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### AuthorTopic: What's the AOV of stitched 17mm PC lens pano?  (Read 5630 times)

#### AFairley

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##### What's the AOV of stitched 17mm PC lens pano?
« on: July 21, 2016, 12:42:47 pm »

Can any one tell me what the angle of view is of a horizontal panorama made by shifting a 17mm lens (such as the Canon) on a 24x36 sensor camera?  Thanks.
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#### Bart_van_der_Wolf

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #1 on: July 21, 2016, 04:18:03 pm »

Can any one tell me what the angle of view is of a horizontal panorama made by shifting a 17mm lens (such as the Canon) on a 24x36 sensor camera?  Thanks.

Hi Al,

On a 36mm wide sensor, with 2x 12mm shift added, it will create a virtual sensor width of 60mm at 17mm focal length.

That means that the approx. AOV is:  2x aTan((60/2) / 17) = 120.9 degrees at infinity focus.

Cheers,
Bart
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#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #2 on: July 21, 2016, 08:48:01 pm »

That means that the approx. AOV is:  2x aTan((60/2) / 17) = 120.9 degrees at infinity focus.

For horizontal AOV, yes, that's 120.9 degrees.

As to "equivalent FOV" (i.e. "what would be the FOV of the lens if measured as manufactures usually do, across the diagonal of the frame"), that would be

deg(2*atan((sqrt((60/2)**2 + (24/2)**2)) / 17)) = 124.5 degrees.
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#### Slobodan Blagojevic

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #3 on: July 21, 2016, 10:51:43 pm »

For horizontal AOV, yes, that's 120.9 degrees.

As to "equivalent FOV" (i.e. "what would be the FOV of the lens if measured as manufactures usually do, across the diagonal of the frame"), that would be

deg(2*atan((sqrt((60/2)**2 + (24/2)**2)) / 17)) = 124.5 degrees.

And what is then an equivalent focal length for 124.5 degrees? And the same calculation for the 24 t/s, please?

#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #4 on: July 22, 2016, 12:59:44 am »

And what is then an equivalent focal length for 124.5 degrees?

One way of looking at it is to see what lens produces 124.5 degrees of FOV on 24x36mm sensor, which would give us

sqrt(24**2+36**2)/2 * tan(rad(90-(124.5/2))) = 11.38 mm

but that is, of couse, not entirely correct... The thing is that you'd have to crop the image from top and bottom to produce the same aspect ratio that "virtual 60x24" frame gives us... So we have to further shrink the short side of the frame to account for that "virtual extension" that shift gives us. So we get

sqrt((24*36/60)**2+36**2)/2 * tan(rad(90-(124.5/2))) = 10.2 mm

All in all, it means that you can produce similarly-looking frame by snapping 10mm hyper-wide Voigtlander and then cropping the image to 60:24 == 5:2 aspect ratio.

And the same calculation for the 24 t/s, please?

By how many millimeters it shifts?
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#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #5 on: July 22, 2016, 01:09:29 am »

By how many millimeters it shifts?

Looked it up... According to DPR it's those same 12mm.

So, equivalent FOV:

deg(2*atan((sqrt((60/2)**2 + (24/2)**2)) / 24)) = 106.79 degrees

Equivalent focal length on FF sensor:

sqrt(24**2+36**2)/2 * tan(rad(90-(106.79/2))) = 16.07 mm

Equivalent focal length on FF sensor if cropped to the same aspect ratio:

sqrt((24*36/60)**2+36**2)/2 * tan(rad(90-(106.79/2))) = 14.4 mm

That is, Canon's own 14mm prime would do.

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#### georgem

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #6 on: July 22, 2016, 02:06:03 am »

Can any one tell me what the angle of view is of a horizontal panorama made by shifting a 17mm lens (such as the Canon) on a 24x36 sensor camera?  Thanks.

Towards the end of this page http://www.cambridgeincolour.com/tutorials/tilt-shift-lenses1.htm there is a convenient shift calculator. You can even select camera orientation and shift direction.
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#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #7 on: July 22, 2016, 09:07:38 am »

Towards the end of this page http://www.cambridgeincolour.com/tutorials/tilt-shift-lenses1.htm there is a convenient shift calculator. You can even select camera orientation and shift direction.

Doesn't mention diagonal FOVs (am I the only one who tend to think about lenses and images they produce in terms of diagonal FOV?), but at least the numbers those guys arrived at for focal lengths necessary to produce equivalent (including aspect ratio) images on FF without shifts match mine (10.2 and 14.4), which is always good to know...
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#### AFairley

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #8 on: July 22, 2016, 10:41:13 am »

Thanks, Bart and George, horizontal FOV was the number for me as that describes where the edges of the image will be.
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#### mcbroomf

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #9 on: July 25, 2016, 09:54:56 am »

You don't really need to use a complicated calculation for figuring out the new FL equivalent when shifting, just use the ratio of the FF vs new frame with shifts, egs;

12mm left and right shift on FF using a 17mm lens

FF width = 36mm
Shifted width is 36 + 12 + 12 = 60mm

New FL equiv is 17 * 36/60 = 10.2mm

12mm left and right shift on FF using a 24mm lens

24 * 36/60 = 14.4mm

10mm left and right shift on FF using a 28mm lens
New frame width is 36 + 10 + 10 = 56mm

28 * 36/56 = 18mm
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#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #10 on: July 25, 2016, 11:00:09 am »

You don't really need to use a complicated calculation for figuring out the new FL equivalent when shifting, just use the ratio of the FF vs new frame with shifts, egs;

12mm left and right shift on FF using a 17mm lens

FF width = 36mm
Shifted width is 36 + 12 + 12 = 60mm

New FL equiv is 17 * 36/60 = 10.2mm

12mm left and right shift on FF using a 24mm lens

24 * 36/60 = 14.4mm

10mm left and right shift on FF using a 28mm lens
New frame width is 36 + 10 + 10 = 56mm

28 * 36/56 = 18mm

Indeed.

But it's much less fun that way, isn't it?
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#### Slobodan Blagojevic

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #11 on: July 25, 2016, 11:20:11 am »

You don't really need to use a complicated calculation...

Damn, Mike, you are entering a dangerous territory. You remind me of a medieval passerby, overhearing scholars discussing how many teeth a horse might have and suggesting to simply open the horse's mouth and count. They beat the crap out of him for being un-scientific

#### Zorki5

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #12 on: July 25, 2016, 11:29:45 am »

You remind me of a medieval passerby, overhearing scholars discussing how many teeth a horse might have

Yeah, those were the days... <sigh>
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#### mcbroomf

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##### Re: What's the AOV of stitched 17mm PC lens pano?
« Reply #13 on: July 25, 2016, 06:20:30 pm »

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