# Birds and Angular Resolution

Started Dec 2, 2011 | Discussions
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 Birds and Angular Resolution Dec 2, 2011

I have had an SX30IS for almost a year and this is my first posting to Canon Talk Forum. I have been particularly impressed by the bird photos posted on this site by several regular contributors. I have been unable to duplicate the sharp detail that they have achieved. My own pictures have been mainly through window-glass with the birds at a feeder 20 ft away, most often on dull days. A few pictures have been taken outside on bright sunny days from a distance of approximately 15 ft and these are better quality, but still not as good as those posted on this site. I have concluded that lighting is very important and that you experts must be usually less than 15 ft away from the birds and that you must have a lot of skill and patience and that the birds are not as afraid of you as they are of me. I would appreciate any comments about these conclusions.

(I am a retired physicist who is trying to talk about good pictures, whereas you people actually do it.)

Theoretical Angular Resolution of SX30IS
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Theoretically, the best angular resolution is with the maximum-diameter aperture, which occurs at F5.8 when the optical zoom is set to 35x.

So the aperture diameter is: (f / 5.8) = (150.5 mm / 5.8) = 25.95 mm. (Say 26 mm)

The Rayleigh Criterion specifies the angular resolution as = (wavelength / diameter).

A wavelength of 636 nm can be used to represent white light, which is actually composed of of a whole spectrum of various wavelengths.

Theoretically, for a perfect lens, the best possible angular resolution is therefore (636 x 10^-9 m / 25.95 x 10^-3 m) = 0.0000245 radians = 24.5 microradians.

Measured Angular Resolution of SX30IS
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Soon after getting my SX30IS, I wanted to determine its angular resolution at maximum optical zoom. I downloaded a USAF 1951 test pattern, printed it, and used it to test the camera outdoors on a bright sunny day. The test pattern consists of three black lines separated by white spaces that are the same width as the black lines.

The pattern of three lines is repeated in many different sizes. The angular resolution was taken from the smallest pattern for which the 3 separate lines could be distinguished, afterwards, in photos taken by the camera. The angle, in radians, is the line-pair separation divided by the distance of the target from the camera. (One radian is approximately 57 degrees, but it is easier to just work with radians, or microradians, which are millionths of a radian)

Example Calculation: [ 1.827 mm line-pair separation / (200 ft distance x 304.8 mm/ft) ] = 0.000030 radians = 30 microradians

The result of a series of tests was:

MEASURED ANGULAR RESOLUTION = 30 microradians at full optical zoom and F/5.8.

I think it is impressive that this value is almost as good as the theoretical Rayleigh Criterion for a perfect lens.

(The pattern was completely extinguished at 26.7 microradians, where the three-line pattern became just a single grey blob.)

I also tested printed text (arial bold) and found that it was just barely legible in photographs when the printing was 49 microradians high.

The printing could be read without difficulty when the printing height was 55 microradians (12-point printing at a distance of 178 ft.)

Relevance regarding Details in Photographs
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For the SX30IS using L format 14 MP (4320 x 3240 pixels) and 35x zoom, The full picture height covers an angle 0.0335 radians.

For M1 format 7 MP (3072 x 2304 pixels) and 35x zoom, there are 14.5 microradians per pixel.

Since the smallest angle that can be resolved is 30 microradians, it is impossible to see any meaningful detail at 35x zoom that is closer together than 3 pixels for L format or 2 pixels for M1 format.

Using 4x digital zoom brings the total zoom to 140X, which means that there will be 10.3/4 = 2.6 microradians per pixel but you will see no meaningful detail unless there is a separation of 30/2.6 = 11.5 pixels which is just lots of pixels with no meaningful information. The only use that I can see for the optical zoom is for large blow-ups where you want to avoid seeing individual pixels.

Indoor Experiment with a Bird Feather
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The feather that I used had regular dark striations every 0.25 mm apart and I took photos of it from a distance of 20 ft under normal incandescent lighting (P mode: typically 1/20s, F/5.8, 800 ISO)

The angle between striations is [0.25 mm / (20ft x 304.8 mm/ft)] = 0.00041 radians = 41 microradians. Even though this angle is larger than the 30 microradian resolution, the striations were NOT VISIBLE in the photos.

I then repeated the experiment with a light bulb close to the feather so that it was brightly illuminated (P Mode: typically 1/200 s, F/5.8 125 ISO). The striations were then CLEARLY VISIBLE in the photographs. (Note that, if the angle is less than 30 microradians, the striations would never be visible, no matter how strong the light source.)

I think that the reason for the poor resolution in low light is not the high ISO but the relatively long exposure times, which resulted in blur from the hand-held camera movement. Even though the IS of the camera is excellent, it can't compensate enough to give maximum angular resolution over 1/20 second.

SX40HS (I don't have one.)
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The angular resolution for the SX40HS should be the same as for the SX30IS at he same F/5.8. I don't know if the SX40HS allows a lower stop at 35x zoom, which would improve the resolution. Also, the greater sensitivity of the CMOS sensor should shorten the exposure time and thus lessen the blur of fine details.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

I am replying to my own post, which is probably not good etiquette, but it is 4 AM and I can't sleep. My post describes an indoor feather experiment, which I conducted just before posting. I concluded that, in less than bright light, the SX30IS's image stabilization was inadequate to take full advantage of the lens' angular resolution.

It occurs to me now that maybe I have been trusting the IS too much in all light conditions and that maybe a good tripod is absolutely essential for taking good detailed zoom shots of birds. Is that right?

I have a tripod that I bought for \$40 and it has a plastic head that keeps drifting even after it is locked in place. As a result, I have to steady the handle with my hand when using zoom and this re-introduces shake into the camera. Although the tripod is better than nothing, it is not much better than bracing the camera body against something steady, which is what I usually do. How much do you have to spend for a tripod that will be good enough for an SX30IS at full optical zoom on a dull day? An amount comparable to the price of the camera?

I have noticed a lot of sneering at super-zoom cameras on various forums. Canon's 800 mm lens costs about \$14,000 on sale and I suppose that you would need to get a pretty special SLR to go with that. Then, because the angular resolution is so good, you would need a rock solid tripod too.

For now, I intend to stick with my SX30IS, so any advice on tripods would be much appreciated. Thanks.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Re tripods. Plastic tripod heads are always unsatisfactory. Velbon Sherpa (see Amazon) is a metal headed one popular with birdwatchers - who appreciate a steady view at a reasonable price. However you may be able to improve the stability of your present tripod by hanging a suitable weight from it - a rucsac full of sandwiches and waterproofs etc is traditional. If you do buy a new one get the biggest you can manage. Shop around - I got mine for half the price of other sellers (on the web). Good luck.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Very interesting, thanks for posting. If using a relatively slow shutterspeed at full zoom (like e.g. 1/100 sec, in order to keep the ISO/noise down), you could try shooting a 3-5 shots burst. That'll improve the chances that at least one of the images are sharp. An easy way to find/select the sharpest image afterwards is to simply look at the JPEG file sizes. The largest file (mb) will also be the sharpest image (assuming same focus, framing, exposure, etc.).

P.S. - Most of your post was hidden below 'show signature'.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Stephen Barrett wrote:

For now, I intend to stick with my SX30IS, so any advice on tripods would be much appreciated. Thanks.

Get a Manfrotto 701 fluid head, on whatever tripod legs you choose.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Stephen Barrett wrote:

The Rayleigh Criterion specifies the angular resolution as = (wavelength / diameter).

Don't rely on the Rayleigh Criterion for resolution. Different scenarios required different parameters. Rayleigh is for splitting double stars - extremely high contrast subjects. Also, don't rely on 636nm. There are red birds, green birds, and blue birds, if it's birds you're shooting. Finally, the Bayer pattern is the probable reason for the difference in your test versus extinction resolution, not lens aberrations which are close to nil in the center of the frame, which is likely where you did your test.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Hi Stephen,

I have taken a few pictures through glass and they look extremely soft. I have been able to get sharp, detailed pics with the SX40 in both good light and not-so-good light without a tripod. I do use a monopod on occasion, but I really don't think its necessary unless the light is really poor. I am usually 10 feet away or less, but I have gotten acceptably sharp images from futher than that. The cardinal below was taken at about 30 feet, the chickadee at about 8 feet. You should also note that Kenn Thread always shoots handheld with the SX30. This is proof enough that a tripod is not necessary for amazingly sharp and detailed images. Patience is of course a cardinal virtue in bird photography (sorry). I have found that chickadees, nuthatches and woodpeckers don't mind my close presence nearly as much as do cardinals and other birds. My ratio of sharp to blurry pics is about 10-15/1. This is primarily because my birds don't sit still long enough to achieve and lock focus. The SX30/40's lens is sharper than we have a right to expect from such an inexpensive camera. I would say, work on getting the birds to the feeder, then acclimated to your presence, and then on achieving sharp focus.

Good luck and, BTW, are superluminal neutrinos real?

Roy

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 Re: Birds and Angular Resolution In reply to RoyAmatore, Dec 2, 2011

Thank you for the tips, Roy.

Your photos and Kenn's are just amazing. I particularly like the one that you took of a bird with a seed in its mouth and another of a young jay where you can see the hairs at the base of its beak.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Thank you, Retiredoc, Steen Bay, jfinger and Roy,

Re super-luminal neutrinos, there is a lot of skepicism about them.

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 Re: Birds and Angular Resolution In reply to Lee Jay, Dec 2, 2011

ljfinger wrote:

Stephen Barrett wrote:

The Rayleigh Criterion specifies the angular resolution as = (wavelength / diameter).

Don't rely on the Rayleigh Criterion for resolution. Different scenarios required different parameters. Rayleigh is for splitting double stars - extremely high contrast subjects. Also, don't rely on 636nm. There are red birds, green birds, and blue birds, if it's birds you're shooting. Finally, the Bayer pattern is the probable reason for the difference in your test versus extinction resolution, not lens aberrations which are close to nil in the center of the frame, which is likely where you did your test.

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Re: Rayleigh Criterion

I agree that you can get a little bit better detail for a blue bird and a little less for a red bird, but I still think that the best angular resolution for the SX30IS is somewhere around 30 microradians. You are right that there are other things that can make the detail worse than this. The point that I wanted to make is that you can't resolve smaller angles than this (except a bit by photographing only blue and purple birds). You can't disregard the Rayleigh criterion any more than you can disregard the law of gravity. This criterion shows that the SX30IS and the SX40HS are very close to the physical limits that can be achieved without going to a larger-diameter aperture. In other words it would do no good to replace the 14 MP and 12 MP sensors with 50MP sensors. You would get no more detail in the zoom shots, just more fuzzy pixels in between. Neither would it do any good to redesign the lens to have 40X or 140X optical zoom. Again, this would just add to the number of fuzzy pixels.

The only thing that will significantly reduce the resolution-angle is a larger-diameter aperture, which will result in a bigger, heavier, more expensive lens. I think that the Canon engineers have done a great job and there is no point in clamoring for more pixels or more zoom.

In my "feather experiment", I suggested that the lack of resolution in low light might be from camera shake (not lens aberration) but you may be right that there is some other factor causing it.
Thanks for the discussion.

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 2, 2011

Stephen Barrett wrote:

You can't disregard the Rayleigh criterion any more than you can disregard the law of gravity.

Sure you can.

The Rayleigh criterion equates to an MTF of 9%. What is special about 9%? Why not 5% or 10% or 50%? Or, more to the point, why not 0%, where you're really at extinction?

0%: http://en.wikipedia.org/wiki/Spatial_cutoff_frequency
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 Re: Birds and Angular Resolution... A little Physics humor :) In reply to Stephen Barrett, Dec 2, 2011

Stephen Barrett wrote:

ljfinger wrote:

The Rayleigh Criterion specifies the angular resolution as = (wavelength / diameter).
...

Re: Rayleigh Criterion

I agree that you can get a little bit better detail for a blue bird and a little less for a red bird, but I still think that the best angular resolution for the SX30IS is somewhere around 30 microradians. ...

Hi Stephen and Lee,

I certainly can't argue the physics or the optics, but this is certainly an interesting discussion.

We do have Eastern Bluebirds, (which aren't all blue) :

And we don't have any really red birds, but our male Cardinal comes closest:

Anyway, I'm not sure I can confirm from experience that the SX30 captures better detail based on different colors. But I have learned that Q1*Q2/4pi*Epsilon sub zero*Rsquared definitely proves to be true...
In that: The closer we get to the birds, the more attractive they become.

best regards,

Kenn

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 Re: Birds and Angular Resolution... A little Physics humor :) In reply to kenn threed, Dec 2, 2011

Wow! Those are amazing.

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 Re: Birds and Angular Resolution... A little Physics humor :) In reply to kenn threed, Dec 3, 2011

I dropped out of physics because of a really bad teacher. He tried to tell us that pies are square, or something like that.

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 Re: Birds and Angular Resolution... A little Physics humor :) In reply to RoyAmatore, Dec 3, 2011

RoyAmatore wrote:

I dropped out of physics because of a really bad teacher. He tried to tell us that pies are square, or something like that.

LOL - Hi Roy,

My (hopefully humorous) reference was to Coulomb's Law, which formulates the force of attraction or repulsion between two charged particles in space as being relative to the inverse square of the distance between them.

Kenn

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 Re: Birds and Angular Resolution In reply to Stephen Barrett, Dec 3, 2011

Very interesting calculations! Although as Lee Jay points out, MTF-wise, hard to know what's a gray area when shooting color. I think it is fair to assume that a black/white line pair represents maximum contrast, but even with a Bayer sensor I would be a little concerned about alignment effects for a rectangular sensor grid affecting the eyeballed MTF.

Your thoughts on the lack of detail gain from longer focal lengths are particularly interesting, as I had not thought of that limitation when playing with teleconveters on my SX30/40. Although there are other variables in lens design and quality, it is clear that the best performance I have seen from a TC is from a Canon design with a 90mm objective, which slightly lowers the f-number of the lens system on my SX40 even while extending the focal length from 150 to 225mm.

Regarding your original question, about achieving strong feather-detail in your bird shots, Roy and Kenn are showing (and telling) you what you already know: closer uber alles. Shutter speed should not be discounted though, the shot below, although at a slow shutter, was illuminated by a slave strobe giving very high effective shutter speed, and has resolution I have found difficult to match under normal lighting at the 41ft distance of the shot.

Keep experimenting and posting!

cheers

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 Re: Birds and Angular Resolution In reply to Vince Doran, Dec 3, 2011

Vince Doran wrote:

...was illuminated by a slave strobe giving very high effective shutter speed...

I just wanted to tell you something I found by testing a while ago.

My 550EX and 580EX have an effective illumination time of about 1/800th when fired at full-power. Not slow, to be sure, but not exactly very high either.

When fired at minimum power, I could get around 1/20,000th, but oddly, they would fire even lower than 1/128 (the minimum manual setting) in an automatic mode with suitable exposure to require it. They could get down to about 1/60,000th that way.

Just thought that might interest you.

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 Re: Birds and Angular Resolution In reply to Vince Doran, Dec 3, 2011

Vince Doran wrote:

Your thoughts on the lack of detail gain from longer focal lengths are particularly interesting, as I had not thought of that limitation when playing with teleconveters on my SX30/40. Although there are other variables in lens design and quality, it is clear that the best performance I have seen from a TC is from a Canon design with a 90mm objective, which slightly lowers the f-number of the lens system on my SX40 even while extending the focal length from 150 to 225mm.

The lack of detail gain was only if assuming a constant aperture diameter, I think. A longer FL with the same f-stop, like e.g. 1680mm equiv. f/5.8, would deliver more detail on the subject.

..but how about a shorter FL, with the same aperture diameter (app. 26mm) as now? Would a 100mm (558mm equiv.) f/3.85 lens in practice deliver the same amount of detail as 150.5mm f/5.8 does?

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 Re: Birds and Angular Resolution In reply to Lee Jay, Dec 3, 2011

Interesting indeed. Was your measurement setup difficult? That shot was with a cheap optically triggered slave sitting inside the feeder, and I've assumed that its burst was 1/1000 - 1/2000, but have made no measurements.

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 Re: Birds and Angular Resolution In reply to Vince Doran, Dec 3, 2011

Vince Doran wrote:

Interesting indeed. Was your measurement setup difficult? That shot was with a cheap optically triggered slave sitting inside the feeder, and I've assumed that its burst was 1/1000 - 1/2000, but have made no measurements.

Not difficult. I set up something spinning, and shot it with a known set of shutter speeds in bright light, then shot it with the flash and compared to find a match. For the really fast shots, I shot a 30,000 RPM Dremel wheel and measured the angular blur:

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