[RioRico]

For those interested it is based on the fact that if the camera rotates off-axis to a certain angle the image moves across the sensor a certain distance image.error where:

image.error = angle x focal.length

Note: this is the same simple equation that gives rise to the shutter.speed ~ 1/Focal.length rule. When macros are involved focal length should be multiplied by (1+magnification) - ie, the actual distance between lens and sensor.

Elsewhere here (https://www.pentaxforums.com/forums/pentax-slr-lens-discussion/183204-fast-wi...ml#post1919555 and followups) I expounded a bit on applying the 1/FL rule to fisheyes.

We use 1/FL as a shortcut that works with rectilinear lenses but not necessarily with fisheyes, because of their wider AOV at any specific FL. I still don't quite see how to derive a 1/FL equation from AOVs, but I think a 10/3.5 fisheye (AOV=175 degrees on my K20D sensor) is effectively 1.66x as 'fast' as a 10/3.5 rectilinear (AOV=109 degrees) in terms of stopping motion. 175/109= 1.666.

NOTE: I use those AOVs because although a nominal APS-C frame has a 30.1mm diagonal, my K20D and other Pentax sensors have a 28.1mm diagonal. And a caveat: I don't use 1/FL as a rule for *best* sharpness but for *acceptable* or *equivalent* sharpness. For best sharpness, I use 1/FL with SR on, or 1/(~4FL) with SR off.

So my question is: How do we factor AOV rather than FL into the SR and 1/FL equations?

[newarts]

So my question is: How do we factor AOV rather than FL into the SR and 1/FL equations?

I don't think any changes to the 1/fl rule are needed because the angles involved are very small; it isn't really the focal length of the lens that's important, it is the distance from lens to sensor. Besides the 1/fl rule is just an approximation.

Here's how it works; when the camera turns at a particular rate (like it was sitting on a turntable turning at some RPM). As the camera rotates, an image point moves across the sensor:

image.point.motion = 2Pi*RPM/60*Exposure.time*focal.length

To avoid motion smear the image point must move less than about 1/1000 of the sensor width (equivalent to one display pixel), or about 0.025mm..Rearranging the equation to solve for exposure.time,

Exposure.time.sec = (0.025mm*60)/(2Pi*RPM)/Focal.length.mm

It turns out (for most people) that

Exposure.time.sec ~ 1/focal.length.mm

This implies that the average camera rotation rate (like it was sitting on a turntable) is about 1/4 RPM

Clearly this is not a precise rule and there will be a large dependence on the individual and situation. The result also depends on the sensor size but not so much as one might think because for the same scene one chooses focal lengths that are proportional to sensor size so there's no predicted crop factor effect. (I didn't realize that clearly until writing this post.)

I hope this is not too confusing...
Dave

[theunartist]

I took my A 35-70/4.0 out for a spin and did a simple test. I've always used 70mm for SR since I take most of my pictures at or near this range. If I did use the 35mm end at this setting I always thought it was a bit soft. Below are a couple of pictures where I did change the SR length and I am pleasantly surprised by the 35mm shot/sharpness, both shot at ISO1250 f5.6, very tight crops and jpegs no PP. Or it may just be psychological effects of the change on my mind

35mm


70mm


*Otherwise with all the formulas previously posted, I will need to get "SR Focal Length for Dummies"

[MSL]

I took my A 35-70/4.0 out for a spin and did a simple test. I've always used 70mm for SR since I take most of my pictures at or near this range. If I did use the 35mm end at this setting I always thought it was a bit soft. Below are a couple of pictures where I did change the SR length and I am pleasantly surprised by the 35mm shot/sharpness, both shot at ISO1250 f5.6, very tight crops and jpegs no PP. Or it may just be psychological effects of the change on my mind

I'm not sure this test tells us much. What shutter speed did you use as if it was fast enough SR isn't doing anything to help. If I understand right, you shot each of the photos with the correct SR setting for the focal length. What would be more interesting would be to add 4 more photos - taking the same shots with the opposite SR correction (35 for the 70, 70 for the 35), and taking the same shots with SR off.

[theunartist]

I'm not sure this test tells us much. What shutter speed did you use as if it was fast enough SR isn't doing anything to help. If I understand right, you shot each of the photos with the correct SR setting for the focal length. What would be more interesting would be to add 4 more photos - taking the same shots with the opposite SR correction (35 for the 70, 70 for the 35), and taking the same shots with SR off.

Handheld 1/25 for each shot even at ISO1250, dim backroom lighting.

For the A35-70, I rarely used the wide end thinking it was too soft but after seeing the results above, I'm pretty sure setting the correct SR Length did help in this instance. That doesn't mean I will stop and change length for each shot, I will probably try 2 "middle zones" instead to keep my sanity plus less wear on toggles, buttons and wheels...

[RioRico]

@Rick,
Fortunately my 35-70 is an F not an A, heh heh. But if it was MF I'd have to choose between:

1) setting the exact FL each time
2) using the mean: 52.5mm, rounded to 50 or 55
3) using the algorithm: 4900/105= 47mm, rounded to 45 or 50

So I might try 50mm and see if each extreme are 1) acceptable and 2) similarly soft|sharp. Or I might just leave SR off and insist on using the 1/(~4FL) for sharp images or 1/FL for acceptable.
___________________________________

@Dave,
I still don't see that the motion-stopping shutter speed would be the same for a 10mm fisheye (AOV = 175 degrees) and a 10mm rectilinear (AOV = 109 degrees). If both look at the same subject from the same distance with the same motion, the subject would make a larger arc on the rectilinear, larger by 175/109= 1.666x.

One approach might be to use the de-fished effective FL of a fisheye. That makes my Zenitar 16/2.8 an effective 12mm, and my DA10-17 @10mm an effective 4mm. I'll try 1/4 second handheld with SR off, see how sharp images seem. I don't think I can tell the K20D's SR'bot to use 4mm though.

--Rico

[newarts]

...
@Dave,
I still don't see that the motion-stopping shutter speed would be the same for a 10mm fisheye (AOV = 175 degrees) and a 10mm rectilinear (AOV = 109 degrees). If both look at the same subject from the same distance with the same motion, the subject would make a larger arc on the rectilinear, larger by 175/109= 1.666x.

One approach might be to use the de-fished effective FL of a fisheye. That makes my Zenitar 16/2.8 an effective 12mm, and my DA10-17 @10mm an effective 4mm. I'll try 1/4 second handheld with SR off, see how sharp images seem. I don't think I can tell the K20D's SR'bot to use 4mm though.

--Rico

I don't know what's going on in the cases you describe for very wide angle lenses. Maybe you could do a simple test for us where you use such lenses to focus on something at infinity in the center of the screen, then see what happens when the camera is turned just a little on the tripod (like nodding your head no) use some small, repeatable rotation like 5 degrees. Is the shift at the center on the image proportional to the focal length? (other things may be happening at the edges because of distortion due to lens design.)

I have no uwa lenses to try, but the underlying theory is so straightforward that it is hard for me to imagine that it is wrong.

Dave