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Technically speaking, to achieve the sharpest photos possible one generally should follow the simple rule of "two or three stops down from your lens'" maximum aperture. But why is this?
When I first started photographing a variety of subjects with my first DSLR; I used aperture-priority mode (dubbed "Av" in most cases) to open the lens wide open and isolate my subject. This is a great tactic when taking portraits as often times you want to blur everything but the subject, creating a milky blur in the background (better known as "bokeh" ). However, when outdoors and trying to keep everything in the frame as sharp and crisp as possible, I found that the opposite wasn't true for "across the image" sharpness.
The Sweet Spot
Often times, using the simple rule of stopping down two or three stops from your lens' max. aperture is an easy way to get the sharpest images possible. This would mean that with an f/4 lens, using f/8 or f/11 would yield the best results. In fact, there's a saying that photojournalists follow: "f/8 and be there" which is some good advice for those who have a profession in getting everything clear... after all, it's their job.
Diffraction
Why is it though that our lenses continue to f/16, f/22, and even f/32 in some cases if we can achieve ultimate sharpness at f/8 or f/11? Why won't these produce the sharpest images? Well something called "diffraction" comes into play. When your "pinhole" gets too small--light slightly bends around the edges and with a gap too narrow, that can be pronounced as a loss of edge detail. Think of squinting your eyes to see more clearly. At one point, you may squint too much and things may tend to blur a little bit.
Then what are f/22 or f/32 for?
Sometimes you may have a bit too much light. Say you're out on a bright sunny day and you want to slow down your shutter to get some motion blur. A classic example is of a cascading river, where you want to prolong your shutter speed in order to make the water look "creamy". On a bright day, you may want an exposure of 1/4 second, but even at ISO 100, you're hooped at f/8 and can't go any slower on your shutter. This is where you can limit the amount of light and get that desired shutter speed, by stopping up to f/22 or f/32. You may be the victim of diffraction, but hey, you still have a good shot. (Note: use neutral density filters to help stop down in bright conditions)
A safe range for sharpness is between f/5.6 and f/11, especially during the day while traveling. You may not always want to follow this rule, but it's always good to know for being your default f-stop when it comes to getting a sharp photo.
You can always use a tripod and take the same photo at different f-stops, then check corner-to-corner sharpness later on with your computer. Try this with each lens to find their individual "sweet spots".
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A quick note on how apertures are calculated:
Apertures follow the same exposure values as ISO and shutter speed, doubling the amount of light that hits the sensor by each step. For example, shutter speeds will jump from 1/15 to 1/30 to 1/60... and ISO will follow a similar scale with 100 to 200 to 400...; however, what's with f/1.4, f/2, f/2.8, f/5.6, f/8, f/11... etc? Well because aperture is calculating the amount of light that's getting through a circle, we have to use the old area of a circle equation where we are squaring the radius. Pretty much, all that means is you can take the same steps: 2, 4, 8, 16, 32, 64, 128, 256 and square root each one to get those f-stops you've been confused about... weird but it works! (Most DSLRs also have midpoints like f/7.1 to offer the photographer more flexibility)
Image credit: Silverstrand Photography
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