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Interferometry and Telescopes A practical guide to building and using your own interferometer Copyright 1994 - 2003 by Ceravolo Optical Systems This work may be freely distributed and quoted. Table Of Contents Introduction Interferometry Basics Types of Interferometers The Spherical Wave Interferometer Designing and Making the Reference Element Mounting the Components The Laser Assembling and Aligning the Interferometer Viewing and Recording the Fringe Pattern Using the Interferometer Analyzing the Fringe Pattern Peak to Valley or RMS? Parts List and Suppliers 3 4 6 1 1 2 2 2 2 2 3 3 3

0 8 1 3 5 6 8 3 6 8

Further Reading Optical Shop Testing Second Edition, Edited by Daniel Malacara, John Wiley and Sons Telescope Optics, by Rutten and van Venrooij, Willmann-Bell Modern Optical Engineering Second Edition, by Warren J Smith, McGraw-Hill


Preface This booklet has been written to assist commercial and amateur telescope makers in discovering the modern testing technique of laser interferometry. Much of the material dealing with interferometry found in the professional literature is very technical and does not deal effectively with the practical techniques and concerns of testing optics. This booklet will attempt to explain, in simple language, how interferometers work, how to build an interferometer and how to test telescope optics by interferometry. In writing this booklet, the emphasis was placed on presenting hard to find information in a easy to understand way. It is assumed that the reader has had some experience with testing mirrors, or is familiar with optical testing techniques like the Foucault and Ronchi tests. If not, the persistent worker will still be able to assemble an interferometer and use it in experiments, and even engage in the testing of telescope optics. Interferometry is a very technical subject with no shortage of specialized lingo and concepts which may be difficult to understand without having seen an interferometer in use. If you have difficulty understanding the technical matters, ignore them! At least for the time being. The best way to learn about interferometry is to actually do it. And do not be intimidated by the misconception that one needs finely machined components to do interferometry. The first time I laid out the interferometer described in this booklet I used masking tape to hold everything together! Remember, during those frustrating times when things don't seem to work, fringes are fun! I recall how thrilling it was to see fringes when I first slapped together my first interferometer, even though I routinely work with high-tech commercial units. There is something special about making a piece of equipment which does essentially the same job as a commercial instrument costing tens of thousands of dollars!

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Introduction The optical tests amateur telescope makers use have changed little in the last hundred years. The Foucault test, invented in the mid 1800's, is unusual in that even a crude apparatus made of wood, a razor blade and a light bulb becomes an extremely powerful device capable of magnifying otherwise invisible defects on a mirror many thousands of times. Unlike amateur testing techniques, the last thirty years have seen great advances in professional optical testing techniques, and the invention of the laser revolutionized the field of interferometry. However, these modern techniques were largely out of reach of the amateur telescope maker because of the very expensive equipment and extensive engineering know-how needed to perform these tests. Today, due to the availability of inexpensive lasers and computers, modern interferometry can now be practiced by advanced telescope makers in their home workshops. Interferometry offers many advantages over the well known Foucault knife-edge and Ronchi tests, the main fault of the latter two being their subjective nature. The Foucault test's shadow pattern is qualitative; figure errors are easily detected, but their magnitude is not easily measured. In contrast, interferometry easily lends itself to objective computer analysis, avoiding the biases and inexperience of the operator. While the Foucault and Ronchi tests easily reveal small errors in figure, the magnitude of aberrations can be difficult to measure accurately, particularly when the aberrations are subtle. Non-rotationally symmetric aberrations such as coma and astigmatism can be difficult to see and impossible to measure accurately. The interferometer's fringe pattern is quantitative in nature. The distortion of the fringes from straightness is directly related to the magnitude of aberration. While the intensity of shadows in the Foucault test is hard to quantify, the straightness of a fringe in an interferogram is easily measured. Another drawback of the Foucault and Ronchi tests is the variability of sensitivity with the focal ratio of the optic being tested. The greater the focal ratio, the greater the sensitivity. A 1/4 wave figure error on an f/8 mirror will be more apparent than a 1/4 wave figure error on an f/2 mirror. However, the sensitivity of interferometry is constant with respect to the focal ratio of the optic being tested. One type of optical testing that is not done with interferometry is the testing of color correction in refractors. By its very nature, interferometry requires monochromatic light. Only aberrations which reveal their presence at the particular color being used will be seen. Interferometry is also more difficult apply to optical testing than the Foucault and Ronchi tests. It is convenient to slap together a Foucault setup by stacking phone books to get the tester at the right height, but interferometry requires more care in making sure the optics and tester are held firmly in place without flexure, since excessive motion of the interference pattern can make testing difficult, if not impossible.

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Interferometry Basics In the Foucault test, a razor blade cuts into the converging beam reflected off a concave mirror. If the lights rays reach a common focus, a smooth graying of the mirror will be observed. If, however, the mirror is flawed, the knife edge will intercept some rays while letting others pass by, causing defects on a mirror to appear as shadows on its surface. With the Foucault test, the spherical mirror at the center of curvature is tested "against itself" since no additional optics are required.

Interferometry is different in nature. The light reflected off the test mirror (the test wavefront) is compared to the light reflected off a reference surface (the reference wavefront) of known quality. When the test and reference wavefronts are combined they form interference fringes whose form are an indication of the optical quality of the mirror under test. A telescope's optical performance can be assessed by analyzing the degree of straightness of the fringes: the straighter the fringes, the higher the quality. The interference pattern contains quantitative information derived from a measure of the spacing of the fringes. When a telescope mirror is tested at the center of curvature, one fringe spacing corresponds to 1/2 wave on the mirror's surface. If a depression on the mirror's surface causes a fringe to distort by one fringe spacing, the defect is 1/2 wave deep. In order for interference fringes to be clearly visible the light source must be monochromatic. If the test surface can be placed in contact with the reference surface, as when checking a Newtonian diagonal against an optical flat, a simple, reasonably monochromatic low pressure sodium vapor lamp (i.e. an outdoor security light) can be used, since the test and reference surfaces are nearly in contact.

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But when non-contact interferometry is required, as when testing the wavefront quality of a complete telescope for example, a laser must be used. The highly monochromatic nature of laser light allows a large separation, or optical path difference, between the test and reference surfaces. Optical systems as a whole, not just their individual elements, can then be analyzed by interferometry. Interferometry is much more sensitive to environmental disturbances than the Foucault or Ronchi tests. Even slight air currents and vibration can make interferometry difficult. While it is easy to jury rig a Foucault test, an interferometer requires solid optical mounts to reduce vibrations, and a shrouded optical path to dampen air currents. Even so, interferometry is not beyond the means of the resourceful hobbyist.

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Types of Interferometers Over the decades many types of interferometers have been designed to fulfill a variety of testing requirements. The original and simplest interferometer is the Newton interferometer. It is commonly known as the "test plate method" of testing optical surfaces, where the test and reference surfaces are in contact. The fringes are formed by the narrow air gap between the test and reference surface, and are generally viewed by the eye alone. Test plates have been used by opticians for at least a century and are still in wide use today, especially in high volume production optical shops.

One of the main disadvantages of the Newton interferometer is the possibility of scratching surfaces when they are in contact. Test plates are also only useful for checking the quality of individual surfaces. It is not possible to check the total system quality of a telescope with the Newton interferometer. One of the first modern interferometers was the Tymann-Green modification of the Michelson interferometer. Monochromatic light is collimated by a lens and is then split in two by a beamsplitter to form the reference and test beams. The beams reflect off the master and test flats, to be recombined by the beamsplitter. The fringes are viewed at the focus of the imaging lens. The Tymann-Green interferometer is capable of producing fringes without the necessity of having contact at the test and reference surfaces.

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Non contact testing without laser light was possible because the optical path length, or distance the light travels, in the test and reference arms of the interferometer were made nearly identical. As far as the light is concerned, the test and reference surfaces are effectively in contact, allowing fringes to form. This balancing of the light path permitted the Tymann-Green interferometer to test complete telescopes, not just their individual surfaces. The significant difficulty with the Tymann-Green interferometer is the requirement of very high quality beamsplitter and auxiliary optics in the test arm. Of the many types of interferometers that can be applied to optical testing, the simplest to build and the one that is found in most modern optical shops is the Fizeau interferometer. The important difference between the Newton test plate method and the Fizeau interferometer is in the lens used to collimate the light striking the reference and test surfaces. If the fringes in the Newton interferometer are viewed from too close a distance they will be distorted. For maximum accuracy the monochromatic light must strike the surfaces at normal incidence, or perpendicularly, which basically means that the wavefront of the illuminating light must have roughly the same shape as the optics being tested. In the case of testing flats, the wavefront of the illuminating light must be flat. The lens in the Fizeau interferometer collimates the light rays diverging from the source, causing them to strike the flats at right angles.

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The fringes in the Fizeau interferometer are observed at the focus of the collimator. This viewing position ensures that the eye (or camera) is seeing properly collimated light, eliminating the possibility of distortion caused by incorrect viewing distance. The Fizeau interferometer design requires that only the reference surface of the interferometer to be of high quality; all surfaces before it may be of lesser quality because they only affect the collimation of the light. The collimation optics can be as bad as several waves before otherwise straight fringes suffer a significant amount of distortion. Remember, the fringes are formed in the interferometer "cavity", the space between the reference and test surfaces. The Tymann-Green interferometer requires very high quality optics in the cavity, mainly the beamsplitter and any focusing lenses. The quality of these optics have a direct affect on the fringes. The Fizeau interferometer requires no optics in the interferometer cavity to function. The Fizeau modification of the Newton interferometer was limited to testing flats in near contact since the fringes would disappear when using conventional monochromatic lamps and when the air space between surfaces was increased beyond a millimeter or so. Using a laser with its high purity light allowed the simpler Fizeau interferometer to test spherical and flat surfaces which are widely separated from the reference. The laser Fizeau quickly superseded the Tymann-Green interferometer as the instrument of choice in optical shops. There are a number of other unique interferometer designs that have been developed which excel in simplicity and effectiveness. Two that stand out are the point diffraction interferometer (PDI) and the Shack cube interferometer.
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The PDI is known as a common path interferometer; the reference beam is generated the same optics being tested, so it is much less sensitive to vibration and air currents. PDI requires a pinhole in a semi-transparent medium, such as partially exposed film, a small, high quality beamsplitter. The pinhole must be smaller than the Airy disk of system being tested. Such a small pinhole is difficult to make and alignment can be difficult.

by The and the

One great advantage of the PDI is its ability to form fringes under polychromatic, or "white, light. In fact the PDI has been used to test large telescopes in the observatory using starlight. Amateur use of the PDI was described in the February, 1985 issue of Sky and Telescope magazine. Despite its simplicity, the PDI can be difficult to implement and has not seen widespread use. The Shack cube interferometer is of the Fizeau type, but it is dedicated to testing the converging wavefronts of a mirror at the center of curvature, or of a telescope under autocollimation. The Shack cube interferometer inherited its name from Roland Shack, of the University of Arizona, who combined a beamsplitter cube with a high-precision plano convex lens. The Shack interferometer is capable of producing a high quality, very fast cone of light for testing strongly curved wavefronts. The Shack interferometer is described in the SPIE conference proceedings, Interferometry, vol 192 (1979), pg. 35. The spherical wave interferometer to be discussed in this booklet is of the Fizeau type and is similar in nature to the Shack interferometer, but considerably easier to build. The spherical wave interferometer, like the Shack, is limited to testing converging wave fronts. It can be used everywhere a Foucault tester is used, and since it is simple in design it is ideal for amateur construction. The spherical wave interferometer was developed by the author to meet in-house testing needs at Ceravolo Optical Systems.

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The Spherical Wave Interferometer

Kitchen table interferometry! The spherical wave interferometer is well suited to amateur construction since it is relatively simple in principle and requires a minimum of precision components. Because this interferometer is located close to the telescope's focus it can be physically small and compact, thus reducing the cost of the precision optics required. In fact, the interferometer can be designed to slide into the telescope's focuser tube, thus making testing very convenient by reducing the extra mounting hardware necessary to support the interferometer. This interferometer is of very simple construction when compared to the instruments used in professional optical shops. The interferometer's simplicity is the result of specifically tailoring it to the testing needs of telescope mirrors and complete telescopes. As stated earlier, this interferometer can be used wherever the ordinary Foucault tester is employed. The interferometer consists of a small laser for the light source, a polarizing filter, a gradient index (grin) lens to diverge the laser beam, a beamsplitter to make the fringe pattern accessible, and the reference element, whose convex surface is the master surface the test wavefront is compared to. All items, except the reference element, can be purchased from optical and surplus house catalog listings.

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The optical elements will be described in detail later on, but let's briefly go over the way the interferometer works. The laser beam passes through a rotatable polarizing filter used to adjust fringe contrast (see the chapter "The Laser"), and is then made to diverge from parallelism by passing through a gradient index (grin) lens. The diverging beam travels through a beamsplitter and onward to the reference element. The concave surface of the reference element causes the cone of light to diverge a little more, but without introducing aberrations. The light then passes through the convex master surface of the reference element, without further deviation, toward the telescope or test mirror. Some of the light is reflected off the reference surface and retraces its path back into the interferometer. This is the reference wavefront. The remainder of the light returning from the telescope or test mirror retraces its original path back through the interferometer and interferes with the reference wavefront, thus generating the fringe pattern. The interfering test and reference beams pass through the beamsplitter, and are reflected 90 degrees to the secondary focus where the fringes are viewed or photographed. The target screens placed around the grin lens, laser and the secondary focus of the interferometer will greatly aid in the alignment of the interferometer components, and also aid in aligning the optics to be tested. The function of the target screens is explained in the chapter, "Assembling and Aligning The Interferometer". The nature and function of the optical components will now be described in detail.
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The experimental laser interferometer fashioned from bits and pieces of aluminum lying around the shop. A very short focus test mirror is mounted in an adjustable holder, and both are mounted on a small optical bench.

The light path in the interferometer is revealed by smoke blown into the light beam in this time exposure.

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The Grin Lens The grin lens is a tiny glass rod about 2mm in diameter and about 4mm long. The index of refraction of the glass is not constant within the rod, but varies radially. This variation in refractive index causes the rod to act as a lens, even though it has flat, not curved, surfaces.

The use of a grin lens provides a very simple and convenient way to generate a diverging cone of light. The faces of the grin lens should be anti-reflection coated, otherwise spurious background interference fringes will form. Such spurious fringes may seriously affect the accuracy of test results. The focusing power of the grin lens is described by its numerical aperture (NA). The NA can be converted to a focal ratio by the simple equation: f/# = 1/ 2 NA Since the grin lens must full illumination across the reference element, it must be carefully selected so as to match the reference element's f/#. In fact it is better to over-fill the reference element since "noise" at the outer edge of the beam is "filtered" out of the interferometer. A 1.8mm diameter grin with an NA = 0.46 has a focal ratio of f/1. But this is only true if one is filling the full 1.8mm aperture with laser light. Most lasers emit a very narrow beam, typically 0.5 mm. The grin, when used with such a laser, is underfilled and yields about an f/4 cone of light. The Beamsplitter To allow the fringe pattern to be viewed, the return beams from the reference element and the optic under test must be separated or "split" from their original paths and then be redirected to an accessible observation point. A beamsplitter accomplishes this by both partially transmitting and reflecting light passing through it.

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A cube beamsplitter is made from two identical right angle prisms cemented together at their hypotenuse faces. On the hypotenuse of one of the prisms is applied either a partially reflecting coating of aluminum or a modern multi-layer dielectric (non metal) coating. Unlike a dielectric beamsplitter, a metal coated beamsplitter will absorb a significant portion of the light. This is unimportant, however, since even a low power laser will deliver plenty of light for most testing requirements. The cube beamsplitter has two significant effects on the light cone emanating from the grin lens, and which must be considered when designing the interferometer. First and most important is the introduction of spherical aberration. A cube beamsplitter is essentially a thick glass plate. When such a plate is inserted in a converging (or diverging) cone of light, the outer rays strike the flat surface of the beamsplitter at a greater angle than those rays close to the optical axis. This causes spherical aberration, which worsens with "faster" beams. Because the laser light passes through the beamsplitter twice in the interferometer, the aberration is doubled. The spherical aberration introduced by the beamsplitter can be minimized by doing one or both of the following. Reduce the size of the beamsplitter and place it closer to the interferometer's focus, or limit the speed of the cone of light emerging from the interferometer. The second effect to consider is the shift of focus along the axis caused by the glass thickness of the beamsplitter, the magnitude of which is given by the simple formula: focus shift = t (n-1)/n, where t is the cube beamsplitter's thickness, and n is its refractive index.

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Cube beamsplitters are expensive purchased new, however cubes can be purchased from surplus suppliers listed at the alternative is the plate beamsplitter, a thin glass plate tilted be thin, otherwise a significant amount of astigmatism will plate, and which may affect test results.

inexpensive 12mm (1/2 inch) end of this document. An at 45 degrees. This plate must be generated by the inclined

The plate beamsplitter should only be used for checking slow cones of light. An f/4 or slower mirror checked at the center of curvature (i.e., an f/8 beam) should not pose a problem with a beamsplitter plate that is no more than several millimeters thick. The plate should be placed close to the focus so that only a small area of its surface is usedѕplate beamsplitters are seldom very flat.

The plate beamsplitter causes, in addition to an axial shift of focus, a lateral displacement of focus away from the optical axis which should be considered when the interferometer is laid out.

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There are many unwanted reflections which occur in the beamsplitter, causing spurious fringes and a general fogging of the fringe pattern. This source of noise can be largely blocked by a screen pricked with a pinhole. The pinhole passes the light from the reference element and test optics, while the screen blocks the stray light from getting to the eye or camera. Such a card with a pinhole is called a "spatial filter" by optical engineers. The Reference Element The reference element, the heart of the spherical wave interferometer, is essentially a small, high-precision negative lens. The light diverging from the grin lens passes through the concave surface of the element. This is what is known as an aplanatic surface; it causes the light to diverge slightly without introducing aberrations, provided it is figured well. Because a laser is used in the interferometer, many spurious interference patterns are generated between beamsplitter and lens surfaces. Coating all glass surfaces except for the test and reference surfaces will help to reduce these undesirable fringe patterns. The aplanatic surface of the reference element should be coated with a high efficiency (less than 0.5% reflectivity) multi-layer dielectric coating.

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The convex side is the master surface. Its radius is chosen such that light will pass through it without further deviation. A fraction of the light is reflected off the master surface and back into the interferometer; this is the reference wavefront. The rest of the light proceeds to the optic under test where it is reflected back to the interferometer so that it may interfere with the reference wavefront. Since the reference element is a negative lens, it shifts the focus back from its origional position and slows the apparent focal ratio of the mirror or telescope being tested by a factor equal to its refrative index. In other words, an f/8 beam will appear as an f/12 beam if the index of the reference element glass is 1.5.

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Designing and Making the Reference Element Designing the reference element is very simple. But making it can be quite difficult. For those who wish to purchase the reference element, CERAVOLO Optical Systems is making a limited number available for the price of $375. The 1" clear aperture reference element, made from optical grade Zerodur, generates an f/3.2 diverging beam. The critical master surface is tested by computerized interferometry to meet or exceed the l/10 criterion over the full f/3.2 aperture, and is even better at slower focal ratios. Each reference element is supplied with a quality assurance test data sheet specifying that particular reference element's optical quality. When designing the reference element there are two parameters which must be established. The first is the limiting focal ratio of the interferometer, and the second is the diameter of the master surface. The COS reference element is designed to yield an f/3.2 beam, since most telescopes are not faster than f/4. Also remember an f/4 mirror at the center of curvature produces an f/8 beam. So the COS reference element can actually test a mirror as fast as f/2 at the center of curvature. It is always advisable to make the interferometer faster than the fastest telescope likely to be tested so as to provide a "buffer" around the edge of the interferometer field. The 1" clear aperture implies the master surface will be placed about 3.2" inside focus (or ahead of the radius of curvature) of the mirror being tested.

Given that we have established the distance inside focus (S), determining the reference element's two surface radii is easy: The master surface radius (R1) is equal to the distance inside focus, R1 = S The radius of aplanatic concave surface (R2) is given by,
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R2 = n( S - t ) / (n + 1) where n equals the refractive index of the material used, and t is the center thickness of the element. Note: the reference is a negative lens, causing the focus to shift farther back. The resultant back focus, from the vertex of R2 to the focus is BFL = n (R1 - t). The reference element must be made of an optical grade material, since variations in homogeneity of the glass will distort otherwise straight fringes. The crown glass normally used in refractor objectives can be used, but a more thermally stable substrate like ultrahigh quality fused silica or Zerodur is preferred, especially if the reference element is larger than 2" in diameter. The lens should also be thick enough to resist any stresses when interferometer. The standard 1:6 aspect ratio will be sufficient if mounting. Lenses smaller that 2" may be difficult to figure with techniques, so make it at least large enough to be comfortable to mounted in the care is exercised in its the traditional ATM work on.

The master surface is the most critical part of the reference element, since the test optic is directly compared to it. In order for the interferometry results to be accurate, the master surface must be made as precisely spherical as possible. The concave surface of the reference element is not as sensitive to errors as the reference surface, and provided that the radii and glass thickness are strictly adhered to, need only be accurate to 1/2 wave or so. This is because this surface only affects the collimation of the light relative to the master surface. The master surface is convex and therefore the Foucault test. However, if the reference the radii and the thickness of the lens as clo by figuring the concave side as accurately s convex master surface through the concave cannot be tested directly by reflection with element is made precisely, that is by grinding se as possible to the design parameters, and pherical as possible, we can then test the surface with the ordinary Foucault test.

A word of caution. The difficulty of making excellent spherical surfaces must not be underestimated. One of the myths of telescope making is that spherical surfaces come naturally. Take it from someone who has made hundreds of spherical surfaces--they do not always come easy! The procedure for making the reference element is no different from that of making any other precision lens, so we will not go into any great detail here (see Telescope Making Magazine #3). Both surfaces are first accurately ground, de-wedged and completely polished before any figuring is attempted. The concave side is first figured as accurately as possible with the
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Foucault t Foucault t beam, the curvature. steep.

est. There should be absolutely no visible zones, since the sen est is poor with fast cones of light. If the reference element is concave side of the lens will have approximately an f/2 curve It will be difficult to see the whole aperture because the cone

sitivity of the to cover an f/3 at the center of of light is so

With the concave surface accurately figured, we can now test the convex side through the concave surface as a Mangin or second surface mirror. The knife-edge should be positioned where the grin lens will be mounted. It is important to remember here that what appears to be a bump is in fact a depression on the surface, since we are checking this surface from the "other side". The internal reflection works in our favor because the visibility of zones is amplified by a factor equal to the refractive index of the lens. But this must be weighed against the fact that the light must fi