GUIDE - EQUIVALENCE
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This page explains what kind of lenses are emulated by using this technique. When creating a panorama the cameras sensor size and lenses image circle are effectively increased. The aperture diameter remains the same however (because the camera rotates around this point). Because the resulting stitch represents a wider angle lens and the f-stop value gets amplified because of it's relative size to that wider angle. In a nutshell it enables you to turn a reasonably sized/priced portrait lens (left), into something totally insane (right):
If you’re thinking “what the hell is that lens on the right”, no, you haven’t missed something special. It was made as a joke. You can read up on it at PetaPixel here. It’s alleged 40mm f/0.33 would have an aperture diameter is 121mm - twice that of an 85mm f/1.4!! That's such a crazy figure the lens in this image isn't nearly big enough. Even using the panorama technique it would be difficult to do, although not impossible. You can actually surpass it by using a 400mm f/2.8, but that would require taking and stitching literally hundreds of images. If you have plenty of money, muscle and patience you could give it go, but I wouldn't advise it. Von Wong has a Youtube video about it here, although I doubt he managed a 40mm equivalent.
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This crazy & fictitious optic works well to illustrate a point: That a carefully chosen, affordable lens plus some time/effort can give results that aren't achievable even if you have hypercar money to spend on glass. OK, on with the maths…
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Let’s say, for example you use an 85mm f/1.8 lens to take 9 shot (3×3), with 50% overlap. You will end up with an image that has twice the dimensions. This ‘doubling’ makes it a bit easier to work out, it means you can half each of the lens’ values (1/x, x=2, so 1/2). This makes an 85mm f/1.8 become 42.5mm f/0.9
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PHYSICAL APERTURE SIZE
When you rotate the camera and lens around the lenses entrance pupil (roughly the aperture blades) it means that the physical size of that aperture remains constant, even in the final stitched image. Thus the physical aperture size is the most important factor for this technique (and lens choice). The bigger it is – the better.
You can work out a lenses physical aperture size by dividing the focal length by the aperture. Using the same lens as an example: 85 / 1.8 = 47.2mm. By looking at the maths involved for the panorama (above) you can start to see how all this comes around, because 42.5 / 0.9 = 47.2 – the same physical aperture size.
CAMERA SENSOR SIZE
The maths you see above for working out lens equivalency and physical aperture size is based on using a full frame camera (36x24mm). This makes it all easier because the lens values are made for use on a full frame camera. If you’re using a camera with a smaller sensor it will make the maths a bit harder to work out.
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When taking a single image from an APS-C sensor (24x18mm / 1.5x crop) it will lose 1 stop of ‘depth of field’ capability. For example: A 50mm f/1.4 may perform like a 75mm f/1.4 as far as light transmission is concerned, but for depth of field it will perform like a 75mm f/2. A Micro 4/3 sensor (18x12mm / 2x crop) will lose 2 stops, making the same lens a 100mm f/2.8, again purely where depth of field is concerned.
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However, one of the beauties of this technique is that it emulates a larger sensor camera. So all of these cameras have the potential to end up with exactly the same results. The smaller the sensor’s handycap is simply in the number of images it will need to take to reach the same goal.
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3 shots from an APS-C camera will make up 1 frame from a full frame (given a 50% overlap rule). Using the same logic – 9 shots from the M4/3 sensor will make up one from the full frame. If you remember the maths from above on a 3×3 panorama you can again reverse engineer the numbers from the 100mm f/2.8 to get to 50mm f/1.4 by halving both the values.
The above example shows the reverse calculation. How a small sensor used in a camera phone equates to a much smaller aperture value when worked out for a full frame image. This camera phone lens doesn't have a variable aperture, so it's stuck at f/2.2 all the time. However it's equivalent depth of field is on an f/17 lens. The sensor and aperture sizes are shown relative to each other here.
POTENTIAL
All these number only work if you’re using the lens wide open of course, but an 85mm f/1.8 is not an extremely fast or expensive lens, nor is 9 shots a lot of images to take for a panorama. If you are lucky enough to have a lens with an even larger aperture or have the patience to take and stitch many more images together then you can get some even more crazy values and this effect can really show up in your images.
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MAXIMISE THE EFFECT
What makes this technique great is seeing a wide image with great subject isolation, but be careful how wide you go. The shallow depth ‘effect’ comes from getting as close to your subject as possible. As your stitched image gets wider (by taking more shots) you’re effectively stepping back from that image. The amount of blur will fall as you step back, so there is a ‘sweet spot’ to this effect. Just what that is can be hard to pin down because of the variables, but just try to keep this in mind.
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