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December 13th, 2006, 12:06 PM  #1 
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XH A1 Zoom Number vs 35mm Equivalent Focal Length
The relationship between Zoom Number and focal length in Canon cameras is curvilinear. Method:
 Measured the width of the field of view (FOV) every ten Z Numbers.  Plotted the Z=0 and Z=99 FOV against the published focal lengths in an Excel chart, and let Excel calculate the linear regression for the expected FOV intermediate focal lengths.  Used the regression to convert intermediate FOV numbers to focal lengths.  Also converted actual camera focal lengths to 35mm equivalents (7.22 conversion factor).  Replotted focal lengths against Z Number. Here is the XH A1 chart. I didn't test the Wide Angle, but you should be able to multiply by 0.8 and get the 35mm equivalent focal length.
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December 13th, 2006, 01:22 PM  #2 
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That will come in handy. Thank you for that.

December 13th, 2006, 01:39 PM  #3 
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Thank you very much!
With my primary work being 35mm/digital photography, I have been trying to figure out a way to visualize this for a while. Thank you very much for your work on this.
I am going to print it and tape a laminated copy on my tripod leg for easy reference... 
December 13th, 2006, 01:41 PM  #4 
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Fov?
Is the FOV intentionally in inches or really in supposed to be in degrees?

December 13th, 2006, 04:30 PM  #5 
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Wow! Thanks. Very useful.
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December 13th, 2006, 05:55 PM  #6  
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Quote:
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January 26th, 2008, 12:24 AM  #7 
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Thread Resurrection!!!
wow, this is amazingly useful! If I wanted to find out the 35mm equivalencies for the zoom numbers 110 would I have to rerun the experiment with single zoom number increments to get accurate estimates, or could I just plug the values listed here for Z1 and Z10 into excel and run an identical analysis and get accurate answers? If so how would I do this? I am pretty much excel illiterate. Pete, if your still around  how did you do this?

January 26th, 2008, 04:41 AM  #8 
Wrangler

Thanks Pete! Very, very useful! Totally missed it the first time around. Based on your numbers, here's a rough, dirty, linear estimate of the 35mm equivalents between Z01Z10.
Z# / 35mm 10 / 148 09 / 136 (135mm) 08 / 125 07 / 113 06 / 102 (100mm) 05 / 090 (85mm) 04 / 078 03 / 067 02 / 055 (50mm) 01 / 044 00 / 032 (35mm)
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January 26th, 2008, 10:41 AM  #9 
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Great Michael! Can I ask how you extrapolated these?

January 26th, 2008, 01:58 PM  #10 
Wrangler

I guesstimated using Pete's calculations: 32mm at Z0 & 148mm at Z10. Turns out 11.6mm neatly adds up to 148mm. Not super accurate, but probably "good enough".
Z00/32mm + 11.6mm = ~44mm Z01/44mm + 11.6mm = ~55mm Z02/55mm + 11.6mm = ~67mm etc. Like they say ... mas o menos ...
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January 27th, 2008, 01:41 PM  #11 
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ok so I've run my own tests on the Z#s 115 to get as accurate results as possible. The only problem is I based my test on the FOV of the lens being 58 degrees at full wide and now I think this was a false assumption. I should have no problem converting all my data if I can find out the true FOV at full wide. Does anyone know this?
Also, the native resolution of the A1 being 1440x1080 vs 1900x1080 would result in the 1/3" sensor not having a practical sampling area of 3.6mmx4.8mm as traditional 1/3" chips do right? So would this need to be taken into account for determining FOV or does the automatic uprezing to full 1080 negate this? 
January 27th, 2008, 01:55 PM  #12 
Obstreperous Rex

Here's what I did to determine the focal length value for each Znumber, it's entirely different from Pete's mathematical methodology and surprisingly the results were also very different. Which leaves me very confused, since Pete is a rocket scientist in real life and not often prone to be wrong. So I don't know what's going on here. At any rate, my results were curvilinear too, but in the other direction from Pete's findings:
Code:
Z# F.L. 35mm  Z99 90 650 Z90 53 383 Z80 33 238 Z70 23 165 Z60 16.7 120 Z50 12.4 90 Z40 9.8 71 Z30 7.8 56 Z20 6.4 46 Z10 5.3 38 Z00 4.5 32.5 How did I get these numbers? I enabled Still Image Recording and shot a .jpeg to the SD card at each Z number, and then noted the focal length as reported in the EXIF data which accompanies each image. My target was a brick wall about fifteen feet away. Anybody want to take a stab as to why the EXIF data is so very different from the F.O.V. test? Could the reason be related to the distance of the target? (See all of my target images w/EXIF data at http://www.dvinfo.net/gallery/browseimages.php?c=53)
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January 27th, 2008, 04:22 PM  #13 
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chris, your findings seem much more inline with mine. Though I started with an incorrect FOV for full wide, the ratio of FOV values from one to the next as well as across the overall range seem very similar to your values. I basically started with the [false] assumption that at 32.5mm (4.5mm nonadjusted) the field of view would be 58 degrees and placed a ruler at a distance from the lens such that exactly 29cm were visible thus calibrating every 1/2 cm to equal a full degree. Then I just noted how many "degrees" were visible a each z#.
But you say that when you take a still it embeds the focal length info? I certainly can't think of any reason why this would not be the most accurate data to go off of since it's coming straight from the camera. 
January 27th, 2008, 04:55 PM  #14 
Obstreperous Rex

There's a lot of shooting information in the EXIF data embedded in each still image:
Code:
File Name Z99.JPG Camera Model Name Canon XH A1 Shooting Date/Time 12/17/2006 6:08:34 PM Shooting Mode Manual Tv (Shutter Speed) 1/30 Av (Aperture Value) 4.0 Light Metering Center Weighted Avg. ISO Speed Auto Lens 4.5  90.0 mm Focal Length 90.0 mm Digital Zoom None IS Mode Off Image Size 960x540 Image Quality Superfine Flash Off White Balance Auto AF Mode Continuous AF Color Space sRGB File Size 239 KB Drive Mode Singleframe shooting
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January 27th, 2008, 09:38 PM  #15 
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Chris and I had actually been communicating via email about this discepancy. We were really scratching our heads but then I have to admit that when the thread went dead before we figured out the reason for the difference, I let it drop.
Still don't understand it, but then I'm nobody's expert in optics. Figure it either has to be a flaw in my technique or something peculiar about these complex multielement lenses. Having only the 90mm and 4.5mm focal lengths and nothing in between, I did have to assume standard "rectilinear lens" equations applied (See this wiki page: http://en.wikipedia.org/wiki/Angle_of_view). That may or may not be the case, perhaps having to do with the behavior of a big zoom lens like this. One mistake I did make was to do my set up fairly close so I could get pretty accurate measurements using a 48" carpenter's rule. Chris had his brick wall closer to infinity but the measurement accuracy was a little more difficult..."was that image 6.25 or 6.33 bricks wide?" Surprisingly, though, when I gave it a go, his numbers came out similar to mine and letting Excel run a polynomial regression on the curve (that's the red line) makes the curve pretty darn clean (see attached screenshot of the graph). BUT, I used the same technique as described below, so any assumptions or errors would be duplicated. I guess what I can say is the proportions of the image width at each Znumber ARE pretty much correct (and I'd use the FOV numbers from the graph of Chris data since the distance he shot was closer to infinity). The question is whether there is some trick I'm missing in converting the image width into a lens focal length. I have to admit, seeing a minimal difference in the width of the frame going from Z99 to Z95 makes it hard for me to believe the EXIF data that drops the zoom by almost half. And conversely it makes more intuitive sense to me that the wide end, with a much greater relative change in image width from, say, Z0 to Z5, would have a larger focal length increase. Best I can understand, a doubling of focal length ought to halve the field of view for a rectilinear lens focused at/near infinity. But things ain't always what they SEEM, and I think it is a safe bet the the folks who design the lenses and the camera firmware that spits out the EXIF data know a bit more about optics than I do! Anyone a realdeal whiz at optics that can solve this puzzle?
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