Thursday, June 09, 2011

Choosing An Optimal Aperture To Avoid Diffraction

Stopping down your lens aperture to get greater depth of field can result in such a small opening for light that diffraction begins to limit the image quality. This is a well-known phenomenon, but what is less appreciated is how soon this effect kicks in. Photographers who commonly stop down to f/22 or f/32 for macro shots (one typical example) will want to read on. And sensor size also plays its part, which is why I am considering this topic now, in proximity with my equivalence article.

Rather than repeating information, I recommend you read Cambridge In Colour for a clear explanation of the diffraction limit effect. You will see from that article that it is not actually the sensor size that is the important factor, but rather the size of the pixels that make up the sensor. As sensors become smaller so do pixels, in general, but the relationship is not exact.

The following is a chart of many popular cameras, including some for historical interest. After each the sensor size is given along with the diagonal pixel pitch (in micrometers). The chart is ordered from smallest to largest pixels and you will see that this mostly matches up with sensor size. In the final column is the maximum aperture before diffraction starts reducing resolution. The first figure is the actual calculation and the second figure rounds this off to the nearest actual f-stop number (including half and third stops) you can use to avoid diffraction effects.

This number was determined by multiplying the pixel size by 1.054, using the formula provided by Nathan Myhrvold in Luminous Landscape's equivalent lens article.

Update 24 June 2011 Rather than simply use the pixel pitch from DXO Mark I now calculate this from the maximum resolution figures for the given sensor. I have also added the Pentax Q as a lower limit.

--------------CAMERA    -SENSOR   PIXEL   ----APERTURE
            Pentax Q     1/2.3"    1.53    1.62   1.60
           Canon G10    1/1.63"    1.79    1.88   1.80
            Canon G9    1/1.63"    1.98    2.09   2.00
       Canon G11/S90     1/1.7"    2.04    2.15   2.00
       Panasonic LX3    1/1.63"    2.18    2.30   2.20
       Panasonic GH2        MFT    3.67    3.87   3.50
        Panasonic G3        MFT    3.75    3.96   3.50
            Canon 7D     APS-CC    4.16    4.39   4.00
           Canon 60D     APS-CC    4.27    4.50   4.00
       Olympus E-P1*        MFT    4.29    4.53   4.50
      Panasonic G1**        MFT    4.31    4.54   4.50
         Nikon D7000      APS-C    4.75    5.00   4.80
          Pentax K-5      APS-C    4.74    5.00   4.80
          Pentax K-7      APS-C    4.99    5.26   5.00
    Samsung NX100/10      APS-C    5.02    5.29   5.00
         Pentax K20D      APS-C    5.03    5.30   5.00
        Sony NEX-3/5      APS-C    5.12    5.39   5.00
         Nikon D300S      APS-C    5.44    5.73   5.60
          Pentax K-r      APS-C    5.44    5.73   5.60
           Sony A700      APS-C    5.50    5.80   5.60
          Pentax K-x      APS-C    5.48    5.77   5.60
           Nikon D90      APS-C    5.48    5.77   5.60
         Pentax 645D       645D    5.93    6.25   5.60
           Sony A900       35mm    5.95    6.27   5.60
  Canon 1Ds Mark III       35mm    6.32    6.66   6.30
    Canon 5D Mark II       35mm    6.39    6.74   6.70
   Canon 1Ds Mark II       35mm    7.08    7.47   7.10
            Canon 5D       35mm    8.07    8.50   8.00
            Nikon D3       35mm    8.41    8.86   8.00
          Nikon D700       35mm    8.41    8.86   8.00

* also E-PL1, E-PL2, E-P2, E-30
** also G2, GF1, GF2, GH1, G10
The results are quite surprising. Increasing the f-number beyond f/4 on the Olympus E-P1 degrades quality due to diffraction. The Pentax K-x allows f/5.8 and even the Nikon D700 only f/9. The Pentax 645D does more poorly than one might expect, a result of cramming the sensor with megapixels.

One conclusion we can draw is that commonly used zoom lenses on the E-P1, those whose fastest aperture is f/4 or higher, are diffraction limited all of the time! And this is unavoidable, since it is based on an immutable law of physics. Technology improvements cannot help us here!

However, one should not take this to mean that no smaller apertures should ever be used. Obviously one will need to stop down more to gain depth of field in many typical use cases. Realise however the trade-offs in doing so.

Further, this information can be useful in choosing optimal apertures for a lens. Knowing this, I will now try to use the 20/1.7 between f/2 and f/4, where possible.



robin said...

I have updated the chart to improve the consistency of the figures and include the Pentax Q as a lower limit.

Charles Nam said...

Hi there,
Interesting article.
However, I see a fatal flaw in this. Basically, what you have not considered is the effect of the lens. The figures you have quoted above are the theoretical optimal values for PERFECT LENSES which are at its sharpest at all apertures.

But obviously, typical zoom lenses start at F3.5, etc, and is nowhere as sharp as the sensor allows. The lens may be much sharper when stopped down to say, F8.

What I'm saying is, even though e.g. the K-5 sensor might be at its sharpest at F5 or below, if the lens mounted on it is poor at F5, then this calculation becomes utterly meaningless. The user then has to stop down the aperture to the LENS'S optimal aperture, rather than the sensor's.

robin said...

You are correct that one has to take the diffraction information I present here in tandem with any other constraints. This does not make the information I present "fatally flawed" or "utterly meaningless"; it is simply part of the decision-making process one must make.

This is explicitly acknowledged in the last paragraphs of the article. It would be silly to decide to shoot only wide open with the 20/1.7, so as to avoid diffraction effects at all costs. Instead, I made the decision to aim for apertures that are a compromise between optimum lens performance and diffraction effects. Unless I need to stop down for extra depth of field, in which case I will!

Though your comments imply such, this article in no way advocates any sort of absolutist application of diffraction information.

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