Internet Info 1994 March/Internet Info CD-ROM (Walnut Creek) (March 1994).iso/answers/rec/rec-photo/lenses/faq

Text File | 1994-03-21 | 12KB | 301 lines

Newsgroups: rec.photo,rec.answers,news.answers
Path: bloom-beacon.mit.edu!hookup!swrinde!sdd.hp.com!hpscit.sc.hp.com!hplextra!cello!jacobson
From: [e-mail] (David Jacobson)
Subject: Photographic Lenses FAQ
Summary:  This posting contains a list of Frequently Asked Questions
    about lenses.  It is intended for photographers.  It
    defines terms, gives a large number of formulas, discusses
    depth of field issues, diffraction, and lens aberrations.
Message-ID: <[e-mail]>
Supersedes: <[e-mail]>
Approved: [e-mail]
Date: Tue, 22 Mar 1994 03:28:03 GMT
Expires: Fri, 22 Apr 1994 06:00:00 GMT
Organization: Hewlett-Packard Laboratories
Followup-To: rec.photo
Lines: 282
Xref: bloom-beacon.mit.edu rec.photo:44485 rec.answers:4566 news.answers:16723

Archive-name: rec-photo/lenses/faq
Last-modified 1994/02/10
Version: 1.0

Frequently Asked Questions regarding lenses.
By David Jacobson
[e-mail]


Q. What is the meaning of the symbols in the rest of this FAQ?

A.  f       focal length
    So      distance from front principal point to subject (object)
    Sfar    distance from front principal point to farthest point in focus
    Sclose  distance from front principal point to closest point in focus
    Si      distance from rear principal point to film (image) plane
    M       magnification
    N       f-number or f-stop
    Ne      effective f-number (corrected for bellows factor)
    c       diameter of largest acceptable circle of confusion
    h       hyperfocal distance

See the technical notes at the end for more infomation on subject
distances, more information on the meaning of f-number and
limitations to be observed when applying these formulas to lenses in
which the aperture does not appear the same size front and rear.

Q. What meant by f-stop?

A. The focal length of the lens divided by the diameter of the
aperture (as seen from the front).  It is also called an f-number.
The brightness of the image on the film is inversely proportional
to the f-number squared.

Q.  What is the basic formula for the conditions under which an image
is in focus?

A.  There are several forms.
        1/Si + 1/So = 1/f      (Gaussian form)
        (Si-f)*(So-f) = f^2    (Newtonian form)


Q.  What is the formula for magnification?

A.  There are several forms.
        M = Si/So
        M = (Si-f)/f
        M = f/(So-f)


Q.  How do I correct for bellows factor?

A.  Ne = N*(1+M)


Q.  What is meant by circle of confusion?

A.  When a lens is defocused, a point in the subject gets rendered as
a small circle, called the circle of confusion.  If the circle of
confusion is small enough, the image will look sharp.  There is no one
circle "small enough" for all circumstances, but rather it depends on
how much the image will be enlarged, the quality of the rest of the
system, and even the subject.  Nevertheless, for 35mm work c=.03mm is
generally agreed on as the diameter of the acceptable circle of
confusion.  Another rule of thumb is c=1/1730 of the diagonal of the
frame, which comes to .025mm for 35mm film.  (Zeiss and Sinar are
known to be consistent with this rule.)


Q.  What is hyperfocal distance?

A.  The closest distance that is in acceptable focus when the lens is
focused at infinity.  (See below for a variant use of this term.)

        h = f^2/(N*c)



Q.  What are the closest and farthest points that will be in sharp
focus?

A.  Sclose = h * So / (h + (So - f))
    Sfar   = h * So / (h - (So - f))

If the denominator is zero or negative, Sfar is infinity.

Q.  What is depth of field?

A.  It is convenient to think of a rear depth of field and a front
depth of field.  The rear depth of field is the distance from the
subject to the farthest point that is sharp and the front depth of
field is the distance from the closest point that is sharp to the
subject.  (Here we assume the lens is focused on the subject.)
Sometimes the term depth of field is used for the combination of these
two, i.e. the distance from the closest point that is sharp to the
farthest point that is sharp.

frontdepth = S - Sclose
frontdepth = Ne*c/(M^2 * (1 + (So-f)/h))
frontdepth = Ne*c/(M^2 * (1 + (N*c)/(f*M)))

reardepth = Sfar - S
reardepth = Ne*c/(M^2 * (1 - (So-f)/h))
reardepth = Ne*c/(M^2 * (1 - (N*c)/(f*M)))

In the last two, if the denominator is zero or negative, reardepth is
infinity.


Q.  Where should I focus my lens so I will get everything from some
close point to infinity in focus?

A.  At approximately the hyperfocal distance.  More precisely, at
So = h + f.  In this condition the closest point that will be in focus
is at half the subject distance.  (Some authorities use this as the
definition of hyperfocal distance.)


Q.  I have heard that the depth of field depends only the the f-stop and
the magnification.  Is this true?

A.  Yes, under some conditions.  When the subject distance is small
with respect to the hyperfocal distance, the front and rear depth of
field are almost equal and depend only on the magnification and f-stop.
As the subject distance approaches the hyperfocal distance, the front
depth of field gets smaller and the rear depth gets larger, eventually
extending to infinity.


Q. I have heard that one should use a long lens to get a shallow depth
of field and a short lens to get a large depth of field.  Is this
true?

A.  Assuming that you frame the subject the same way, using a long
lens does not make the depth of field very much shorter.  It does make
the front and rear depths more even, but you probably didn't care
about that very much.  Using a short lens can make the rear depth of
field very large, or even infinite.  (See the previous question.)  Now
back to the long lens issue.  Even though making the lens very long
has little effect on the maximum distance behind the subject at which
points still appear to be sharp, it has a big effect on how fuzzy very
distant points appear.  Specifically, if the lens is focused on some
nearby point rendered with magnification M, a distant point at
infinity will be rendered as a circle of diameter C, given by

C = f M / N

which shows that the distant background point will be fuzzed out in
direct proportion to the focal length.


Q.  If I focus on some point, and then recompose with that point not
in the center, will the focus be off?

A.  Yes, but maybe only a little bit.  If the object is far enough
away, the depth of field will cover the shift in distance.

An approximate formula for the minimum distance such that the error
will be covered by depth of field is given by

d = w^2/(2 N c)

where
    d = minimum distance to make the point be sharply rendered
        d is measured from the film plane
    w = distance image point on the film is from center of the image

Thus for 35mm you can recompose the image moving the subject clear to
the edge of the frame and still have it be sharp if the subject
distance (at the center) was at least 5.4 meters (18 feet) divided by
the f-number.  See the technical notes at the end for a bunch of
assumptions.


Q.  What is diffraction?

A.  When a beam of light passes through any aperture it spreads out.
This effect limits how sharp a lens can possibly be.


Q.  What is the diffraction limit of a lens.

A.  A lens is diffraction limited at about 1500/N line pairs per mm.


Q.  What are aberrations?

A.  Aberrations are image defects that result from limitations in the
way lenses can be designed.  Better lenses have smaller aberrations,
but aberrations can never be completely eliminated, just reduced.

The classic aberrations are:

* Spherical aberration.  Light passing through the edge of the lens is
focused at a different distance (closer in simple lenses) than light
striking the lens near the center.

* Coma.  The distance from the axis at which an off-axis object point
is rendered varies with the distance from the center of the lens at
which the light passes.  In other words, magnification varies with the
distance from the center of the lens.  Off axis points are rendered
with tails, reminiscent of comets, hence the name.

* Astigmatism.  Off-axis points are blurred in their the radial or
tangential direction, and focusing can reduce one at the expense
of the other, but cannot bring both into focus at the same time.
(Optometrists apply the word "astigmatism" to a defect in the human
eye that causes *on-axis* points to be blurred along one axis or at 90
degrees to that axis.  That astigmatism is not quite the same as
astigmatism in photographic lenses.)


* Curvature of field.  Points in a plane get focused sharply on a
curved surface, rather than a plane (the film).  Or equivalently, the
set of points in the subject space that are sharp makes a curved
surface rather than a plane.  With a plane subject or a subject at
infinite distance the net effect is that when the center is in focus
the edges are out of focus, and if the edges are in focus the center
is out of focus.

* Distortion (pincushion and barrel).  The image of a square object
has sides that curve in or out.  (This should not be confused with the
natural perspective effects that become particularly noticeable with
wide angle lenses.)  This happens because the magnification is not a
constant, but rather varies with the angle from the axis.

* Chromatic aberration.  The position (forward and back) of sharp focus
varies with the wavelength.

* Lateral color.  The magnification varies with wavelength.


Q. Can I eliminate these aberrations by stopping down the lens?

A.  The effect of all aberrations except distortion and lateral color
is reduced by stopping down.


Q. What are "elements" and "groups", and are more better?

A. The number of elements is the number of pieces of glass used in the
lens.  If two or more are cemented together, that whole set is called
a group.  Thus a lens that has 8 elements in 7 groups has 8 pieces of
glass with 2 cemented together.  It is impossible to completely
correct all aberrations.  Each additional element the designer has at
his/her disposal gives a few more degrees of freedom to design out an
aberration.  So one would expect a 4 element Tessar to be better than
a 3 element Triotar.  However, each element also reflects a little
light, causing flare.  So too many elements is not good either.  Note
that an unscrupulous manufacturer could slap together 13 pieces of
glass and claim to have a 13 element lens, but it might be terrible.
So by itself the number of elements is no guarantee of quality.


Technical notes:

The subject distance, So, as used in the formulas is measured from the
subject to the lens's front principal point.  On most cameras the
focusing scale is calibrated to read the distance from the subject to
the film plane.  There is no easy way to precisely convert between the
focusing scale distance and So.

The formulas presented here all assume that the aperture looks the
same size front and rear.  If it does not, which is particularly
common in wide angle lenses, use the front diameter and note that the
formulas for bellows correction and depth of field will not be correct
at macro distances.  Formulas that are exact even with this condition
are given in the lens tutorial, posted separately.

The conditions under which the formula for the minimum distance at
which the effect of focusing and recomponsing will be covered by depth
of field are:

1.  w is no more than the focal length of the lens.  At the edge
w=18mm for 35mm, so this will very seldom be a problem.  2.  The
lens's two nodal points are not very widely separated.  But if the
front nodal point is in front of the rear nodal point, which I think
is the more common case, the formula is too conservative, so this is
not a problem either.  3.  The camera is rotated about the front nodal
point.  Almost always the camera will be rotated about an axis behind
the front nodal point which again makes the formula too conservative.
For guide number given assumes c=.03mm.