Diffraction Effects

Copyright – P. J. Smith

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


Geometrical Optics never gives the full picture when performing an optical test.   This is especially true of the simple Ronchi tests because it uses a grating.

How deleterious this is to the test depends on various parameters and the purpose of the test.  In some cases, the Ronchi test is entirely adequate, in others it may fall short of requirements.  

By knowing what to expect we may understand these limitations and thus avoid certain pitfalls.

As a general statement, Geometric Optics is perfectly adequate to interpret Ronchigrams for many purposes, but one should be alert to limitations and even impossibilities.


Wave Optics impacts the Ronchi Test in three main ways.


1.      The edges of all surfaces appear slightly modified.  This is true in all tests such as the Foucault and Ronchi test and will not be pursued in detail.


2.      Ronchi Gratings, like all gratings, produce multiple images.  If the grating lines are vertical, this is most evident at the extreme left and right, but on careful examination extends completely across the image.


3.      Fine structure is evident between Ronchi Bands, particularly at certain grating positions.  This usually shows as diffraction bands running more or less parallel to, and between all the main Ronchi bands.  On very close inspection, using a minimum width slit or pinhole, these become even more complex   The Ronchi band spacing depends on grating position, but the multiple imaging spacing is constant.   In certain positions, the Ronchi bands and multiple images due to diffraction are overlaid with linear scales a simple multiple of each other.   Thus, weaker bands between the normal Ronchi fringes may be easily visible.  In some grating positions, the Ronchigram looks sharp, in others more confused.  This is a manifestation of the Talbot effect. Using white light makes it less visible.  One should understand that this happens and search out the best viewing positions for the grating, but this is not the main topic of this section.


The second effect - Multiple Images.


Anyone who has examined an object such as a light source through a transmission grating will know that on each side of the main image are weaker 1st, 2nd, 3rd etc. order images of diminishing intensity.

 Looking through a piece of finely woven material such as a Ronchi grating, or even flyscreen, will confirm this.  With a dull Ronchi image, it is difficult to see more than the direct image plus each 1st order diffraction image.

These images are widely separated with very fine Gratings (500 – 2000 line pairs/mm), but with typical coarse Ronchi gratings (2 – 8 line pairs/mm) the Ronchi Images overlap.

Some choose very coarse gratings in the belief this effect will be so small as to be invisible.   It may be reduced, but so is the test sensitivity.  Others believe that white light and certain sources suppress it. 

The effect is still present.  It is always present [1].  If you cannot see it the chances are your set-up can be improved. 

But, don’t get worried because, when the effect is understood, it is not really a problem.  As with most things, a working compromise must be struck.  Most use gratings between 80 to 150 lp/inch.

Below is a simulation showing the effect from Jim Burrow’s program “Diffract” (available for download from Jim Burrow’s site – see    Diffract  ).  Some other illustrations also use this excellent program.  It is invaluable to rigorously check certain aspects of Ronchi testing, but is not needed for normal working Ronchigram evaluation.

Note the two 1st order images surrounding the central image.

Now compare with some real Ronchigrams.


These photographs of a sphere with a 150 lp/inch grating are deliberately overexposed to

show the diffraction effects at left and right.  This has produced poor detail in the bands.


Another photograph at first glance seems to show a double edge but closer inspection reveals a third image. [2]


This is taken with a much higher quality camera.

It is possible to minimise the magnitude of diffraction effects – primarily the multiple image – by using blue instead of red light.  The multiple image spacing is reduced to about 2/3 of that for red light.

The diffraction effecs is, however, still quite visible, and no matter what we do we have to learn to live with these diffraction effects.  Since red is more suitable for cheap web cameras, and I find it more distinctive, I tend to prefer Red LED’s as a source.  Others may like to switch to blue LED’s.


Another obvious effect (below) is how the multiple diffraction effects at left and right remain constant

 even though the grating is scanned across the mirror.


This effect may influence our interpretation of the shape at the ends of Ronchi bands.

The following simulated Ronchigrams of Spheres show how, on cursory examination, the ends of the bands seem to hook outwards but in fact this is an illusion caused by the overlapping images. Around the rim of the mirror, the ends of the multiple images do not line up.  Because the area of the overlapped rim is greatest further from the centre, this is more obvious to the eye.  Thus, the eye is predominantly drawn outwards no matter where the grating is positioned.

In a real situation, this effect is easily demonstrated by masking off a large outer portion of a known very good spherical mirror.

Since a bend at the ends of Ronchi bands is a very sensitive indicator of turned edge, careful study of these simulations and photographs shows how we may be mislead by diffraction effects when assessing turned edge.  The intensity of light used in the test, the method of recording the Ronchigram, and any subsequent image manipulation all play a part.  Now that digital imaging and reprocessing is common, this will often appear and be discussed in more detail.

Consider the Ronchigram (150 lp/in) below of a near sphere with a close to perfect edge.

Some may doubt the accuracy of this statement but this can be guaranteed because

about 40 % of the edge has been masked off. There is a small defect in the centre.

Diffraction always gives the illusion that the bands hook slightly.  Coarse gratings shows the effect less.

The effect is only really noticeable when a surface is close to being finished. When you look very carefully, the ends of
the Ronchi bands are slightly streaked around the rim of the mirror.  Most (but not all) of this is outwards towards the left on the left and the right on the right.  It does not matter if you are inside or outside COC, the streak is mainly outwards.  It is very slight and will mainly be of interest to the experienced optician.  For a mirror with obvious imperfections, just forget about this and concentrate on whipping the surface into order first.  Exposure and processing  have a major effect on how visible is the effect.


Here is a different type of Ronchigram by Michael Spooner [3].

It is a superb 8" f/5 parabola being tested in autocollimation - thus the bands are straight as befits a null test.

Uses a 100 lp/inch grating.


This Ronchigram illustrates some of the features previously mentioned.

·        The multiple images in Michael's photos are clearly visible in the center because of the central perforation - a situation not many ATM's normally see.  It is obvious because in this region there is a 'black hole' and the adjacent, well-illuminated area (triple imaged) contrasts against the dark background. On the left and right edges of the perforation, these edges are multiple imaged and displaced perpendicular with the edge so this shows up well.  At top and bottom of the perforation, the displacement is parallel to the edge so is not obvious.


·        Easily visible at top left is a small area on or near the rim where the Ronchi band edge is slightly smeared outward.  It is not evident at the bottom because the illumination is less and the recording medium has not registered the effect.  If this had been overexposed, the effect would begin to dominate, fooling the eye into thinking this excellent edge is far from perfect.


Air turbulence during testing may give the impression of defective edges to Ronchi bands.   The naked eye usually distinguishes this problem, but photographs taken at a bad moment can be misleading.  As the optician strives for perfection, and pores over Ronchigrams on the look out for small defects, the effect can become worrying unless understood.

The effect is also evident with Paraboloids.

One way to distinguish between diffraction effects and Ronchi bands at the edges is to move the grating longitudinally.   The Ronchi Band spacing changes but the left and right diffraction band spacing does not.  This is easily seen in the simulations for the spherical mirror above.

By examining the geometric simulations below [4] it is easy to see how a turned edge may be confused with diffraction effects.  

Geometrically predicted Ronchi Bands for an 8 inch F:6

 Paraboloid with ¼ wave of Turned Down Edge.

Aspheric with Turned  Down  Edge 

(OUTSIDE  COC above,   INSIDE  COC below)

When the edge rolls off gently it is not hard to see that the band spacing at the edge changes as the grating is repositioned.  Diffraction effects give constant band spacing at the edges.

Be careful with this distinguishing test because, with a very steep turned edge, there are many closely spaced Ronchi bands on the left and right, and it is not easy to see the change of spacing with longitudinal grating movement.  This is especially true when examining Aspheric surfaces. 

An extremely narrow but very steep Turned Down Edge gives Ronchi bands so closely spaced at the edges that it is difficult to see the spacing change as the grating is repositioned.  With this type of turned down edge it may be possible to detect it by simply viewing the mirror obliquely, looking at the reflected image of a light near the edge.  It is always worth doing this as it is more sensitive than most think.  If any Turned Down Edge is detected this way it must of course be fixed by better technique or removed by edging or masking.

Consider this actual Ronchigram [5] taken inside COC.

Is this diffraction or actual Ronchi bands at the edges ?

We should expect some multiple imaging to show on the extreme left and right.

But, do not immediately assume this is all due to diffraction.

We can investigate this further because the shape of the second set of Ronchi fringes, where they depart the mirror, is a dead giveaway.  This is the best place to estimate turned edge – as the Ronchi bands depart the mirror about 1/3 of the way out from the centerline.  The far left and right parts of the pattern are best ignored.

We will consider the edge in more detail in an attempt to reconcile theory with the above photograph.

By considering the shape of the bands, it is easy to build up an assessment of the surface shape.  When this shape is used to simulate the expected Ronchigram, the following results are obtained.  It clearly shows that Geometrical theory predicts 2 to 3 very closely spaced bands be visible at the extreme left and right edges.



This has been produced by my program RonchiZ. 

 Zemax gives very similar results.

I am beginning to think that some, whenever they see close packed lines on left and right, simply dismiss them as diffraction lines.  When there is a severe turned area towards the edge, it is possible to have many closely packed Ronchi lines there as well as diffraction effects.

This is more reason to keep away from this region at extreme left and right

and look at the band ends maybe ¼ to 1/3 distance out from the centerline.


The third way diffraction impacts Ronchigrams is

 primarily dependent on the slit width used in the test.[6]


As the slit width is reduced, Ronchi Bands narrow and may separate into multiple images.  This effect is more noticeable at certain positions so it may be worth moving the grating.  These effects are usually worse when testing Paraboloids just inside the COC.  The simulations below show the effects of reducing the width of a slit source with the grating inside the Centre of Curvature.


As the slit width is reduced below a minimum value, no extra diffraction details appear.


In some positions of the grating, diffraction effects are much worse.

This is illustrated in the actual Ronchigram below.  It is worth moving the grating to a different position.

The following are simulations outside the Centre of Curvature.

I prefer quite fine Ronchi bands and am not worried by some diffraction effects from a small source.  The practice of blurring out the Ronchi bands to hide diffraction effects is often taken to extremes with some detriment to the test sensitivity.  On the other hand, there is no point using an absolute minimum source width.  If nothing else, this dulls the image noticeably.


One final thing about the fine line diffraction effects is that it is reassuring to see them.  If a mirror has a surface rough beyond a certain point, they simply will not show up in the test.






[1] Some modern complex variants separate the multiple images fully.  This is beyond an ATM.  See history section.

[2] Photograph reproduced by permission of Bill Hanagan.

[3] Photograph by kind permission of Michael Spooner.  More photographs at

[4] Made with my program “RonchiNu” which you may download complete with various surface deformation files.

[5] Contributed by Jack Day.  Taken in the early stages before the polishing action spread evenly across the surface.

[6] Different types of sources are covered in more detail elsewhere.