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.


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.



[1] 1958. A. A. Sherwood. J. Br. Astron. Assoc. 68, 180, (1958).    "A Quantitative Analysis of the Ronchi Test in  Terms of Ray Optics"


[2]   See Chapters on Software,  also on History.

[3] This uses the conventional (Strehl = 0.8) criterion.  Discerning observers benefit from higher standards.  Strehl of 0.8 is still  a respectable mirror, however, and will certainly impress all but the most experienced observers.  Users can generate their own limiting Ronchigrams from “RonchiNu” with the aid of its analysis section which gives Strehl values for different mirrors. 

[4] More detail may be found in conjunction with the software by Mel Bartels and John Upton.  See under Software.

[5] See under Materials and Gratings for excellent substitutes for the traditional grating.