RONCHI
Conclusions
Summary of conclusions for simple Ronchi Testing of optical systems.
Copyright – P. J.
Smith
But permission is
given to distribute this material in unaltered form as long as it is not sold
for profit.
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Purpose
Before discussing the suitability of Ronchi
testing, we should be very clear on its purpose.
This can range between :-
·
Verifying
wavefront aberrations.
·
Verifying
precision Aspheres.
·
Verifying
precision Spheres.
·
Final
figuring – which is more or less equivalent to the above.
·
Rough
figuring – which is simply information so we can roughly modify the surface in
the right direction. Until the surface
shapes up, there is no point in any better tests. Indeed, better tests may even be impossible at this stage.
·
Fine
grinding checks. [1] Few will
interested in this.
A Ronchi test may be brilliant for one purpose but
deficient in another role.
Of course, in some cases, there may be no
alternate method available. [2]
Normal Ronchi Testing only operates on one
diameter of the surface. This means it
assumes radial symmetry.
Thus, it cannot easily be applied to surface
testing in 2 dimensions.
For this reason, any claims of ridiculous
accuracy should automatically be suspect.
Inevitably, questions will be asked about this
assembled material on Ronchi testing
relating to the suitability and accuracy of the Ronchi test.
This is an incredibly wide ranging and complex
question, especially if complex null tests are involved. A tolerance analysis using a Raytracing
program is probably the best approach in this case.
If you wish to make your own assessment, the best thing is to :-
·
Consider
the allowable image degradation and the corresponding wavefront defect. This is not easy, especially with combined
aberrations and must be somewhat arbitrary.
Raytracing programs which estimate Strehl, and the downloadable program Aberrator
may help. See software.
·
Estimate
reasonable limits of sensitivity which may be detected for each type of
aberration on the wavefront using the Ronchi test. Included in this may be certain specific types of defects met
with during production such as Turned Down Edge and isolated defects which are
covered in more detail in my program RonchiEstimates. See software.
·
Consider
the contribution of different surfaces to these wavefront defects. This will, of course, take into account the
type of surface and the angle of rays.
It can be done with a Raytracing program.
My
downloadable program RonchiZ (see software
) has a facility to help you to match Ronchigrams with surface defects. If the surface is a paraboloid to be used as
a telescope mirror, the program also estimates RMS and Strehl for the surface,
also for the surface with areas masked from both inner and outer edges.
Some thoughts on Ronchi Testing Limits.
Rather than attempt a detailed assessment, I
will simply state what
I
believe to be reasonable in some common situations.
I cannot fully substantiate some of this
material. If anyone disagrees and
can substantiate their argument I am certainly
interested.
Note that the following refers to estimated PV errors. I am perfectly aware that RMS figures are more directly related to performance. I think that estimates made by eyeballing Ronchigrams are more realistically made as PV errors. If a series of measurements are made by some other method, or by advanced Ronchigram reduction, RMS errors may be possible and more appropriate. On the other hand, an intelligent consideration of where on the surface errors produce most impact will go someway towards redeeming the shortcomings of PV estimates.
Ronchi bands that suddenly change shape show an obvious defect, but bands that show a less obvious deviation from perfect shape over a long span may actually indicate worse surface deviation.
Always try to visualise the area involved in shifting the Ronchi bands rather than just the amount of shift. This is a mental way of integrating to mentally convert a slope based to a height based test. This explains why it is difficult to evaluate degree of parabolisation – one has to read a slight line shift extending completely across the mirror. On the other hand, TDE effects only cover a small distance so look more fearsome.
Type of Aberration
Spherical
aberration. The Ronchi test is good for detecting
the presence of spherical aberration.
In other words, used as a null test, it is quite powerful. 1/20 wave
is achievable on the wavefront.
Estimating
the amount is very much harder. It requires experience and careful comparison
with example Ronchigrams. This is
typical of the case met when parabolizing.
The depth of the parabola has a huge effect. The resulting pattern works at different sensitivity [3]
in different areas, which compounds the problem.
Turned
edge is a
symmetric production problem shown well by Ronchi testing. The width and shape of Ronchi bands may
cover different spans, and be of a wide range of shapes, so it is difficult to give
a simple estimate, but typical, small, steep, TDE’s of 1/20 wave ( surface
[4]
), should be detectable. If the TDE covers a wider span the slope error will be
too small for a Ronchi test to pick it up.
This
requires an understanding of the part diffraction plays in interpreting
edge effects. See Diffraction.
With
respect to turned edge, it may be worth looking at expected image degradation
from a defective paraboloid when used in an 8 inch telescope, ramping linearly to the specified turned edge
PV surface value, over a span of 10 mm.
|
TDE in waves |
1/20 |
1/5 |
1/4 |
1/2 |
|
Strehl |
0.99 |
0.86 |
0.78 |
0.4 |
This may at first seem surprising. The explanation
lies in the fact that, despite the moderate area covered by the defect, since
it tapers from zero defect to maximum, the average surface depression is much
less than expected.
In a Ronchigram, ¼ wave of TDE of this type literally leaps
out at you and just cannot be mistaken for anything else.
The table above clearly shows that, while TDE may be a
problem, it can be sensibly addressed. Simply because it is hard to quantify,
people have been worrying just a bit too much about it. One of the few ways
ATM’s have to roughly quantify TDE is by using my program RonchiEstimates. See software.
PLEASE.
I do not want this material to be used to justify a batch of mirrors
with excessive TDE. Correct it nicely, but
do not become paranoid about the edge.
A rational balance of all defects is more important.
Isolated defects such as
small pimples and holes can be quantified using a Ronchi test, which is about
the only way an ATM can attempt this.
Quantitative estimation of the
amount of Turned Edge and Isolated Defect
is aided by my program, RonchiEstimates. See software.
Investigation
of the non symmetrical aberrations such as coma and astigmatism
becomes harder and is not as suited to Ronchi
testing as some other tests.
Astigmatism, especially, requires a systematic
search by examining the surface with the grating at a series of angles. The test is most sensitive when the grating
is at 45 degrees to the astigmatism but at 0 or 90 degrees shows no obvious
Ronchigram pattern.
For
Spheres, I believe the Ronchi test can detect moderate astigmatism but there is
a much better method available – examination of a pinhole image inside and
outside of focus with an eyepiece. Astigmatism is much harder to detect with
aspherics and on deeper ones almost impossible. There is no easy way for ATM’s to detect Astigmatism in the case
of Aspherics [5]. Astigmatism is usually caused by a warped
surface.
For the
record, the following is the general pattern for gross astigmatism in the
presence of spherical aberration, which is equivalent to astigmatism on an
aspheric surface. The main
characteristic is rotation of the bands to a new angle. On an aspheric, the bands also take on an S
shape as shown. If the surface is a
sphere, the bands are angled, but straight.
The limit
of detection is probably about 1/10 wave PV on the wavefront.
Astigmatism on a paraboloid.
Depending on angle, it may be totally invisible.
Coma is seen
when the test is performed far off axis.
Below are examples of typical patterns, depending on the angle.
Coma
examples with a
sphere.
Performing the Ronchi Test very far off axis produces these effects depending
on whether the slit source is placed in line with (left Ronchigram), or
adjacent to (right Ronchigram), the grating.
The limit for visual detection is probably about 1/10 wave PV on the
wavefront.
With a mix of these
aberrations, visual analysis is very difficult except in the most simplistic
cases.
Typical ATM applications
Spheres
Careful
work can achieve 1/10 wave surface PV with medium depth spheres and I believe
painstaking work may do better with respect to the simple, symmetrical aberrations. This is of course a null test. With spheres, it is possible to draw the
grating closer to COC and still see a meaningful test on the mirror. With deep spheres the situation is
worse. Another problem is the
difficulty of testing on axis. Beam splitters
may help but beware - they can introduce aberrations. [6]
Paraboloids
Careful
work will bring you to, or close to the final surface. If the F:NO of the mirror is more than 8 or
9, very good results are possible with no further testing. Below F:6 means it is very hard to test the
degree of parabolization using a Ronchi test.
Matching to simulations extends the usefulness but other tests become
mandatory. See more under aspherizing. All other defects are harder to isolate in the presence of the
spherical aberration introduced when testing aspheres [7].
Of course,
null tests of paraboloids using autocollimation or the ‘Waineo’ test [8]
are free of these problems and behave in the same way as when testing a sphere
at COC.
Lenses
One
interesting thing to consider is the fact that, concave surfaces tested by
reflection, but subsequently used in a refractive role, should be expected to
perform very well. Test sensitivity is
effectively boosted about 4 times. This
situation exists when testing the concave surface in refractors, or making test
plates to subsequently test convex surfaces.
Echoes from 1936
One of the reports
in the columns of Scientific American (Edited by Ingalls) reports on some
testing done by Selby in a serious attempt to estimate the sensitivity limits
of Ronchi Testing is probably as true today as it was then. It is included in the History section but
will not be amiss repeated here.
Apr 36 HERE are some solid data from Horace n H. Selby, a chemist, of
San Diego. "Since last you wrote," he says, "I've
attempted to compare the Foucault test with the Ronchi, on several surfaces,
both directly and with a flat. Briefly, my conclusions are:
"1: The two methods are equa1 in sensitivity at f/6 direct, and at
f/12 with a flat.
"2: Ronchi is better at large aperture ratios: f/l, f/2.3, f/4.5.
"3: Foucault is better at small ratios: f/6.8, f/8, f/10.
"4: Neither is sensitive enough (
0.1
wave) below f/4.5.
"5: Straight-edge, diffraction (Everest test) and Ronchi are equal
for edge.
"6: When using a flat or a Hindle sphere, these surfaces must be
pretty near to fairly good: 0.1
wave is none too close.
"All of the above was done with 120-line- per-inch Lower wire
grating and smoked razor blade. In all comparisons, source (pinhole) and eye
were precisely together on the axis. Surfaces used had apertures of 1.09, 1.4,
2.3, 3.5, 4.5, 6, 8, 10 and 11.3. Sensitivity was judged by polishing grooves
in surfaces with pitch laps l/8" diameter, loaded 50 grams per square
centimeter, and using black rouge washed from worn-down stock.
"Don't forget," Selby adds, "that other may not get the
same results."
Everest commented - "I choose the old tin can and razor blade."
Sheib- "Interesting. I agree with Selby on No. 3, also No. 4 and No. 5. I
am not sure I agree with him on No. 1 or No. 2."
Whatever Ingalls says, the tests made by Selby seem an
admirable attempt to obtain good experimental data. They are probably quite reliable. Everest was probably a little prejudiced against the Ronchi test
but he was most certainly a very experienced and capable mirror worker.
Selby was involved in many advanced ATM projects (see ATM 1, 2, and
especially 3) and participated in WW2 optical work both at production and
research levels so was a very capable worker.
In general, this material agrees reasonably with my conclusions. It should be noted that Selby used a quality
wire grating (120 lp/inch) and a pinhole.
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