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Diffraction in Consumer Digicams: When Megapixels Go Poof

Last updated 2010-01-10 - Send Feedback
Related: diffraction, digital sensor technology, optics
When a 6 megapixel camera really is a 2.1 megapixel camera

I am fond of carrying my Panasonic Lumix DMC-FX01 digicam in the pocket of my jersey while biking for it’s light weight, diminutive size, and generally pleasing images. However, like all digicams, there is a little secret that camera manufacturers won’t mention in their advertising or camera manual: even for top-performing cameras, optical diffraction can limit resolution to less than the claimed amount.

Diffraction is an optical phenomenon which places an absolute limit on achievable lens resolution. The complete story is quite complicated, but the short summary is that resolution of a lens is limited to 1600/f line pairs per millimeter, where ‘ f’ is the f-stop. For example, the resolution limit at f8 is about 200 line pairs/mm or roughly speaking 400 “dots”.

The Panasonic Lumix DMC-FX01

Let’s use the Panasonic Lumix DMC-FX01 digicam as an example. Its 1/2.5" sensor measures 5.76mm X 4.29mm, with 2816 X 2112 pixels (5.95 megapixels) jammed into that tiny area. There are about 489 pixels per millimeter, or 244 line pairs per millimeter, which means that the sensor is optically limited at about f6.5. At the wide end, the camera offers an f2.8 maximum aperture, whereas at the long end f5.6 is the maximum aperture, so stopping down at full telephoto by only about 1/3 stop suddenly reaches the theoretical resolution limit!

It turns out that the DMC-FX01 is not too smart about choosing an appropriate aperture. Knowing the fixed optical limits, the camera ought to first raise the shutter speed before it begins stopping down such that resolution begins to be limited by the lens. It also turns out that it might not matter—see the Conclusions.

An example at f11

I took a snapshot [below] over the weekend in which the camera chose a shutter speed of 1/160 second at f11 (zoomed to telephoto of 16.8mm, according to the embedded EXIF data). At f11, resolution is limited to about 145 line pairs/mm. But the sensor resolution is 244 line pairs/mm! In other words, the “6 megapixel” picture I took had 6 megapixels (2816 X 2112), but was optically limited to about 2.1 megapixels (1670 X 1250), or about 1/3 the claimed resolution of the camera (using the term “resolution” to mean megapixels).

The image is suitable for a 6 X 4 print (280 dpi), or perhaps a low quality 10 X 8 (167 dpi). In reality, it’s rather unlikely that the actual recorded resolution is even close to the theoretical values, especially given the JPEG compression the camera uses.

The original image

Shown below are two crops from the red outlined area above. One is from the original photo and the other is from the original photo first downsized to 2.1 megapixels, then upsized back to its original size, demonstrating that the “6 megapixel” image, while containing about 6 million mushy dots, really has no more than about 2.1 megapixels of resolution (and probably less).

Of course, a 2.1-megapixel camera would not produce sharper results than a 6-megapixel camera, but if two such cameras have the same size sensors fabricated with the same sensor technology, the 2-megapixel camera would compare very favorably, exceeding quality from the 6MP camera in areas such as dynamic range, contrast, tonality, color rendition and noise levels, all of which make strong contributions to perceived (human) picture quality.

Actual pixel crop
original
Actual pixels crop
downsized to 2.1MP, then upsized to original size

Sharpening both images (see below) shows a slight visual difference. The difference has more to do with elimination of image noise (colored speckles) than with actual detail; noise (digital grain) has the effect of increasing apparent sharpness. Close examination of both images shows little, if any, actual detail advantage of the original over the resampled image.

Actual pixel crop
original
Unsharp Mask {200,0.3,0}
Actual pixels crop
downsized to 2.1MP, then upsized to original size
Unsharp Mask {200,0.3,0}

An example at f5.6

Here is another example, this time taken at f5.6. It was taken at a wider focal length, so optical performance could be different. Still, the results are instructive.

The original image

At f5.6, it’s clear that the camera is producing something closer to its claimed resolution (though still rather disappointing compared to a 6 megapixel digital SLR). The crops below show a clear difference in detail, and applying further sharpening brings that detail out more clearly.

Actual pixel crop
original
Actual pixels crop
downsized to 2.1MP, then upsized to original size
   

Actual pixel crop
original
Unsharp Mask {200,0.3,0}

Actual pixels crop
downsized to 2.1MP, then upsized to original size
Unsharp Mask {200,0.3,0}

   
SSD upgrade that takes full advantage of APFS

Extending the f5.6 example

Let’s resample the f5.6 example to 5, 4, 3, 2, 1 megapixels to see the differences (from the original 5.95 megapixels). This is easier to compare as a horizontal strip, so click to see it. There is only a little difference between the 5-megapixel resampled image and the 5.95-megapixel original, and even the 4-megapixel variant shows only modest differences. Consider such things before laying out the money for 6/7/8/10 megapixel consumer digicams.

A resolution chart

A black and white high contrast target offers the best possible opportunity for the camera to show its optimal resolving power.

For this shot, I used a tripod (which probably weighs 100 times as much as the camera!). I used a 3 stop neutral density filter to force the camera to use f5.6 instead of f11. The camera was zoomed in as far as possible (telephoto, 16.8mm). I shot 3 frames at each aperture at ISO 80, allowing the camera to refocus each time using center spot focus. Center and corners were checked for consistency; all frames were consistent in sharpness.

The results below show that f5.6 is a little better, but not by much. There is a slight improvement in sharpness, but also better contrast at f5.6. Based on previous testing with digital SLRs such as the Nikon D2X and the Canon EOS 1Ds Mark II, the best possible result that could be expected would be to see the “35” bars resolved (with this particular framing of the resolution chart).

At f5.6, we see the “20” bars resolved (clear separation of black/white), with the “25” bars hinting at being resolved, but they are blurred between bars and part of what appears to be detail is actually aliasing, or false detail.

At f11, the “20” bars are still resolved, but barely. Diffraction should limit resolving power to a bit more than the 20 bars, and indeed it does.

Why don’t we see a big difference between f5.6 and f11 as expected? There are several factors involved, all of which likely contribute in varying amounts:

(1) the camera offers only JPEG output, and these are compressed, losing some detail;
(2) digital camera noise and/or noise reduction obscures detail;
(3) the lens is incapable of resolving to the full sensor resolution.

The fact that we can resize (Photoshop bicubic sharper) the 5.95 megapixel original (2816 X 2112) to 4 megapixels (2309 X 1731), or even 3 megapixels (2000 X 1500), then resize it back up to 5.95 megapixels with only minor loss of detail (see below), shows that the camera is not producing 5.95 megapixels of detail. So the results at f11 can’t be expected to be much worse than at f5.6.

Actual pixels
  f5.6 f11
Original
Resized down to 4 megapixels, the upsized to original size
Resized down to 3 megapixels, the resized up to original size

Same as above, but displayed at 200%
  f5.6 f11
Original (5.95 megapixels)
Resized down to 4 megapixels, the resized up to original size
Resized down to 3 megapixels, the resized up to original size

One might reasonably conclude that resampling an image to a lower resolution improves picture quality by removing objectionable artifacts (see the 4 megapixel example above and compare it to the original, with its speckles and “gunk”).

Conclusions

Consumer digicams such as the Panasonic Lumix DMC-FX01 might stop the lens down well beyond the point at which theoretical image detail is lost. But when the camera does not produce anything near the theoretical amount of detail, this makes little difference.

When I started this article, I incorrectly assumed that the choice of a small aperture by the camera was the culprit for missing detail. In actual fact, other factors are limiting resolution to considerably less than the advertised maximum (5.95 megapixels for the DMC-FX01), and an aperture of f11 shows little degradation over an aperture of f5.6. At the telephoto end (16.8mm) actual delivered resolution is closer to 5 megapixels than the claimed 6 megapixels, and there is little to commend it over a 4 megapixel downsampling. Of course, lens performance varies over the zoom range, so this finding might differ for the wide and mid-range parts of the zoom range.

The Panasonic Lumix DMC-FX01 is obstinate about choosing f11—at ISO 80, I was unable to cause it to use f5.6 and a fast shutter speed, even with flash off, image stabilization off and Scene Mode set to “Sports”. It is clearly capable of 1/2000 second, because it will use that speed if necessary (I tried with a bright white target and higher ISO). Instead, it prefers f11 at 1/250 or 1/320 in my testing, no matter which mode I used, whereas the camera could have used f5.6 at 1/1000 or f8 at 1/500 instead, especially in “Sports” mode.

Formula for the diffraction-limited aperture

1. Determine the sensor size using the handy table at dpreview.com. Your camera owner’s manual will document the sensor size as a confusing 1/2.5" or 1/1.8", etc. Use the dpreview table to turn that into a usable measurement of X by Y millimeters.

2. Divide the number of pixels wide by the sensor width in millimeters. This yields pixels/mm. Divide that by 2 to yield line pairs per millimeter (lp/mm).

3. Divide 1600/(lp/mm), where lp/mm is the value from step 2. The resulting value is the smallest aperture that should be used before the image begins to degrade from diffraction.

Some examples (including some professional SLRs)

You’ll need to shoot your own examples to determine if your particular camera meets its resolution limits for reasons other than diffraction.

Digicams
Camera

Sensor
(size, mm)

Resolution Sensor LP/mm Diffraction-limited
f-stop

Panasonic Lumix DMC-FX01
5.95 megapixels

1/2.5"
5.76 X 4.29
2816 X 2112
244
f6.5

Panasonic Lumix DMC-TZ
4.92 megapixels

1/2.5"
5.76 X 4.29
2560 X 1920
222
f7.2

Panasonic Lumix DMC-LC1
4.92 megapixels

2/3"
8.8 X 6.6
2560 X 1920
145
f13.8

FujiFilm FinePix F30 Zoom
6.08 megapixels

1/1.7"
7.6 X 5.7
2848 X 2136
149
f10.6
Canon PowerShot SD700 IS
5.95 megapixels
1/2.5"
5.76 X 4.29
2816 X 2112
244
f6.5
Sony DSC-W100
7.98 megapixels
1/1.8"
7.18 X 5.32
3264 X 2448
227
f7
Nikon CoolPix P4
7.98 megapixels
1/1.8"
7.18 X 5.32
3264 X 2448
227
f7

Professional Cameras
Camera

Sensor
(size, mm)

Resolution Sensor LP/mm Diffraction-limited
f-stop
Nikon D200
10.0 megapixel
APS
23.6 X 15.8
3872 X 2592
82
f19.5
Nikon D2X
12.2 megapixel
APS
23.7 X 15.7
4288 X 2848
90
f17.8
Canon EOS 30D
8.2 megapixel
APS
22.5 X 15.0
3504 X 2336
78
f20.5
Canon EOS 5D
12.7 megapixel
full frame
36 X 24
4368 X 2912
61
f26.2
Canon EOS 1Ds Mark II
16.6 megapixel
full frame
36 X 24
4992 X 3328
69
f23
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