Angle of view for stitched photos

[Pieter 12]

Trying to wrap my brain around estimating the angle of view for multiple, stitched photos. Is it factor of the lens AOV times the number of exposures, allowing for overlap? Or more complicated than that? And would one use the diagonal AOV or more likely the AOV corresponding to the frame orientation?

 

[guphotography]

Lens Visualizer Tools - DT Photo

www.photo-digitaltransitions.com

 

[dougpeterson]

I did the coding for that if you have any questions.

When doing stitching with stitching you’re basically just making a physically larger virtual sensor.

For example if you stitch an IQ4 150mp ~51x40mm sensor to do a left-right stitch of +/- 12mm shift on the long side your virtual sensor size is now (51+12+12) x 40mm.

 

[Pieter 12]

I did the coding for that if you have any questions.

When doing stitching with stitching you’re basically just making a physically larger virtual sensor.

For example if you stitch an IQ4 150mp ~51x40mm sensor to do a left-right stitch of +/- 12mm shift on the long side your virtual sensor size is now (51+12+12) x 40mm.

Got it. What I’d like to know is the then equivalent angle view for the lens.

 

[MGrayson]

There are a few choices when converting angles of view with different aspect ratios. In @dougpeterson's example, since you're describing a 75x40 rectangle instead of a 51x40, you can use the diagonal or the long edge, and these will give different answers. The long edge is a 47% increase (75/51) = 1.47. The diagonal is a 31% increase. (85/65) = 1.31. With a larger aspect ratio like 75x40 (almost 2:1), the diagonal is probably what you care about, and so the angle of view would be that of a 50/1.31 = 38mm lens. That is, a single image from a 38mm lens, cropped to the same shape as the panorama, would have the same image, only with fewer pixels.

The formula is (equivalent focal length of panorama) = (focal length of taking lens)*(diagonal of single frame)/(diagonal of panorama)

Plugging in the numbers here looks like 38 = 50 * 65 / 85

Best,

Matt

(If you really want angles and not equivalent focal lengths, then it's 2*ArcTan( d / f ), where f is the focal length of the taking lens and d is the diagonal of the panorama.)

 

[Pieter 12]

There are a few choices when converting angles of view with different aspect ratios. In @dougpeterson's example, since you're describing a 75x40 rectangle instead of a 51x40, you can use the diagonal or the long edge, and these will give different answers. The long edge is a 47% increase (75/51) = 1.47. The diagonal is a 31% increase. (85/65) = 1.31. With a larger aspect ratio like 75x40 (almost 2:1), the diagonal is probably what you care about, and so the angle of view would be that of a 50/1.31 = 38mm lens. That is, a single image from a 38mm lens, cropped to the same shape as the panorama, would have the same image, only with fewer pixels.

The formula is (equivalent focal length of panorama) = (focal length of taking lens)*(diagonal of single frame)/(diagonal of panorama)

Plugging in the numbers here looks like 38 = 50 * 65 / 85

Best,

Matt

(If you really want angles and not equivalent focal lengths, then it's 2*ArcTan( d / f ), where f is the focal length of the taking lens and d is the diagonal of the panorama.)

Thank you. Come to think of it, I thought there was a website where you could plug in the numbers and get equivalent focal length and angle of view.

 

[daz7]

you can calculate it quite easily using basic trigonometry - the triangle basis is your new image width and you know the height since you know the original width and the original angle of view (angle at the apex). Tangent of that angle equals the original witdth divided by the height.
There is a lot of webpages offering ready made triangle calculators, too.

 

[dougpeterson]

Thank you. Come to think of it, I thought there was a website where you could plug in the numbers and get equivalent focal length and angle of view.

That’s exactly what the DT Visualizer (linked above) does.

Enter any combination of sensor, lens, and stitching configuration and it gives the AOV, equivalent focal length (based on vertical, horizontal, or diagonal) in another format. It also shows you the result visually.

Maybe you didn’t notice the Focal Length Visualizer as it’s the second such tool at the provided link?

 

[Pieter 12]

That’s exactly what the DT Visualizer (linked above) does.

Enter any combination of sensor, lens, and stitching configuration and it gives the AOV, equivalent focal length (based on vertical, horizontal, or diagonal) in another format. It also shows you the result visually.

Maybe you didn’t notice the Focal Length Visualizer as it’s the second such tool at the provided link?

Maybe I'm missing something here, but the tools seem to be limited to certain lenses and sensors, none of which I am using. I don't see the option of entering my own configuration(s).

 

[Whisp3r]

Maybe I'm missing something here, but the tools seem to be limited to certain lenses and sensors, none of which I am using. I don't see the option of entering my own configuration(s).

Hello Pieter,

I think you're referring to the Image Circle Visualiser, it's the first tool on that particular page, and it indeed offers a selection of Rodenstock and SK lenses, in addition to various sensor sizes.
But if you scroll down from there, you'll discover the Focal Length Visualizer, which might be the specific tool you're looking for. I hope

Here's a screenshot:

 

[corvus]

If you have a small drawing program - or use conventional paper, ruler, compass and pencil - you can do this yourself for each combination. I usually work out the relationships graphically, as I can usually visualize it better that way. Here is a simple example of a full-frame 4x shot with a 58mm large-format lens. I have also entered the individual shift values that make sense for the format.