Calculation of mosaic step angles

Discussion forum for techniques and issues relating to the creation of panoramic and/or "mosaic" images

Moderator: spamkiller

Post Reply
Posts: 44
Joined: Sat Jan 17, 2009 4:48 am
Location: Newcastle, Australia

Calculation of mosaic step angles

Post by Growing » Wed Nov 02, 2011 9:09 am

I made a mistake today which had me scratching my head for a while.

Armed with a brand new pano head with selectable detents, I headed out to capture a panorama. I was using a 10mm rectilinear lens on a 1.6x crop sensor in vertical orientation. I calculated an FOV of 96.7 degrees by 73.7 degrees . For example, see, or use 2 * atan( 0.5 * sensor_width / focal_length )

So expecting my lens to cover 73.7 degrees horizontally, I selected the 60 degree click-stop detents on my new pano head, and shot my 2 row panorama (12 shots for 360x180), expecting around 18% horizontal overlap between images.

Back at my PC, I was alarmed to discover gaps in my panorama. How could this be?!? How could my lens fail to cover 60 horizontal degrees, when my calculations said it should cover 73.7 degrees?

When I checked the calculations, I realised that while the FOV across the centre of the frame was 73.7 degrees, the FOV across the short edge of the frame was (I think) only 53.0 degrees = 2 * atan ( 0.5 * sensor_width / sqrt( focal_length^2 * (0.5 * sensor_height)^2 ))

I guess other people haven't noticed that because with less extreme wide-angle lenses, the centre FOV and the edge FOV are similar. And 20% overlap hides a multitude of sins. But in my case, my 18% calculated overlap was insufficient when combined with a 10mm lens and a horizon that was not through the centre of the frame.

The moral of the story is that the traditional formula for rectilinear Field-Of-View gives misleading results when used to calculate optimal spacing of a panoramic mosaic when either the desired overlap is small, or the lens is extremely wide. In future, I will be using the FoV across the edge of the frame rather than the FoV through the centre of the frame in order to calculate the optimal mosaic spacing.


Posts: 2118
Joined: Sun Jul 20, 2003 2:43 pm
Location: UK

Re: Calculation of mosaic step angles

Post by johnh » Fri Dec 02, 2011 5:19 am

Calculating fov values becomes even more problematical when using fisheye lenses, which are commonly used for 360x180 panoramas. Instead of calculations, you can trial shooting patterns by loading some dummy images and applying various lens and image parameters. The overlaps are then easily understood by reference to the preview window. Recommended shooting patterns for various lenses can be found at


Posts: 1
Joined: Tue Apr 06, 2010 12:46 pm
Location: Italy

Re: Calculation of mosaic step angles

Post by rosco » Wed Apr 18, 2012 6:50 am

Growing, can you please help me understand what you mean, speaking about the difference between FOV across the centre an FOV across the short edge of the frame.

FOV is given by this formula: Fov (rad) = 2 * arctan (d / (2f)), where d represents the size of the film (or sensor) in the direction measured and f the effective focal length.

So, where does the new formula in the previous message come from? Also, i think there should be a + or a - insdide the ( ) under the sqrt., or am i wrong?

Thanks for your help.


Posts: 1
Joined: Sat Mar 09, 2013 6:10 am

Re: Calculation of mosaic step angles

Post by hadriyagee » Sat Mar 09, 2013 6:12 am

I am really grateful to receive information from experienced people and i hope that this post will help others as well !

Post Reply

Who is online

Users browsing this forum: No registered users and 1 guest