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Author Topic: Lenses, sensors, and spatial resolution  (Read 3916 times)

jrista

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Lenses, sensors, and spatial resolution
« on: December 08, 2011, 08:29:19 PM »
This thread is for continued discussion of a topic started in a CR thread on the T4i. Moving here to continue without commandeering the CR thread.

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Lenses, sensors, and spatial resolution
« on: December 08, 2011, 08:29:19 PM »

jrista

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Re: Lenses, sensors, and spatial resolution
« Reply #1 on: December 08, 2011, 10:11:14 PM »
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Yep....and that limit is reached when pixel density reaches infinity.  What you end up approaching is the limit created by optical aberrations + diffraction.  Many of the best lenses have almost no aberrations and thus you're approaching this limit:

@Lee Jay: You might want to check your facts. Assuming a perfect lens, there is a limit on how many line pairs per millimeter (lp/mm, or cycles/mm) that you can resolve with any optical system, and even assuming an optically perfect system at its maximum aperture (i.e. no aberrations), diffraction still limits the resolution of the image projected by the lens. For example, a "perfect" f/2.8 lens at Rayleigh can resolve an absolute maximum of 532 lp/mm, and the same lens stopped down to f/22 can only resolve 68 lp/mm. Image detail at Rayleigh is the lowest level of contrast that can reasonably be differentiated by the human eye, or 9% contrast. For reference, the 7D's 18mp sensor resolves 116 lp/mm, so that perfect lens at f/22 resolves only about half of the resolution the sensor can capture, or almost twice its nyquist rate. At a more reasonable level of contrast, say 80% (a pretty common target level for camera lens MTF charts), the same lens would only be capable of resolving about 13lp/mm @ f/22!!

This article on Luminous Landscape might shed some insight on optical resolution and its physical limitations:

http://www.luminous-landscape.com/tutorials/resolution.shtml

Assuming no optical aberrations, the physical size of the aperture affects the maximum resolution, and that maximum SHRINKS as f/# is increased since the airy disc grows with smaller apertures. Note that when I say image, I mean the virtual image of the world the lens captured and projected. The only reason to increase sensor resolution beyond the resolution of the projected image is to minimize artifacts that may be produced by the sensor itself, such as moire (in B&W or Foveon sensors) and color moire (in bayer sensors), but only to a certain point. Many smaller camera sensors used in compacts already FAR outresolve their lenses with incredibly tiny 2 micron or smaller pixels. The lenses for such cameras tend to have such small apertures that they are effectively pinhole cameras, which produces enough diffraction to go well beyond the diffraction limit of the sensor. At that point, the entire system is diffraction limited, and you are getting NEGATIVE returns...very soft images that almost look watercolor in appearance in the worst case. The simple fact of physics is that diffraction always exists, at any aperture, and the tighter the aperture, the larger the airy disc.

Most astrophotography I've done myself or done by friends is usually at an aperture of f/8 or f/10, since those are very common apertures of high quality consumer-grade telescopes. The types of sensors in CCD imaging devices and DSLR's attached with a T-ring are usually diffraction limited at around f/11-f/16, and end up encountering detrimental softening at f/22-f/28 and beyond. That's nothing to speak of the effects of atmospheric interference that further degrade the quality of light. The only f/30 images I've seen from telescopes came from a Celestron EDGE telescope, and while the definition of edges of celestial objects seemed sharper, other detail was visibly soft.

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This is why a lot of astro folks shooting planets with 5.6 micron pixels (roughly 40D size) will shoot at f/28-f/40 (f/30 is common) - that's where they can extract all the detail their aperture can give them.  For example, these were shot by a dedicated amateur with a backyard scope of 14" of aperture at somewhere close to f/30:

http://www.damianpeach.com/barbados10/2010_09_12pic.jpg
http://www.damianpeach.com/barbados10/20100912whole.wmv

Regarding the links, there does not appear to be any embedded EXIF metadata, so I can't verify the aperture. The shot of Jupiter appears fairly soft, but I'm honestly not sure if that is due to atmospheric interference or a small aperture. Even in astrophotography circles that I know, its well known that reducing aperture beyond a certain point reduces spatial resolution, it does not increase it (reducing aperture increases resolution it early on because optical aberrations overpower diffraction at wide apertures.) The resolution of any imaging system, lens and sensor/film included, is not an ever increasing linear curve, its more of a bell curve. Image clarity (resolution and acutance) peaks and optical aberration bottom at a certain midpoint. Before that midpoint optical aberrations diminish sharpness, while after that midpoint diffraction diminishes sharpness. The sweet spot is usually only around a stop wide given lens+sensor. The following link demonstrates the impact on image resolution with the Canon 450D. It has a 5.2 micron sensor (similar to the 40D), which is diffraction limited at just over f/10. I've configured the tool to compare f/2.8 to f/11 to demonstrate how diffraction visibly degrades resolution at the smaller aperture (mouse over the image to see f/11, mouse off to see f/2.8).

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=458&Camera=460&Sample=0&FLI=0&API=2&LensComp=458&CameraComp=460&SampleComp=0&FLIComp=0&APIComp=6

I've heard of astronomers using smaller aperture telescopes to view very bright objects, however I think thats a matter of reducing exit pupil size of the telescope relative to the pupil size of your eyes, rather than as a matter of increasing the detail in the image projected by the lens. A slightly smaller exit pupil in a telescope (or binoculars) relative to the entrance pupil of your eyes helps prevent your eyes from reacting to a perceptibly "bright" object by shrinking the pupil even farther. That tends to darkens the image too much, which has the effect of reducing contrast, which affects how easy it is to see detail in whatever it is your observing. I don't know that the same rules apply when photographing stellar objects, and from a physics standpoint, assuming you used a Canon 7D to photograph stellar objects, I would assume an f/8 telescope would probably produce the clearest images with the best detail.

Lee Jay

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Re: Lenses, sensors, and spatial resolution
« Reply #2 on: December 12, 2011, 08:31:06 PM »
Quote
Yep....and that limit is reached when pixel density reaches infinity.  What you end up approaching is the limit created by optical aberrations + diffraction.  Many of the best lenses have almost no aberrations and thus you're approaching this limit:

@Lee Jay: You might want to check your facts. Assuming a perfect lens, there is a limit on how many line pairs per millimeter (lp/mm, or cycles/mm) that you can resolve with any optical system, and even assuming an optically perfect system at its maximum aperture (i.e. no aberrations), diffraction still limits the resolution of the image projected by the lens.

Of course, and I posted that:

http://en.wikipedia.org/wiki/Spatial_cutoff_frequency

Quote
Quote
This is why a lot of astro folks shooting planets with 5.6 micron pixels (roughly 40D size) will shoot at f/28-f/40 (f/30 is common) - that's where they can extract all the detail their aperture can give them.  For example, these were shot by a dedicated amateur with a backyard scope of 14" of aperture at somewhere close to f/30:

http://www.damianpeach.com/barbados10/2010_09_12pic.jpg
http://www.damianpeach.com/barbados10/20100912whole.wmv

Regarding the links, there does not appear to be any embedded EXIF metadata, so I can't verify the aperture.


Damian shot with a C14 at about 10m of focal length.  10,000mm/355.6mm = f/28.

Quote
The shot of Jupiter appears fairly soft, but I'm honestly not sure if that is due to atmospheric interference or a small aperture. Even in astrophotography circles that I know, its well known that reducing aperture beyond a certain point reduces spatial resolution, it does not increase it

He's not reducing aperture - it's 14 inches fixed.  He's increasing focal length.

RayS2121

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Re: Lenses, sensors, and spatial resolution
« Reply #3 on: December 12, 2011, 09:12:01 PM »
Jrista, with all due respect, within a span of few days you among others have started multiple new threads ALL of which directly or indirectly rehash the dead old horse of MP vs ISO, an already well covered and beaten-to-a-pulp suject here in these forms...  by the second reply we are back to the I want higher MP lament. We get it! Some of you guys want more MP. Has this not been dredged enough? what more can be said on this subject that will convince the group? This subject is like watching a Friday the 13th horror flick...where you slay Jason and he is back in the next frame! :) I stopped commenting but new threads which are "continuations" of something are back. Very tiring. Again, this not meant to be mean...  Cheers!

jrista

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Re: Lenses, sensors, and spatial resolution
« Reply #4 on: December 12, 2011, 09:19:35 PM »
Well, I started two. This one, which was to pull off a conversation from an official CR thread that I did not want to take over (I was trying to be polite.) It seems it died the day I started it. I started another one, as I had to address some of the crazy anecdotes that are flying around here (and I've been thouroughly smited for it, too! :p). Beyond that, I can't be held accountable for what other people do, although I am a bit surprised the whole MP thing seems to have taken off like wildfire.

jrista

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Re: Lenses, sensors, and spatial resolution
« Reply #5 on: December 12, 2011, 09:53:31 PM »
He's not reducing aperture - it's 14 inches fixed.  He's increasing focal length.

Yes, very true. Its the f/# that really matters though or (the proper term is entrance pupil, I believe, although pupil diameters in telescopes always confuse me, since you have eyepieces and camera adapters and god knows what else, all with their own entrances and exits.) The size of the airy disc is magnified along with everything else as you increase focal length (otherwise telephoto lenses would perform spectacularly well at f/22 on modern DSLR's, however they tend to perform about the same as ultra wide angle lenses.) So, if you go from a 5m focal length to a 10m focal length, your entrance pupil relative to the focal length has shrunk, and that does affect diffraction.

Denabears

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Re: Lenses, sensors, and spatial resolution
« Reply #6 on: December 13, 2011, 04:03:03 AM »
The sweet spot is usually only around a stop wide given lens+sensor. The following link demonstrates the impact on image resolution with the Canon 450D. It has a 5.2 micron sensor (similar to the 40D), which is diffraction limited at just over f/10. I've configured the tool to compare f/2.8 to f/11 to demonstrate how diffraction visibly degrades resolution at the smaller aperture (mouse over the image to see f/11, mouse off to see f/2.8).

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=458&Camera=460&Sample=0&FLI=0&API=2&LensComp=458&CameraComp=460&SampleComp=0&FLIComp=0&APIComp=6


It is interesting to change the left hand camera on the tool to be a 60D set to f/11.   What I see is the 60D resolves at least 2800 lph while the 450D reaches about 2500 lph.  There is some aliasing, so I count the highest frequency that all lines are seen correctly as the result, but try with your own criteria, or method  - but don't be fooled by the change of image scale which makes the 60D look blurrier on first glance, even when it is sharper at the image level as evidenced by counting lines.

At f/11 the lens is diffraction limited. The square root of the number of ratio of pixel counts suggests a potential increase in resolution of up to 22% (and lest anyone says I'm stupid, no I don't expect that to be achieved).  Instead I see about 10% benefit. 

Now at f/2,  I see 3000lph with the 60D (starting to alias), and 2600 lph with the 450D (again there is aliasing) this time the 60D is 15% better. 

Keep in mind that the aliasing we see here tells us that for that amount of optical sharpness (diffraction, lens and AA filter limited) more pixels are needed just to sample the image properly.

Offered without comment, but at least I find it interesting.


Edits: I wrote lpw, probably should be lph, but I mean the topmost pattern with the number multiplied by 100. And the final results are ratios, so the units don't matter.
« Last Edit: December 13, 2011, 04:07:54 AM by Denabears »

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Re: Lenses, sensors, and spatial resolution
« Reply #6 on: December 13, 2011, 04:03:03 AM »