RONCHI
Aspherizing
Assessment of Conic Constant.
Copyright – P. J.
Smith
But permission is
given to distribute this material in unaltered form as long as it is not sold
for profit.
GOTO RONCHI INDEX
Originally the Ronchi test
was used on spherical mirrors where it performs very well. The optician aims for straight and parallel
Ronchi bands. Any bending in the
Ronchi bands indicates some departure from a sphere.
Makers of Aspheric surfaces
soon looked at the possibility of assessing the state of Parabolization by
estimating the amount of bending of Ronchi bands. Since ATM’ usually target aspheric surfaces, they were in the forefront of this
movement.
It looks easy to simply figure a surface to match the Ronchigrams above.
This requires three steps.
1.
Calculation
of the required Ronchi band shape at some definite position of the grating.
2.
Positioning
the grating at this location.
3.
Estimating
the match between theoretical and observed shapes.
Ronchi Band
Shape Calculation.
Since this was first
attempted in the 1930’s, before computers or even electronic calculators,
calculation of the shapes was no trivial matter. Most opticians using this method depended on published families
of graphs that were still in use in the 1960’s.
One much used resource was
Sherwood’s tables and Graphics. He was
one of the first to rigorously calculate the band shapes and his work was
published in Italy, Australia, and Britain.
A small extract of one of these publications[1]
is shown below for the historical record.
Software which generates
these curves is now easily available.
All of the Geometric simulations seen here are produced using my program
RonchiZ but others are available.[2] Users simply generate their required
Ronchigram shapes. It should also be
mentioned that Raytracing software will also compute expected Ronchi band
shapes.
Positioning the
grating.
When testing Spheres,
positioning the grating is easy. All
one has to do is move the grating towards or away from the mirror and note the
number of Ronchi bands visible. Some
seen unaware that when the Grating period and the F:NO of the test beam are
fixed, it becomes possible to extract
the mirror shape (in one dimension) and the defocus. Various automated Ronchi fringe analysis programs have been
developed to do this. There is of
course a limit to what the eye can detect, complicated by the uncertainty introduced
by diffraction effects.
In practice, it is best to
move the grating until one set of bands just drop off the edge of the surface.
When assessing the
asphericity of near spheres, this method is entirely adequate for excellent
performance.
Consider a just
“Diffraction Limited”[3] 8 inch (200 mm) F:8 mirror.
Users may wish to choose
different grating positions showing more or less bands, but this gives some
idea of the allowable variation at two different positions, one inside
COC, the other outside.
Even allowing for
Ronchigram degradation from diffraction etc. this indicates that a classical
“diffraction limited” mirror should easily be discernable by eye. Note the wide range of allowable conic
tolerable for a 200 mm F:8 mirror. It
is instructive to compare with 200 mm F:10 and F:4 mirrors of the. Both are just “diffraction limited”.
An F:10 mirror allows
of a much wider conic tolerance range.
But an F:4 mirror
requires much tighter conic control.
The differences between Ronchi
patterns spanning the allowable tolerance is now almost impossible for the eye
to discern.
Careful choice of the
grating position may enhance examination of specific portions of the mirror
when viewing aspherics. Since inner and
outer zones of aspheric mirrors have different radius of curvatures, which are
different distances from the grating, the sensitivity of the Ronchi test varies
in these different zones. This is more
evident in the images below showing band “centres”.
Edge most
sensitive Centre most sensitive
In each case, the band
spacing at centre and edge is marked.
The test sensitivity is directly related to this band spacing and we can
see it varies as we scan the mirror.
One argument for assessing asphericity outside COC for deeper parabolas
is that the sensitivity of the test is greatest near the edge where the area of
the mirror is a maximum.
Another approach taken by
some is to generate Ronchi patterns for specifically chosen positions and
actually measure the longitudinal position of the grating before comparison of
the patterns are made.
The setting may be done by
measuring from Centre of curvature of the central zone to the grating
positions. Since the paraxial COC is
hard to accurately locate in practice, this is harder than it sounds.
An alternate, potentially
more accurate method is to match best the outside position image by positioning
the grating, then move it the full measured distance to the other chosen
position.
Pattern changes
between measured grating positions are more distinctive.
This variation has become
known recently as the Matching Ronchi Test[4]. It allows aspheric correction to be read
adequately from Ronchi tests for deeper aspherics.
While the difference in the
above images outside COC looks very obvious, the bands change extremely quickly
at the edge and setting is much harder than it looks.
Unfortunately, the test
also becomes more complex, requiring some well calibrated measuring and
translating mechanism.
In my opinion, it is better
to leave the Ronchi test in a form where no special grating[5]
or measuring rig is needed – thus its main advantage is utter simplicity.
If we acquire this more
complex equipment, it can of course be used to extend the Ronchi test, but is
probably more usefully used with other testing methods.
Certainly, one should not
feel that a precision positioning rig is a necessity for Ronchi Testing.
Custom Inverse
Gratings
Mention should be made of
another method of Aspherizing via the Ronchi test. This uses custom shaped
Gratings, which, when used in a particular position, produce a perfect looking
Ronchi pattern when applied to the target surface shape.
Usually the target is a
Paraboloid and a non-linear line Grating is used. This is commonly called a Mobsby Grating. It should produce a
parallel line Ronchi pattern.
Another variation is a
modified circular grating by Popov.
Both of these processes can
be modified to produce Ronchi Hartmann variants.
More details of all these
are given under Non Linear Gratings.
GOTO RONCHI INDEX