Topic: Photography, Mathematics, and Boredom (Read 3150 times)

RazorTM · « **on:** October 03, 2009, 09:11:02 am »

I was bored at work today, so I started browsing the web, looking at various photography-related web pages. I saw someone mention the old 1/focal length recommendation for handheld photography and wondered just how accurate it is. Also, is it more or less effective at longer focal lengths? How about shorter focal lengths? Why not explore the mathematics behind it so there is no question about the effectiveness of this rule?

First, let's look at the well-known formula for the diagonal angular field of view in degrees in relation to focal length for a full frame 35mm camera. The correct formula and a graph are below.

The next step is to modify the 1/focal length rule to keep the effectiveness constant across all focal lengths. Any takers?

RazorTM · « **Reply #1 on:** October 03, 2009, 09:14:43 am »

Also, looks like I skipped right over the Techniques forum when I was looking for one. Could somebody move this topic to that forum? Sorry!

Eric Myrvaagnes · « **Reply #2 on:** October 03, 2009, 09:36:54 am »

Interesting analysis.

In practical terms, I take three conclusions from your work:

(1) The "1 over f-stop" rule applies only to an individual holding the camera/lens with the same care at each focal length (intuitively obvious).

(2) The rule is probably a useful approximation when using lenses of about 40mm focal length or longer.

(3) The rule shouldn't be read as saying that "at 1/100 second my pictures will be sharp on a 100mm lens", but rather that "if I hold the camera just about as steady for each lens, the amount of blur I get at 1/100 with a 100mm lens will be roughly similar to what I'll get with 1/200 and a 200mm lens."

As you rightly point out, the amount of blur depends substantially on the photographer's own steadiness (or lack thereof).

-Eric

P.S. When I got bored at work (before I retired) I usually just skipped work and went out photographing.

RazorTM · « **Reply #3 on:** October 03, 2009, 09:50:30 am »

Quote from: EricM

P.S. When I got bored at work (before I retired) I usually just skipped work and went out photographing.

I wish I had that liberty

Thanks for reading!

Roger Calixto · « **Reply #4 on:** October 03, 2009, 10:33:47 am »

Hmm... seems like you should adjust your exponentials with a new constant C^IS to account for image stabilization... I'd think that'd flatten the knee out a little and make it more parabolic, no?

=)

{}
KT

RazorTM · « **Reply #5 on:** October 03, 2009, 10:48:55 am »

Quote from: kingtutt

Hmm... seems like you should adjust your exponentials with a new constant C^IS to account for image stabilization... I'd think that'd flatten the knee out a little and make it more parabolic, no?

=)

{}
KT

Yes, but those with IS lenses probably pay no heed to the "rule." I sure don't!

Panopeeper · « **Reply #6 on:** October 03, 2009, 04:19:26 pm »

Quote from: RazorTM

I was bored at work today

...

The next step is to modify the 1/focal length rule to keep the effectiveness constant across all focal lengths. Any takers?

I have another suggestion for the case you are still bored and want to fine tune the recognitions from your thoughts.

Think of following experiment: you have a wall large enough to fill the image. The wall is plastered with some grainy stoff, the grains are of varying color; you go so far, that each grain is captured by one pixel. All lenses you considered are rectilinear, thus one grain is one pixel in the center and in the farthest corner (apart from lens distortion, let's ignore that), assumed the lense's axis is perpendicular to the wall.

Now, the point: one grain in the center occupies much more "angular space" than in the corner. Or, in general, the angle of view covered by one pixel is greater in the center than in the corners. Accordingly, the effect of camera shake depends not only on the lens, but on the location in the image: the center gets much less blurred than the corners. Moreover, the rate of change from the center to the corner depends on the focal length: long lenses show a more uniform effect than wide angle.

robert zimmerman · « **Reply #7 on:** October 03, 2009, 04:35:11 pm »

Okay, i have no clue about the math but it seems like you do, so i'll ask a question about a symilar subject if you don't mind.

How can i figure out how to match the field of view at different distances, with different focal lenths?

For example: I'm shooting a group of people in the studio with a 50mm at a distance 3 meters, and I want to place them in a landscape, via photoshop, 6 meters from the camera. What focal lenth should I use for the landscape shot to match the field of view. Or is it easier to figure out in reverse? A landscape shot with a 50mm is my starting point. What focal lenth should I use for the group shot at a distance of three meter to match the FOV when placed in the Landscape shot?

Thanks for the help,

kipling

RazorTM · « **Reply #8 on:** October 03, 2009, 06:15:58 pm »

kipling, I think that in order to maintain the same perspective, you should use the same focal length for both shots but step 6 feet away from the patch of ground on which you would like to place the group of people in the landscape photo. 6 feet is a close distance, so I maybe you should shoot with a wide lens like a 35 or 24mm?

michaelnotar · « **Reply #9 on:** October 04, 2009, 01:37:43 am »

Quote from: RazorTM

kipling, I think that in order to maintain the same perspective, you should use the same focal length for both shots but step 6 feet away from the patch of ground on which you would like to place the group of people in the landscape photo. 6 feet is a close distance, so I maybe you should shoot with a wide lens like a 35 or 24mm?

so what i get from this is that the 1/FL applies most of the time, mostly in the mid FLs... would be interested in seeing numbers/graphs for those.

interesting take on the super wides and 1/FL. true 1/10 arc is more of a movement with a WA lens.

isnt all this based on "good enough" or "sharp enough" not critical focus. i think "good enough" comes into play on the wides since the blur would be so little.

Rob C · « **Reply #10 on:** October 04, 2009, 03:36:26 am »

Boredom at work would indicate the need for a new job. No maths required to figure that calculation.

;-)

Rob C

robert zimmerman · « **Reply #11 on:** October 04, 2009, 09:27:08 am »

Quote from: RazorTM

kipling, I think that in order to maintain the same perspective, you should use the same focal length for both shots but step 6 feet away from the patch of ground on which you would like to place the group of people in the landscape photo. 6 feet is a close distance, so I maybe you should shoot with a wide lens like a 35 or 24mm?

Razor,
yes, I could do that, but it's not always a good solution.

For example, if I shoot a landscape with a 35mm lens, and I have to stand 10 meter away from where the subject will be placed later in the composed picture.
Then, when shooting the subject in a studio I only have 5 meters distance to work within. If I use the 35mm I'll have a different perspective due to the closer distance of the subject to the camera.
If doing this I'd guesstimate and shoot the subject with a 50mm to have a similar perspective.

But this gets even trickier if you take in to account that sometimes you have to shoot subject matter (a model boat for example) that is 1/10th the size of how it will be used in the composed picture.

I'm sure there must be a way to calculate the correct focal length to match a given subject/focal length/distance. But I'm math illiterate...

Thank anyway,

Kipling

Author Topic: Photography, Mathematics, and Boredom (Read 3150 times)