Only treats concave mirrors Roncigrams.

Be aware that refractive surfaces, systems in autocollimation etc.

may have the Ronchi pattern reversed.


Copyright – P. J. Smith

But permission is given to distribute this material in unaltered form as long as it is not sold for profit.

A Ronchigram by itself is useless.


We must also know

1.      Grating frequency – eg. 4 line pairs per mm.


2.      F:NO of the test beam passing through the grating.  This is usually twice the F:NO of the surface if it is to be used like a Paraboloid in a telescope.  Usually this is defined when users specify the mirror diameter and radius of curvature and no more details are required.  There are more details in the program Ronchi Estimates and Advanced tests.


3.      Whether inside or outside the centre of curvature.


4.      Whether refractive or reflective surfaces, single pass or double pass path etc..  This will not be considered further here – see under advanced tests.


If 1 2, and 3 are known, it is unnecessary to measure the exact position of the grating as this defocus information is now fully defined by the Ronchigram.   Because the eye finds it difficult to judge subtle Ronchi band shape during aspherizing, some do measure this defocus distance as a cross check 


During rough figuring, we want a quick method to indicate the shape of a surface with respect to a sphere. 

If the final target is a sphere, this method may be continued through final figuring, but if we aim for a Paraboloid, a change of tactics is needed.  Most Paraboloids are figured after obtaining an excellent sphere, so, no matter what type of surface we aim for, the ability to test with respect to a sphere is paramount.  No measuring rig is needed for this and the Ronchi test is a simple solution.


As previously stated, the most basic prerequisite is

knowing if the grid is inside or outside the Centre of Curvature of the surface.


In practice, it is easy to move the grid towards the mirror until more and more narrower lines are seen.  The Ronchi grid is now inside the Centre of Curvature as in the diagram above. An experienced mirror tester simply moves the grating either well inside (closer to mirror) or well outside (further from mirror) and then finds which way it must be moved to decrease the number of bands. 


So, if by moving the grating back, the number of bands decreases, you are inside the centre of curvature.


Near the crossover point, the Ronchi pattern will become coarser and disappear into a blur.  When you know how, this position can give a lot of information in the same way as a Foucalt test.  But, since this is primarily about interpreting the Ronchi bands, we will ignore this situation.

For sensitive work, you must move the grating so only a few bands are visible. Very seldom will you want more than 8 bands over the mirror and often you will want only four, three, two, or even less for critical work.  Many of the following simulations show more bands to help illustrate band shape but in practice you will use less for precise work.

There is no reason the outside region may not be used, but for consistency, only one set is considered here.  Results for the other region are simply assessed in the opposite sense.

Sometimes, outside testing may be advantageous.  Often clearer bands are visible just outside rather than inside.  When examining an aspheric surface, choosing different positions increases sensitivity on certain parts of the surface.  For example, when examining a deep Paraboloid, the inside position is best for central surface detail, the outside for edge detail.

I have chosen to consider the inside as opposed to the outside Grating position because this results in far more eyerelief when working with small deep mirrors.  Non-glasses wearers may think this a trivial reason – others will disagree.

Examination of these diagrams will show how the forward position of the Ronchi Grating allows a wider cone of light to converge on the pupil. 

Spectacle wearers would have no difficulty working in the rear area with an F:8 mirror.   Because normal concave mirror testing is usually performed at the centre of curvature rather than the principal focus, the ray cone is actually working at F:16 during the test.  If you are testing a very fast mirror, it may be mandatory to work exclusively in the forward region.

Certain features are more visible when working in the outside region, but it is more a matter of knowing what to look for.  Here we are more interested in a consistent, easily remembered, system, and I have chosen the forward region.


Simple, easily remembered system best.


It is tempting to initially approach the interpretation of Ronchigrams by analysing offsets, zonal curvature etc. but a better first step is simply to learn a handful of key patterns.  We were initially taught our alphabet by rote.  Later this was built on for more complex operations.  Luckily, we do not need to learn many basic patterns to be very useful.  Later, we can extend this by more detailed analysis. 

Remember, that we did not need to relearn our multiplication tables to handle negative numbers.  A consistent, simply applied inversion protocol, takes care of the problem.

Similarly, once we learn a few basic Ronchi patterns, by noting grating position and whether a refractive or reflective surface, we then deduce profile by applying the correct number of inversions.  Finally, we may extend the test by analysing less usual patterns.


Finally, beware of one system often mentioned to interpret Ronchigrams assuming the bands present some sort of contour map of the surface.  This is incorrect in theory because the bands represent slope, not profile and this can be misleading in practice because the slope information must be integrated and the result is not intuitive. 

If you assume the bands represent a contour, the inside of a mirror surface does bear some relation to the correct results.  Edge results, especially,  may be quite wrong.


The best advice I can give a newcomer is to learn off by heart about five common patterns so you never make any gross errors when assessing surface profile.  Then interpret variations from these main patterns.  By limiting ourselves to the inside Ronchigrams, there is far less chance for memory lapses and confusion.



The Sphere


A Sphere gives straight, evenly spaced Ronchi Bands

No matter where the grating is positioned, a reflective Sphere will result in straight, evenly spaced Ronchi bands when examined at the Centre of Curvature because the resulting Wavefront is Spherical.  The spacing is a measure of the defocus from the Centre of Curvature.  The Sphere on the right has its Centre of Curvature closer to the grating than has the left Ronchigram.

It does not matter if a dark or light band is in the centre, or there is an even or odd number of bands, or even if the bands are displaced sideways, this always holds true.

It is possible for a complex optical instrument with no Spherical surfaces to give a Spherical Wavefront which, of course tests as a Sphere.  This is the case with any Null test which is the best possible testing situation.  Auxiliary optical reflective and or refractive surfaces are introduced in the ray path.  See under Null figuring.

A Sphere is always our reference, so if the bands are not straight and evenly spaced,  we attempt to estimate departure from spherical.


Sphere within a Sphere

A very common situation is represented above.  Here, the inner and the outer portion of the concave mirror are both spherical since the lines are straight and evenly spaced in both areas.  In this case, the inner area has its centre of curvature closer to the grating giving wider spaced lines.  If the grating is inside, the COC inner zones have a shorter radius of curvature.

The transition area is seen as a circular zone where the slope of the surface suddenly changes.  Although surface height changes, it is the change of slope, which directly repositions the lines rather than the difference in height of the surface.

Note how the region of abrupt slope change corresponds with the maximum distortion of the bands [1].


Isolated  Ridge

Determine how this differs from the previous Sphere within a Sphere diagram.

At first glance, they look the same.  But on close inspection, there are two differences.

1.      The lines actually reverse curve instead of just kinking outwards.

2.      The spacing of the inner and outer regions are identical.

Since the band spacing is the same in the outer and inner regions, they represent portions of the same sphere.

The region of band distortion in this example represents a raised ridge.



If inside COC,  if the bands kink inwards, ie. closer together, the surface defect is a raised ridge

Turned Down Edge


Turned down edge is very common.  It should not be confused with the incomplete polish situation covered previously.  In this case, the edge becomes steeper and steeper as we move outwards.  It usually spans quite a very small range at the very outside of the mirror.  Please note the span in this example is exaggerated for clarity.

Turned Down Edge viewed Inside Centre of Curvature

causes Ronchi bands to hook inward at the edges

The mirror profile is drawn with respect to a reference Sphere.

In this case the edge falls off so drastically that the slope changes at an alarming rate.  This accounts for added bands at the extreme left and right edges.  You should not confuse the extra bands at the edges with diffraction effects seen on the extreme left and right of the mirror.2  In this case, the edge is intolerable and must be eliminated in some way.

The best area to diagnose this situation is the bend of the ends of bands

 departing the mirror at maybe 1/3 of the way out from the centreline.

It is better if you never use this extreme left and right region when interpreting Ronchigrams.


Gentle Overall Depression.

Apart from some irregularity, the mirror depicted below indicates a depressed centre with respect to a sphere. 

ATM’s will recognise this as approaching a parabola in shape.

The shape of these lines depends on the dimensions of the mirror and position of the grating and each case should be examined in detail.  Fortunately, many computer simulations are now available to generate these patterns so there is no excuse for the mirror maker to simply guess the band shapes.



Each of these represents a Ronchigram of a Paraboloid.

The Grating has been moved to different positions resulting in

the same number of bands, so making comparison simpler.


This has dominated the type of optics made by ATMs and is given far more attention under Advanced interpretation and Aspherizing.  Until you have a good sphere without a turned edge, it is best to leave this until later.


The inverse patterns


The situations presented so far have been oversimplified
because a large number of combinations are possible.



This is because :-



Fortunately, we do not have to learn each pattern because

we simply invert the pattern for each of these changes.



It is a worthwhile exercise to prepare a simple wall chart including the inverted patterns.  There is no need for this to be in any way fancy.  A crude sketch is perfectly adequate and will serve a better purpose than simply copying something fancy from a book or the Internet. 


My program RonchiZ will be found useful to explore this further and

 generate patterns for gratings in different positions.  See software.  It is, however,

not needed, because simple inversions of the patterns are easy to generate mentally.





































[1] Far more detail is given under advanced interpretation, but you should become thoroughly familiar with this simple material first.

2 Diffraction effects may be confused with TDE.  See the section on diffraction for more details.