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Diffraction limits of Resolution | Andre Gunther Photography

Diffraction limits of Resolution

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Diffraction affects your image sharpness by limiting Depth of Field and useful Resolution. See how our camera and lens choices influence these limits.

2 Airy discs with small overlapTo increase Depth of Field we simply decrease aperture (larger f-stop). However, we cannot get infinite Depth of Field by decreasing our aperture infinitely. Diffraction establishes the upper limit to Depth of Field.

The subject may seem very technical, but the solution is far from being difficult. To understand this tutorial better, consider reading my Correct Exposure Series of Tutorials and my previous tutorial on Hyperfocal Distance, which explains the relationship of aperture and Depth of Field.

Diffraction is an optical effect limits the resolution / sharpness of our photograph. Since it is an optical effect, higher resolution sensors will not improve resolution further. Higher resolution cameras are thus more demanding on our optics and eventually will yield little to no improvement in total resolution. Diffraction plagues landscape photographers who are striving for a large depth of field and high-resolution images. Many of us are not even aware of this, blindly selecting a small aperture according to our calculators and charts.


  What is Diffraction?

Diffraction describes the interaction between waves and obstacles. It describes how waves deform to fill the space behind the object (the wave shadow so to speak). "Sound waves can diffract around objects, this is the reason we can still hear someone calling us even if we are hiding behind a tree." - quoted from Wikipedia.

Waveform Large ApertureWaveform small aperture

(generated from this site)

In the two extreme examples above, I illustrated diffraction:
An object like the lens diaphragm will shape a wave passing it. The object deforms the wave. The smaller the opening of our diaphragm (or the smaller the aperture) the more the wave will be affected. The distortion of the wave will create a pattern on the sensor. We call this pattern the Airy Disc (after George Airy and not the lofty nature of the subject). It takes the form shown in the next figure.

Airy Disc
Shape of the Airy Disc on the sensor plane

The diameter of the Airy Disc starts to increase with a decreasing aperture size. When the cone (the red and yellow) area is as large as your smallest resolution unit is, you will start to lose sharpness due to diffraction. The smallest resolution unit is the larger of your pixel size or your circle of confusion for a desired Depth of Field. In order to maximize the output resolution of your camera, the Airy Disc should not be much larger than your pixel. The pixel size for a Canon 20D is roughly 39 square microns.
To calculate the pixel size, simply divide the sensor area by the number of pixels. Although it is only a simplification, it is accurate enough for our purposes.
The sensor of the 20D is 22.5mmx15mm with 8.5 million total pixels. So (22500um x 15000um / 8,500,000 = 39um^2). Assuming square pixels, we get an edge of about 6.2um.
With this, we can approximate the diameter of the airy disk:

Equation 1

where λ is the wavelength of the light (about 450nm=0.45um), f/d is the f/stop of our aperture. For f/16 x=8.78um. The Airy Disc is thus already larger then our pixel limiting the resolution of our system. The theoretical limit for the 20D lies between f/11 to f/13.
Decreasing the aperture further to improve our Depth of Field will result in an overall sharpness loss throughout the picture.
By comparison, a Sony W200 (1/2.5" sensor with 12 Megapixel) has a pixel width of about 2um and will start showing the limits of diffraction at apertures smaller than 3.5. The benefit of 12 Megapixels in such a small sensor over its 8MP counterpart the W90 is virtually nonexistent.
Since we are actually interpolating the color information of each pixel from its adjacent pixels through a process called Bayer Interpolation, we already get a certain amount of un-sharpness. Knowing this, one can assume an absolute upper limit of two four pixels (Bayer Pattern) or two pixel widths. For my 20D this translates into a smallest usable aperture of f/22.
This means that the effect of diffraction will start to have an impact below f/11, but for apertures larger then f/22 the effect will be less visible due to the way the sensors work. With some sharpening, we can still improve the image.

The following pictures illustrate how the sensor can resolve two adjacent features.
2 Airy discs with small overlap
Two adjacent non-overlapping airy discs that can be resolved


2 airy discs that cannot be resolved 
Two adjacent overlapping airy discs that cannot be resolved

Without lengthy analysis, we can conclude that two adjacent lines start to blur together at around f/11 for the 20D (at the onset of diffraction).

Diffraction Limited Lens

Optical aberrations - often plaguing consumer grade lenses - require "stopping down" in order to reduce their effect. These lenses have a limited "useful" aperture range. Aberrations limit one end of the scale, Diffraction the other.
Very high quality lenses are sharp even at wide-open apertures. Due to the effects of diffraction, they are sharpest wide open.
I recommend performing a series of tests for your lens - camera combination.

Using some of the above mentioned limitations of the camera itself, and neglecting any other effects, I calculated the Minimum usable Aperture for a range of popular camera systems. Column 3 lists the minimum Aperture for highest quality. 
 

Camera

Pixel Size

Min Aperture

Min Aperture 2pixels

comments

Nikon D3S 8.17um 15 30 SLR

Canon 5D Mark 2

6.4um

11

22

SLR

Nikon D3x

5.9um

11

22

SLR

Nikon D700

8.45um

16

32

SLR

Canon 20D
Canon 30D
Canon 350D (Rebel XT)

6.2um

11

22

SLR

Sony DSLR-A300
Nikon D3000
5.9um 11 22 SLR

Nikon D60/D40x
Sony DSLR-A900
Sony DSLR-A850
Sony DSLR-A230
Sony DSLR-A330

5.8um 11 22 SLR

Canon 40D
Canon 400D (Rebel XTi)

5.6um

10

20

SLR

Canon 1DMIV 5.5um 10 20 SLR
Nikon D300
Nikon D300S
Nikon D5000
Sony DSLR-A500
5.3um 10 19 SLR

Canon 450D (Rebel XSi)

5.1um

9

18

SLR

Sony DSLR-A350
Sony DSLR-A380
Sony DSLR-A550
Sony DSLR-A450
Sony DSLR-A290
Sony DSLR-A390

5um 9 18 SLR

Canon 50D

4.7um

9

17

SLR

Canon 500D (Rebel T1i) 4.63um 8 16 SLR

Olympus E-420
Olympus E-450
Panasonic Lumix DMC-L10

4.5um 8 16 SLR
Olympus E-620
Olympus E-600
4.3um 8 16 SLR
Canon 7D
Canon 550D (Rebel T2i)
4.2um 8 16 SLR

Leica V-LUX 1

1.9um

3.5

7

Advanced P&S

Fujifilm Finepix S100fs

2.2um

4

8

Advanced P&S

Casio Exilim Pro EX-F1

2.4um

4

8

Advanced P&S

Canon Powershot G11 2.04um 3.7 7.4 Advanced P&S

Canon Powershot G9
(David caught a mistake)

2.9 1.9um

5 3.5

10 7

Advanced P&S

Canon Powershot G10

1.72um

3.2

6.4

Advanced P&S

Nikon Coolpix P100 1.63um 3 6 Advanced P&S
Canon Powershot SX20
Nikon Coolpix L110
Nikon Coolpix P90
1.51um 2.8 5.5 Advanced P&S

This table does not indicate a maximum depth of field. Smaller sensors have a larger Depth of Field due to their focal length multiplication. Since the lens diameter and the distance from the sensor also limit the maximum aperture, the useful range for those cameras is very small.

I rounded some values in this table. Cameras grouped together do not always have exactly the same pixel size but you can easily compare them against each other using these numbers.

Example Calculation

For a 1/2.5" sensor I calculated the pixel size like this:
The sensor diagonal dimension is z=25400um/2.5. With  y=3/4x (the aspect ratio) and with

Equation3

I easily calculated x=8128um and y=6096um. I can now calculate the pixel area to be:

Equation3

, and by finding the square root, I came up with the pixel dimension. Using the formula above, I calculated the aperture for an Airy disc with a diameter of the size of a single pixel and for the Airy disc the size of two pixels.

Conclusion

I think it is important not to read too much into all those numbers, but it is nice to understand why pictures are sometimes not as sharp as we might expect.
When you are buying your next digital camera, do not obsess too much about resolution and technical mambo jumbo. If you funds are limited, buy a cheap DSLR instead of the latest flashy point and shoot model. You will end up with much more creative options and better-looking pictures.
Limiting the useful range of apertures, Point and Shoot cameras make it next to impossible to create shallow depth of field images. Cluttered portraits with in-focus backgrounds distract from the subjects. At the other end of the scale, you cannot get more depth of field by simply using smaller apertures. Many P&S already limit the minimum aperture via software.

Postscript

I wrote this article as a reference for future tutorials on the correct exposure. It is not necessary to understand everything, but it is helpful to know there is such a thing as diffraction limit and how to deal with it.
 

 

What, no 1D Mark III??

Ha Ha, just kidding. Thanks for this info Andre. Not sure I get the whole thing and I am horrible at math but it's a still good article.

Frank

Hello Frank, I will

Hello Frank,

I will calculate the numbers for your camera. I think it is one of the cameras with the largest pixel sites and should barely be affected.

hello andre, i am just a new

hello andre,
i am just a new kid out in this world of photography and i feel i could take some of ur help....tell me how to start photographying and what are the basic things i need to know to atleast be called an amatuer photographer. i have read ur some of ur article but could not make much out of it....further more the camera selction link did not work so i also need your help in which camera i should buy .........

Edge diffraction

"The smaller the opening of our diaphragm (or the smaller the aperture) the more the wave will be affected"

Actually shouldn't this read, "the more the *image* will be affected."? Light waves are all affected the same as they diffract past an edge. At smaller apertures, a greater proportion of the the waves pass by the edge of the lens diaphragm relative to the unaffected waves that pass through clear glass. As you stop down, the edge circumference decreases linearly, but the lens surface decreases by the square.

Hence, the *image* suffers at small apertures from the greater ratio of diffracted light waves. Even wide open, light is still diffracted around the edges of a lens, but that amount of diffracted light is very small relative to all the other waves passing through clear glass.

If I reduce the resolution, will the diffraction limits change?

First of all, congrats on your great article!! This was very instructive for me, and I am certain that I will become an regular visitor!

My point is related to this part of your text:
(...)
"To calculate the pixel size, simply divide the sensor area by the number of pixels. Although it is only a simplification, it is accurate enough for our purposes. The sensor of the 20D is 22.5mmx15mm with 8.5 million total pixels. So (22500um x 15000um / 8,500,000 = 39um^2). Assuming square pixels, we get an edge of about 6.2um. With this, we can approximate the diameter of the airy disk"
(...)

So... using the above mentioned 20D, if I lower the resolution for 6mp(or any possible lower resolution on the camera settings), will this action set the diffraction limits on a narrower f stop?? Or the pixel size is allways related to the maximum resolution of the sensor?

Yes

You are absolutely right JH. For instance compare the 20D (8MP) to the 50D (15MP). As you can see, the pixel size makes a difference.
If you reduce the resolution of the 20D to 2MP, the pixel sides will effectively double (4 times larger area). Think of four pixels that now contribute information to one pixel of the 2MP image.

Congrats, this is great. A

Congrats, this is great. A lot of people dont know this!

Also great work on calculating the Fstop limit for popular cameras! I suggest that you continue expanding it when new cameras come!

Tnx.

Thanks for the reminder Tim.

Thanks for the reminder Tim. It is about time for an update on the table. I will provide one soon.

Expanded the Table

I expanded the table with the latest Camera Models.

highly helpful stuff!

I learned quite a lot today, thanks to your article. I must admit, though, that some of these facts are a bit too technical for me, being a mere novice in the industry. However, I'll be sure to be back so I can learn some more. Thanks!

This photos diffraction is

This photos diffraction is so amazing; this work is very difficult so first study their technology then applies. Really I can’t do this, so thanks for something different types of post.

İs calculation correct ?

Hi,

There is one point I couldn't understand clearly. In approximate Airy disk calculation you have used f/d as f/16 as an example. But this value only denotes how much aperture is open compaed to local length of lens and longer the lens is for the same aperture opening f stop we have larger aperture opening, isn't it?

This means that if we simply take f/d, f/16 (as example) in our calculation we will have same Airy disk value for all lenses, but isn't it wider the aperture, lesser the diffraction ?

Regards,

You quote the Airy disk

You quote the Airy disk calculation multiple as 1.22. However it is 2.44 elsewhere. I think you are confusing this with:
"The Rayleigh resolution criterion states that two point objects can be resolved if the peak of one falls on the first zero of the other:

Resolution = 1.22λf ⁄#W"

source http://spie.org/x32321.xml

I agree your formula gives the right answer for the cameras concerned.

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It is really important for

It is really important for you to know that, when you come to the poing of mastering, then the color combination for that must be at the apperture ratios of 45:15.

I have nikon coolpix cameras and it is because i was not having a budget to buy a SLR. So, i get a .jpeg file. At the time i efit it on Photoshop , according to the lightning i keep the ratio nwhich is 3/4.

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Although the above diagrams help give a feel for the concept of diffraction, only real-world photography can show its visual impact. The following series of images were taken on the Canon EOS 20D, which typically exhibits softening from diffraction beyond about f/11.
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Warning: Duplicate entry '6424945' for key 'PRIMARY' query: INSERT INTO watchdog (uid, type, message, severity, link, location, referer, hostname, timestamp) VALUES (0, 'php', '<em></em> in <em>/home/agunther/public_html/includes/database.mysqli.inc</em> on line <em>151</em>.', 2, '', 'http://www.aguntherphotography.com/tutorial/diffraction-limits-of-resolution.html', '', '54.145.181.138', 1432494663) in /home/agunther/public_html/includes/database.mysqli.inc on line 151