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Copyright P. J. Smith

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


Simple Folded Shearing Interferometer.

 

 by Peter John Smith.

 

An incredibly simple working interferometer made from a few readily available items.

 

In common with other shearing interferometers, no accurate reference surface is needed.

There is little chance of inaccuracy from compromised components.

 

This has to represent the 'destitute man's interferometer'.

 


Background.

Interferometric tests fall into two main groups. Some compare against a reference surface of unimpeachable accuracy. Others generate a reference wavefront some other way. Until recently, these have been out of reach of most amateur opticians.

We often attribute magic to interferometry and underestimate the precision attainable from Foucault and Ronchi tests. Amateur Telescope Makers (ATM's) have wrung the last drop of performance from these simple shadow tests.

While shadow tests may be modified to give quantitative data, they are inherently qualitative and somewhat subjective. They also give surface slope rather than height information which should be computed by integration..

Interferometers on the other hand give surface deviation directly in wavelengths.

 

The ATM has quite unusual testing requirements.

Professional opticians primarily deal with spherical refracting surfaces. These are more tolerant of surface error.

ATM's consider deep aspheric reflecting surfaces quite normal. Thus non null tests become commonplace.

Much of the modern magic of interferometers resides in analysis software applied to captured images. Without this, interoferometric methods of evaluation offer far less than most ATM's realise.

Interferograms are much simpler to interpret when close to a null such as when testing sphere. Since ATM's deal with paraboloids or worse, simple interferometric testing now becomes complex to implement!

 While experimenting with a variation of Ronchi testing, interference fringes were observed. Their appearance was purely accidental. The set up was recognised as a shearing interferometer. After library research and some thought a simple simulation program was written which seems to mimic the results - at least when close to a null. This has given me enough confidence to present this test for others to use.

 I was originally worried that interpretation of shearing interferograms would be difficult. While there are some complications, this does not seem a major problem. The simulation program allows one to investigate this interpretation aspect more fully.

Of course, the closer to a null, the easier it is to interpret results.

Thus the test is more useful for spheres than odd shapes.

 


Special Advantages Of This Interferometer.

 

No reference elements are needed.

Path lengths are essentially equal. Thus monochromatic light is not required. A laser is not needed. Even White light may be used when close to a null

Red LEDs work very well. While by no means monochromatic the results are excellent.

The test is incredibly stable because of 'equal' path lengths. Vibrations from inadequate support have little or no effect in comparison to other types of interferometers.

Set up is very similar to a knife edge test.

It can be applied to any image producing optical instrument. Where the image is accessible but the optics are difficult to test directly because of size, this has appeal. Thus shearing interferometer have often been applied to very large mirrors and extremely small microscope objectives.  

If you have unlimited money and facilities, there are usually better methods.

 


Limitations.

 

In some situations this test is useful. In others it makes little sense and. Certainly it is no magic panacea and should be used in conjunction with other appropriate tests.

Uses include quantifying zones, craters, hills, coating thickness, and turned edges in terms of wavelengths.

It gives a quantitative assessment of small departures from spherical, but without analysis software will not definitively measure parabolic correction. In other words, it is mainly useful in null tests.

The view only covers about half of the mirror surface.  If the surface is symmetric, this is far less of a limitation than may be supposed.

  


Requirements.

 

1. Fine slit which must be narrower than commonly used during shadowgraph testing. 

There should be a means to rotate the slit so it is parallel to item 3. This may be as basic as a 1/2 inch tube lying in a V groove cut into the top of a block of wood. Sensitive rotational adjustment is important. A lever from the tube hanging down is an easy adjustment system. Two razor or pencil sharpener blades may be pushed together and clamped when correctly spaced. A variable slit is a very nice to aid set up, but is not essential.

Another convenient way to make a reasonably narrow slit is by drawing a sharp needle along freshly painted glass. Leave to partially dry first. Some experiments may be worthwhile with the partial drying time. Eventually the paint may flake off but it is very easy to redo.

2. Light source - preferably monochromatic.

A LED is fine. No Laser is needed. I prefer a red LED. Yellow ones are often a mixture of colours and are far from monochromatic.

3. A small reflecting surface about 1 inch square. This may be a piece of selected plate glass as the active portion is small. Some binocular prisms are very satisfactory. One surface is not (nor should be) antireflection coated.

No aluminising is needed because reflection occurs at grazing incidence when reflection from a glass surface is very efficient. I have found a glass 'Knife Edge' mirror surface produces cleaner fringes than an aluminised one. It is much easier to clean and gives an equally bright image.

In the simplest implementation, this may be a square of plate glass 'blue-tacked' to the top of the wooden block.

4. Some means of translational and rotational adjustment.  The incredible stability of the image makes a block of wood moved by hand quite satisfactory. Because translation AND rotation are needed, the simple block of wood is very suitable and is recommended for first time use even when more elaborate equipment is at hand.

 


Setting up the test.

 

The set up is almost the same as a simple knife edge test.  

 Imagine a knife edge test with the knife edge replaced by a vertical reflecting surface. The only testing elements are the vertical mirror surface and the vertical slit.

The image of the slit must be adjacent to the centre of the folding or 'Knife Edge' mirror surface.

This mirror is turned about a vertical axis so one ray reaches the eye by reflection, the other directly from the mirror surface being tested. Thus the mirror is rotated so the reflected and direct view of the sphere under test are superimposed.

Now move the slit and mirror assembly slightly sideways until both returning beams merge. At this point interference fringes appear. Slight rotation of the block about a vertical axis highlights different portions of the mirror. The manipulations are reminiscent of Foucault testing but with extra manipulations of the testing block about a vertical axis. Precise back and forth movement is not required.

The slit may need slight vertical tilt adjustment. After fringes appear this should be readjusted.

Like all testing procedures, thus is very difficult to describe, but simple once the idea is grasped.

There is a range of backward and forward positions which work. An excellent starting point is to arrange the centre of the 'knife edge' mirror at the same position as a knife edge.  


Some results.

The following photographs of mirrors under tests show what may be expected. They were recorded with a cheap Quick Cam and considerable patience. The original lens was replaced with one of longer focal length. Unfortunately, I could not find a lens of ideal focal length so some of the mirror's image is missing. The lens used was actually a 5X microscope objective in reverse.

Much detail has been lost. The test can return considerably better accuracy than these pictures show.

The included 'foucogram' was actually made with a Ronchi screen working in conjunction with a very fine slit. When drawn back to focus so one grid line performs the occultation, the setup effectively becomes a foucault tester. This Ronchi screen is actually a piece of two dimensionally woven bronze gauze which produces excellent results if the source is a slit.

Ronchigrams (2 bands over the mirror at 80 lines per inch) show some surface imperfections and a poor edge, but these errors are more apparent in either the shearing interferometer bands or the foucogram. For this reason, ronchigrams have not been included.

This mirror is obviously not up to scratch - which makes the interferograms far more interesting. It is a 7 inch diameter 'sphere' of 28 inch focal length. It is in fact debatable that much time should be spent on testing such a poor mirror but it conveniently demonstrates various aspects of this test.

The foucogram is only roughly aligned with the other photographs to make comparisons easier. Some guesswork is needed to determine the edges of the mirror. The horizontal picture is a rotated copy of the left hand one.

A halved image caused by the folding mirror does not worry me in the least. The main problem is to carefully check where the cut off point is represented on the mirror surface. Depending on the overlap resulting from vertically pivoting the folding mirror, the edge band usually represents a line which is not a diameter.

This is evident in the right hand photographs.

The bottom left inset shows in more detail a disgraceful edge. For some reason, the camera must have been tilted when this was taken.

Obviously, this mirror has imperfections. But how bad are they ??

Consider this enlargement of the previous left hand photograph.  Fringe deviation gives a direct measure of surface errors.

It is relatively easy to estimate the fringe deviation from this photograph.

Each fringe represents 1 wavelength on the wavefront.

Or alternately, we may be more interested that each fringe represents 0.5 wavelength on the surface.

It is very difficult to quantify these errors from a Foucault test on an irregular mirror where experience is the main guide. Herein probably lies one of the main uses for this test.  


Theory and simulation.

 

If you are not interested in the theory of the test, skip this and move to the simulations. 

To confirm the mechanism behind this test, and to assist interpretation of the fringe pattern, a crude simulation was attempted. The results are encouraging in that they correspond well with observations.

 Rays from a slit arriving directly and via the mirror travel slightly different distances.

They almost travel a common path. Thus air currents have the same effect on each and a very stable interference pattern results.

 This is equivalent to having a second imaginary source identical to the original slit but displaced slightly from it.

If the optical surface under test is interposed in the light path, a second 'imaginary' or 'virtual' conic surface is partially superimposed over the real surface. The final converging rays travel different distances depending on which points on the conic surfaces are superimposed.

Some will recognise this as related to 'Lloyds' mirror' sometimes used in interference experiments

 

Normal Shearing Interferometer.

 

It is easier to understand this folded Shearing Interferometer after considering how a normal shearing interferometer functions.

All shearing interferometers have some mechanism for superimposing the test surface and a modified image of itself. This may involve lateral or radial translation, rotation, or folding. The word 'shearing' originally implied a translation which was used in the first of these interferometers. It is instructive to realise that the 'shear' is not a simple linear translation. It is really a movement along a base circle.

 Consider the case of a spherical mirror imaged to form a virtual mirror slid around it's base sphere. The properties of this sphere are such that all points on it form a perfect image at the centre of the sphere. Thus the returning rays from both the mirror and its sheared image are in phase. This is the case with a normal shearing interferometer where a single bright spot forms from a perfectly spherical mirror.

 

An interferogram is easier to interpret if a 'tilt' is introduced. This is similar to the way most people manipulate Newton's fringes during testing.

 

The 'tilt' is a deliberate movement of the surface of the virtual mirror so it is not quite tangential to the base circle. In the case of a normal shearing interferometer this is done with auxiliary optics which will not be discussed here.

 The effect of this tilt is to produce straight fringes in the interferogram which facilitate interpretation. Here 2.5 wavelengths of tilt have been introduced to the virtual mirror surface with reference to the base sphere. This results in 5 waves of tilt in the final wavefront as indicated by the 5 fringes. Each fringe represents one wavelength at the wavefront or 1/2 wavelength at the surface.

Non Spherical Mirror

If the mirror under test is not spherical the surface of the mirror and the virtual mirror do not coincide because there is a height difference in the overlap region.

Surface heights are most conveniently measured with respect to the Polar Sphere.

This has the great advantage that distances to the centre are always radial, so the changing orientation of the virtual mirror has no effect.

Simpler path difference calculations result from referencing all heights the polar sphere which would produce a perfect wavefront .

.

Any point on the real conic corresponds to another point on the imaginary superimposed conic. These correspond to rays reflected from points at different radii from the corresponding centres of each test surface.  By knowing the radius, we may calculate the 'high' of points on each conic surface.

These different surface heights introduce a path difference to the returning rays of twice the height difference. If a 'knife edge' mirror is used, to this must be added a 1/2 wavelength because of phase change at this extra reflective surface.

If the calculated effective path difference is a whole number (ie. an even multiple of 1/2), the corresponding point on the mirror will appear bright. If, on the other hand, the effective paths differ by some odd multiple of 1/2 wavelength, cancellation occurs and the area appears dark.

 

 

The folding interferometer described in this paper is different in the following ways from a normal shearing interferometer.

 

1. The 'folding' or 'knife edge' mirror blocks approximately half of the view. This may be the reason it has never (to my knowlwdge) been used for testing optics before. Folding with an auxiliary mirror has been used in interferometers for other purposes.

2. One extra reflection introduces a phase reversal. Thus with no tilt, the overlapped portion of a perfectly spherical mirrors appears dark, not bright as seen with a normal shearing interferometer. With tilt, fringes appear but the light and dark fringes are interchanged.

3. This tilt is introduced by moving the 'Knife Edge' mirror slightly sideways so the centres of the Test mirror and its Virtual image are now slightly displaced. This must be accompanied by just enough rotation of the 'KE' mirror to maintain any required overlap.

4. Tilt cannot be reduced to less than about 4 fringes because at zero tilt, the rays from the virtual mirror become parallel to the 'KE' mirror's surface.

NOTE. Although the image of the virtual mirror is inverted, for radially symmetric surfaces this should have no impact.

 

.  


Simulations.

 A Pascal program (source code) is available which uses the above ideas. Different Diameters, Overlaps, Radius of curvature, Conic type, Tilts etc. may be investigated.

These simulations are outputs from this program for a selected number of test situations.

Spherical mirror.

By moving the test block sideways, different amounts of tilt may be introduced.

Tilts are wavelengths across the full diameter.

Normal shearing interferometers produce the inverse.

 

 

Note how some degree of tilt is desirable to facilitate interpretation of the results.

 

 

Different Overlaps.

 In practice, slight rotation of the 'knife edge' mirror block about a vertical axis changes different overlap. Tilt is varied by moving the 'knife edge' mirror block slightly sideways.

Zonal Errors.

Surface errors have been introduced into the simulation. When these zonal errors are very small, the patterns are reasonable.

This was simulated by introducing extra zonal path differences into the calculations. This has been poorly blended into the surface and probably should be implemented differently. The appearance reasonably matches observation.

Edges.

 

An edge of different height shows well and agrees with observation.  

Depressed Centre.

 

A depressed central area shows more or less as expected.

Parabola - different tilts.

This represents an 8 inch F:6 paraboloid where surface deviation from spherical is about 1.4 waves.

Observation on a real mirror confirms this quite well.

  

 

ATM's are probably better off with another test when confirming degree of aspheric correction. Sophisticated fringe analysis software is needed. Since this must be more complex to disentangle shearing interferograms, other interferometric methods become more attractive.

Different Parabolas.

Paraboloids of different F:NO's Are shown. The further from a true null, obviously the less useful is this test without elaborate capture and analysis hardware and software.

 

Ripple.

 This represents 0.1 wavelength of ripple on an 8 inch F:6 mirror.

 

Note how the shearing process makes the defect more evident in some places than others. This is related to the overlap.

 

Maybe someone has a mirror like this for confirmation ??

   


Summary.

 

Other interferometers may be better but this comes at the expense of cost, stabilty and complexity.

The test described is interesting and instructive to anyone with limited resources who is interested in experimenting and gaining experience with interferometric methods. Estimation of surface deviations directly in wavelengths is possible in many situations.

It is far more useful when close to a null. This is of course true of any test. 

Measuring aspheric deviation during Parabolising is impossible without complex additional fringe capture and analysis facilities. Traditional shadow test methods are more useful in this respect.

The complete simulation program is available to anyone who is interested. It now comes with a facility for the user to specify any mirror shape - ie. deviation from a specified conic, and then examine the expected interferometric fringe pattern. This deviation is entered by mouse by drawing a mirror deviation profile via clamped cubic splines which is then impressed on the defined conic.

 

The simulation program is available for download at http://www.atmsite.org/contrib/Smith/.

 

The zipped file is about 260 Kb long. Simply unzip and run.

It is designed for an 800 X 600 monitor. There are a very few small bugs and annoyances in the program but since it is eminently useable I will wait for more user input before making any changes.

For any further details or comments e-mail me at pjifl@bigpond.com.au

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