Notes on Image Quality, Sensor- and Pixel Sizes

Figure 1: Image by Pentax

There is more to camera sensors than merely the number of effective pixels.

When I compare specifications for my three older compact cameras and my wife's somewhat newer, I find amongst others the following information: 

Table 1: Selected specifications for our household's "current compact camera park"

Of these specs, we can readily understand the image size numbers. They are the dimensions in width and height of our pictures and multiplied together, they give us the "pixel sizes" that you will always see advertised (i.e.: here we get in rough numbers 5, 5, 4 and 7 mega. pixels)

Why I mention lens specifications here, when this is supposed to be a note on sensor and pixel sizes will become obvious soon; suffice to say now, that optical and sensor specifications are intimately linked together in a well designed digital imaging system.

But the sensor types then; what is the meaning of 1/1.8-inch, 1/2.5-inch and 1/2.33-inch??? The "inch" indicate that it has got something to do with the physical dimensions of the CCDs and that is exactly so: They are a kind of technical slang left over from the days of TV cathode ray tubes. There is no direct mathematical correlation between type designation and absolute size, but it is a unique designation that one can look up in a table and below are shown some of the most frequently applied sensor types in compact digital cameras.

Table 2: CCD sensor types and their dimensions

But before that, we had better refresh some trivial but important facts about lens sizes and focal lenghts. Firstly, it shall be remembered that a lens not only "bends" the light for us to produce an image; it also serves as a "light-bucket" and the larger it is in absolute size, the more photons / the more light will it collect for our camera and sensor:

Figure 2: Light capture from a remote, point-like source as function of absolute lens aperture

Figure 3: Image size as function of lens focal length

Figure 4: Sensor/image size as function of lens focal length for a given field of view

Let us take a quick "historical overview": I got my first digital camera, the Olympus C-900 Zoom in 1999. It had a 1/2.7-inch CCD and had provided an image size of 1280 x 980 pixels in uncompressed TIFF or best JPEG-mode. Focal lengths and ratios were between 5.4 mm, f/2.8 and 16.2 mm, f/4.4. Table 2 then lets me calculate that this CCD had some 240 pixels per millimetre (mm).

Table 3: Sensor dimensions, relative pixel sizes and image sizes (in pixels and megabytes) for selected cameras

To begin with, let us see the difference between the Olympus C-50 Z and the mju 760: We got 40% more pixels. Great, then we also got 40% better resolution? No, not quite so, because the 1/2.3-inch sensor size is only 86% in linear dimensions compared to the dimensions of the 1/1.8-inch CCD. This means that while we have to magnify the image from the C-50 Z by a factor of 5 to reach a print size comparable to standard 35 mm film, we have to magnify that of the mju 760 by a factor of 5.8, c.f. Table 3 above.

This is the linear magnification required. By area, the smaller sensor is only 74% the size of the larger. In other words, one might say that we spend 36% of the extra pixels to compensate for the extra magnification required to reach a comparable print-size.

The above issue may in a certain sense be considered as related to the issue of proper sampling. By sampling we mean how many pixels it take to record a (small object) properly. If we are to capture a small, bright circular disk on a sensor with large pixels compared to the image size of that disk chances are that photons will be captured on only a few pixels and hence, look oddly and angular shaped. In this case, we need smaller pixels to record the image properly. This is illustrated in the example below:

Figure 7: Photos of star Castor in Gemini (The Twins)

Left: 8 sec. exposure at 7.8 mm focal length - Right: 8 sec. exposure at 23.5 mm focal length

Both pictures captured with Olympus C-50 Z at ISO 320

For further comparison I have inserted a similar picture of another star (Arcturus) captured with an entirely different system: A Pentax *ist DL equipped with a 350 mm f/5.6 mirror tele lens but enlarged to about the same stellar disk-size:

Figure 8: Photo of star Arcturus in Bootes

Image captured with a Pentax *ist DL camera and a Tamron SP 350 mm f/5.6 catadioptric lens

2 sec exposure at ISO 400

"Well", you might say, "I can understand that pixels must not be too large for a given set of optics to achieve proper sampling but, surely, I can make my pixels as small and get as many as possible - for my particular overall sensor size - as technological advances allows"? Again, yes and no. We are discussing a double-sided truth because there are also other things such as sensitivity and noise to consider..........

Furthermore, you should be aware that the reasoning about four times exposure times for the smaller pixels were based upon the assumption that the total number of photons was the same in the two cases. But that is just not the case in practice. Take a look at the absolute apertures calculated in Table 3, (they are easily computed as the focal length divided by the f-number). The newer cameras have apertures near to 2 mm at the wide-field settings of the zoom lens, while the older have apertures near to 2.8 mm. Since the number of photons available is directly proportional to the open lens area, we see that only (2/2.8)² = 51% of the photons available for the older cameras are available for the newer ones. This is not the "CCD's fault". It is the overall design goals for the cameras that dictates this development. Again we see, that CCD- and optical characteristics cannot be dealt with independently.

You might of course then ask, why the manufactures do not increase lens sizes to get a higher, effective aperture. This is a question about cost and manufacturing techniques. It is very difficult - or at least costly - to manufacture a highly curved lens - i.e. a with short focal length - with a large surface. DSLR owners who can change their optics "at will" may confirm that glass may indeed be as very costly commodity: A high-quality, large aperture wide-field lens for a DSLR may easily cost more than a kit of a camera-body + run-of-the-mill zoom lens itself !

We may now begin to understand, why contemporary cameras of the very compact type and with many-many-megapixels are acclaimed to give excellent pictures in well lit outdoor scenes, while indoor shootings at ambient light may sometimes be characterized as somewhat disappointing.........

......and then there is also an issue about noise.

The problem with noise in digital photography is, as I understand it (and I am only a lay.-man), a three-headed monster:

Firstly, you have "hot" or "stuck" or "dead" pixels. This may not really be "noise" in the strict, physical sense of the word, but for us as consumers, it may be as annoying for our pictures as "real noise": Due to almost inevitable tiny flaws in the manufacturing process, a few pixels will not respond to incoming light the way they should. "Hot" or "Stuck" pixels will give excessively high read-outs upon exposure to light, while "Dead" pixels will not respond to light at all. "Dead" pixels will usually not be very prominent in your image and there is nothing much you can do about them. "Hot" or "Stuck" pixels will show up in your picture as highly localized small dots of light (often coloured) covering some 3-5 adjacent pixels. The effect usually becomes pronounced after a couple of seconds of exposure - that is, at long exposures in low-light situations.

As said, this is a manufacturing quality issue and is not dependant upon sensor- or pixel sizes or -design as such. The effect may change over time as the CCD ages and it may also be dependant upon exposure time and temperature. For critical applications, you may eliminate this effect by taking a "Dark Frame" at the same exposure time, ISO-setting and temperature and subtract that dark frame from your image. Since the effect may vary as the CCD ages, the dark frame should preferably be made immediately after the exposure of your image. Some cameras have this procedure built-in as an automated noise-reduction feature as soon as longer exposure times (typically from 2 seconds and up) are being used.

Figure 10: Hot pixels  usually appear as point-like light sources

Olympus C-50 Z image of belt stars in Orion

for details, see Figure 11 below

Figure 11: Automatic (aggressive) noise-reduction or not?

Belt stars and sword in Orion shot with:

a.: Olympus C-50 Z at 7.8 mm FL f/2.8; 8 sec. exposure at ISO 160

b. Pentax Optio 550 at 7.8 mm FL f/2.8; 2 sec. exposure at ISO 400

for further explanations see text below

And as we have learned above, smaller pixels have a lower sensitivity than larger ones. Therefore one requires more light one way or the other before the smaller pixels can build up a decent picture. Again, we see that smaller cameras may have trouble with low light situations where DSLRs with their generously large sensors, pixels and optics perform to the photographers' creative desires. So, complaints about low-light performance in the smaller cameras may not be attributable to poor craftsmanship from the designers' or manufacturers'  side but rather to the laws of nature.

This noise increases (the deviations from the proper signal value grow) as the number of captured photons grow. But it only grows proportionally with the square root of the number of photons, while the signal itself grows proportionally with the number of captured photons itself. Hence the signal-to-noise ratio grows (the quality of the signal grows) proportionally with the square root of the number of captured photons: Signal-to-noise-ratio = S/N = P / sqrt(P) = sqrt(P), where P is the number of photons captured during the exposure. It is the a bit the same as with the 1912 versus 478 raindrops above: You will expect a higher accuracy from you rain gauge the larger the sampling area (aperture) is and thus, the more raindrops that you collect. In mathematical terms we talk bout the requirement to have "a statistically significant sample" (of all the raindrops that fell to the ground) to work with.

Figure 12: Pictures of clear, blue sky and (statistical) image noise

a. Olympus C-50 Z photo; b: Pentax Optio 550 photo

Upper part: Crops of un-processed, un-enlarged original images

Middle part: Crops of the above, greatly enlarged but otherwise unprocessed

Lower part: Same crops enhanced using AutoContrast in PhotoImpact

Figure 13: Photos of the night sky (Orion)

a: Olympus C-50 Z shot; 8 sec. exposure at ISO 160 b: Pentax Optio 550 shot; 4 sec. exposure at ISO 100

Upper parts are crops of of original images merged and enhanced using Level in PhotoImpact.

Lower parts are crops, highly enlarged from the above.

Click on image to see more details

The two pictures in Figure 13 are not fully comparable (exposure x ISO being much higher in a than in b), but that is also not the main point. Here's the story I want to tell: Normally, unprocessed images straight out of the camera take about the same amount of disk space, around 2 - 2.5 MB. And, indeed, so do the original images of the otherwise "blank" bkue sky used for Figure 12 above, because, as we saw, there are subtle differences in the colour values from pixel to pixel in these images. However, in these shots, the original Olympus shot occupies 2 mega bytes, while the Pentax shot only occupies a little less than 200 kilo bytes - i.e.: 10 times smaller ! Clearly something has happened here. The images have been enhanced quite a bit, as one usually has to for astrophotos on small CCDs in order to more than just the brightest stars. But the Olympus image responds quite different than the Pentax to this post-processing: In the Olympus picture the image-noise becomes obvious, whereas the Pentax image has become a flat, basically 2-bit black and white image.

So what is the explanation? Clearly, from all other comparisons that we have made and the knowledge we have compiled so far, the CCD cannot be that different (in fact, for these two camera models, the CCD manufacturer was one and the same). The answer lies in the different ways manufacturers deal with image noise in small pixels - particular at the lower ISO settings.

Figure 14: Schematic presentation of noise sources in a digital image

Once again, the manufacturers may build in algorithms that allow for more advanced noise removal in the processing within the camera before the final image is delivered. But to me, this is a dubious approach as you will inevitably also level out subtle differences - such as texture - that are real, c.f. Figure 13.b above. Here, the noise reduction has been so efficient that I am am left wit a velvet black night sky (which it never is at my place) at the expense of extinguishing all but the brightest stars . Another example from the realm of macro photography is shown in Figure 15.

I certainly prefer to have as much differentiation as possible to work with at first and then do the noise reduction at a later stage. You may pick up a beautiful stone at the beach and polish it vigorously to get a nice, silky smooth surface. But that smooth stone will not tell you what pebbles and stones at the seaside are truly like.

Figure 15: A closer look at my handkerchief

a. Cropped and enlarged part of an image straight out of my camera (Pentax Optio 550 in macro mode - 1/1000 sec f/7.7 at ISO 200)

b. Same part after very aggressive (manual and deliberate) noise reduction in PhotoImpact

Irrespective of all that is said above about pixel sizes, the higher the number of pixels we have the more information will our digital image contain - simply because of the increased number of colour levels that we have to define the image. Right?

Of course that is right - to a certain extent!

If we only had one large pixel covering the whole of our CCD area available we would at best get information about the average grey scale (i.e. between black and light) level of light available for our exposure. If we had four, one red, one blue and two green, we might at best get the average light temperature (colour) too - whatever sense that would make? So, of course we need many, many more pixels to define a proper image, and the more we add the better we are off.

But remember what we have learned above: That really only holds, if we are allowed to increase our sensor size and optical size without limit and only provided that we carefully match sensor/pixel size and optics. But in practice we do impose constraints in respect of camera dimensions and sensor sizes. Further, we have seen that the smaller the pixels get, the poorer will our signal-to-noise ratio be.

This leads me to one, last note on pixel sizes and image quality: In normal consumer use, output images are of the JPEG file format. File sizes are typically around 1.5 MegaBytes (MB) for a 4 Megapixel (MP) camera; 2-2.5 MB for a 5 MP camera; 3.5 for a 7 MP camera and 6 MB for a 12 MP camera.

However, the maximum limit in information contents for a picture of a given pixel sites is 3*8 bits (256 levels) or 3 bytes (1 byte = 8 bit) times the number of effective pixels used to produce the image. If you consult Table 3 above, you will find the maximum image sizes in MegaBytes for all the cameras listed there. Thus, a 5 MP camera will have around 14 MB as maximum image file size while a 12 MP camera will have around 34 MB as the maximum image file size. So what happens with all this theoretically available information when going from 34 MB maximum limit to a practical output of 6 MB for a 12 MP camera? The answer is, that this information is being lost during reduction and compression in the camera's internal routines for production of the final JPEG-image. This is because JPEG is a so-called lossy file format: Producing a JPEG picture involves compression of the original image data by grouping pixels of slightly varying colours and assigning each such group a single average colour value. The principle is illustrated in the following schematics:

Figure 16: Principle for lossy image (JPEG) compression

Now, my older Olympus and Pentax compact cameras provide me with the option to have my image output as uncompressed 8-bit TIFF-files, i.e.: they represent the original image and no information is lost and they do provide files that are about 14 MB large! Modern DSLR cameras such as the two types mentioned in Table 3 do not provide uncompressed TIFF-images as an option - alongside with JPEG - but rather RAW-files which are lossless file types. The RAW format(s) represent an advanced compression technique where data is sorted and packed in such a manner that file sizes are smaller than the maximum file sizes, ( though not as small as JPEG-compression yields ), but when they are unpacked in the imaging software provided with the cameras, the original images may be regenerated without loss in information. One may thereafter save them as uncompressed TIFF or as compressed JPEG at one's own discretion.

But the newer compact cameras in the 7 - 12 MB range then? They DO NOT provide neither uncompressed TIFF, nor lossless compressed RAW - only lossy JPEG! In other words in these newer cameras, information is irretrievably being thrown away.

It is often argued, that 34 MB file sizes are uncomfortably large to work with and store. But DSLR owners are supposed to work with uncompressed TIFF files of the same size (or even twice as large in 16 bit TIFF formats). And why not give consumers the choice of output type so that they may work with the files first and then compress images afterwards? Why 12 MP in the first place??

Part of the explanation may be that all those extra MB of information are in fact used to provide a better definition of the resulting JPEG image "before they are thrown away". However, I also suspect - but this is purely guesswork from my side - that the provision of uncompressed data like with my older compact's is no longer feasible. Perhaps, uncompressed images from a modern compact camera would look strangely noisy, considering what we now know about small pixels and noise ??? I don't know. The camera manufacturers should be able to tell us.

All in all, there is definitely a limit beyond which it becomes senseless to implant more and more smaller and smaller pixels into a constant, and in practice very confined CCD-area. Has this limit been reached? I am not competent to say for sure; the camera designers would know. But to me, the reported problems with sensitivity and noise in low light situations is a hint that we may be close to the limit with the current compact camera designs.