Technical Discussions

Sensor Size Matters – Part 2

By
Published February 5, 2012

Why Sensor Size Matters

Part 1 of this series discussed what the different sensor sizes actually are and encouraged you to think in terms of the surface area of the sensors. It assured you the size of the sensor was important, but really didn’t explain how it was important (other than the crop-factor effect). This article will go into more detail about how sensor size, and its derivative, pixel size, affect our images. For the purists among you, yes, I know “sensel” is the proper term rather than “pixel.” This stuff is confusing enough without using a term 98% of photographers don’t use, so cut me some slack.

I’ve made this an overview for people who aren’t really into the physics and mathematics of quantum electrodynamics. It will cover simply “what happens” and some very basic “why it happens.”  I’ve avoided complex mathematics, and don’t mention every possible exception to the general rule (there are plenty). I’ve added an appendix at the end of the article that will go into more detail about “why it happens” for each topic and some references for those who want more depth.

I’ll warn you now that this post is too long – it should have been split into two articles. But I just couldn’t find a logical place to split it. My first literary agent gave me great advice for writing about complex subjects: “Tell them what you’re gonna tell them. Then tell them. And finally, tell them what you told them.” So for those of you who don’t want to tackle 4500 words, here’s what I’m going to tell you about sensor and pixel size:

  • Noise and high ISO performance: Smaller pixels are worse. Sensor size doesn’t matter.
  • Dynamic Range: Very small pixels (point and shoot size) suffer at higher ISO, sensor size doesn’t matter.
  • Depth of field: Is larger for smaller size sensors for an image framed the same way as on a larger sensor. Pixel size doesn’t matter.
  • Diffraction effects: Occur at wider apertures for both smaller sensors and for smaller pixels.
  • Smaller sensors do offer some advantages, though, and for many types of photography their downside isn’t very important.

If you have other things to do, are in a rush, and trust me to be reasonably accurate, then there’s no need to read further. But if you want to see why those 5 statements are true (most of the time) read on! (Plus, in old-time-gamer-programming style, I’ve left an Easter Egg 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 the effects seen with different sensor sizes are the result of smaller or larger pixels rather than absolute sensor size. Obviously if a smaller sensor has the same number of pixels as a large sensor, the pixel pitch (the distance between the center of two adjacent pixels) must be smaller. But the pixel pitch is less obvious when a smaller sensor has 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 camera’s sensor and the size of its image in pixels. Simply dividing the length of the sensor by the number of pixels along that length gives us the pixel pitch. For example, the full-frame Canon 5D Mk II has an image that is 5616 x 3744 pixels in size, and a sensor that is 36mm x 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 of sensors have square pixels.

To give some examples, I’ve calculated the pixel pitch for a number of popular cameras and put them in the table below.

Table 1: Pixel sizes for various cameras

 

 

 

Pixel size Camera
(microns)
8.4 Nikon D700, D3s
7.3 Nikon D4
6.9 Canon 1D-X
6.4 Canon 5D Mk II
5.9 Sony A900, Nikon D3x
5.7 Canon 1D Mk IV
5.5 Nikon D300s, Fuji X100
4.8 Nikon D7000, D800, Sony NEX 5n, Fuji X Pro 1
4.4 Panasonic AG AF100,
4.3 Canon GX1, 7D; Olympus E-P3
3.8 Panasonic GH-2, Sony NEX-7
3.4 Nikon J1 / V1
2.2 Fuji X10
2.0 Canon G12

A really small pixel size, like those found in cell phone cameras and tiny point and shoots, would be around 1.4 microns (1). To put that in perspective, if a full-frame camera had 1.4 micron pixels it would give an image of 25,700 x 17,142 pixels, which would be a 440 Megapixel sensor. Makes the D800 look puny, now, doesn’t it? Unless you’ve got some really impressive computing power you probably don’t have much use for a 440 megapixel image, though. Anyway, you don’t have any lenses that would resolve it.

Effects on Noise and ISO Performance

We all know what high ISO noise looks like in our photographs. Pixel size (not sensor size) has a huge effect (although not the only effect) on noise. The reason is pretty simple. Let’s assume every photon that strikes the sensor is converted to an electron for the camera to record. For a given image (same light, aperture, etc.) X number of photons hits each of our Canon G12’s pixels (these are 2 microns on each side, so the pixel is 4 square microns in surface area). If we expose 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 by 10 times as many photons, sending 10 times the number of electrons to the image processor.

There are other electrons bouncing around in our camera that were not created by photons striking the image sensor (see appendix). These random electrons create background noise – the image processor doesn’t know if the electron came from the image on the sensor or from random noise.

Just for an example, let’s pretend in our original image one photon strikes every square micron of our sensor, and both cameras have a background noise equivalent to one electron per pixel. The smaller pixels of the G12 will receive 4 electrons from light rays reaching each pixel of the sensor (4 square microns) for each pixel of noise (4:1 signal-to-noise ratio) while the 5DII will receive 41 electrons from each pixel (41:1 signal-to-noise ratio). The electronic wizardry built into our camera may be able to make 4:1 and 41:1 look pretty similar.

But let’s then cut the amount of light in half, so only half as many photons 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 in the camera. And if we cut the light in half again and the SNR is now 1:1 and 10:1. The 5DII still has a better SNR ratio at this lower light than the G12 had in the original image. But the G12 has no image at all: the signal (image) strength is no greater than the noise.

That’s an exaggerated example, the difference isn’t actually that dramatic. The sensor absorbs far more than 40 photons per pixel and there are several other factors that influence how well a given camera handles high ISO and noise. If you want more detail and facts, there’s plenty in the appendix and the references. But the takeaway message is smaller pixels have lower signal to noise ratios than larger pixels.

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

It is very obvious that newer cameras handle high ISO noise better than cameras from 3 years ago. And just as obvious is that some manufacturers do a better job handling high ISO than others (Some of them cheat a lot to do it, with in-camera noise reduction even in RAW images that can cause loss of detail – but that’s another article someday).

People often get carried away with this, thinking newer cameras have overcome the laws of physics and can shoot at any ISO you would please. They are better, there’s no question about it, but the improvements are incremental and steady. DxO optics has tested a lot of sensors for a pretty long time and has graphed the improvement they’ve seen in signal to noise ratio, normalized for pixel size. The improvement over the last few years is obvious, but on the order of 20% or so, not a doubling or tripling for pixels of the same size.

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

 

Other things being equal (same manufacturer, similar time since release), a camera with bigger pixels has less noise than one with smaller pixels. DxO graphs ISO performance for all the cameras they test. If you look at the cameras with the best ISO performance (top of the graph) they aren’t the newest cameras, they’re the ones with the largest pixels. In fact, most of them were released several years ago.

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

The “miracle” increase in high ISO performance isn’t just about increased technology. It’s largely about decisions by designers at Canon, Nikon, and Sony in 2008 and 2009 to make cameras with large sensors containing large pixels. There is a simple mathematical formula for comparing the signal-to-noise ratio for different pixel sizes: the signal to noise ratio is proportional to the square root of the pixel pitch. There is more detail about it in the appendix.

Effects on Dynamic Range

You might think the effects of pixel size on dynamic range should be similar to that of noise, discussed above. However, dynamic range seems to be the area where manufacturers are making the greatest strides – at least with reasonably sized pixels. When measured at ideal ISO (ISO 200 for most cameras) dynamic range varies more by how recently the camera was produced than by how large the pixels are (at least until the pixels get quite small). If you look at DxO Mark’s data for sensor dynamic range the cameras with the best dynamic range are basically newer cameras, not those with the largest pixels.

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

 

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

Effects on Depth of Field

Depth of field is a complex subject and takes some complex math to calculate. But the principles behind it are simple. To put it in words, rather than math, every lens is sharpest at the exact distance where it is focused. It gets a bit less sharp nearer and further from that plane. For some distance nearer and further from the plane of focus, however, our equipment and eyes can’t detect the difference in sharpness and for all practical purposes everything within that range appears to 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 the camera. Pixel size has no effect on depth of field, but sensor size has a direct effect on the circle of confusion, and the crop factor may also affect our choice of focal length and shooting distance. Depending on how you look at things, the sensor size can make the depth of field larger, shallower, or not change it at all. Let’s try to clarify things a bit.

Circle of Confusion

The circle of confusion causes a lot of confusion. But basically it is a measure of how large of a circle appears, to our vision, to be just a point (rather than a circle). It is determined (with a lot of argument about the specifics) from its size on a print. Obviously to make a print of a given size, you have to magnify a small sensor more than a large sensor. That means a smaller circle on the smaller sensor would be the limits of our vision, hence the circle of confusion is smaller for smaller sensor sizes.

There is more depth to the discussion in the appendix (and it’s actually rather interesting). But if you don’t 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 CoC
Full Frame 0.029 mm
APS-C 0.018 mm
1.5″ 0.016 mm
4/3 0.015 mm
Nikon CX 0.011 mm
1/1.7″ 0.006 mm

The bottom line is that the smaller the sensor size, the smaller the circle of confusion. The smaller the circle of confusion, the shallower the depth of field – IF we’re shooting the same focal length at the same distance. For example, let’s assume I take a picture with a 100mm lens at f/4 of an object 100 feet away. On a 4/3 sensor camera the depth of field would be 37.7 feet. On a full frame camera it would be 80.4 feet. The smaller sensor would have the shallower depth of field. Of course, the images would be entirely different – the one shot on the 4/3 camera would only have an angle of view half as large as the full frame.

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

Lens Focal Length and Shooting Distance

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

In the above example, I take a picture with a full-frame camera using a 100mm lens at a subject 100 feet distant at f/4. The depth of field was 80.4 feet. If I want to frame the picture the same way on a 4/3 camera I could use a 50mm lens (same distance and aperture). The depth of field would then be 313 feet. If instead I kept the 100mm lens but backed up to 200 feet distance to keep the same angle of view, the depth of field would be 168 feet. Either way, the depth of field 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 a large 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, can’t we just 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. In the example above the best depth of field I could get with a 4/3 sensor was 168 feet by keeping the 100mm lens and moving back to 200 feet. If I additionally opened the aperture to f/2.8 and then f/2.0 it would decrease the depth of field to 141 feet and 84 feet respectively. So in this case I’d need to open the aperture two stops to get a similar depth of field as I would using a full frame camera.

The relationships between shooting distance, focal length and aperture 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 field calculator is a must. And just to be clear: the effects on depth of field have nothing to do with pixel size, it’s 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 image begins to get soft from diffraction effects. Most of us understand roughly what diffraction is (light rays passing through an opening begin to spread out and interfere with each other). A few have gone past that and enjoy stimulating after-dinner discussions about Airy disc angular diameter calculations and determing Raleigh Criteria. A very few.

For the rest of us, here’s the simple version:  When light passes through an opening (even a big opening), the rays bend a bit at the edges of the opening (diffraction). This diffraction causes what was originally a point of light (like a star, for example) to impact on our sensor as a small disc or circle of light with fainter concentric rings around it. This is known as the Airy disc (first described by George Airy in the mid 1800s).

A computer generated Airy Disc (courtesy Wikepedia Commons)

The formula for calculating the diameter of the Airy disc is (don’t be afraid, I have a simple point here, I’m not going all mathematical on you): \theta \approx 1.22 \frac{\lambda}{d}

The point of the formula is to show you that the diameter of the airy disc is determined entirely by ? (the wavelength of light) and d (the diameter of the aperture). We can ignore the wavelength of light and just say in words that the Airy disc gets larger as the aperture gets smaller. At some point, obviously, the Airy disc gets large enough to cause diffraction softening.

At what point? Well, using the formula we can calculate the size of the Airy disc for every aperture (we have to choose one wavelength so we’ll use green light).

Table 3: Airy disc size for various apertures

Airy disc
Aperture (Microns)
f/1.2 1.6
f/1.4 1.9
f/1.8 2.4
f/2 2.7
f/2.8 3.7
f/4 5.3
f/5.6 7.5
f/8 10.7
f/11 14.7
f/13 17.3
f/16 21.3
f/22 29.3

Remember the circle of confusion we spoke of earlier? If the Airy disc is larger than the circle of confusion then we have reached the diffraction limit – the point at which making the aperture smaller is actually softening the image. In Table 2 I listed the size of the CoC for various sensor sizes. A smaller sensor means a smaller CoC so the diffraction limit occurs at a smaller aperture. Comparing the CoC (Table 2) with Airy disc size (Table 3) it’s apparent that a 4/3 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 we can use before diffraction softening sets in. If the pixels are small they 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 – it’s arguable) pixel widths then diffraction softening can occur. If we calculate when the Airy disc is larger than 2.5 x the pixel pitch rather than when it is larger than the sensor’s circle of confusion things look a bit different.

Table 4: Diffraction limit for various pixel pitches

 

 

 

Pixel Pitch 2.5 * PP Example camera Diffraction at
8.4 21 Nikon D700, D3s f/16
7.3 18.3 Nikon D4 f/13
6.9 17.3 Canon 1D-X f/13
6.4 16.0 Canon 5D Mk II f/12
5.9 14.8 Sony A900, Nikon D3x f/11
5.7 14.3 Canon 1D Mk IV f/11
5.5 13.8 Nikon D300s, Fuji X100 f/10
4.8 12.0 Nikon D7000, D800, Sony NEX 5n, Fuji X Pro 1 f/9
4.4 11.0 Panasonic AG AF100, f/8
4.3 10.8 Canon GX1, 7D; Olympus E-P3 f/8
3.8 9.5 Panasonic GH-2, Sony NEX-7 f/8
3.4 8.5 Nikon J1 / V1 f/6.3
2.2 5.5 Fuji X10 f/4.5
2 5.0 Canon G12 f/3.5

Let me emphasize that neither of the tables above are absolute values. There are a lot of variables that go into determining where diffraction softening starts. But whatever variables you choose, the relationship between diffraction values and sensor or pixel size remains: smaller sensors and smaller pixels suffer diffraction softening at lower apertures than do larger sensors with larger pixels.

Advantages of Smaller Sensors (yes, there are some)

There are several advantages that smaller sensors and even smaller pixels bring to the table. All of us realize the crop factor can be useful in telephoto work (and please don’t start a 30 post discussion on crop factor vs magnification vs cropping). The practical reality is many people can use a smaller or less expensive lens for sports or wildlife photography on a crop-sensor camera than they could on a full-frame.

One positive of smaller pixels is increased resolution. This seems self-evident, of course, since more resolution is generally a good thing. One thing that is often ignored, particularly when considering noise, is that noise from small pixels is often less objectionable and easier to remove than noise from larger pixels.  It may not be quite as good as it sounds in some cases, however, especially if the lens in front of the small pixels can’t resolve sufficient detail to let those pixels be effective.

An increased depth-of-field can also be a positive. While we often wax poetic about narrow depth of field and dreamy bokeh for portraiture, a huge depth of field with nearly everything in focus is a definite advantage with landscape and architectural work. And there are simple practical considerations: smaller sensors can use smaller and less expensive lenses, or use only the ‘sweet spot’ – the best performing center of larger lenses.

Like everything in photography: a different tool gives us different advantages and disadvantages. Good photographers use those differences 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 to larger sensors.
  • Depending on what your style of photography these things may be disadvantages, advantages, or matter not at all.

Given the current state of technology, a lot of people way smarter than me have done calculations that indicate what pixel size is ideal – large enough to retain the best image quality but small enough to give high resolution. Surprisingly they usually come up with similar numbers: between 5.4 and 6.5 microns (Ferrel, Chen). When pixels are smaller than this the signal-to-noise ratio and dynamic range starts to drop, and the final resolution (what you can actually see in a print) is not as high as the number of pixels should theoretically deliver.

Does that mean you shouldn’t buy a camera with pixel sizes smaller than 5.4 microns? No, not at all. There’s a lot more that goes into the choice of a camera than that. And this seems to be the pixel size where disadvantages start to occur. It’s not like a switch is suddenly thrown and everything goes south immediately. But it is a number to be aware of. With smaller pixels than this you will see some compromises in performance – at least in large prints and for certain types of photography. It’s probably no coincidence that so many manufacturers have chosen the 4.8 micron pixel pitch as the smallest pixel size in their better cameras.

APPENDIX AND AMPLIFICATIONS

Effects on Noise and ISO Performance

A camera’s electronic noise comes from 3 major sources. Read noise is generated by the camera’s electronic circuitry and is fairly random (for a given camera – some cameras have better shielding than others). Fixed pattern noise comes from the amplification within the sensor circuitry (so the more we amplify the signal, which is what we’re doing when we increase ISO, the more noise is generated). Dark currents or thermal noise are electrons that are generated from the sensor (not from the rest of the camera or the amplifiers) without any photons impacting it. Dark current is temperature dependent to some degree so is more likely with long exposures or high ambient temperatures.

The example I used in this section is very simplistic and the electron and photon numbers are far smaller than reality. The actual SNR (or Photon/Noise ratio) is  P/(P + r2 + t2)1/2 where P = photons, r= read noise and t= thermal noise. The photon Full Well Capacity (how many photons completely saturate the pixel’s ability to convert them to electrons), read noise and dark noise can all be measured and the actual data for a sensor or pixel calculated at different ISOs. The Reference Articles by Clark listed below present this in an in-depth yet readable manner and also present some actual data samples for several cameras.

If you want to compare how much difference pixel size makes for camera noise, you can do so pretty simply: the signal to noise ratio is 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 pixel pitch, SqRt = 2.9) with the D3X (5.9 micron PP, SqRt = 2.4) and say the D3X should have a signal to noise ratio that is 2.4/2.9 = 83% of the 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 the release of the D700 and the release of the J1.

Effects on Dynamic Range

At their best ISO (usually about ISO 200) most cameras, no matter how small the sensor size, have an excellent dynamic range of 12 stops or more. As ISO increases, larger pixel cameras retain much of their initial dynamic range, but smaller pixels loose dynamic range steadily. Some of the improvement in dynamic range in more recent cameras come from improved Analogue to Digital (A/D) converters using 14 bits rather than 12 bits, but there are certainly other improvements going on.

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 focal length of the lens) such as in macro work and for normal to far distances. Depth of field even varies by the wavelength of light in question. Even then, calculations are basically for light rays entering from near the optical axis. In certain circumstances off-axis (wide angle) rays may behave differently. And after the calculations are made, practical photography considerations like diffraction blurring must be taken into account.

For an excellent and thorough discussion I recommend the Paul van Walree’s (Toothwalker) article listed in the references. For the two people who want to know all the formulas involved, the wikepedia reference 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 were chosen since 8 X 10 prints were common and 10 inches distance placed it at the normal human viewing angle of 60 degrees) a circle of 0.2mm or less appeared to be a point. Make the circle 0.25mm and 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 small that we can’t see it at all).

Even if a photograph is blurred slightly, as long as the blur is less than the circle of confusion, we can’t tell the difference just by looking at it. For example in the image below the middle circle is actually smaller and sharper than the two on either side of the middle, but your eyes and viewing screen resolution prevent you from noticing any difference. If the dots represent a photograph from near (left side) to far (right side) we would say the depth of field covers the 3 central dots: the blur is less than the circle of confusion and they look equally sharp. The dots on either side of the central 3 are blurred enough that we can notice it. They would be outside the depth of field.

To determine the Circle of Confusion on a camera’s sensor we have to magnify the sensor up to the size of an 8 X 10 image. A small sensor will have to be magnified more than a large sensor to reach that size, obviously.

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

Effects on Diffraction

Discussing diffraction means either gross simplification (like I did above) or pages of equations. Frighteningly (for me at least) Airy caclulations are the least of it. There also  is either Fraunhofer diffraction or Fresnel diffraction depending on the aperture and distance from the aperture in question, and a whole host of other equations with Germanic and old English names. If you’re into it, you already know all this stuff. If not, I’d start with Richard Feynman’s book QED: The Strange Theory of Light and Matter before tackling the references below.

If you want just a little more information, though, written in exceptionally understandable English with nice illustrations, I recommend Sean McHugh’s article from Camridge in Colour listed in 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 an Airy disc larger than 1 pixel doesn’t cause diffraction softening, why we choose 2, 2.5 or 3 pixels instead. It’s because the Bayer array and AA filter mean one pixel on the sensor is not the same as one pixel in the print (damn, that’s the first time ever I’ve thought that ‘sensel’ would be a better word than ‘pixel’). The effects of Bayer filters and AA filters are complex and vary from camera to camera, so there is endless argument about which number of pixels is correct. It’s over my head – every one of the arguments makes sense to me so I’m just repeating them.

Oh, Yeah, the Easter Egg

If you’ve made it this far, here’s something you might find interesting.

You’ve probably heard of the Lytro Light-Field Camera that supposedly lets you take a picture and then decide where to focus later. Lytro is being very careful not to release any meaningful specifications (probably because of skeptics like me who are already bashing the hype). But Devin Coldewey at TechCrunch.com has looked at the FCC photos of the insides of the camera and found the sensor is really quite small.

Sensor size of the Lytro Light Field Camera, courtesy TechCrunch.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 the odor of strong fertilizer issuing forth from yon marketing department.” Focus on one part of the image after the shot? Even with an f/2.0 lens in front of it, at that sensor size the whole image should be in focus. Perhaps blur everywhere else after the shot? Why, wait a minute . . . you could just do that in software, now couldn’t you?

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 Sensitivity Tradeoff with Pixel Size.

P. van Walree: Depth of Field

Depth of Field – An Insider’s LookBehind The Scenes Zeiss Camera Lens 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. García: Do Sensors Outresolve Lenses?

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

 

Roger Cicala

Lensrentals.com

February, 2012

Author: Roger Cicala

I’m Roger and I am the founder of Lensrentals.com. Hailed as one of the optic nerds here, I enjoy shooting collimated light through 30X microscope objectives in my spare time. When I do take real pictures I like using something different: a Medium format, or Pentax K1, or a Sony RX1R.

Tweet
Posted in Technical Discussions
← 
Newer Comments  →

  • Hello Roger,

    Unfortunately your statements regarding the effect of pixel pitch are not wholly consistent with results. It appears that for a given sensor size, the generation of the sensor has more significance than the pixel size alone. So if you look at APS-C format sensors across generations, although the D7000 sensor has many more pixels than the Nikon D70, and its pixels are much smaller at 4.73 microns versus 7.8 microns for the D70, the D7000 delivers higher quality images at higher ISOs with lower noise. So this immediately contradicts your first claim.

    Regards
    Dibyendu

  • Roger Cicala

    As I mentioned, oh, about a dozen times in the article, this isn’t meant as an deep discussion of physics, simply as an overview with the notation, again several times, that there are a lot of arguments, different opinions and exceptions. I tried, within the scope of limited space (which I greatly exceeded) to give some secondary sources that could take people further into the fun journey of arguing optical physics, quantum electrodynamics, signal conversion and any of a host of topics which this post was only intending to touch on.

    But if I understand your reference to pixel size claims, I believe I used Ferrel and Chen as the primary sources for that statement, not Clark. I would never try to explain that Roger Clark is wrong. But there are other, equally qualified people who disagree with him. Am I qualified to say who is correct? Absolutely not, my doctorate isn’t in optical physics, theirs are (or at least closer to it than mine).

    I didn’t have a premise in this blog post. Simply wanted to discuss that there were a lot of things that matter about sensors and pixels, particularly for readers who are being told this new camera has a big sensor when in fact it doesn’t, or on an even more basic level that 16 megapixels are 16 megapixels no matter the sensor size. If I had a premise for this article, that was about it.

    Roger

  • knickerhawk

    Roger Clark, who is cited as the primary authority for the pixel size claims, has this to say:

    My Apparent Image Quality (AIQ) model, discussed in more detail in Digital Camera Sensor Performance Summary shows an optimum pixel size (Figure 9). For cameras with diffraction limited lenses operating at f/8, the model predicts a maximum AIQ around pixels of 5 microns. Many APS-C cameras are operating near that level, but as of this writing, full frame 35 mm digital cameras have a way to go (peaking near 33 megapixels).

    That statement pretty much blows up the entire premise of your blog post, Roger. You should either explain why Clark is wrong (good luck with that) or retract your blog post because all of the technical experts who actually know what they’re talking about (including presumably the engineers at Nikon, Sony, Canon, etc.) don’t agree with you.

  • b8004

    This site/blog is becoming my new dpreview. Since acquisition by amazon dp site isn’t going any better 🙁

  • Carl

    Alek, thanks for the info. Your link is nicely presented and written. After perusing your website, you appear to have a lot of time to review camera gear and go on safari, so I applaud your enthusiasm and your travel experience! I want to travel to Europe myself, to go on Formula One safari, haha…

    However, your link doesn’t address lens internal dust at all…kind of deceptive of you! You mean well, but trust me, what I’ve seen isn’t dust on the sensor. It appears in different areas with different lenses, and is repeatable. And the same “field of dust” could be seen as being enlarged by using a teleconverter (i.e., the same pattern of particles is spread farther apart and wider on the picture, with the ones at the outer edges not appearing at all, after attaching the TC…clearly the field of dust was being scaled up).

    Dust on the sensor’s surface would NOT do that. Also, it seems to me that a narrower aperture wouldn’t show dust on the sensor’s surface more clearly than a wide open aperture would (nor would it change the size and focus of the dust…nor would it change from no dust, to some dust, to different dust, back to none again…by changing to various lenses).

    The clearest explanation for this I can come up with, is that sensor surface dust is imaging itself as a “contact print” would, irrespective of the lens and aperture in front of it…is it not? Or are there laws of optics rewriting themselves, to make the burden more “fair” for everyone? (ok that’s a political joke!)

    So anyway, I still wonder if anyone has noticed lens internal dust, and if so, doesn’t it frustrate you that you know it’s there, even if it hides at wider apertures? I noticed this on the month-old (practically new) supertelephoto lens I rented from LR back in October. Once I attached it to my camera, it was never unattached (other than to try the TC). Front and rear lens elements appeared as clean as any I have ever used, the lens has weather sealing, and I performed the change indoors. The pattern of dust was not the same as that of any other lenses where I noticed the phenomenon, and rather they all appear different, with some having basically none at all. Otherwise, the above supertelephoto lens delivered the best overall image quality of any lens I have ever tried. Dust or not, a boat-load of money is the only thing keeping me from buying such photographic pleasure!

  • Carl: rest assured other people notice “internal dust” – probably more frequently dust on the sensor. I got a little carried away and did a whole analysis at different apertures and before/after – http://www.komar.org/faq/camera/canon-sensor-dust-cleaning/

    A real world example (the HULK at Devil’s Tower) is shown at the bottom.

  • Frank LLoyd

    Lets look at your ‘executive summary’:

    Noise and high ISO performance: Smaller pixels are worse. Sensor size doesn’t matter.

    Absolute nonsense, the reverse of what is true. No real demonstrable correlation with pixel size, it’s all about sensor size. Maybe you picked that one up from Roger Clarke’s free and easy swapping of the twi thins.

    Dynamic Range: Very small pixels (point and shoot size) suffer at higher ISO, sensor size doesn’t matter.

    Absolute nonsense. Point and shoot sensors suffer solely because of their small size – their efficiencies are generally above those of larger pixelled sensors.

    Depth of field: Is larger for smaller size sensors for an image framed the same way as on a larger sensor. Pixel size doesn’t matter.

    A dodgy statement. The truth is that you require different f-numbers with different size sensors t achieve the same DOF. A large sensor can achieve as deep a DOF as a small one, so long as the lens has a high enough f-number available.

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

    Absolute nonsense. The diffraction blurring for a aperture of a given ‘width’ given the same angle of view in the final image is the same for any format. Pixel size has no effect on diffraction blurring, though small pixels might allow a camera to render a diffraction blurred image slightly more crisply than would larger ones.

    Smaller sensors do offer some advantages, though, and for many types of photography their downside isn’t very important.

    In the same size sensor, it seems like the only downside is readout times and file size. So, his statement is not wrong, but he has completely misrepresented the downside.

  • Carl

    And finally, how come no one other than me, seems to have noticed a lens’ internal dust that shows up in the image, as apertures get closed down a lot (let’s say f/32 on a telephoto lens)? I admit you kind of have to be shooting something uniform, and diffusely lit up like sky, to see them well…I do apologize if no one finds that relevant to the larger discussion of sensor size or resolution!

  • Carl

    Looking at DXO Mark’s sensor comparisons, it seems odd that Nikon was able to achieve such a huge increase in ISO noise performance (at least with the method used in the DXO test), going from the D3…to the D3s, with only what, two years between the release of these cameras? They both have the same pixel size, but obviously there was improvement…perhaps more in the hardware than the processing side? I suppose Nikon could have also held back on some of the innovation of the D3, only to provide it later with the D3s, to help encourage users to buy the new one? I don’t see the “mere” 720p video ability of the D3s, as enough of an advantage over the D3 alone (especially not to pro sports photographers who don’t really buy such expensive cameras to shoot video with)…I could be wrong.

    The S/N ratio is really generated by the hardware, and only dealt with by software after the fact. I suppose the A/D conversion could the main factor? (It certainly makes a difference in audio.) The D3s still stands at the top in the ISO category at DXO, so it will be interesting to see if they measure the new D4 (with its smaller pixels) as better than the D3s, in the ISO category. They’re both still using 14 bit A/D conversion, though. Or maybe I’m wrong…is the D4 using 16 bit A/D conversion, but writing the NEF file at only 14 bits (to save space and keep the speed fast enough)?

  • Carl

    Roger, good point about the Lytro camera! I learned long ago, that the methods to the madness of “college professors” who “suddenly see the light” of innovation, and do the public a “favor” by bringing their innovation onto the marketplace, are practicing the black art of selling snake oil. Their products appeal to the less technically sophisticated…to those who pay little attention to what actual industry is doing. But free market capitalism always wins in the end…which flies in the face of the philosophy of 99% of college professors!

    MY QUESTION about diffraction (I only want the simple answer…but make it longer than “yes” or “no”…haha): Is the apparent softening of a lens as I close down aperture (let’s say on two of my fast lenses, a 58mm f/1.4, and a 135mm f/2…both are obviously less sharp by f/10 or so on my 15 MP aps-c)….TOTALLY due to diffraction effects of the aperture itself, or is there more to it than that? Is there some kind of reaction (or interference) the various glass elements (and their overall design/layout) pose on the light, relative to the size of the aperture opening, as it decreases in size? I ask because, diffraction seems like it would be present in a “pinhole” camera with no glass lens elements, would it not? And yet similar lenses of various brands, with even the same focal length, can exhibit different amounts of apparent “diffraction effects” at the same aperture…at least from the tests I have looked at online.

  • anon

    btw, where does the Leica M9 fall in regard to pixel size?

  • Roger Cicala

    Hi Xaris,

    I actually should have said “at wider apertures than it would on a larger sensor with larger pixels”.

    Roger

  • At the beginning you write:
    “Diffraction effects: Occur at wider apertures for both smaller sensors and for smaller pixels.”

    but I guess you mean “…Occur at narrower appertures…”

    I liked the section about the Circle of Confusion.

    Nice work!

    Thanks,
    Xaris

  • Exceptionally well written!

  • Roger Cicala

    Samuel – well done! You made it much simpler and more straightforward than I did.

    Roger

  • regarding DoF formulas, and how going back and forth between formats makes it impossible to work out what the shot will look like without a DoF calculator:

    I have my very own DoF calculator

    and still I call: nonsense!

    the difficult part is having one frame of reference: knowing how DoF and perspective will look with different focal lengths and apertures on a full frame camera

    but once practice makes you know that, translating it into a different format is straightforward: just multply by the crop factor, like you do with focal length

    Say you have three different cameras: a full frame stills camera (1x crop factor), an APS-C stills camera (1.6x crop factor) and a 2/3″ camera (3.9x crop factor). Resolution is the same on all of them. Glass is ideally perfect on all three of them. You plant your tripod on a particular spot, and shoot from there using all three cameras. Then, you’ll get exactly the same images (FoV, DoF, exposure, etc), if you use the following settings:
    * 50mm lens set at f/5.6, 1/50s and ISO 1600 on a full frame camera
    * 31mm lens set at f/3.5, 1/50s and ISO 600 on an APS-C camera
    * 13mm lens set at f/1.4, 1/50s and ISO 100 on a 2/3″ camera

    a few more details, and some sample shots to prove this, here:
    http://www.similaar.com/foto/doftest/doftest.html

  • Yet another informative article Roger – great job again.

    In your “Effects on Dynamic Range”, you wrote “When measured at ideal ISO (ISO 200 for most cameras)” … how ’bout a future article about why/what is the ideal ISO?

    For instance, I’ve read the Canon C300 has a “native” ISO of 850 … but I believe that is an exception to most DSLR’s such as my Canon 7D.
    alek

    P.S. Verryyyy interesting “Easter Egg” on the Lytro Light-Field Camera … now that I think about it, yea, how they heck could they be getting such narrow depth of field with such a small sensor – me thinks some trickery may be going on! 😉

  • Roger Cicala

    Mike, I’m going to steal your “physics really does not CARE about opinions, because you can’t fabricate an opinion” quote. I absolutely love it.

    It’s above my qualifications, but I do think microlenses work around some of the light blocking that occurs with CMOS sensors. I’m not certain how much. And backlight will be better, but again, I’m not sure how much (although I’m sure it will be less than 100%). And there’s the whole organic thing that Fuji is doing. Bottom line is the next couple of years should be exciting.

    Roger

  • Roger,

    Thanks for your clear explanation of a very complex topic concerning image sensors – bravo! I think when you separate “commercial” from “science” or even opinion from fact, the naked truth become so refreshing!

    Yes, I have an INTEREST! With over $30K in digital cameras, lens, printers, computers and software, I am on the edge of my seat trying to reach out and grab a better resolution, a better low light solution and hopefully both in one camera, and all in an effort to improve the IQ of the large prints I produce. So YES, pixels are important to me and I am starting to lean towards MF (medium frame) solutions as a method of getting better image files. I can say this, that after 20 years of working as an engineer in semi-conductor fabs, I realize that physics really does not CARE about opinions, because you can’t fabricate an opinion.

    So here is my question – Back Illuminated sensors – do you think designers will be able to shrink pixel size perhaps 30% or more while maintaining IQ?

    According to what I have been able to read, the front illuminated CMOS sensor suffers from a percentage of the light gathering pixel being shaded by circuitry layers that exist ABOVE the pixel sensor. Hence a 6.5uc pixel may only have an effective light gathering surface area of 4.uc – 5uc depending upon above the pixel layer circuit obstructions.

    I would love to hear what you may have heard concerning back illuminated image technology and how this might positively affect future resolution capabilities in FF 35mm Cameras. It seems to stand to reason that if 6uc pixels can only net 4uc of light gathering (due to circuit obstructions), then the published signal to noise ratios are actually worse seeing that so many photons can’t reach the image sensor. If this assumption is correct then it appears the maximum number of pixels a FF “back illuminated” sensor can house while maintaining high ISO/Low noise would be somewhere in the neighborhood of 24mp to 30mp.

    Again this assumption would be based upon a back illuminated pixel being able to see 100% of the incoming light (no obstructions) and so in reality a font illuminated 6.5uc really only ever equaled ~4uc so theoretically a ~4uc “back illuminated” pixel size would gather the same light as the larger pixel hence allowing designers to decrease pixel size while maintaining current larger pixel size IQ.

    Any thoughts/comments on this would be greatly appreciated.

  • Roger Cicala

    Thank you Jay! I typoed that (probably trying to transcribe my horrid handwriting). It should be 18, not 15. (I split the difference between the smaller and larger APS-C sensors and used 27.2mm = 18.13)

    Roger

  • Jay Frew

    Thanks for the article Roger.

    I think there is an error in Table 2: Circle of Confusion for Various Sensor Sizes.

    Using the formula listed in your article (d/1500 = CoC), the CoC for APS-C sensors should be closer to 0.018mm.

    Of course, that figure depends on the actual APS-C sensor size (as they are not all the same). For example, my 40D sensor diagonal = 26.68mm while the Nikon D3100 sensor diagonal = 27.76mm

    Cheers! Jay

  • great article, but I have some doubts…

    for a start: why does diffraction depend on aperture measured in f/, instead of measured in mm?
    the hole through which light has to pass at f/10 on a 300mm lens is 10 times wider than the hole through which light has to pass at f/10 on a 30mm lens

    maybe on a 300mm that hole has to be farther away from the sensor and this neutralizes the difference? or maybe you gave us the numers for, say, a 50mm lens?

  • Roger Cicala

    David,
    I totally agree with most of what you say, and would add that sensor microlenses make a huge difference. I think DxO’s downsampling to 8 Mpix is a step too far, but the principle that smaller, high frequency noise from smaller sensels causes less interference with resolution is valid, no question. But the article had gotten so long and the topic would have added another 1,000 words or so – and the principle isn’t changed. I’m sure the new full frame cameras will be better than the old, and better than everything else – except probably the Ds3 and D700 with those huge pixels. If they’re better than those, though, I’ll go back and revise the article.

    Roger

  • Roger Cicala

    Vaibhav,

    I don’t know where sensors go from here, and although I’m sure we haven’t reached absolute limits perhaps we are nearing them. But I think your comments are a superb summary of where we probably go. Thank you!

    Roger

  • an avid reader of yours

    Well done. Thank you, again.

  • An interesting point about the Lytro. You *could* use software to simulate shallow depth of field in a conventional image. But you have to guess distance information and unless the scene is geometrically simple, it usually doesn’t look quite right. However, if you measure the light field, which is what the Lytro camera does, you have all the distance information you need to make it look just like the real thing! You can have as much or as little depth of field as you want, regardless of the sensor size.

  • While I enjoyed much of this article, the discussion of pixel size and noise (high ISO performance) is confused and perpetuates the myth that more megapixels equals more noise. Yes, smaller pixels have more noise than bigger pixels. And if you are comparing images *at the pixel level*, then the lower megapixel sensor will generally outperform the higher megapixel sensor. But except for the pixel peepers, we tend not to look at images at the pixel level. We tend to downsample them and view them online, or print them. And in that case, all other things being equal, there is no noise disadvantage to having more megapixels. Indeed, a higher megapixel camera collects more information than a lower megapixel camera, which can then be used to average out the noise.

    DxOMark recognises this, and when making their ISO comparisons they essentially downsample all images to 8 Mpx.

    There is, however, a more subtle factor, which is that low megapixel sensors tend to have fewer wires and other areas of inactive silicon on their surface, and are therefore a little more efficient at collecting light, though this is a technological factor that is clearly becoming less important with developments such as back side illumination.

    You claim that “If you look at the cameras with the best ISO performance (top of the graph) they aren’t the newest cameras, they’re the ones with the largest pixels. In fact, most of them were released several years ago.” But these are full frame cameras. And there hasn’t been a full frame camera released and tested by DxOMark for a few years. The 5DII, 1DsIII, D3s, D3x and A900 are all about three or more years old. It will be interesting to see how the 1Dx, D4 and D800 fare in the next round of testing to see how much the full frame sensors have improved, particulalry in the area of high ISO performance.

  • Great, great, great. You could charge some pennies for your articles. All the articles are interesting, informative and very well written. Thanks for your work!

  • anon

    you’re my hero! 😉

  • Vaibhav Haldavnekar

    Roger an excellent synopsis of sensors and laying the bricks and mortars of the eye of the camera. After the first article I was eagerly waiting for a summation of your research with this article and you have performed it as succinctly as possible.

    My point of the issue has more to do with the development of digital sensors. Am I assuming incorrectly if I say current digital sensors have reached their peak of development based on pixel pitch? Is this why the top cameras from both Nikon (D4) and Canon (1DX) dialed back on the pixel pitch from their respective predecessors, a situation unheard of just 2 years ago, to concentrate on working on other frontiers of the camera system?

    Chen’s research is an excellent simplified yet theoretical approach, but one point where the research falls short (even authors acknowledge) is by bringing into context the effects of lenses, which of course is covered by Osuna and Garcia.

    So where do manufacturers go from here, if the above two researches among other similar ones are valid? A – bring high quality lenses to market – seeing that 85% jump in EF 24-70 II is now more palatable after above readings. B – start the race of accessories, similar to automobile manufacturers when limits of combustion engines, drivetrain are more or less achieved plateau, the current battle is for getting media, 12 gear transmissions, 25 speaker sound systems, 256 way power seats into the cars. Or C something out of extraordinary that would defy existing laws of optics.

    One thing remains – i.e., no matter how much science we put in the cameras, if the spirit is not there in the photographer, the pictures will be mechanical. Just ask Adams, Bourke-Whites of the world who used far inferior systems than we are currently calling cutting edge. Modern photographers seem to be more obsessed with the science part than the spirit part of this hobby.

←  
Newer Comments  →
Follow on Feedly