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Author Topic: Lens 'resolving power' vs sensors.  (Read 14180 times)

sanj

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Lens 'resolving power' vs sensors.
« on: February 14, 2012, 09:06:38 AM »
Hello experts.
I keep hearing that current Canon lenses are not 'good enough' for newer/better sensors. I would really appreciate a lesson on how this works.
Thx...

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Lens 'resolving power' vs sensors.
« on: February 14, 2012, 09:06:38 AM »

jrista

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Re: Lens 'resolving power' vs sensors.
« Reply #1 on: February 15, 2012, 03:09:00 AM »
To start, its best to measure resolution in lp/mm, or line pairs per millimeter. This is a measure of spatial frequencies...light/dark oscillations or waveforms that compose a two dimensional image, be that the virtual image projected by a lens, the image recorded by film or a digital sensor, etc. Measurement in line pairs, or a light line paired with a dark line, is essential to measure microcontrast, or the ability to discern the difference between a light line and a dark line that are right next to each other.

(NOTES: For reference, the human eye is able to discern a line pair when contrast is as low as 9% (this is called Rayleigh Criterion). Modern sensors capable of barely resolving detail around the same level, probably closer to 12-15%, however at such levels details can become inconsistent and often "useless". Low-pass filters are usually used to cut off spatial frequencies somewhere below this level to eliminate what effectively becomes additional image noise and possibly moire in the presence of regular repeated patterns. Sensors can only really resolve a line pair as consistently separate light and dark lines when contrast is about 50%. For any imaging medium to resolve a line pair, it must have twice the resolution as the frequency being sampled...so for a sensor to resolve 100 lp/mm, it must have at least 200 rows of pixels per millimeter. This called the Nyquist Rate, and the maximum resolution of an image that can be captured...the maximum frequency that can be usefully sampled...is the Nyquist Limit.)

Both lenses and sensors have resolution, and they can be measured independently of each other, as well as part of a greater whole. When it comes to sensors, its pretty easy to compute the theoretical resolution. This is usually pretty close, although not exactly the same as, real-world resolution. Real-world resolution can differ a bit when you factor in bayer interpolation, low pass filters, bayer array layout, etc. I'm going to quote from another answer I gave on another topic, as it has relevant information about sensor resolution:

I'm wondering though, how the line widths/ picture height (LW/PH) figures from lense tests translate to sensor resolution.
So 18MP result in 3456 "lines per picture height", while the highest LW/PH scores for APS-C I found were around 2600. If this was a 1:1 conversion, no APS-C sensor above 12MP would be of much use. So I'm guessing that's probably not it. I'd like to find a way to calculate the corresponding sensor resolution to any given lens resolution (and vice versa) OR know why this is not possible. Can anyone help?

If I understand how your measuring LW/PH, then an 18mp APS-C sensor resolves the same as an 18mp FF...both the 7D and the 1D X produce images that have 3456 lines. Generally speaking, a more tech-agnostic way to measure resolution is with lp/mm, or line pairs per millimeter (its important to use the term line pair, which denotes the waveform nature of spatial frequencies, a light line (white) followed by a dark line (black)...for camera sensors, line pairs generally need an MTF of 50% contrast, or not fully resolved but about half way there...to be clearly imaged as a full "line pair"...anything less and you are losing resolution to diffraction). In that respect, the highest resolution APS-C's are able to resolve more detail than an 18mp FF sensor, which is exactly correct...the 7D (or for that matter the Sony A77 @ 24mp APS-C) is a higher resolution sensor from the level of fineness of detail resolved than the 1D X...its just in a smaller package with a crop factor. In resolvable lp/mm, an 18mp APS-C sensor can resolve 115.97 lp/mm (3456 lines/14.9mm sensor height = 231.94 l/mm, divide by two to get lp/mm). The 18mp FF sensor of the 1D X, however, can resolve 72 lp/mm (3456 lines/24mm sensor height = 144 l/mm, divide by two to get lp/mm). It is possible to derive the necessary FF megapixels that would produce the same fineness of detail as an 18mp APS-C sensor if you were interested. Take the height and width of the APS-C, calculate the lp/mm for both dimensions, and derive the image width and height for FF from that by multiplying by the correlated sensor dimensions:

 3456L/14.9mm = 231.94 l/mm
 5184L/22.3mm = 232.47 l/mm

 231.94 l/mm * 24mm = 5566 L
 232.47 l/mm * 36mm = 8368 L

 5566 * 8368 = 46,576,288 pixels ~= 46.6mp

You would need a 47mp FF sensor to capture the same lp/mm, or "resolution", as an 18mp APS-C sensor. For reference, the 36.3mp Nikon D800 sensor resolves about 102.3 lp/mm, so even though it has greater megapixels than an 18mp 7D, the 7D is still resolving slightly more detail at a pixel level (barring any intrusive factors such as sensor noise...can't say exactly how the noise of the D800 will be in real-world tests.)

The story is not quite as cut and dry as that, given that (excluding Foveon) most sensors are bayer arrays, usually with a low pass filter in front of them, so that mucks with the final resolution a little bit, and makes it tough to nail down nyquist limit...but from a theoretical standpoint, there you have it.

Lenses themselves are projecting a virtual image that is simply recorded by the sensor, however the resolution of the image projected by a lens does not have a single "resolution". Depending on the aperture setting, and whether you measure resolution at the center of the lens or the edge of the lens, lens resolution will vary considerably. Assuming an ideal, or "perfect" lens, one that is entirely free of any form of optical aberration, the maximum possible resolution at maximum apertures above f/4 can FAR outresolve current sensors at minimum detectable contrast, and considerably outresolve them at 50% contrast (a key level, as noted above.)

Perfect lenses are also called "diffraction-limited" lenses, in that the resolution possible is only limited by diffraction and not optical aberrations. Real-world lenses tend to be aberration-limited at wide apertures, and diffraction limited at narrower apertures, and the narrower the aperture, the more diffraction will limit maximum resolution. Thus the reason why a photo will start to soften beyond f/11, and exhibit pronounced degredation beyond f/22, on an APS-C sensor. Because of optical aberrations at wide apertures, lenses exhibit idealistic behavior at middle apertures, such as f/8. However thats just about where things get dicey from a whos-outresolving-who standpoint.

The highest resolution Canon sensor on the market today, their 18mp APS-C sensors, resolve 116 lp/mm (see quote above for reference and details about how this number is derived.) If we assume a perfect lens, at f/2.8 and 50% contrast, you can resolve about 247 lp/mm, which is slightly more than twice what Canon's highest resolution sensors are capable of resolving (for reference, you would need a 210mp FF or 81mp APS-C sensor to resolve that much detail.) Given that real-world lenses are aberration-limited at wide apertures like f/2.8, lets take a more realistic aperture. The Canon 7D 18mp APS-C sensor is diffraction-limited at f/6.9, so if we assume an f/7.1 aperture, we can resolve roughly around 95-100lp/mm. The sensor is now outresolving the lens at this aperture, and all apertures smaller than f/7.1. At f/8 the lens can only resolve 86 lp/mm, f/11 it drops down to 63 lp/mm, and at f/22 it is at a mediocre 30 lp/mm!! The same lens at f/6.3 would probably resolve just about 118 lp/mm, just ever so slightly better than what the sensor is capable of resolving itself.

When it comes to resolution, its not quite a simple as "Lens A outresolves Sensor A, but Lens B does not". For pretty much any lens these days, at f/8, pretty much all modern sensors with at least 15mp are capable of resolving enough detail to match the lens. Its at wider apertures where lenses have the potential to resolve considerably more detail, and how much more depends on how well aberrations (and flare) are controlled. The more aberration and flare control a lens has, the sharper it will be at wider apertures, and the more likely the lens will be to outresolve even the highest density sensors.

As for Canon lenses, it depends on what you mean by current. Canon made a claim (I forget where...I've been searching for the reference) that their "newest" L-series lenses, which at the time seemed to mean their Mark II lenses and all "new entrants", or brand new designs like the 8-15mm L Fisheye, are capable of resolving approximately enough resolution for a 45mp full-frame sensor. This accounts for a fair number of lenses released in the last several years, possibly as far back as 2006-2007. I believe a large part of the reason Canon is starting to release more updated lenses, such as the new 24-70mm f/2.8 L USM II, despite the fact that its predecessor was considered one of their best lenses ever...is to get resolution "up to snuff", and ensure they are capable of resolving enough detail for upcomming (and even current, when accounting for their 18mp APS-C sensors) ultra high resolution sensor designs.

For top end superteles like the 500mm L II and 600mm L II, given the stunning near-perfect MTF charts, I would effectively consider them "perfect", diffraction limited lenses at all apertures, and therefor capable of about 173 lp/mm at f/4. Thats enough resolution for a 103mp FF sensor, or a 40mp APS-C sensor.
« Last Edit: February 15, 2012, 03:14:57 AM by jrista »

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Re: Lens 'resolving power' vs sensors.
« Reply #2 on: February 17, 2012, 12:27:04 AM »
In non technical terms, what exactly do you mean by "resolving". I have read how the 7D images can look a bit soft at 100% but "resolve" well because there are so many pixels. In this case I assumed "resolved" meant going to 300dpi when printing. You have mentioned lenses resolving to sensors. It all got a bit too technical for me so I'm unclear.  I've been wondering what you guys mean by resolve for a while.
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jrista

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Re: Lens 'resolving power' vs sensors.
« Reply #3 on: February 17, 2012, 12:45:39 AM »
In non technical terms, what exactly do you mean by "resolving". I have read how the 7D images can look a bit soft at 100% but "resolve" well because there are so many pixels. In this case I assumed "resolved" meant going to 300dpi when printing. You have mentioned lenses resolving to sensors. It all got a bit too technical for me so I'm unclear.  I've been wondering what you guys mean by resolve for a while.

When referring to optical imaging systems...such as cameras, but not limited to them (telescopes, microscopes, etc.), "to resolve" means to "distinguish details", or to make details distinguishable. A lenses power to resolve details in a scene is limited, both by optical aberrations (physical effects caused by lens design, such as chromatic aberration, spherical aberration, field curvature, etc.), and resolving power essentially refers to where that limit lies.

Regarding the 7D's "softness", there are a few reasons for that. For one, the 7D does seem to have a slightly over-aggressive low-pass filter (AA, or anti-aliasing filter), so it blurs "useful" frequencies that actually represent good detail that can still be imaged by the sensor. Thats not the sole reason for the 7D's perceived softness though. Two additional factors, camera shake and quite literally insufficient lens resolving power, also limit its sharpness when viewing RAW images at 100%.

The higher the resolution of a sensor, the more important a stable camera is going to be to ensuring pixel-level sharpness. An 18mp APS-C sensor is one of the highest density DSLR sensors on the market, and it resolves an incredible amount of detail (116 lp/mm). Even the slightest amount of camera shake will affect detail, assuming the lens is even resolving enough to start with.

The extremely high resolution of the 7D also means that outside of the best of the most recent Canon L-series lenses, namely Mark II's and new designs like the 8-15mm L Fisheye, the 7D is very likely outresolving most lenses except for their very centers. Sharpness can fall off quickly from center to corner, particularly in lower-end lenses. Maximum sharpness is often lower than maximum contrast in many Canon lenses as well, so while...for the detail resolved...most Canon lenses offer excellent contrast, sometimes they don't resolve as much detail as is really required for a sensor that offers as much resolution as the 7D.

(I believe this is why Canon has been releasing updated versions of many of its lenses lately, even those that were previously considered their best lenses ever...like the 24-70mm L. When you compare MTF charts for Mark I and Mark II versions of the same lens, center sharpness is improved somewhat, however corner sharpness is often improved considerably. Its corner resolution where the resolving power of a lens really matters these days with high resolution sensors.)

jrista

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Re: Lens 'resolving power' vs sensors.
« Reply #4 on: February 17, 2012, 01:39:58 AM »
Just for reference, here are the resolutions, in lp/mm (line pairs per millimeter) for the highest resolution sensors on the market for prosumer and professional grade interchangeable lens cameras, ranked in order of physical resolution, not image resolution:

(Note: Excludes point and shoot or bridge cameras, which may have resolutions as high as 200 lp/mm, but represent an entirely different class of camera.)

Nikon v1 Mirrorless 10.1mp CX format
3872x2592 pixels; 13.2x8.8mm dimensions
Resolution: 147.27 lp/mm

Sony 24.3mp APS-C "Exmor" HD CMOS
6000x4000 pixels; 23.5x15.6mm dimensions
Resolution: 128.20 lp/mm

Olympus E-5 12.3mp Hi-Speed Live 4/3 MOS
4032x3024 pixels; 17.3x13mm dimensions
Resolution: 116.31 lp/mm

Canon 7D 18mp APS-C
5184x3456 pixels; 22.3x14.9mm dimensions
Resolution: 115.97 lp/mm

Canon 500D 15.1mp APS-C
4752x3168 pixels; 22.3x14.9mm dimensions
Resolution: 106.31 lp/mm

Nikon D7000 16.2mp APS-C (DX)
4928x3264 pixels; 23.6x15.6mm dimensions
Resolution: 104.62 lp/mm

Pentax K-5 16.3mp APS-C
4982x3264 pixels; 23.4x15.6mm dimensions
Resolution: 104.62 lp/mm

Nikon D800 36.3mp Full Frame (FX)
6144x4912 pixels; 35.9x24mm dimensions
Resolution: 102.33 lp/mm

Canon 1D IV 16.1mp APS-H
4896x3264 pixels; 27.9x18.6mm dimensions
Resolution: 87.74 lp/mm

Nikon D3x 24.5mp Full Frame (FX)
6048x4032 pixels; 35.9x24mm dimensions
Resolution: 84 lp/mm

Sony 24.6mp "Exmor" Full Frame
6048x4032 pixels; 35.9x24mm dimensions
Resolution: 84 lp/mm

Hasselblad H4D-60 Medium Format Full Frame
8956x6708 pixels; 53.7x40.2mm dimensions
Resolution: 83.43 lp/mm

Pentax 645D 40mp Medium Format "Cropped" DSLR
7264x5440 pixels; 44x33mm dimensions
Resolution: 82.42 lp/mm

Canon 1Ds III/5D II 21.1mp Full Frame
5616x3744 pixels; 36x24mm dimensions
Resolution: 78.63 lp/mm

Canon 1D X 18.1mp Full Frame
5184x3456 pixels; 36x24mm dimensions
Resolution: 72 lp/mm

Nikon D4 16.2mp Full Frame (FX)
4982x3280 pixels; 36x23.9mm dimensions
Resolution: 68.62 lp/mm

From that list, we have the Nikon D800 36.3mp sensor as the highest density full-frame sensor on the market, the Sony 24mp Exmor sensor as the highest density APS-C sensor on the market, the Canon 1D IV 16.1mp sensor as the highest density APS-H sensor on the market (obviously), and the Olympus E-5 12.3mp sensor as the highest density 4/3rds format sensor (4/3rds or micro 4/3rds, not sure which it is, as I don't really use that system.) I threw in the Pentas 645D and Hasselblad H4D-60 medium format sensors and the Nikon v1 CX sensor just for a basis of comparison.

Intriguingly, the Nikon v1 sensor has the highest physical resolution of all the sensors at 147 lp/mm. Unless the v1 system has unbelievable optics in the lenses, I'm a bit skeptical that any lens for that system can actually resolve that much detail except maybe at f/2.8 or f/3.5, and you would have to have some SERIOUS aberration control. I haven't seen any MTF charts for v1 lenses, so I really cant say anything definitively there...but I am indeed skeptical. The same would pretty much go for the Sony 24mm APS-C Exmor at 128 lp/mm...I haven't seen anything in any MTF charts that would indicate Sony/Minolta lenses are approaching perfection at f/3.5 or wider by any means, so I'm assuming that sensor thoroughly outresolves any lens you might throw at it.

The Pentax 645D is an intriguing control case, as it partially demonstrates why medium format sensors are capable of resolving such clean, noise-free detail despite their large image size. They have rather large pixels, spread over a very large sensor area. Its about the same density as the Hassy H4D-60, which is more of a true "full-frame" digital medium format camera at 54x40mm.
« Last Edit: February 17, 2012, 01:42:30 AM by jrista »

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Re: Lens 'resolving power' vs sensors.
« Reply #5 on: June 04, 2012, 04:30:52 PM »
If we assume a perfect lens, at f/2.8 and 50% contrast, you can resolve about 247 lp/mm...

How do you determine that number? The common formula of "1600/f-stop = lp/mm" means a perfect lens at f/2.8 would resolve about 571 lp/mm, over twice your figure of 247 lp/mm.
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Re: Lens 'resolving power' vs sensors.
« Reply #6 on: June 04, 2012, 04:39:06 PM »
Meh, Don't stress over resolving power and sensors too much. It usually works out fine when you do a good job getting correct settings.

I took the 7D which has one of the most demanding sensors from its lenses and shot with an old 1970's Cosina 200mm F/4 adapted from pentax K mount. It had horrid color and was optimized for B&W shooting. I took a couple of really nice sharp photos with it.
« Last Edit: June 04, 2012, 05:00:55 PM by RLPhoto »

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Re: Lens 'resolving power' vs sensors.
« Reply #6 on: June 04, 2012, 04:39:06 PM »

jrista

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Re: Lens 'resolving power' vs sensors.
« Reply #7 on: June 04, 2012, 04:50:33 PM »
If we assume a perfect lens, at f/2.8 and 50% contrast, you can resolve about 247 lp/mm...

How do you determine that number? The common formula of "1600/f-stop = lp/mm" means a perfect lens at f/2.8 would resolve about 571 lp/mm, over twice your figure of 247 lp/mm.

I am basing my numbers on an MTF of 50% (hence the "at f/2.8 and 50% contrast"). I believe the 1600/f-stop is based on rayleigh, or an MTF of 9%. MTF 50% is commonly used with photography, where as Rayleigh/MTF 9% is usually used in reference to human visual acuity (and then, usually referring to our ability to barely resolve two closely spaced points of dim light on a black background...i.e. stars). I prefer MTF 50%, as that relates better to the clear, sharply defined kind of detail people prefer in their photography, where as MTF 9% might apply assuming you were ok with detail of extremely low contrast (i.e. barely discernible differences.) To be exact, MTF at 9% is about 532 lp/mm, so the 1600/f-stop is really pushing it for cameras.

Once you get to that level, or when you start talking about MTF 0% (which technically is just barely above 0%), there are only a few cases where such low contrast is applicable. The most notable being the detection of binary stars from a what otherwise resolves as a single point-light source in astronomy & astrophotography...at just above MTF 0% you can detect whether a resolved point in a photograph represents a single star or a binary (or even ternary) star based on how the diffraction pattern presents.

Currently, there isn't a commercial-grade camera that can even come close to resolving that much detail, it usually requires high resolution, scientific-grade cooled CCD's and appropriate detection software. You can also use superresolution techniques with commercial-grade gear to produce images that can then be processed to identify binary stars at MTF 0%, which is something the amateur binary star discoverer can do these days if they wish, although its not as effective (superresolution is still a newer technique, and its not guaranteed to leave the presentation of a multi-star airy disc in tact in all cases.) The best consumer-grade sensors on the planet are barely capable of 130lp/mm, and when you factor in the nature of multi-component optical systems, the actual final spatial resolution of a whole camera system tends to be quite a bit lower than that of the highest resolution component (be it lens, sensor, whatever.) So...MTF 50%...in my opinion, it is more realistic for real-world photographers.



As a side note, modern lenses are not restricted to projecting light at any given contrast level. Measurements of resolution, in the form of MTF, determine spatial resolution at a given contrast level...the contrast level is a factor of the measurement, but it is not a limitation of the lens itself. As such, there is nothing to prevent a LENS from projecting an image at any contrast level...0% to 100%. It is entirely possible to project an extremely fine white line on a black background that is 1/(571*2)mm thick (0.000876mm) with a lens. The contrast of that line could be extremely low (so blurred that it barely registers more than pure black)...even below the level at which the human eye can detect (which would be 9% contrast), and well below the level at which the best modern DSLR or even medium format sensors could resolve in any meaningful sense.

There are some films that are capable of resolving far more than the best sensors today, such as a Zeiss film capable of resolving about 400lp/mm at ISO 25 (which, as far as I know, was only ever used for the purposes of testing a (possibly..it may still exist) short-lived and somewhat legendary...in certain circles...400lp/mm ultra fast lens.) It should be noted, however, that the nature of film and a very meticulous and expensive manufacturing process makes it a bit easier to support such incredible spatial resolutions (which would only be possible at very wide apertures, or at barely discernible contrast levels and narrower apertures). Most digital sensors follow a bayer array design, and usually have low-pass filters in front of the sensor. That puts a hard limit on the amount of resolution you can achieve digitally. Canon has claimed their newer L-series lenses (not exactly sure what "newer" means...from the time I read that, it was around 2008 or 2009, so perhaps within a few years of that date) are capable of resolving 45mp worth of full-frame CMOS sensor resolution...which pipes in at arounb 113-116lp/mm (f/5.6 or wider, as any narrower than that and diffraction limits your resolution.) A sensor might barely be able to resolve a
« Last Edit: June 04, 2012, 05:10:03 PM by jrista »

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Re: Lens 'resolving power' vs sensors.
« Reply #8 on: September 16, 2014, 09:11:48 PM »
To add a historical note, I remember the photo magazines of the '70's and 80's publishing test resolution of lenses, usually in lp/mm.   Most normal lenses considered as excellent had a center resolution of 90 - 100 but fell off dramatically towards the edges, the better lenses, macro, and Leica lenses usually reported a resolution spec of about 80-90 lp/mm but uniform from edge to edge.  I have used my old Leica and Nikon lenses with the EOS M (18 mp APS-C sensor) with excellent results (oh, but much slower work, no autofocus).  The old Nikon 55mm macro and the Leica Sumicron-C were truly perfect from edge to edge with the EOS M compared to the small errors seen in the magnified image with the two EF-M lenses.  The 4 Canon lenses I use have shown better overall resolving power by a combination of more modern optics and image stabilization (telephoto moon shots, macro bug and flower shots).  Based on the simple sensor size explanations of "jrista" a 40+ mp full frame sensor is needed to match the resolving power of the 18 mp APS-c and will not be outperformed by those old lenses but just could be by Canon's modern lenses.  At least one would hope so before Canon introduces a 40-50 mp FF sensor

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Re: Lens 'resolving power' vs sensors - what's fine these days
« Reply #9 on: September 17, 2014, 02:32:47 AM »
@ JRista

Just updating a couple of your sensor rez data examples.

Present MFT is over 16MP.
E.g.  OMD EM10, 4640x3472 in 17.3x13.0mm sensor = 134.1 lp/mm
The more I use this camera, the more I'm impressed with it!  I can only imagine a FF with pixels like this. (~9650x6450)


A very good lens for the moment is the 75/1.8


that's at 60 and 20 lp/mm

or the Sigma 60mm Art for $210, fantastic, not even considering the price!




Nikon 1 v3/j4 is over 18MP
5248x3502 in 13.2x8.8mm sensor = 198.8 lp/mm

There's some very good glass available, one of them's the cheap 30-110mm kit lens, under $300. (80-270mm FF equiv)
MTF below:





and their 10-30 kit lens:






Oh, ya, and the Pentax Q7 is a mere
4000 x 3000 on a 7.4 x 5.6mm sensor = ~270 lp/mm
I've got one of these things too; can't say I've got a lens that can keep up to it tho, altho the 8.5mm f/1.8 prime is decent.
The only thing reducing the quality of the images from these little camera systems is the per-pixel noise as their full-well counts are so low that shot noise is an issue much sooner than with larger sensors.

Edit: tired fingers and brain. at least one type fixed
« Last Edit: September 17, 2014, 02:35:09 AM by Aglet »

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Re: Lens 'resolving power' vs sensors.
« Reply #10 on: September 17, 2014, 05:32:15 AM »
Once you agree on what "resolution" means, there are a number of answers which can be verified in the real world.

There is the ability of a lens to render light to dark transitions "accurately."  Independent of how well contrast is rendered, you can have a very very sharp optic.  You often see this in tessar-formula, artar-formula, and planar-formula lenses from the time before optical coatings.

There is the ability of a lens to come as close as possible to matching the physical theoretic limits of diffraction.  Commercial available lenses used at f-stops between wide open and f/11 have diffraction limits (theoretic and practical) that are so far beyond a sensor's ability to capture that kind of resolution you don't need to worry about a thing.

These two way of looking at what I call pure resolution.  The human mind, however, "processes" more information than just physical resolution.  To a point, the human mind also interprets contrast as "sharpness."

This is why you have MTF charts.  They attempt to share how much contrast is passed through a lens.  Looking at manufacturing and various "test" websites data can be very confusing, as important details are many times left out.  You may be left wondering what you do with the data once you've seen it.

There are, minimally, three other optical effects which will impact the interpretation of "sharpness" by a viewer.  These are coma, chromatic aberrations, and field curvature.  Broadly speaking, coma takes a point of light and distorts it.  Chromatic aberrations take light to dark transitions and adds different colors to a scene, depending on which edge you're looking at (toward or away from the optical center).  Field curvature defines what portions of a scene are actually rendered in focus.

Coming back to the human mind and the way it interprets "sharpness", we need to consider how large an image is being viewed and at what distance.  We also need to consider how old the viewer is.  The older the viewer, the less stringent the "sharpness" criteria.

Why all this build up to providing a simple answer?  It's to, again, recognize that definitions are important.  Precisely what are we to consider?  Which leads me back to your question.

In terms of pure optical resolution (ignoring all other lens effects, unless you buy me a few beers and we have a few hours to consider the topic), and considering APS-C, Full Frame, or Medium Format sensors (an important point here), the sensor is the limiting factor to resolution when using a lens wide open down through f/11 (or for lower density sensors f/16).  Further, using jrista's sensor resolution calculations you can see what your sensor is capable of.

That's it.  It's that simple.  You can sleep well and call it "good to go."  The "sharpness" of a lens simply does not matter.

Ah, you say.  But the devil is in the details, right?  Yes and no. 

A couple things to remember: 
1) Camera manufacturers and stores are in the business of selling you things.  If they can get you thinking you need a "better" lens to shoot whatever new sensor is on offer, they get money and you feel safe, even as your wallet is significantly lighter. 

Looked at differently, humans have been making sharp lenses for hundreds of years.  The ability to design, grind, align, and build great optics has been with us a very long time.  All the little details have been worked out. 

It's come down to design for manufacturability, the all up Bill of Materials, and Gross Margin targets.  That's where the trade-offs are made.  Which is why when you "test" a cheap kit lens by shooting a brick wall you might be disappointed with the results when shooting wide open (for instance).  Yet when shot at f/5.6 or f/8 you probably can't tell the difference between the cheap kit and the hugely expensive L-glass output (I certainly can't and I've looked at this stuff for decades).

2) If you believe that the 1/r formula brings the lens back into the resolution equation, then explain why, in physical (as in science) real world testing (as in the things we can engage in directly) using a Canon 7D that resolves 116lpmm you see 116lpmm resolution as measured using a USAF Resolution Test Chart.  For 1/r to "work", wouldn't you get a much lower resolution number?

Further, how is it that I have a USAF spec'd 75mm f/5.6 Biogon design lens that is, in fact, diffraction limited from wide open?  Three different companies made these and they were quite common in army surplus stores back in the day.  The optic covers 5x5 inches.  That's right, inches.

Tested six ways to Sunday using a wide variety of silver based films, including high contrast 1000lpmm technical films the results are the same?  It's either the resolution of the film or it's the diffraction limits of the lens (if the film can handle it).  It's never been, is not now, and never will be explained using 1/r.
- It's the brain behind the eye behind the eyepiece that counts.
- The sharpest lens I own is a tripod.
- Equipment sitting there on the table, while amazing by any and all human measures, can't produce a brilliant piece of work without serious human intervention.

AlanF

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Re: Lens 'resolving power' vs sensors.
« Reply #11 on: September 17, 2014, 06:16:48 AM »
The theoretical resolution of the 12.1 mp 1/2.3" sensor of the SX50 is 323 lp/mm (1.54 µ pixels).
The theoretical resolution of the 16.1 mp 1/2.3" sensor of the SX60 is 371 lp/mm (1.34 µ pixels).

But, the Airy disk diameter for f/6.5, the widest aperture at telephoto lengths, is 8.7 µ, and the SX50 becomes diffraction limited at f/2.5 and the SX60 at f/2.2. The system is mainly diffraction limited, not sensor limited

In other words, there is no real gain in resolution using the 16.1 mp sensor and it will be noisier!
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jrista

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Re: Lens 'resolving power' vs sensors.
« Reply #12 on: September 17, 2014, 12:39:25 PM »
There is the ability of a lens to come as close as possible to matching the physical theoretic limits of diffraction.  Commercial available lenses used at f-stops between wide open and f/11 have diffraction limits (theoretic and practical) that are so far beyond a sensor's ability to capture that kind of resolution you don't need to worry about a thing.

It isn't as simple as that. Resolving power is always measured relative to a contrast level. Historically, MTF50, or the transfer function at a contrast level of 50%, has historically been used to measure the resolving power of lenses, sensors, and systems. You can measure at contrast levels below 50%, however the closer you get to Rayleigh (MTF9), the more difficult it becomes to differentiate real detail from noise. Additionally, at lower contrast levels, it is generally implicit that the "edge detection" of whatever is doing the resolving is lower...the loss of contrast comes from softer edges.

Now, even at the rayleigh limit, at f/11, your resolving power is 135lp/mm. We have sensors today that are capable of resolving more than that. Just scroll up a couple of posts to Alan and my own lists of sensor resolutions (in luminance...color resolution would be lower, but luminance is really where detail comes from.) Sensors are only going to be getting more and more dense with smaller and smaller pixels. Across the board, in a few years, there will probably be few sensors out there that couldn't resolve 135lp/mm.

You also have to remember, output resolution is relative to the RMS of the input resolutions. If you have a sensor capable of resolving 135lp/mm, you couldn't actually produce 135lp/mm resolution in an image when using a diffraction limited lens at f/11. The most you could resolve with such a system is 95lp/mm (at MTF9, which is a VERY low contrast level...possibly below the noise limit of the camera, meaning you wouldn't be able to accurately resolve detail at that contrast level with the exception of a very few special scientific use cases (i.e. ultra high magnification star diffraction spot analysis).)  To actually get the most out of that 135lp/mm sensor, you would need a lens capable of resolving a LOT more...which means you would have to have a lens that is diffraction limited, at MTF9, at f/8 (227lp/mm) to get 116lp/mm, and at f/4 (455lp/mm) to get 129lp/mm. You would need a truly diffraction limited lens at f/4 MTF9 to resolve even 130lp/mm out of the 135lp/mm the sensor is capable of...you would probably need an f/2 or f/1.8 lens to get that last 5lp/mm...and such a lens would be extremely expensive (were talking Otus-grade or better here.)

This all assumes that noise levels in the camera don't swamp real detail at a low contrast level of 9%. Something like a D810 or A7s at their lowest ISO levels should have enough dynamic range at midtones and brighter, however as you get down into the lower midtones, shadows and blacks, noise levels are still going to be high enough that it could be difficult to actually differentiate real detail from noise. Once you move up to MTF20 or MTF50, then the resolving power of lenses drops considerably. An f/11 diffraction limited lens is only capable of resolving 63lp/mm at MTF50, where we can easily pick out the microcontrast between pixels, and images look readily and acceptably "detailed and sharp" to our eyes.

As far as I am concerned, a lens at f/11 is woefully inadequate for anything where I really need detail. That would primarily be landscapes, but I also try to avoid stopping down below about f/9 for my birds and wildlife for the same reasons...I SEE the difference, the loss in detail, in my images when I do. I'd rather use a T/S lens at a much wider aperture for landscapes, where I could stop down to the ideal aperture of the lens (usually somewhere between f/4 and f/5.6) to get maximum resolution, while avoiding the DLA of the sensor. Again, I can see the results in my images when I do that. There is a meaningful difference between f/11 and f/4 through f/8 when it comes to resolution:



I labeled f/8 as the sharpest, as it's sharp through a greater DOF...however compare f/8 and f/4...at f/4 more detail is resolved, and the difference between f/4 and f/11 is visually obvious.

Tested six ways to Sunday using a wide variety of silver based films, including high contrast 1000lpmm technical films the results are the same?  It's either the resolution of the film or it's the diffraction limits of the lens (if the film can handle it).  It's never been, is not now, and never will be explained using 1/r.

I do agree that the 1/r equation is probably a bit simplistic and not accounting for all the factors.

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Re: Lens 'resolving power' vs sensors.
« Reply #12 on: September 17, 2014, 12:39:25 PM »

Mt Spokane Photography

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Re: Lens 'resolving power' vs sensors.
« Reply #13 on: September 17, 2014, 03:35:55 PM »
Hello experts.
I keep hearing that current Canon lenses are not 'good enough' for newer/better sensors. I would really appreciate a lesson on how this works.
Thx...

Who did you hear it from, and how did they take their measurements of the lens MTF?  Most of the online lens testers, including DXO test a lens on a camera, and in every case I've seen, the camera sensor has been the limiting factor.
 
Roger Cicala at Lens Rentals has the capability to test a lens by itself (No camera attached), and has posted  a couple of actual lens MTF values for some conditions.  A lens like the 24-70 f/2.8 L MK II or the 70-200mm f/2.8 MK II is supurb.  Easily capable of handling high MP sensors.  The Canon lenses may be slightly better than the Nikon equivalent, but they are both fantastic lenses.
 
Here is some more reading on the subject.  Jrista throws out a lot of terms that you might not understand, this will help understand what they mean, as well as the other factors that are involved in grading a lens.
 
http://www.cambridgeincolour.com/tutorials/lens-quality-mtf-resolution.htm

Marsu42

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Re: Lens 'resolving power' vs sensors.
« Reply #14 on: September 17, 2014, 03:41:09 PM »
Again, I can see the results in my images when I do that. There is a meaningful difference between f/11 and f/4 through f/8 when it comes to resolution

Thanks for the nice demonstration animation! And I agree, diffraction even at "medium" f-stops is visible - that's why do macro focus stacking @f8 even though stopping down would need way less exposures. Plus of course with macro, the bokeh gets worse on small apertures.

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Re: Lens 'resolving power' vs sensors.
« Reply #14 on: September 17, 2014, 03:41:09 PM »