ATM Autres follies de Foucault (More Foucault Follies)

[Roger Ceragioli <rogerc@dakotacom.net>]

In response to a recent post, I have been asked to supply the raw data for
my 6" f/4, because the knife edge readings seemed to indicate
UNDERCORRECTION, while a star test indicated very good correction.

Here is the requested data:

Diameter of Mirror: 5.94"
Radius of Curvature: 47.88"

Edge Radii of Couder Mask:
Zone 1 (inner radius): 0.00"
        (outer radius): 0.79"
Zone 2 (outer radius): 1.61"
Zone 3                : 2.17"
Zone 4                : 2.60"
Zone 5                  : 2.97"

The mask is pretty much a standard Couder Mask, and was not hard to read
from 4 ft. away.

The raw data from the final test were as follows:

Zone 1:  -.072/-.075
Zone 2:  -.063
Zone 3:  -.046
Zone 4:  -.027
Zone 5:  -.007/-.006

Explanation of these numbers:  I use an X-Y micrometer table to move my
light source (a slit) and my knife edge together.  The micrometer reads in
such a way that the numbers DECREASE from zone 1 to zone 5, instead of
INCREASE (as Texereau's standard method of analysis requires).  So in order
to use my numbers in TEX or ADMIR, I must enter the negatives of what I
actually measure (so that the numbers INCREASE), which is fine since we're
only REALLY interested in the DIFFERENCES in zonal measurements, and not
their absolute values.  Zone 1 in fact focuses IN FRONT of Zone 2, and 2 in
front of 3, etc., just as they are supposed to do in a paraboloidal mirror.

For zone 1 and zone 5 I give alternative knife edge readings because I
couldn't make up my mind.  I don't bother with Texereau's elaborate method
of taking many readings blindly, because past experience has shown me that
when I do that, my numbers tend to reproduce themselves closely.  The final
arbiter for me is the star test, which is pitiless and much less subjective
than reading the relative grayness of zones.

So I tell myself as I'm measuring the zones that I want to know the TRUTH,
not just see a pleasing numbers.  Then I try to find a good balance of
grayness between the zones.  Then I look to see what reading I get.  And
THEN, I purposely change the reading by a few thousanths and look again at
the relative greyness.  I keep changing the micromter setting and looking
again and again, until I'm satisfied that I've gotten close to a good
balance of grayness.

Over a number of years of testing, I've gradually discovered more and more
how error-prone the knife edge test is:  1) you have to allign the knife
edge and slit; 2) you have to allign the tester with the optical axis of
the mirror; 3) you have to cut a Couder mask and measure its radii; 4) you
have to position the mask correctly in front of the mirror; 5) you have to
move the lamp house until the corresponding zones on opposite sides of the
mirror look equally bright (very subjective); 6) you have to make the
readings by balancing the greyness on the corresponding zones (very
subjective).

I often find that I can make a good-faith reading, look away, turn the
flashlight on, write the result down, look back again without moving the
micrometer, and the zones don't look balanced anymore.  The brain/eye
system just ain't good at absolute measurements: physiology/psychology
affect the results in varying ways.  And forget making measurements if
you're tired! 

If you plug my above numbers into TEX, you get an overall rating of about
1/3 wave UNDERCORRECTED: the zonal graph DESCENDS from zone 1 to zone 5.
Same for ADMIR.  Yet, the star test shows definitively that the spherical
correction is close to perfect.  And after past figuring spells, when I got
the "correct" readings from the knife edge test that produced beautiful
wave numbers from TEX and ADMIR, the star test showed my little mirror to
be about 1/4 wave OVERCORRECTED.  But the star test is the absolute, final
judge, 'cause we make mirrors to look at stars not at knife edge shadows!

What I'm writing here isn't meant to attack the knife edge test, which I in
fact really LOVE.  It's a great test: shows you turned down edge easily,
shows surface roughness vividly, zones stand out, and the Couder mask for
me is an enormous help in figuring.  So it's really versatile, and I will
go on using it with pleasure.  But it is limited, and needs help from other
tests, in my opinion.  So that's where star testing comes in.  I suspect
that as the sages have long said: the Foucault test begins to break down
below at about f/5.
So, IMHO, don't worry too much about your numbers, look at the stars instead!

Best holiday wishes to all,
Roger Ceragioli