Monday, June 06, 2011

Equivalence of Camera Systems

Olympus E-P1 with FA43 Limited
Now that I can use both the K20D and E-P1 with the same lenses, I thought it interesting to directly compare images taken with each. This might reveal something about the different sensors and in particular shed light on the thorny matter of equivalence. This article is an update and extension of my previous Sensor Sizes Explained. I will correct some errors1 made there and deal more plainly with equivalence. Unlike some of the other large and confusing tomes on this subject2, I will be as simple and clear as possible.

Lenses Are Invariant
To get the obvious out of the way first, a 20mm lens is 20mm no matter what camera it is attached to. And the maximum f/1.7 aperture is the same as well. The lens does not magically change attributes when attached to a different body. It has the same magnification ability, the same light transmittance and so on. It is, after all, the same lens!

Second, consider that the aperture (f-number) indicates the intensity of the light that makes it through the lens. The larger the sensor the more light it captures at a given aperture. And the more light that gets to the sensor the better the image, all else being equal. Here "better" could mean signal to noise ratio, resolution, dynamic range or some other measure.

Looking at this another way, a smaller sensor needs to be magnified more than a larger sensor to get to the same size final output, whether this target is a print or image for screen display. This means greater distortion (in the pure technical sense of that term) and hence lower image quality (IQ). All else being equal, a larger sensor produces better IQ.

So why don't we all simply use the largest sensors possible? The first reason is cost. In practice a larger sensor also means a larger camera, one that is bulky and calls more attention to itself. Portability, cost and discretion are valid reasons to choose a smaller sensor, so long as one realises that IQ will, of necessity, suffer. Often that's a fair trade-off.

It is remarkable how often these basic principles are forgotten in debates on internet forums!

Field Of View and Depth Of Field Equivalence
The next proposal may come as more of a shock. As photographers, we don't care about focal length or aperture. We choose a focal length to frame a scene, from top to bottom and left to right. Thus what we really care about is field of view (FOV). Likewise we choose an aperture to specify how much of the scene (front to back) is in focus. What we really care about is depth of field (DOF).

Both FOV and DOF depend on the sensor size, and that is the crux of the matter. When moving between different camera systems we must take into account the sensor size in order to determine the photographic equivalence between these systems. Equivalence simply refers to the parameters we need to get exactly the same resulting photograph of the same subject out of two different cameras.

It follows that if you are not planning on sharing lenses between different systems, you have no reason to care about equivalence! Simply learn the lens characteristics on your camera, and how these impact your shooting. The lens performance on some hypothetical "other system" is irrelevant. But let's continue, assuming that we will be sharing lenses across systems (as I am).

I propose that the measure usually used to perform equivalence is subtly wrong.

To consider why, examine the following table of sensors. In this chart the sensor diagonals have been calculated and normalised against full-frame -- the usual, though arbitrary, reference. The same has been done with sensor area and the square root of area (both are normalised). If you wish you may add in 6x7, 8x10 and other larger formats. Units are millimetre. APS-CC is the Canon APS-C format. 645 is the original film format; various digital variants are smaller.

   645  56.00 x 41.50      0.62   0.37       0.61
   H3D  48.00 x 36.00      0.72   0.50       0.71
  645D  44.00 x 33.00      0.79   0.60       0.77
  35mm  36.00 x 24.00      1.00   1.00       1.00
 APS-C  23.60 x 15.70      1.53   2.33       1.53
APS-CC  22.20 x 14.80      1.62   2.63       1.62
   MFT  17.30 x 13.00      2.00   3.84       1.96
  2/3"   8.80 x  6.60      3.93  14.88       3.86
1/1.63"  8.00 x  6.00      4.33  18.00       4.24
1/1.7"   7.60 x  5.70      4.55  19.94       4.47
1/2.3"   6.17 x  4.55      5.64  30.78       5.55
1/2.5"   5.76 x  4.29      6.02  34.97       5.91

When a writer states that a FF camera has a sensor twice as big as an MFT camera, they justify this by observing the sensor diagonal is twice the length. Equivalent focal length and aperture (f-number) are said to scale with this diagonal. To take but one example, you will find it commonly stated that the Panasonic 20mm f/1.7 lens on MFT acts like a 50mm f/3.4 on full-frame. To repeat for emphasis, this means the 20/1.7 produces the equivalent field of view and depth of field of some hypothetical 50/3.4 lens on FF.

But the use of the diagonal ignores differences in aspect ratio. A more accurate measure is to use the square root of the area, since this is independent of aspect. Look at the chart and notice how this value is quite similar to the diagonal. In fact the square root of area and the length of the diagonal are exactly equal when the sensor is a square. The further the aspect ratio deviates from the square, the more these two measures differ.

It may seem like a pedantic matter, but for panoramic shots the difference is significant. Besides the mathematical accuracy, the emphasis on sensor area helps focus our attention on this, the most important parameter determining overall IQ.

ISO Equivalence
In the discussion thus far I have not mentioned the third photographic parameter, sensitivity or ISO. It turns out that this varies directly with the area. Thus, shooting MFT at ISO200 is equivalent to shooting FF at ISO768, since the ratio of the areas of these sensors is 3.84.

I note that all of this is only an approximation, as it does not take into account number of pixels, noise characteristics, the fact that lens focal length measurements are only roughly as the manufacturer might state, and so on.

Finally, you will need to read documentation of a far more technical nature if you wish proof of the conjectures that FOV and DOF scale with the root of area and ISO with the area itself. I leave that as an exercise.

1. Lens Focal Length and Aperture are invariant no matter what sensor they are attached to.

2. A smaller sensor acts exactly like a cropped version of a larger sensor (all else being equal). The image quality decreases in proportion to the amount of the crop.

3. Equivalent ISO can be calculated using the same ratio of sensor area.

4. Equivalent Field Of View and Depth Of Field can be calculated using the ratio of the square root of sensor area.


1 Thanks to Peter Harris and Tompsk who critiqued my previous article.
2 See Joseph James for more information than you ever needed.

1/2.3" added to chart and two typos fixed



robin said...

In the last few days I've updated the text for clarity, added headings and augmented the table with three more sensor sizes. I am referring to this article a lot and want it to be as complete as possible.

robin said...

Updated the chart to add in 2/3" sensors, like that in the new Fuji X10. Fixed chart so that 35mm is the baseline for comparison.

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