6

As the title says, can the diffraction limit be overcome with superresolution techniques? Or is this the absolute hard limit in optical photography without making special assumptions? If this is the hard limit, what is an illustration of why this is the case?

"Without making special assumptions" in this case means the techniques of superresolution microscopy - structured light, laser beams etc.

To illustrate the point: Can superresolution beyond the diffraction limit be achieved by taking multiple exposures from slightly different angles and positions and feeding them into [SR approach here]? Even with the added assumption of a diffraction-limited system (High resolution camera and lens)?

UPDATE Thank you for your answers. However it feels to me more like you explained to me what diffraction means rather than if it is possible to overcome the diffraction limit under reasonable assumptions. To clarify further: In a relatively controlled environment, where you can expect the subject to be stationary and the lens/aperture diffraction to be the limiting factor of resolution (as opposed to sensor resolution), do techniques exist to increase detail beyond this diffraction limit without the aforementioned "special assumptions"?

  • In part it depends on what you mean when you say "diffraction limit?" The diffraction limited aperture when the effects of diffraction are first barely perceptible or the much narrower diffraction cutoff frequency? – Michael C Feb 10 '17 at 16:34
  • 1
    Perceptible diffraction is always based upon the sensor's (or film's) resolution limit. Whatever diffraction happens at aperture settings wider than the DLA of the sensor are beyond the ability of the sensor to record. It makes no difference if you have a perfect dot .001µm wide or a blurry disc 2µm wide if the sensor's pixels are 4µm wide. Both will look the exactly the same as recorded by that sensor. – Michael C Feb 11 '17 at 17:51
3

Can the diffraction limit be overcome with superresolution techniques?

Sort of, to a limited degree. Using sub-pixel shifting of the imaging sensor, in effect you are increasing each pixel size while keeping their spacing the same. Of course, it is not physically possible to build sensors where individual pixels are larger than their pitch (center-to-center spacing). But mathematically, this is basically what's happening.

That sounds great, but how does that overcome diffraction limits?

As Michael Clark stated in his answer, a camera system is diffraction limited when the size of the Airy disk (the blur) caused by diffraction becomes larger than the size of a digital camera's sensor pixels.

The size and nature of the Airy disk is not something you can overcome — it's a function of the wave-like behavior of light, the aperture size (usually assumed to be circular), and the wavelength of the particular light in question).

But if you can increase the size of the pixels while still packing the same number of pixels in the same area, you can "push back" the diffraction limit a bit farther. And that's what sub-pixel shifting of the image sensor does.

So it's not overcoming the diffraction limit per se, it's more like moving the goalposts a little bit.

The upper limit of sub-pixel shifting superresolution is an apparent twofold increase in resolution.

You don't get something for nothing. What's the tradeoff?

Well, as you mentioned, it requires a non-moving subject, that's one of the limits of applicability. As John stated in his answer, you are using the temporal-based certainty (i.e., there is no motion in the scene, so it exists independent of time) to take multiple images (which takes time, but who cares, you have plenty of it when the subject isn't moving) that help you increase your spatial information / knowledge about the scene.

  • "...usually assumed to be circular..." Not always. Very detailed lens correction profiles take the actual shape of the aperture opening at each f-stop setting (and the alignment of that shape with the sensor) for each lens and apply deblurring based upon the specific shape and orientation of the diaphragm. That's partly what Canon's DLO does. – Michael C Feb 11 '17 at 17:44
  • @MichaelClark I was speaking only in the context of nominal Airy disk size, where the aperture is usually circular (otherwise, complex Bessel integrals become unnecessarily complex (even more so)). But when it comes to computational lens correction to maximize resolution/sharpness, you're absolutely right. – scottbb Feb 12 '17 at 3:12
  • So if the imaging system is limited by diffraction blur and not aliasing (for example, pixel pitch is very small so that there can be more than 10 pixels representing the Airy disk (i.e. the point spread function), does "sub-pixel shifting super resolution" help reconstructing the blurred image to high resolution image at all? – YEEFANG XIAO Nov 4 '17 at 18:40
  • @YEEFANGXIAO No. In your example of 10:1 pixels per Airy disc diameter, no pixel in a near neighborhood of ±5px can actually determine which photon hits which pixel. sub-pixel superresolution might be able to reduce that uncertainty by less than 2px (diameter). But that still means that you have > 8:1 pixels per Airy disc diameter. – scottbb Nov 5 '17 at 17:11
  • "The upper limit of sub-pixel shifting superresolution is an apparent twofold increase in resolution."? Where did you find that? – Navin Feb 11 '18 at 10:01
1

All camera optics are plagued by twin demons of interference and diffraction. These yield stray light rays that comingle with the image forming rays. Diffraction is caused when light rays from the vista being imaged, just brush by the edge of the aperture stop. Some close passes are shadowed but not completely blocked. The ricochets comingle and degrade the image. Interference is due to the wave nature of light crossing paths and adding and canceling each other.

Well studied by Lord John Rayleigh, Astronomer Royal British 1842 ~ 1919 Nobel Prize physics 1904.

His calculations, remain valid. We are talking about the resolving power of a lens system. Following is a table for 589, about the center of our color spectrum.

Called the Rayleigh Criterion (to my knowledge, never exceeded)

f/1 1392 lines per mm

f/2 696 lines per mm

f/2.8 487 lines per mm

f/4 320 lines per mm

f/5.6 249 lines per mm

f/8 184 lines per mm

f/11 127 line per mm

f/16 87 lines per mm

f/22 63 lines per mm

f/32 44 lines per mm

0

Several post-processing techniques that increase the resolution limits of a camera/lens system can be used to ameliorate the effects of diffraction. Stacking multiple images taken from slightly different positions as you suggest is one way. A tool such as Canon's Digital Lens Optimizer that uses very detailed lens profiles is another.

Diffraction is a lot like the edges of depth of field. The more we magnify an image the easier it is to see. Diffraction starts at apertures where only very high magnification will reveal any effects at all. As the aperture is closed down further the effects begin to be perceptible at lower and lower magnifications.

What we often refer to as the Diffraction Limited Aperture (DLA) for a specific digital sensor is the aperture at which the effects of diffraction are noticeable when the resulting image file is viewed at a magnification that yields 1-pixel in the image file equals 1-pixel on the monitor and those individual pixels are right at the limits of the viewer's perception to differentiate them. The DLA is the point at which the effects of diffraction are barely perceptible at such a magnification. This begins to occur when the size of the blur caused by diffraction becomes larger than the size of a digital camera's sensor pixels.

What we refer to as the Diffraction Cutoff Frequency requires a much narrower aperture setting than the DLA for a specific sensor (or film - the size of the grains in various films affects the DLA with film!).

For more on how the DLA is affected by the resolution limits of the recording medium, please see: Does sensor size impact the diffraction limit of a lens?

  • I suspect that post-processing such as Google is doing with AI will be applied to all sorts of fun problems. Deconvolution, repairing damaged photos, diffraction, abberations, noise reduction, and so on. – Lumigraphics Feb 11 '17 at 5:16
  • There's no real AI going on with Canon's DLO. Just a lot of very detailed and complex math based on very detailed information about the exact shape, position, and characteristics of the lens elements and aperture blades in the lens. – Michael C Feb 11 '17 at 15:31
  • And? My comment wasn't about DLO. – Lumigraphics Feb 11 '17 at 17:02
  • Your comment was about an answer that mentioned two techniques, one of which was DLO as representative of extremely detailed lens correction. If your comment wasn't in response to this answer then why was it placed here instead of as a comment to the question or in your own answer? – Michael C Feb 11 '17 at 17:40
  • Now you are just being a troll. – Lumigraphics Feb 11 '17 at 17:53
0

Yes but you are trading one type of information for another - it doesn't break the laws of physics or information theory. You have to assume the object is stationary and you are trading signal to noise for resolution.

There are many possible approaches. One is simply blocking out the centre of your optical system and only using the edges. The central peak of the transfer function of this is narrower than for a circular aperture so your resolution is increased but you both have less signal received and have wider wings in the transfer function, both reducing signal to noise.

  • Could you expand on how signal-to-noise is being traded for resolution? – junkyardsparkle Feb 10 '17 at 20:54
  • Thank you for your answer, however it should be obvious that you can't break the laws of physics. Can you explain how to achieve higher resolution under your assumptions? – Kapt.Brackbier Feb 11 '17 at 9:54
  • 1
    There are many possible approaches. One is simply blocking out the centre of your optical system and only using the edges. The central peak of the transfer function of this is narrower than for a circular aperture so your resolution is increased but you both have less signal received and have wider wings in the transfer function, both reducing signal to noise. – John Feb 11 '17 at 18:49
  • @John add it to the answer, it is an interesting piece of information. It would be nice to include a short exmplanation of transfer function too. – Euri Pinhollow Feb 12 '17 at 11:37
  • This only filters the spatial frequencies received at the focal plane. It's the optical analog of a high-pass filter in electronics. It has nothing to do with exceeding the Airy disc limit. – Carl Witthoft Feb 13 '17 at 12:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.