The Holding Tank

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Depth of Field, Image Quality and Sensor Size

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Harold M. Merklinger has published a very interesting article "Depth of Field Revisited" where he argues for an alternative approach to the traditional hyperfocal focusing method.

Essentially, considering the traditional landscape situation, Merklinger notes that distant objects, being at smaller magnification than close objects, contain more detail and thus need more resolution. Conversely the close objects can appear sharp with lower resolution because the detail is closer.

The suggested solution is to focus close to infinity to maximize the detail in distant tree leaves for example whilst, the use of a small aperture will render good detail on close objects like blades of grass.

This contrasts with the traditional hyperfocal method where the plane of sharp focus is often placed where there is no useful subject and both very close and distant subjects have equal resolution at the sensor plane, but the very distant details are rendered soft.

To quote:

The rule for determining what objects are resolved is ultra-simple. We focus our lens exactly at some distance, D, from our lens. An object one-tenth of the way back from D, towards our camera (that is, at a distance of 0.9 D), will be resolved if it is at least one-tenth as big as the opening in our lens diaphragm. If the object is one-quarter of the way from the point of exact focus to the camera lens, it will have to be one-quarter as big as our lens to be resolved. And so on. The same rule will hold on the far side of that point of exact focus also. An object twice as far from the lens as the point of exact focus will have to be as large as the lens aperture to be resolved.

Mathematically this reduces to the relatively simple formula:

S=d.E/D

where S the size of object resolvable at distance E either side of the plane of sharp focus located at a distance D from the lens. d is the aperture used in the lens, i.e. d=focal length/f-stop#.

This is an interesting concept that I know I have often used with analyzing it when I was worried the hyperfocal method would not render sufficient distance detail, often as a secondary safety shot.

So how does this work out in practice. To look at this we can consider the simplifying assumptions of the camera being mounted level at a height L above the ground which we can assume is a plane. The closest point will then be defined by the lens focal length and format size and orientation. By similar triangles we can calculate the distance as

D'=2.L.F/W,

Where L is the camera height, F is the lens focal length and W is the format size in the down direction. 

The value E can then be calculated as E=abs(D'-D).

Looking at the problem with some plots for APS-C and 35mm formats in vertical and horizontal orientations at two height 2ft and 0.5ft:

 

 

So the question is how well does this compare to the traditional hyperfocal method. We can discover this by plotting the resolution relative to the resolution achieved at the same distance if the lens were hyperfocally focused at the same f-stop using the appropriate circle of confusion parameter for 35mm and APS-C of 0.03 and 0.019mm respectively.

 

 

Here we can see that the Merklinger method is sacrificing little sharpness at low camera heights, where the penalty is about 20-40%, however at typical handheld heights the sharpness factor can be worse by a factor of 100-300 although for very wide angle lenses it seems the hyperfocal setting can be too close for normal handheld heights.

All in all this method seems to be well worth using except where the main subject of interest is in the foreground and the background has little very fine detail to retain.

 

Last Updated 05/06/2008

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