Re: Focal Length Redux

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me@myplace.to wrote:
> 
> The theory I'm familiar with says a pinhole has infinite DOF _IF_  it is
> infinitely small.

What you are familiar with (in terms of theory) is WRONG

> Practice says for any focal
> length there is an optimal pinhole diameter for image sharpness.

Yes, and that is exactly what theory tells us.  Isaac Newton produced a
pretty good formula that describes the relationship (which I can't
locate at present) :-)

One I've been able to find is:

Diameter of pinhole = 1.56 sqrt( wavelength * focal length )

and if we use 500 nm for wavelength, we get:

  f          d

  4 mm      0.0698 mm
  8 mm      0.0987 mm
  17 mm     0.144 mm

  699 mm    0.922 mm
  736 mm    0.946 mm
  750 mm    0.955 mm 

Now, this compares quite well with Eric Renner's table that you referred
to in another message (which is why I chose those focal lengths)

The difference could be due to the choice of wavelength, or to the
multiplier.  Various formulae use slightly different values, since these
formulae are simplifications of rather more complex equations. 

(Incidentally the results come out very close when 547 nm is chosen as
the focal length)

> >> Every lens has a "normal" format and every format has a "normal" lens.
> >
> >It does?
> 
> Yes and yes.
> 
>  >And how do you calculate this "normal" lens/format? Can it be
> >empirically determined? Or just looked up in an old book?

As far as I can tell, "normal" means that if you look at a print of a
certain size from a certain distance, it overlays the scene exactly. 
i.e. it looks just as your eye would see it.

If we take that certain size to be 10x8 and the distance to be 12
inches, then we can determine focal lengths etc. to give us this.

Obviously many prints these dats are closer to 6x4, many eyes can't
focus that close without glasses :-) and we (as opposed to minilab
operators) don't always print the same fraction of the full frame.

> Consider it an exercise for supercilious twits.

Hmmm.

However, this concept of the "standard print" is the one which our
calculations of DOF are based on, so it's well worth remembering it.  If
you move too far form it, then you may need to change your calculations,
or at least be aware of the surprises :-)

Producing a smaller print is typically less of an issue, since few
viewers will look at it closer than 30 cm, and the increase in apparan
DOF when viewed at 30 cm will not normally be a major issue.

Even larger prints are rarely an issue.  The normal response to a larger
image is to stand back a little further from it, so at a "normal viewing
distance" DOF changes are probably minimal.

Cropping causes issues though...

Steve


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