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12-28-2011, 01:50 AM   #1
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Focal length and after PP cropping calculations - HELP!

Hello Folks

Suppose I shot with x mm focal length and then cropped the photo to y% of the original (keeping the proportions). What is my focal length now?

The reason I ask is that I am looking at my sunset and landscape pictures trying to work out the FL I most commonly use and since many of the photos are cropped, the EXIF which gives the FL doesn't really tell the real story.

So the dudes and dudettes in the know, help will be greatly appreciated!

12-28-2011, 02:03 AM   #2
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After cropping,
the focal length used is just the same
(so the depth of field will remain the same).

Generally speaking,
it helps to keep the original image intact,
and then save edited versions separately.
This will help you recover your unknown y%,
along with x mm from the EXIF.

However, by the way you asked the question,
I get the impression that you might be thinking
in terms of what P&S marketers call "digital zoom."
In that case, for longer focal lengths,
x times 100/y will give you a ballpark
"digital zoom focal length."
(Visions of RioRico tearing his hair out here )

Last edited by lytrytyr; 12-28-2011 at 02:22 AM.
12-28-2011, 03:05 AM   #3
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The focal length remains the same. But cropping changes the FOV, so you could moot a FOV-equivalent focal length based on the crop. And what's the factor? The ratio of diagonals.

For example: You shot a picture with an APS-C sensor. Focal length doesn't matter, but let's say it was a 100mm lens. The diagonal of the captured frame is ~30mm. You crop it down to an image with a 20mm diagonal, keeping the same 3:2 aspect ratio. (I'll let you use the Pythagorean Theorem to calculate the cropped dimensions.) The diagonal ratio is 30:20 or 1.5x, so your shot is FOV-equivalent to a 150mm lens.
12-28-2011, 03:09 AM   #4
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Or to make life easier if you don't like math, just use the long side. It's the same thing if you didn't change the shape. If you cropped from 4000 pixels width to 2667 pixels width, that's the same 1.5 factor RioRico gave in his example.

(And if you changed the shape, just expand your image to the original shape before calculating, because you wanted to know what lens to use on the camera you have, not what lens to use on an imaginary other camera.)

12-28-2011, 04:11 AM   #5
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Thanks heaps, folks!


QuoteOriginally posted by drougge Quote
Or to make life easier if you don't like math, just use the long side. It's the same thing if you didn't change the shape. If you cropped from 4000 pixels width to 2667 pixels width, that's the same 1.5 factor RioRico gave in his example.

(And if you changed the shape, just expand your image to the original shape before calculating, because you wanted to know what lens to use on the camera you have, not what lens to use on an imaginary other camera.)
Yes, I don't like maths all that much, even though that's what I do 9-5.
12-28-2011, 05:00 AM   #6
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FL doesn't change when you crop. What changes is the image's AOV/FOV. What you're really asking is "What FL would give the same AOV/FOV as is in this cropped image?".

If you've resized as well as cropped, and don't have the original, so you're unsure how much of the original frame you have left, there is another way.

Google Earth is your friend. Say you have a far peak "A" on the left of your shot and a nearer peak "B" on the right. You also know where you shot from (say at a lookout). You can bring this up in Google Earth and use the map to work out the tangential distance between the two peaks as seen from your viewpoint:

  1. Draw lines to the two peaks
  2. Draw a tangential line from the closest peak intersecting the line pointing at the further-away peak.
  3. Draw a perpendicular line from the tangential line to you.


Using the map scale you work out the the distance from this "cross-line" to yourself is 3800m & the length of the "cross-line" is 4500m. Then you use an AOV/FOV calculator to work out what FL would produce this FOV. A 20mm FL lens on an APS-C 1.5x CF camera at a distance of 3800m has a horizontal FOV of 4560m. So if the shot had of been taken with a FL of about 20mm, no cropping of the edges would have been required.

Dan.

Last edited by dosdan; 12-28-2011 at 05:47 AM.
12-28-2011, 05:28 AM   #7
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Cropping is equivalent to changing focal length (modulo loss of resolution). The AOV, DOF, etc. of the cropped photo are as if a longer FL had been used. So it makes good sense to ask for the "new focal length" after cropping.

You need to specify whether the percentage "Y" refers to resolution, i.e., the reduction in one of the linear dimensions (long side, short side, or diagonal; it is the same factor for all) or whether the percentage refers to image area.

The new focal lenght x' is the original focal length x times 100/Y (x' = x * 100/Y) if "Y" refers to the percentage left of one of the linear dimensions. If "Y" refers to percentage left of image area then the formula is x' = x * sqrt(100/Y). Note that Y=50 for a reduction by half, Y=10 for a reduction to the tenth of the original size, etc.
12-28-2011, 07:02 AM   #8
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Who really cares.

Since almost every one crops an image to some extent, this debate is irrelevant. You shoot with what you shoot with, and that is all

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