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.




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










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

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]



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.



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.




[1] A very finely ground surface can be made sufficiently transparent for rough Ronchi testing by waxing or lightly oiling the surface.  There is no advantage in this method when our target shape is a sphere, because there are other simple tests – indeed, the feel during fine grinding will tell us how good a sphere we have.  Where we want deep aspheres, or Schmidt plates, there is an unrealistic amount of glass to remove during polishing, so Ronchi testing during fine grinding may be appropriate.  See DeVany’s and Wallard’s early methods of Schmidt corrector plate production for examples.

[2] For example, I know of no other convenient method for an ATM to roughly quantify turned edge.  See the program RonchiEstimates detailed under software.

[3] The sensitivity is directly related to Ronchi band spacing which of course varies when testing aspheres.  For example, inside COC with paraboloids  places maximum sensitivity in the center while outside COC at the edges.  Certainly, there is much advantage to be gained by observing Ronchigrams both inside and outside COC when testing aspheres.  This is far less important when testing spheres.

[4] This has been quoted on the surface because most opticians want to relate it directly to the surface.  Taken on the wavefront we should be able to detect 1/40 wave PV of this type of error.

[5] Of course, finished Paraboloids may be tested for astigmatism on a star with an eyepiece inside and outside of the principal focus which is very sensitive.  Unfortunately, this is not exactly a shop test unless you are null testing.

[6] An otherwise perfect cube beamsplitter introduces aberrations if the slit and grating is ‘behind’ the cube.  For normal optics the effect is minor.  With thicker cubes and deeper spheres, the situation may become untenable.  This situation can be modeled using a raytrace program.

[7] The spherical aberration is introduced by testing a paraboloid at COC.  Of course, when subsequently used with parallel light in a telescope there will be zero (hopefully) spherical aberration.

[8] This is a very common name in the ATM community for a reflection null using a concave spherical nulling mirror.  See null figuring.  The test actually predates Tom Waineo but he pushed its excellent properties and it seems to have been renamed in his honour.