Monday, September 2, 2013

Cameras in Phones - what do we really need?


An awful lot is being said about mobile phone cameras just lately; and we have HTC to thank for opening the conversation with the introduction of their HTC One which has half as many pixels at twice the size of anyone else's. Before we begin I'm going to get some ground rules. I won't use marketing terms; so I will talk about how many pixels a camera sensor has, and what size they are. You won't hear me talking about mega- or ultra- anything. Next is that I will show my meaning with diagrams - I'm a visual person and it helps me to explain. Please bear with me on this post; there's a lot to read but it's worth it at the end.

A digital camera uses a lens to focus an image onto an oblong of special material which has a number of sensors on it; each sensor is called a pixel and usually contains three sub-pixels; a red, a blue (actually two blues but don't worry about that) and a green one. Each of these sends a signal to the camera depending how much light of that colour is falling onto it. Bigger pixels produce a bigger signal for the same amount of light than smaller ones. When signals are small, the amount of noise (erroneous signal levels produced simply by electrons moving around) is a bigger percentage of the whole signal because noise is a constant backdrop. When the signals are bigger therefore, it's easier to pick out the signal, from the noise. More noise means that the signal produced by a smaller pixel is less accurate which means the final photo may not have exactly the same colour from each pixel receiving the same light.

Camera sensors line up their pixels in rows and columns - and the camera's rating is often quoted by counting them. For instance a 10MP camera contains ten million pixels (roughly). These are arranged in a rectangular grid with a side length ratio of 16:9 - so that's 4213 pixels across and 2370 pixels high. If you have a sensor which is 7mm across, each pixel is 7/4213=1.662 microns across (microns = thousandths of a millimetre).

In the real world, standard sensor sizes and pixel sizes exist; a 13 million pixel camera in a phone will have pixels about 1.1 microns across; this gives a sensor width of about 4.55mm (there are 4128 pixels across the image). In the HTC One, the best photos are 2688 pixels across, and the pixels are 2 microns across giving a sensor width of about 5.4mm.
Figure 1 - 4 million large pixels
Figure 1 - 4 million large pixels

Figure 2 - 8 million (smaller) pixels on same size sensor
Figure 2 - 8 million (smaller) pixels on same size sensor
Now we can start looking at construction. Take a look at Figure 1. This shows a camera with large pixels - the lens is focussing the image onto an area exactly the same size as the sensor. In Figure 2, we gave the camera more pixels (which really does give more detail in the image but at the expense of noise and grain - and also less sensitivity at low light levels). Of course; straight away you want more, BIGGER pixels. Figure 3 shows that if you make that happen, the image doesn't cover the whole sensor; the light falls on a little bit of it. So - in Figure 4 we move the sensor further away to ensure the image covers all the pixels.
Figure 3 - 8 million large pixels with no other changes
Figure 3 - 8 million large pixels with no other changes

Figure 4 - Sensor moved away, but the lens size is unchanged.
Figure 4 - Sensor moved away, but the lens size is unchanged.
However; the same amount of light, entering the lens, is now spread over a wider area: this dims the light hitting each individual pixel, which reduces the signal output and increases the noise. The only way to change this is to make the lens bigger - the aperture wider - so that more light gets in. This is shown finally in Figure 5.
Figure 5 - all required changes incorporated.
Figure 5 - all required changes incorporated.
So - how far back do we have to move the lens? Simple trig shows us the answer. Imagine the "field of view" of the lens is about 60° (not unreasonable): the light coming in from the left and right cross over in the centre of the lens and make a triangle with the sensor as the base... an equilateral triangle is formed with all angles at 60° and all sides the same length (let's call it 5.4mm to stick with the HTC One's sensor size). So the lens must be 2.7mm away from the sensor. If we now make the sensor an 8MP one (3800x2140 pixels) that gives a width of 7.6mm - the lens still has a viewing angle of 60° so that means the sensor has to be 3.8mm away from the lens. Obviously I have used 60° as the lens viewing angle because it makes the angles, sines and side lengths easy to calculate - the numbers are probably quite different in real life but you get the idea: to get double the megapixels you have to move the sensor further from the lens, which means you need a bigger lens to gather the light needed to adequately illuminate it. Lenses very rapidly increase in price with size - a lens 4mm across instead of 2mm might cost three or four times as much. (BTW - the large circular opening on the back of the phone is NOT the lens; the lens is the tiny dark speck in the centre of it).

In practical terms for a smartphone? This means that, to get an 8 million pixel camera, with pixels 2 microns across, your phone would need to be about 16-18mm thick (at least at the camera's location); and the phone would cost upwards of US$1000 - possibly even more - JUST because of the lens.

This isn't something which can be corrected with better design, or better lenses; the only way to mitigate this increase in size and cost would be to make smaller pixels which had the properties of larger ones - and that my friends is the nirvana of a pixel scientist! The very best technology available is going into these phones - and with today's tech we're stuck with these limitations. In another article I'll talk about why I believe 4MP at 2 microns across is enough.


This article is also to be found on its author personal blog.

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8 comments:

  1. Can you explain the science between lumia 1020?

    ReplyDelete
    Replies
    1. Teeny Tiny Pixels. Long distance between lens and sensor. Big lens. The problem with it? Teeny tiny pixels.

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    2. Sensor is 8.8mm across; image is 7712 pixels across; that means theoretically the pixel size is 1.1 microns. Same size as the pixels in the Samsung Galaxy S4 but the lens is bigger and further away than in the Samsung, and obviously the sensor is physically bigger.

      Delete
    3. So, they combine teeny tiny pixels to create a big pixel? is that what oversampling does? and isn't it good science?

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    4. That's not what I said at all. The Nokia Lumia 1020 has lots of teeny weeny pixels. The HTC One has many fewer LARGE pixels.

      Delete
  2. But we already have something... Its called a window.... Full-HD, true collour, cheaper....


    No but serieus... As a Dutch student this is some heavy reading.... Let me summ this up

    So HTC is now making bigger pixels (length and width)... With a wider lens and putting the sensor further away.... Correct??? and they call that Mega pixels..

    Bigger pixels is less noise ... Wider lens for more light... And lens further away to keep it focussed (to use the hole sensor)

    So more pixels isn't guaranteed better foto (for having more noise because less light comes In) I already knew half of this but not why.... Thank you very much for clearing this up author and stonelaughter.... Nice article..

    ReplyDelete
  3. To the author: you have no idea how many times and in how many sites I've shared the link to this article, I'm almost fisically sick and tired now of hearing and reading people complain about the 'scanty' 4 million bigger pixels in the htc one and demand more megapixels!.. but I never took the time to thank you and congratulate you for this excellent article, so I thought better late than never (this time I came to copy the title for a comment in a video render for an alleged future successor of the htc one, featuring a 10mp UltraPixel camera!)

    I really thank you for teaching us about this.. and I know it's silly but sometimes when I open this again to copy the link, I read the explanation again (or some parts of it) in order to confirm I'm not the only one who knows this and to feel understood, like telling myself "everything's gonna be okay".. 'cause quite often I feel like I'm loosing my mind, seeing people out there in the world as if they were hungry wolves craving to devour more and more millions of pixels, not knowing or not caring for what they really are

    ReplyDelete
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