You can use the "crop factor" ratios to figure it out. For instance, if it was 85mm f/1.4 and a 4 image panorama with one third overlap, that would be about .6, so the focal length would be 51mm (or about there). The aperture is then 1.4 times .6, or about .84 (at least, I believe it would be). This gives the exact same size of aperture, which is what counts if I'm correct.

hmmm Okay... I think I understand. Thanks for the explanation Eddie

I have some maths I use for this that are a little different so see this makes sense, I made it up so if anyone can see a flaw in this logic please feel free to shout at me.

This formula is related to the 35mm format (24x36 / Full Frame / FX) because that's how lenses are referred to and measured. If you take the photos on crop (DX / APS-C) then the same mathematic rules apply accept you will have to take in to account the smaller sensor (0.5 stops less effective than the 35mm figures*).

OK here goes...

For this example I will start with the resolution of a single image at 6mp (3,000 x 2,000 pixels). If I were to end up with a pano of 12,000 x 8,000 pixels it would be 4x the length in each axis, 16 times (4x4) the volume (96mp).

85mm divided by 4 = 21.25mm
f/1.4 - 2 stops = f/0.7 (4 times as much light)

For the aperture it's more complex than a simple division. 4x is reached in 'stops' by a factor of 2 (2 to the power of 2 = 4). This is why I removed 2 stops from the value above and end up with f/0.7. This could look confusing however, it is a coincidence that the value is halved. The aperture values in full stop increments are as follows:

0.5 ● 0.7 ● 1 ● 1.4 ● 2 ● 2.8 ● 4 ● 5.6 ● 8 ● 11 ● 16 ● 22 ● 32

One position lower on this scale relates to a doubling of light coming through the lens and on to the sensor.

*If you did the same maths as above but on a cropped sensor (18x24mm / DX / 1.5x) then you would have to remove 0.5 stops from the 2 stop figure (1.5 stops). Thus the figures would be equivalent to a 31mm f/0.85

Nice explanation Edd!

thank you for the explanation Edd and Eddie

After trying this effect with a Pentax 135mm f/2.5 and getting a resulting stitch that was 3.3x the diagonal length of a single image (23 shots) I found my old math must be flawed. With the old equation (above) it came out to an equ. of a 40mm f/1.8. I have a lens like that, but it's certainly not capable of producing results like that in a million years. So I have to revise my calculation of using an extra stop for each doubling of image length. I think you just need to devide the f/ number by how many times bigger the diagonal is. This math came out to a 40mm f/0.75, now that's more believable. Here's the image btw:

www.flickr.com/photos/eddnoble/16172387329/


After 6 years I have to say... Eddie was right :)