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The Dawes Limit is the smallest resolvable angle of an optical system. “Resolving Power” is distinguished from “Resolution” in that Resolving Power refers specifically to an angular measurement. The Dawes Limit therefore deals with arc-seconds.

A degree is 1/360 of a full circle. A minute is 1/60 of a degree, and a second is 1/60 of a minute, or ~1/130,000 of a full circle. An arc-second is a very, very small measurement.

There are problems using the Dawes Limit for a lens to describe photographic performance:

• The Dawes Limit does not deal with sharpness because it ignores contrast, and an MTF of exactly zero is the baseline for the Dawes Limit.
• The Dawes Limit is theoretical and doesn’t incorporate atmospheric opacities or lens defects-it assumes that everything, including the nature of the subject is perfect.

However, the Dawes Limit is very useful for reinforcing the concept of the Rayleigh Criterion, and for broadening an understanding of the performance and limits of lenses.

To calculate the Dawes Limit of a lens system, divide 4.56 (seconds of arc) by the Aperture in inches, or 115.8 (seconds of arc) by the Aperture in mm.

In telescopes, binoculars and microscopes the Aperture will be the front element diameter, while in common photography one must do some cipherin’. The result will give the arc-second value of the smallest detail that is resolvable by the lens or system, which may be converted to a more conventional linear size by simple trigonometry-the product is called “Angular Size.” The result will, of course, not refer to completely distinguished detail, and is theoretical in the first place.

Angular Size has been the unrecognized subject of quite a few questions concerning how small the details a “spy” satellite could capture on the earth’s surface. My own undereducated calculations are that the Hubble Space Telescope (the largest visible-band optical system we can place in an affordable, sustainable reasonably low orbit) can capture just under 10cm (just under 4 inches, perhaps as little as 3 inches) when at perigee, and that’s presuming a perfect atmosphere and a minimum distance to a Mean Sea Level object. A near-orthogonal aspect will be necessary in many instances (such as license-plates), drastically reducing the application’s usefulness on vertical features. Now that you’ve developed an understanding of Nyquist, you can easily sense that reading license plates or resolving facial features is out of the question (for visible light systems), even under perfect conditions. I’m really not qualified to make these conclusions-please apply my conclusion diplomatically.

The Dawes Limit was originally formulated around 1850, and constructed using subjective observations predating refined testing. The Rayleigh Criterion was established some 30 years or so later (I believe) and although still subjective, formed within a much more sophisticated body of knowledge concerning light and physics. The formula is therefore more sophisticated and exceeds the scope of this post, however, both the Dawes Limit and the Rayleigh Criterion use subjective analysis to produce their conclusion.

The following links in case you’d like to extend your grasp of The Dawes Limit, The Rayleigh Criterion, or Angular Size. They really aren’t primary to our investigation of whether or not contemporary 35mm lenses are limiting imaging performance on their higher-end counterpart cameras, but they most certainly do aid in understanding the speculations and conclusions behind discussions on the matters. These links are obviously to astronomy sites, which makes perfect sense-it is astronomy where the sciences behind the craft are most widely developed and appreciated (try finding a even a single photographic site with this depth of information on the topics):

• astronomy.org
• Astronomy & Electronics Centre
• Cloudy Nights

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