On 1 Dec 2003 05:45:26 -0800, (andrea tasselli)
wrote:

Let's assume that the color error weighs equally irrespective of the
visual wavelength (it isn't usually so but for sake of semplicity...).
The optimum focus position lies halfaway between the green focus and
the blue/red one. We therefore ask that the focus tolerance is equal
to half of color error between green and red/blue.

The fact that the weighted color error is FAR from equal is why
achromats work as well as they do. Blue and red wavelengths are
only around one tenth the visual weight of yellow-green.
Using your simple example gives the impression that focusing to the
smallest spot size would yield the sharpest focus, which in the case
of virtually any achromat, it wouldn't (although the color would
appear balanced).

Given the formula
above (to be checked !!) one gets the answer it needs:

FR = D/(32*max.error*2*Delta.F), where Delta.F is the distance between
green and red/blue focii and D is the diameter of the refractor.

Conrady's formula F= D(mm)/8.8*delta lambda , where F is focal ratio,
D is dia. in mm, gives f/35 (!) for a 150mm doublet with .5 lambda
from 550nm and is 'a bit' over the top( pun intended:-) At f/18 the
lens would have a delta lambda of ~one wave and such an objective is
quite pleasing on the planets in my experience. My 80mm achromat, at
f/11, has about .7 lambda delta and shows almost no color on anything
in the night sky but Venus and Sirius.
So, the damage done by even as much as 1 wavelength defocus of
blue/red should not be overstated for visual use, with the exception
of Mars and its push towards the red. The abundance of short, cheap
130mm -150mm achromats have exascerbated the seemingly growing
notion of virtually any achromat as a dinosaur less worthy of being a
great visual planetary instrument.

Dan C.