of confusion, the shallowerthe depth of field IFwere shooting the same focal length at the

same distance. For example, lets assume I take a picture with a100mm lens at f/4 of an object 100 feet away. On a 4/3 sensorcamera the depth of field would be 37.7 feet. On a full frame camerait would be 80.4 feet. The smaller sensor would have the shallowerdepth of field. Of course, the images would be entirely different theone shot on the 4/3 camera would only have an angle of view half aslarge as the full frame.

Thats all well and good for the pure technical aspect, but usually wewant to compare a picture of a given composition between cameras.In that case we have to consider changes in focal length or shootingdistance and the effects those have on depth of field.


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Lens Focal Length and Shooting Distance

In order to frame a shot the same way (have the same angle ofview), with a smaller sensor camera we must either use a widerfocal length, step back further from the subject, or a bit of both. If weuse either a wider focal length, or shoot at a greater distance fromthe subject, keeping the same angle of view, then the depth of fieldwill be increased. This increase more than offsets the decreaseddepth of field you get from the smaller circle of confusion.

In the above example, I take a picture with a full-frame camera usinga 100mm lens at a subject 100 feet distant at f/4. The depth of fieldwas 80.4 feet. If I want to frame the picture the same way on a 4/3camera I could use a 50mm lens (same distance and aperture). Thedepth of field would then be 313 feet. If instead I kept the 100mmlens but backed up to 200 feet distance to keep the same angle ofview, the depth of field would be 168 feet. Either way, the depth offield for an image framed the same way will be much greater for the

smaller sensor size than for the larger one.

So if we compare a similar image made with a small sensor or alarge sensor, the smaller sensor will have the larger depth of field.

Compensating with a Larger Aperture

Since increasing the aperture narrows the depth of field, cant wejust open the aperture up to get the same depth of field with a

smaller sensor as with a larger one? Well, to some degree, yes. Inthe example above the best depth of field I could get with a 4/3


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sensor was 168 feet by keeping the 100mm lens and moving backto 200 feet. If I additionally opened the aperture to f/2.8 and thenf/2.0 it would decrease the depth of field to 141 feet and 84 feet

respectively. So in this case Id need to open the aperture two stopsto get a similar depth of field as I would using a full frame camera.

The relationships between shooting distance, focal length andaperture are complex and no one I know can keep it all in their head.If you move back and forth between formats a depth of fieldcalculator is a must. And just to be clear: the effects on depth of field

have nothing to do with pixel size, its simply about sensor size,whether the pixels on the sensor are large or small.

Effects on Diffraction

Everyone knows that when we stop a lens down too far the imagebegins to get soft from diffraction effects. Most of us understandroughly what diffraction is (light rays passing through an openingbegin to spread out and interfere with each other). A few have gonepast that and enjoy stimulating after-dinner discussions about Airydisc angular diameter calculations and determing Raleigh Criteria. Avery few.

For the rest of us, heres the simple version: When light passesthrough an opening (even a big opening), the rays bend a bit at theedges of the opening (diffraction). This diffraction causes what wasoriginally a point of light (like a star, for example) to impact on oursensor as a small disc or circle of light with fainter concentric ringsaround it. This is known as the Airy disc (first described by George

Airy in the mid 1800s).


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A computer generated Airy Disc (courtesy Wikepedia Commons)

The formula for calculating the diameter of the Airy disc is (dont be

afraid, I have a simple point here, Im not going all mathematical onyou):

The point of the formula is to show you that the diameter of the airydisc is determined entirely by (the wavelength of light) and d(thediameter of the aperture). We can ignore the wavelength of light and

just say in words that the Airy disc gets larger as the aperturegets smaller. At some point, obviously, the Airy disc gets largeenough to cause diffraction softening.

At what point? Well, using the formula we can calculate the size ofthe Airy disc for every aperture (we have to choose one wavelength

so well use green light).


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Table 3: Airy disc size for various apertures

Airy discAperture (Microns)

f/1.2 1.6f/1.4 1.9f/1.8 2.4f/2 2.7

f/2.8 3.7f/4 5.3

f/5.6 7.5f/8 10.7

f/11 14.7f/13 17.3f/16 21.3f/22 29.3

Remember the circle of confusion we spoke of earlier? If the Airydisc is larger than the circle of confusion then we have reached thediffraction limit the point at which making the aperture smaller isactually softening the image. In Table 2 I listed the size of the CoCfor various sensor sizes. A smaller sensor means a smaller CoCso the diffraction limit occurs at a smaller aperture. Comparing

the CoC (Table 2) with Airy disc size (Table 3) its apparent that a4/3 sensor is becoming diffraction limited by f/11, a nikon J1 by f/8,and a 1/1.7 crop sensor camera between f/4 and f/5.6.

But the size of the sensor gives us the highest possible f-number wecan use before diffraction softening sets in. If the pixels are smallthey may cause diffraction softening at an even larger aperture(smaller f-number). If the Airy disc diameter is greater than 2 (or 2.5

or 3 its arguable) pixel widths then diffraction softening canoccur. If we calculate when the Airy disc is larger than 2.5 x the pixel


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pitch rather than when it is larger than the sensors circle ofconfusion things look a bit different.

Table 4: Diffraction limit for various pixel pitches

Pixel Pitch 2.5 * PP Example camera Diffraction at8.4 21 Nikon D700, D3s f/167.3 18.3 Nikon D4 f/136.9 17.3 Canon 1D-X f/136.4 16.0 Canon 5D Mk II f/125.9 14.8 Sony A900, Nikon D3x f/115.7 14.3 Canon 1D Mk IV f/115.5 13.8 Nikon D300s, Fuji X100 f/104.8 12.0 Nikon D7000, D800,

Sony NEX 5n, Fuji XPro 1

f/9

4.4 11.0 Panasonic AG AF100, f/84.3 10.8 Canon GX1, 7D;

Olympus E-P3f/8

3.8 9.5 Panasonic GH-2, SonyNEX-7

f/8

3.4 8.5 Nikon J1 / V1 f/6.32.2 5.5 Fuji X10 f/4.52 5.0 Canon G12 f/3.5


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Let me emphasize that neither of the tables above are absolutevalues. There are a lot of variables that go into determining wherediffraction softening starts. But whatever variables you choose, the

relationship between diffraction values and sensor or pixel sizeremains: smaller sensors and smaller pixels suffer diffractionsoftening at lower apertures than do larger sensors with largerpixels.

Advantages of Smaller Sensors (yes, there are some)

There are several advantages that smaller sensors and evensmaller pixels bring to the table. All of us realize the crop factor canbe useful in telephoto work (and please dont start a 30 postdiscussion on crop factor vs magnification vs cropping). The

practical reality is many people can use a smaller or less expensivelens for sports or wildlife photography on a crop-sensor camera thanthey could on a full-frame.

One positive of smaller pixels is increased resolution. This seemsself-evident, of course, since more resolution is generally a goodthing. One thing that is often ignored, particularly when consideringnoise, is that noise from small pixels is often less objectionable and

easier to remove than noise from larger pixels. It may not be quiteas good as it sounds in some cases, however, especially if the lensin front of the small pixels cant resolve sufficient detail to let thosepixels be effective.

An increased depth-of-field can also be a positive. While we oftenwax poetic about narrow depth of field and dreamy bokeh for

portraiture, a huge depth of field with nearly everything in focus is adefinite advantage with landscape and architectural work. And there


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are simple practical considerations: smaller sensors can use smallerand less expensive lenses, or use only the sweet spot the bestperforming center of larger lenses.

Like everything in photography: a different tool gives us differentadvantages and disadvantages. Good photographers use thosedifferences to their benefit.

Summary:

The summary of this overlong article is pretty simple:

Very small pixels reduce dynamic range at higher ISO. Smaller sensor size give an increased depth of field for images

framed the same way (same angle of view). Smaler sensor sizes have diffraction softening at wider

apertures compared to larger sensors. Smaller pixels have increased noise at higher ISOs and can

cause diffraction softening at wider apertures compared tolarger sensors.

Depending on what your style of photography these thingsmay be disadvantages, advantages, or matter not at all.

Given the current state of technology, a lot of people way smarterthan me have done calculations that indicate what pixel size is ideal

large enough to retain the best image quality but small enough togive high resolution. Surprisingly they usually come up with similarnumbers: between 5.4 and 6.5 microns (Ferrel, Chen). When pixelsare smaller than this the signal-to-noise ratio and dynamic rangestarts to drop, and the final resolution (what you can actually see ina print) is not as high as the number of pixels should theoretically

deliver.


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Does that mean you shouldnt buy a camera with pixel sizes smallerthan 5.4 microns? No, not at all. Theres a lot more that goes intothe choice of a camera than that. And this seems to be the pixel size

where disadvantages startto occur. Its not like a switch is suddenlythrown and everything goes south immediately. But it is a number tobe aware of. With smaller pixels than this you will see somecompromises in performance at least in large prints and for certaintypes of photography. Its probably no coincidence that so manymanufacturers have chosen the 4.8 micron pixel pitch as thesmallest pixel size in their better cameras.


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APPENDIX AND AMPLIFICATIONS

Effects on Noise and ISO Performance

A cameras electronic noise comes from 3 major sources. Readnoise is generated by the cameras electronic circuitry and is fairlyrandom (for a given camera some cameras have better shieldingthan others). Fixed pattern noise comes from the amplificationwithin the sensor circuitry (so the more we amplify the signal, whichis what were doing when we increase ISO, the more noise isgenerated). Dark currentsor thermal noise are electrons that aregenerated from the sensor (not from the rest of the camera or the

amplifiers) without any photons impacting it. Dark current istemperature dependent to some degree so is more likely with longexposures or high ambient temperatures.

The example I used in this section is very simplistic and the electronand photon numbers are far smaller than reality. The actual SNR (orPhoton/Noise ratio) is P/(P + r2 + t2)1/2 where P = photons, r= readnoise and t= thermal noise. The photon Full Well Capacity (how

many photons completely saturate the pixels ability to convert themto electrons), read noise and dark noise can all be measured andthe actual data for a sensor or pixel calculated at different ISOs. TheReference Articles by Clark listed below present this in an in-depthyet readable manner and also present some actual data samples forseveral cameras.


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If you want to compare how much difference pixel size makes forcamera noise, you can do so pretty simply: the signal to noise ratiois proportional to the square root of the pixel pitch. For example, it

should be a pretty fair to compare the Nikon D700 (8.4 micron pixelpitch, SqRt = 2.9) with the D3X (5.9 micron PP, SqRt = 2.4) and saythe D3X should have a signal to noise ratio that is 2.4/2.9 = 83% ofthe D700. The J1/V1 cameras with its 3.4 micron pixels (SqRt =1.84) should have a signal-to-noise ratio that is 63% of the D700. If,in reality, the J1 performs better than that when actually measured,we can assume Nikon made some technical advances between therelease of the D700 and the release of the J1.

Effects on Dynamic Range

At their best ISO (usually about ISO 200) most cameras, no matterhow small the sensor size, have an excellent dynamic range of 12stops or more. As ISO increases, larger pixel cameras retain muchof their initial dynamic range, but smaller pixels loose dynamic rangesteadily. Some of the improvement in dynamic range in more recentcameras come from improved Analogue to Digital (A/D) convertersusing 14 bits rather than 12 bits, but there are certainly otherimprovements going on.


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Effects on Depth of Field

The formulas for determining depth of field are complex and varied:different formulas are required for near distance (near the focallength of the lens) such as in macro work and for normal to fardistances. Depth of field even varies by the wavelength of light inquestion. Even then, calculations are basically for light rays enteringfrom near the optical axis. In certain circumstances off-axis (wideangle) rays may behave differently. And after the calculations aremade, practical photography considerations like diffraction blurringmust be taken into account.

For an excellent and thorough discussion I recommend the Paul vanWalrees (Toothwalker) article listed in the references. For the twopeople who want to know all the formulas involved, the wikepediareference contains them all, as well as their derivation.

Circle of Confusion

Way back when, it was decided that if we looked at an 8 X 10 inch

image viewed at 10 inches distance (this size and distance werechosen since 8 X 10 prints were common and 10 inches distanceplaced it at the normal human viewing angle of 60 degrees) a circleof 0.2mm or less appeared to be a point. Make the circle 0.25mmand most people perceive a circle; but 0.2mm, 0.15mm, 0.1mm, etc.all appear to be just a tiny point to our vision (until it gets so smallthat we cant see it at all).

Even if a photograph is blurred slightly, as long as the blur is less

than the circle of confusion, we cant tell the difference just bylooking at it. For example in the image below the middle circle is


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actually smaller and sharper than the two on either side of themiddle, but your eyes and viewing screen resolution prevent youfrom noticing any difference. If the dots represent a photograph from

near (left side) to far (right side) we would say the depth of fieldcovers the 3 central dots: the blur is less than the circle of confusionand they look equally sharp. The dots on either side of the central 3are blurred enough that we can notice it. They would be outside thedepth of field.

To determine the Circle of Confusion on a cameras sensor we haveto magnify the sensor up to the size of an 8 X 10 image. A smallsensor will have to be magnified more than a large sensor to reachthat size, obviously.

There is a simple formula for determining the Circle of Confusion forany sensor size: CoC = d / 1500 where d = diameter of the sensor.(Some authorities use 1730 or another number in place of 1500because they define the minimum point we can visualize differently,but the formula is otherwise unchanged.) But whatever is used, thesmaller the diameter of the sensor, the smaller the circle ofconfusion.


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Effects on Diffraction

Discussing diffraction means either gross simplification (like I didabove) or pages of equations. Frighteningly (for me at least) Airycaclulations are the least of it. There also is either Fraunhoferdiffraction or Fresnel diffraction depending on the aperture anddistance from the aperture in question, and a whole host of otherequations with Germanic and old English names. If youre into it, youalready know all this stuff. If not, Id start with Richard Feynmansbook QED: The Strange Theory of Light and Matter before tacklingthe references below.

If you want just a little more information, though, written inexceptionally understandable English with nice illustrations, Irecommend Sean McHughs article from Camridge in Colour listedin the references. He not only covers it in far more detail than I do,he includes great illustrations and handy calculators in his articles.

One expansion on the text in the article. You may wonder why anAiry disc larger than 1 pixel doesnt cause diffraction softening, whywe choose 2, 2.5 or 3 pixels instead. Its because the Bayer arrayand AA filter mean one pixel on the sensor is not the same as onepixel in the print (damn, thats the first time ever Ive thought thatsensel would be a better word than pixel). The effects of Bayerfilters and AA filters are complex and vary from camera to camera,

so there is endless argument about which number of pixels iscorrect. Its over my head every one of the arguments makessense to me so Im just repeating them.


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Oh, Yeah, the Easter Egg

If youve made it this far, heres something you might findinteresting.

Youve probably heard of the Lytro Light-Field Camera thatsupposedly lets you take a picture and then decide where to focuslater. Lytro is being very careful not to release any meaningfulspecifications (probably because of skeptics like me who are already

bashing the hype). But Devin Coldewey at TechCrunch.com haslooked at the FCC photos of the insides of the camera and found thesensor is really quite small.

Sensor size of the Lytro Light Field Camera, courtesyTechCrunch.com

Lytros has published photos all over the place showing razor-sharp,narrow depth of field obtained with this tiny sensor. Buuuuutttt,given this tiny sensor, as Shakespeare would say, I do smelleth theodor of strong fertilizer issuing forth from yon marketingdepartment. Focus on one part of the image after the shot? Evenwith an f/2.0 lens in front of it, at that sensor size the whole imageshould be in focus. Perhaps blur everywhere else after the shot?Why, wait a minute . . . you could just do that in software, nowcouldnt you?


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REFERENCES:

R. N. Clark: The Signal-to-Noise of Digital Camera Images and

Comparison to Film

R. N. Clark: Digital Camera Sensor Performance Summary

R. N. Clark: Procedure for Evaluating Digital Camera Sensor Noise,Dynamic Range, and Full Well Capacities.

P. H. Davies: Circles of Confusion. Pixiq

R. Fischer and B. Tadic-Galeb: Optical System Design,

2000, McGraw-Hill

E. Hecht: Optics, 2002, Addison Wesley

S. McHugh: Lens Diffraction and Photography. Cambridge in Colour.

P. Padley: Diffraction from a Circular Aperture.

J. Farrell, F. Xiao, and S. Kavusi: Resolution and Light SensitivityTradeoff with Pixel Size.

P. van Walree: Depth of Field

Depth of Field An Insiders LookBehind The Scenes Zeiss CameraLens News #1, 1997

http://en.wikipedia.org/wiki/Circle_of_confusion

Depth of Field

Formulas: http://en.wikipedia.org/wiki/Depth_of_field#DOF_formulas

R. Osuna and E. Garca: Do Sensors Outresolve Lenses?

T. Chen, et al.: How Small Should Pixel Size Be? SPIE

Roger Cicala

February, 2012

cicala, roger - sensor size matters

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