>I need to determine the depth of field for a series of lenses.
>In my optics notes (from the Dark Ages) I have the following equation:
>
>depth of field=  ((n * wavelength)/(2 * N.A.* N.A.)) + ((n * 1000)/(7 * N.A.
>* M))
>
>where N.A. is numerical aperture
>      n= refractive index
>      M= total magnification (eyepiece * objective)
>
>I can fiqure out where most of this comes from, but in trying to derive
>the equation from an optical path diagram I cannot fiqure out:
>
>1. Why the magnification includes both the eyepiece and objective mags?
>2. Where 1000 and 7 terms come from?
>
>Any help would be appreciated. I could of course just plug numbers into
>the equation, but I would prefer to understand. I obviously have
>forgotten something fundamental, but I can't remember what it is!!!!!!
>Thanks in advance. You can reply to me directly at e-mail address below.
>Jay Jerome

Dear Jay,

I find that the diffraction limit is the most helpful parameter to start
with.  It is an unyielding limit, and all else hinges upon it.  It also has
a little bit to do with the resolution and depth of focus of confocal
systems (with quite a few clever twists added on).

The "easy" rule of thumb for diffraction limit I use to calculate laser
spot sizes, for example, is that the "f number" of the system or lens
(let's call it f, for short) times the wavelength of interest (say 0.5
micron) times the factor 1.25 will provide the diameter of the diffraction
limited spot containing about 80% of the focused energy.

Next, as a practical matter, look at the optical path from a purely
geometric point of view, and determine where the diameter of the geometric
light cone is equal to this diameter.  Roughly (and I do mean roughly) the
space between these two intersections is thought of as the "waist" of the
beam.  The length of this waist is, of course, the depth of field.

Finally, the "depth of field" contains personal choice because additional
depth is the depth corresponding to the degree of additional loss of
resolution the user is willing to tolerate, and purely geometric optics is
quite helpful here.

Example:  For a simple, diffraction limited objective lens, such as a
telescope primary -

f=16,  wavelength = 0.5 micron

diffraction spot size = 1.25 x 0.5 micron x 16 = 10 microns.

The rest is Euclid.










Salutations and Regards,


Ed Monberg, Manager
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