Getting off Auto - Crop Factor

This is a slightly deeper look at Crop Factors, after some questions about them on another thread.  I've tried to keep it relatively simple (it can get a bit deeply mathematical if you're not careful), so ask questions if something isn't clear.  It's part of the overall Getting off Auto series, whose Index is available here.

Various size sensors appear in different cameras and it helps to understand how they affect your photography.  For most of us, so called Full Frame sensors are the largest we’re likely to come across and they are referred to as such as they are the same size as a 35mm frame on an old film camera (35mm being roughly the width of the frame on the film itself).  Full frame sensors are expensive however (though prices are coming down), so manufacturers often use sensors that are smaller than that – it saves money of course, but it also makes smaller cameras possible.  A mobile phone with a FF sensor on the back wouldn’t work very well for instance – because sensors need lenses in front of them and the bigger the sensor, the bigger the lens required.

When you use a smaller sensor in the camera however, you lose the ability to capture bits of the image around the edges, even though the lens is capable of it.  

Even the FF sensor throws away some bits – the image thrown by the lens is circular after all and the sensor is square.  But the crop sensor loses even more – and the smaller the sensor, the more of your picture is lost.  Like this

Incidentally, for those familiar with crop-body-only lenses (EF-S ones in the Canon world), that’s how they’re made cheaper and lighter – the bits of glass that normally would be used to expose all that unused area are simply left out (ie smaller, cheaper bits of glass).

However, you never really realise this loss of information, as you don’t view an image at its real size.  You always see a picture ON something – a 6x4 piece of paper, a 22” PC screen, your mobile phone – and the device simply enlarges the image to fit the available space.  As such, what you end up seeing from a smaller sensor is an image that looks larger than that captured on the FF one – as long as both sensors are using the same lens!  Here’s an example – the first image is 400mm lens on Full Frame, the second is the same image as it would be captured by an APS-C sensor (Canon’s term for a cropped sensor). 

Note that even though the pictures are the same size on your device, the crop image is “zoomed in”.  The diagonal measurement of the cropped sensor is 1/1.6 that of the FF one (or FF is 1.6x bigger diagonally than the cropped one, if that’s easier).  This 1.6x multiplier is known as the Crop Factor.  It doesn’t change the ACTUAL focal length of the lens being used, but it DOES change the Field of View (what can be seen).  If you took two pictures, one with a FF sensor using a 160mm lens, one with a 1.6x crop sensor using a 100mm lens you’d get the same Field of View (100mm x 1.6 = 160mm FoV).

So, this is good news!  It means we get more reach from our long lenses for birding, simply by using a camera with a crop sensor – I’d need a 640mm lens on FF to get the same image as a 400mm lens on crop.  Alternatively, if I choose a camera with a very small sensor, I can get away with a lens that’s physically smaller and much cheaper than those monster Big Whites, but still get the effective reach needed for taking pictures of little birds.  This is the approach taken by a typical Bridge camera – a smaller sensor and a fixed (ie not interchangeable) zoom lens.  In our discussion on another thread, we discovered the Canon SX50 has a 215mm lens, but the crop factor of approx. 5.6 gives it a FoV equivalent to 1200mm on a FF camera.  That’s remarkable!

But.  You just knew there’d be a “but”, didn’t you?  Firstly, bigger sensors are generally much better in poor light – they do give better results on murky days.  Secondly, and far more relevant to this thread, is that we have talked extensively about the Focal Length/Field of View equivalence, but not mentioned Aperture. 

A quick re-cap may be helpful at this point, though this is covered in other GoA threads as well.  Focal length is the optical distance between the point of light convergence in the lens (when focussed at infinity) to the camera sensor.  Long focal length normally = bigger physical size.  Yes, Birders have big ones!

The aperture of a lens is the ratio of focal length to the size of the hole that lets in the light.  A 600mm lens with a hole at the front of 150mm will therefore be a f/4 lens (600/150).  The f is just short for Focal Length, the / indicates it’s a ratio.  Which means f/4 is a larger hole than f/8.  Lenses always quote the maximum aperture (ie wide open) they can attain - you can normally close down the aperture on a lens should you wish to.  Smaller apertures give greater depth of field – the amount of the image that is in (acceptable) focus.  This graph may help

And these two images certainly will, one at f/18, one at f/4

Notice how blurred the f/4 image background is?  That’s the benefit of the wider apertures, they allow you to isolate the subject nicely by throwing the background out of focus.

So, what’s all this got to do with our crop factor?  When you multiply the lens focal length by the sensor’s crop factor to work out your effective length and hence Field of View, you ALSO need to multiply the aperture to gain an idea of what the depth of field will be like.

Here’s my DoF calculator to show you – putting a 400mm lens on a crop body is the same FoV as a 640mm lens on FF (OK, I had to use 650mm, the calculator is limited!) – but I have to close down the lens on the FF to f/6.7 to get the same depth of field – f/4 would have given me 22cm.  To work out the aperture required to get the equivalent DoF, you need to multiply the aperture by the crop factor, just like you do the focal length for field of view information (in this case, f/4 x 1.6 = f/6.4 – OK, there are a few errors from approximations in this example, but hopefully you get the gist!)

For birding, who cares? A bit more DoF is often handy, and the difference here isn’t so bad anyway.  However, it gets more noticeable with smaller sensors, especially if you’re after more general shots.  For this example, I dug out an old Ixus 220 point & shoot camera I have in the cupboard – it has a small sensor with the same crop as that SX50, namely 5.6x.  The 4.3-21.5mm lens gives a FF equivalent of 24-120mm.  That tallies well with my full frame camera with a 24-105 on it, so these pics are all shot from the same position at 24mm (equivalent).

The small sensor Ixus, even wide open at f/2.7 is hopeless at blurring the background in this example – contrast it with the full frame at the same focal length, but f/4 (also wide open). 

I have to close the FF down to around f/16 before we see a similar result in the background. 

Whilst the deep depth of field is handy when taking macro shots close up, it’s not so nice when you’re trying to isolate your subject (which is why portrait photographers like larger sensor cameras).  To save you the maths, f/2.7 x 5.6 crop factor = f/15, so our rule of thumb’s still holding up.

So where does all this lead us?  Well, nowhere really!  At the end of the day, you buy the equipment that best suits you, whether that be features, budget, ergonomics or fashion.  As with most things in photography, there are few right answers, only opinions.  Hopefully though, with a little bit of knowledge, decisions can be informed rather than guessed at :-)


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