[Leica] Image sharpness (long)

[George Huczek <ghuczek@sk.sympatico.ca>]

At 03:57 AM 24/05/98 EDT, you wrote:
>Perhaps a Lugger with great knowledge in optics could answer this better (or
>correctly :) ).
>
OK.  I'll give this a try.
As others have said, a sharp image can only be produced on one object plane
at a time, the plane of focus.  In theory at least, there is a one-to-one
correspondence between every point on the object and every point on the
image at this plane, if the lens is behaving in a theoretically perfect
manner (and few lenses actually do).
   Light rays passing through the lens converge to this plane in a cone
shape.  At the sharpest plane of focus all of the rays from the cones have
converged to single points.  Objects that are in front of or behind this
plane of focus do not converge to points at the film plane.  Instead, they
form small circles (circles of confusion) whose size depends, among other
things, on how far away those objects are from the plane of focus.
   The diameter of these circles of confusion will determine how sharp a
portion of the image will appear.  The focal length of the lens being used
influences the size of the circles of confusion in front of or behind the
plane of focus.  Wide angle lenses show a large depth of field.  The
circles of confusion in front of and behind the plane of focus are still
small enough to appear to be in sharp focus.  
   The aperture of the lens also has an influence on this.  Small apertures
produce greater depth of field.  The aperture cuts off the light rays that
would have passed though the edges of the lens.  These have larger circles
of confusion, due to the geometric angle at which they are travelling
through the lens.  The angle of the rays passing through the aperture is
more acute, limiting the size of the circles of confusion.  This is why
stopping down a lens gives greater depth of field.  
   Other factors which influence the appearance of image sharpness are the
distance between the object and image planes, the resolving power of the
lens, and the care with which focusing is done.  (This last point extends
into the discussion that has been going on regarding comparative focusing
ability with a rangefinder and focusing on ground glass with a SLR.)
   What must also be considered is the extent to which the eye is capable
of determining the plane of sharp focus.  Provided that the size of the
circles of confusion is small enough, a portion of the image will still
appear to be sharp, even if it does not lie on the theoretical plane of
focus.  There is always some debate as to how large the circles of
confusion must be before there is an apparent loss of sharpness of a
portion of the image.  It depends to a large extent on how closely the
image is viewed as well as on how the image is viewed.  Generally, the eye
will see a small circle as a point if its size does not exceed 2 minutes of
arc (2/60th of a degree).  This means that the permissible circle of
confusion is about 1/30mm.  I think Leica depth of field tables are based
on this assumption.  It should be noted that the same standard size of the
circle of confusion is not always applied consistently by all lens
manufacturers, leading to some misleading information in depth of field tables.
- -GH