Effective F-Number and Effective Focal Length - Effects upon Diffraction and Depth of Field

_sem_ wrote:

thx1138 wrote: At 1:1 you have a true aperture of f/44 or f/88 FF equivalent.

That is effective aperture, relevant for metering and diffraction.

While nominal aperture remains the same, and matters for DoF, AFAIK.

When a symmetrical or an asymmetrical lens is not focused at infinity, the actual Focal Length reduces to the distance referred to as the Effective Focal Length, which is equal to:

( L ) / ( 1 + M / P )

where:

L is Focal Length when focused at infinity;

M is Image Magnification (image-frame dimension divided by object-dimension);

P is Pupillary Magnification (diameter of the exit pupil divided by the diameter of the entrance pupil).

.

F-Number is Focal Length divided by diameter of the entrance-pupil (the virtual aperture diameter).

The Effective F-Number is that value which, when divided into Effective Focal Length, yields the same virtual aperture diameter. Thus, the Effective F-Number is equal to:

( F ) x ( 1 + M / P )

where:

F is F-Number;

M is Image Magnification (image-frame dimension divided by object-dimension);

P is Pupillary Magnification (diameter of the exit pupil divided by the diameter of the entrance pupil).

.

The diameter of main-lobe of diffraction light-spreading on the Focal Plane surface equals:

( 2.43934 ) x (wavelength in Meters) x ( F ) x ( 1 + M / P )

Diffraction, Page 25, Depth of Field in Depth, Jeff Conrad:

http://www.largeformatphotography.info/articles/DoFinDepth.pdf

The Effective F-Number (as modified by image and pupillary magnification) is relevant to diffraction.

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Depth of Field (stated in terms of Image Magnification, and for the general case of a symmetrical or a non-symmetrical lens) equals:

( ( 2 ) x ( L ) x ( 1 / M + 1 / P ) ) / ( ( L x M ) / ( F x C ) - ( F x C ) / ( L x M ) )

where:

L is Focal Length when focused at infinity;

M is Image Magnification (image-frame dimension divided by object-dimension);

P is Pupillary Magnification (diameter of the exit pupil divided by the diameter of the entrance pupil).

F is F-Number;

C is diameter of the Circle of Confusion (referenced to the Focal Plane).

From Equation 104, Page 24, Depth of Field in Depth, Jeff Conrad:

http://www.largeformatphotography.info/articles/DoFinDepth.pdf

The Effective Focal Length (as modified by image and pupillary magnification) is relevant to the DOF.

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In the case of calculating close-up Depth of Field, note that the distance that needs to be used is the Front Nodal Plane (not Focal Plane) to Plane of Focus Distance (can be significantly different).

Further information about Front Nodal Plane location of a lens system, and general resources here:

http://en.wikipedia.org/wiki/Depth_of_field#Practical_complications

http://johnlind.tripod.com/science/sciencelens.html

http://photo.net/learn/optics/lensTutorial

DM...