Copyright – P. J. Smith –

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

The material presented under Basic Interpretation is extremely

 important but many of the topics need more detailed attention.

Sensitivity and the Blind Spot

Where to look for surface information.

The shape of Ronchi Bands obviously gives surface shape information. But the position of each band is defined by the edges.  Thus it is the band edges that really carry information rather than the bands themselves.

If the edges of a band cross a position on the mirror where the mirror slope is different from the rest of the mirror, the band edge is displaced.

Interpreting the relationship between Ronchi band edges and surface shape can become complex but in the example below is as simple as it could possibly be.

Ronchi Image seen Inside COC.

Since the dimple is near the centre of the mirror, none of the Ronchi Bands outside this region are bent. 

Obviously, only near the centre, where the bands cross the dimple, does this imperfection show.

This very simple fact leads to something less obvious – something that is often not appreciated by beginners.  Look at the following.

Same Mirror, same grating, but moved to a new position.

Note how the defect does not show in both these grating positions.

In the first example the grating is a long way inside COC.  This reduces the sensitivity of the test so that the defect is almost invisible.

The natural reaction is to move the grating back a long way to increase sensitivity a lot.  The second example involves the grating just inside COC.

NOTE how, although the sensitivity is very high (indicated by widely spaced lines), the defect is invisible.  This is obviously because the defect falls between the Ronchi bands.  Thus we have to conclude that

There is a Blind Spot in the centre between the Ronchi Bands.

Anyone performing the Ronchi test will see this defect in certain positions of the grating but some are not aware when viewing a photograph of a Ronchi test that it may contain a blind spot so will not tell the whole story.

Certain solutions to this problem suggest themselves. Below is a Ronchigram taken at the same grating position as the top right image so its sensitivity is the same.  But the Grating is 10 times finer.  In theory , since more band edges traverse the defect more information is visible.  Another way to interpret this that the Blind Spot is now much smaller.

Unfortunately, this is not a very practical solution to the problem because very fine gratings gives huge diffraction problems, especially at the left and right edges of the mirror. More on this under Diffraction.

A much simpler and more effective solution is simply to scan the grating across the mirror as in the following set of diagrams.

A slow Scan from left to right sweeps across the Blind Spot.

A quite coarse grating may be used this way.  When done by an experienced user the detail depicted can be stunning.

I often use a much coarser Grating than others but always scan the mirror surface. This allows high sensitivity yet scans over any hidden blind spot.  As a bonus, the eye is even more sensitive to small changes of velocity of the band shapes. 

No static picture can possibly carry a fraction of the information as a scan.  There is more information on this under scanning the surface.

Finally, as a general rule, remember that when evaluating any zone, look where the edges of the Ronchi bands cross or are adjacent to this zone.  All the band edges cross every zone as long as we are outside the Blind Spot.

Turned Down Edge


Turned down edge is very common.  It has severe impact on image quality.

The situation that can develop from incomplete polishing when a sphere develops within a sphere has a similar impact on image quality.


While there are similarities, it is important to distinguish between these situations because the cause must be isolated so polishing technique may be improved.

With incomplete polish, the edge becomes only slightly steeper as we move outwards.  The turned edge resulting from other causes often rolls off at an ever increasing rate which becomes alarming at the very edge.

While it is to a first approximation possible to state that the inner surface is ‘lower’ than the outer, we immediately run across another problem.  By ‘lower’ we are making some comparison of one thing relative to another.  But which should be relative to what ?

Relative to the outer spherical shape, the inner area has a depressed centre.

But relative to the inner spherical shape, the outer area has a depressed edge.

Either description is quite valid.

We often make quick sketches of surface profile which may look like one of these depending on what we think of as the reference surface.  Of course, both are wrong,   yet either would help us to correct the surface.

The only truly correct way to interpret the surface is in terms of curvature.  The inner zone has more curvature (shorter Radius of curvature) as opposed to the outer zone which has less curvature (longer R of curvature).

If you have any problems interpreting surface shape, always think in terms of surface curvature.[1]

It is worth pointing out that a very similar situation develops when a surface is being polished.  Usually (but not always), the pitch lap initially develops spherical contact at the centre.  This creates an inner sphere of slightly smaller radius which gradually moves outward as the polishing progresses.  Polish is never complete unless this reaches the edge.

Many confuse a ‘serious turned edge’ (ie. the outer edge is lower) with this normal situation resulting from incomplete polishing.  It is the way pitch laps often behave, and the best thing is to simply keep polishing until the inner sphere is in effect, removed.

Although this is more related to polishing techniques, it is worth considering in more detail how this is corrected.

At first, it seems that only a small volume of glass is involved in the edge defect. 

But the only way to correct it is to polish away a large volume until curve A is reached.  In practice, it is almost impossible to do this without removing some from the centre, so a more realistic target is curve B.  This presupposes perfect technique which removes nothing from the edge.  Note that the greatest volume of glass to be removed is near the edge.  It is paradoxical that to cure a turned down edge we must not run away from it and deliberately constrain polishing to the centre .  This only makes matters worse.

What looks like a very small edge defect often takes a lot of polishing to fix.  This is normal, so you should be certain of your test technique and interpretation.

Below grossly exaggerated, are two representations of a true turned down edge, depending on the “reference”.  Both are different representations of the same surface.   In this case, the edge becomes steeper and steeper as we move outwards.  The width has been exaggerated for clarity.  In some cases of very narrow but very steep turned down edge, the defect may be viewed by looking at the image of a light at very oblique angle when the light will appear to bend as its reflection moves closer to the edge. 

The first plot views surface distortion with respect to a spherical surface.

 We should never forget that the second plot really represents the same thing.

 It is convenient to consider changing from one to the other representation by flexing the diagram.  Thus, pushing the centre of the right hand diagram upwards results in the left hand case.  Both views are useful.

The only way to ‘fix’ this error is of course to either sink the top sphere further or to aim for a new sphere of longer Radius of curvature if this is allowable.  In each case, more glass must be removed near the edge than the centre.

A more drastic solution, often used, is to simply reduce the diameter of the surface either by masking or edging away the outer part.

Below is a Ronchigram showing severe turned down edge taken inside of the centre of curvature.  Some like to assess this condition in the outside region, especially when it is impressed onto a Paraboloid when the bands hook outward instead.  Whichever you prefer, it is better to learn a simple consistent system and apply reversals if appropriate.

A Turned Down Edge viewed Inside Centre of Curvature

cause Ronchi bands to hook inward

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

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. In this case, the edge is intolerable and must be eliminated in some way.

It is much harder to diagnose a turned edge on a paraboloid than on a sphere because the edge may blend in with the general shape of the surface.

Aspheric with Turned Down Edge  if OUTSIDE  COC                

Aspheric with Turned  Down  Edge  if  INSIDE  COC                


Some like to assess this condition in the outside region when the bands hook outward, especially when it is impressed onto a Paraboloid.

This is because the bands near the edge are wider apart when a paraboloid is viewed outside the COC so maximum test sensitivity occurs at the edge.

In this case, as the edge falls off, the slope changes at an alarming rate.  This accounts for added bands, which are sometimes seen at the extreme edges.  When you see this, do not immediately assume the multiple bands on the left and right are all caused by diffraction effects  (see diffraction ).  You should not confuse the extra bands at the edges with diffraction effects seen with fine gratings on the extreme left and right of the mirror.2

Think in terms of Curvature and Slopes




Consider this INSIDE of COC Ronchigram which has been generated by my program RonchiZ






The displacement of Ronchi Bands from the position it would occupy with a perfect sphere depends on the SLOPE of the surface rather than its height with respect to the reference sphere.  Of course, they are related.  The slope information can be integrated to obtain a plot of surface height.


Close examination of the above Ronchigram will give some pointers to eyeballing this information from the Ronchi Bands.


The plots drawn below the Ronchigram are of surface height and slope REFERRED TO A SPHERE.


Only absolute slope has been shown because it is less confusing.


The reference grid is calibrated to give zone radius as a percentage of the full radius.


Out to a little over 40% from centre, the surface is spherical.  Referred to this sphere, the height and slope are of course zero.  If you follow the 40% line upward, and then go around the 40% circle, the enclosed area shows straight Ronchi Bands as expected.


Surface height reaches a maximum (C) at about the 70% zone.  If you follow the 70% position upwards and then around the mirror (midway between the 60% and 80% circles), there is no defining feature on the Ronchigram corresponding with the position of this maximum height.


The maximum slope occurs as the high zone rolls down on each side of the ridge.  Maximum Slopes occur at about the 90% and 57% zones at A and B above.



Follow the 90% zone (A) upwards, then around the 90% zone. Now look at all the four points labelled 1.  

Each represents a portion on a different Ronchi band more closely spaced to the centreline than other parts of the same bands.  This represents a zone of longer Radius of Curvature.



Now follow the 57% zone upwards and around to points labelled 2.  These represents the most widely spaced portion of bands (or edges of bands) from the centreline so this is a zone of shorter Radius of Curvature.



If you draw a diagram of the grating inside the Radius of curvature you will confirm that the slopes on each side of the ridge do indeed move the bands in the directions shown.



This is somewhat satisfying.



Applying this idea carefully, you can now eyeball areas of maximum surface height by knowing that the widest and narrowest band positions are NOT maximum surface heights, rather areas of maximum slope on either side of the area of maximum height.



This principle takes some assimilating. It is fundamental to all shadowgram tests, but is probably easier to understand in the case of Ronchi bands.



If this is confusing, remember that, as polishing progresses and errors become less, interpretation is simpler.  Thus, most of the time an exact interpretation of a Ronchi Test is unnecessary, as long as correction is heading in the right direction.




To cement some of these ideas you could attempt the Exercises on interpretation.  Answers are given to these exercises.





[1] Discussed in more detail under Advanced Interpretation.

2 Diffraction effects may be confused with TDE.  See the section on Diffraction.  The best advice is to never use this region when interpreting Ronchigrams.