The following article is a translation of parts of the original publication of Karl-Ludwig Bath in the german astronomical magazine:

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1 The following article is a translation of parts of the original publication of Karl-Ludwig Bath in the german astronomical magazine: Sterne und Weltraum 1973/6, p The publication of this translation on the interferometer wiki ( is with kind permission of the author and the copyright holders of the original article at Sterne und Weltraum, represented by Uwe Reichert, SuW Heidelberg, Germany. Translation by Andreas Derwahl.

2

3 KARL-LUDWIG BATH A simple interferometer for testing astronomical optics Fellow stargazers have access to a whole range of qualitative and quantitative methods for the analysis of astronomical optics. [1]. There are different reasons, however, that interferometric methods are virtually non existent among amateur telescope makers. The following pages describe an interferometer that can be easily assembled and adjusted with little practice, but still gives accurate quantitative results and is made from parts that can be found in every cheap binoculars. cube, beam 1, creates an image Q of the baffle B1 on the concave test mirror, which for simplicity is drawn as spherical. Optical parts: 1) The light source Q: we can use for example a halogen To sum up a few of the specifics: - The interferometer is suitable for all usual f-ratios and focal lengths down to about 25 cm. - It can be used with white, unpolarized light. - The interferometer yields bright interferograms. When using a laser the efficiency at exit port A2 (see fig. 1) is up to 50%. - The fringe contrast is high and always 100% at exit A1 (translator remark: independent on the splitting ratio of the beam splitter). - The interferogram is free of false light and all secondary reflections can be suppressed. - Both exits (A1 and A2) are complementary, meaning at exit A1 the zero order fringe is bright, at exit A2 it is dark. In order to make the instrument usable for people that are not acquainted with interferometric work, it shall be described in maybe greater detail than seems necessary at first sight. Working principle: Let us have a look at fig. 1: the assembly from lamp Q to baffle B2 is used to produce a collimated beam, which is already given when using a laser as a source. The beam is divided by the beam splitter cube into two coherent parts, beam 1 and 2, that are capable of interfering. The beam that is reflected from the splitting surface inside the fig. 1: schematic representation of the interferometer, working principle see text, R is the autocollimation focus. After reflection from the mirror surface and transmission through the small symmetrical biconvex lens L3, beam 1 forms a spherical wave with its centre at P1. The quality of this reference wave, as we might call it, is not influenced by the defects of the test mirror, because the reflection at Q is generated by only a small part of the surface, which can be regarded as defect free. Beam 2 passes through lens L3 on the way to the mirror and illuminates the complete diameter as a spherical wave. The defects of the mirror are imprinted on this wave, forming a second light wave with origin at P2. The two wave fronts with centres P1 and P2 are now mixed by cube W1 and their interference can be observed at exit A2 or - with a second beam splitter cube W2 - at exit A1. The interferometer does not work in strict auto collimation, i.e. the reflected beam 2 does not coincide with beam 2. Therefore the diameter of the usable field of view of the test mirror/objective must be bigger than the P1-P2 distance, otherwise it will show astigmatism and coma, defects that should not be present on axis of the test specimen. incandescent lamp with cylindrical coil, or if not available even a flashlight / torch will do. Best of course is a laser. In order to avoid extraneous interference all surfaces should be cleaned carefully and after adjustment the parts in direct illumination by the collimated beam should be made free of dust with a soft brush. If the laser beam is too small for a given f-ratio, it can be expanded some without disadvantage by a single negative lens in front of the beam splitter. 2) A camera lens of focal length around 50-mm or a binocular eyepiece serves as OBJECTIVE L1. 3) The pinhole B1 is made for example from a piece of tin foil with different sized holes to choose. 4) OBJECTIVE L2 is stepped down to 5 to 10 mm; its focal length is chosen such that the image Q of baffle B1 is smaller than 1/10 of the test mirror diameter. 5) The beam splitter cube W2 is only necessary for exit A1 and should be removed when using exit A2 (A2 provides four times the image brightness of A1). If we don t have a cube if necessary we

4 can cement two Porro prisms with water or use a thickish glass plate as beam splitter. 6) The beam splitter cube W1 should have a minimum edge length of 25 mm. If need be we can build one by cementing two suitable Porro prisms with largely any oil, for example sun flower oil. If we used the oil sparingly the cube is mechanically stable and compared with commercial beam splitter cubes it has the advantage of an accessible fourth face and hence the exit A2 becomes available. 7) The focal length of the symmetrical biconvex lens L3 is less than 1/20 of the test mirror s focal length and under 15 mm in diameter. Its defects are compensated automatically even if it is tilted in the beam path, hence a corrected system would not have any advantage. It should be mentioned that an asymmetrical lens (e.g. plano-convex) can be used. In this case, however, the lens has to be adjusted carefully and the test mirror f-ratio should be at least 10. If, because of a small usable field of view of the test mirror, the P1-P2 distance (i.e. beam separation, remark of the translator) has to be very small, the lens L3 can be ground close to the lens centre. [Comment KLB: with half moon beam 2 is cut from above so that the lower half of the mirror is NOT illuminated.] Assembly: For lens L3 and test mirror PR we require adjustment in all three coordinates. At least one of these two elements has to be fine adjustable in height (perpendicular to the drawing plane). Further, the centers of all elements must be adjustable to the same height. We begin assembly with the lamp. Its coil is tilted a small amount from the interferometer axis. The diaphragm B1 is placed at a distance from the lamp that equals approximately 4.5 times the focal length of lens L1. We center the emerging light cone on the test mirror. Next we insert the objective L1 and project the image of the inside wall of the lamp coil onto baffle B1. This in turn is projected with L2 onto the centre of the test mirror. If the objective does not possess a built in diaphragm we insert another baffle B2 into the beam that is adjustable in both directions perpendicular to the interferometer axis. The assembly of both beam splitter cubes is not critical. Cube W1 acts on beam 2 just like a plane parallel plate, which here can only cause a lateral beam shift. Beam 1 however, which is reflected off the splitting surface, has to be adjusted on the mirror centre by rotating the cube. Because we want to keep the requirements for the field of view of the test mirror small, we will choose a small distance between both beams leaving the cube, for example 10 mm. The position of beam 2 is set by moving baffle B2. The beam separation is adjusted by moving cube W1 along the direction indicated by the arrow in Fig. 1. Finally we insert lens L3 in beam 2 at a distance from W1 equalling its focal length. Only when testing fast mirrors we place the beam splitter cube closer to the lens. In order to avoid light passing the lens on its side we may need to reduce baffle B2 to a smaller beam diameter. It should also be small enough so that the light cone created by L3 does not overilluminate the test mirror by much. The distance of the test mirror from L3 equals its radius of curvature (or its focal length if it is an astronomical objective with a plane mirror). Now the assembly of the interferometer is finished and we can take on the alignment. Fig. 2: Elimination of objectionable reflections Alignment As a small tool we need some strips of stiff paper. We place one strip under each beam splitter cube to be able to turn them in small amounts. Now we move lens L3 or baffle B2 in the plane normal to the beam and center the light cone leaving the lens on the test specimen. If this an objective we cover the flat mirror (Fig. 4) with black paper and adjust the objective axis with the help of the lens reflections to lie on the interferometer axis. Following this we intersect beam 1 with a white paper strip at P2 and adjust the image formed by the test mirror/lens of the lens focus F exactly opposite P1 into the beam center. This is achieved by tipping, tilting and moving the mirror or objective along the optical axis. Now we reach the final phase of adjusting. We look into either exit A1 or A2 into the interferometer (take care when using a laser, translator remark), and we will see all kinds of reflections: one is from cube W2 -- it can be moved by rotating the cube. Another is from cube W1 (see Fig.2). Finally there can be reflections from lens L3; they can be removed by tilting the lens. If we were careful during assembly and adjustment so far, we can now see the two diffraction disks from P1 and P2. P2 is only visible inside the test objects outline and can be recognized more easily by moving our head back 20 to 30 cm. The following fine adjustment positions the interferometer or the test object so that both diffraction disks have equal size and coincide. The size is controlled by changing the L3-PR distance. The discs are made to coincide by tipping and tilting the mirror (or plane mirror if an objective is being tested) by small amounts. Another method is to adjust the lens height of L3 and rotate cube W1. Doing this the beam will move on the test object, but it should not leave it. This second method is more convenient but affects the illumination of the test object. If we managed to get the two spots to the same size and to superimpose we can now see the interference fringes. To get a feeling for this phenomenon we now alter the previous adjustment steps by very small amounts. The focus of the beams

5 that pass the central area of the test specimen - which is of biggest interest to us is called paraxial focus. We can find it easily if we bring the center of the visible ring system to the centre of the fringe pattern (i.e. get the bulls eye, translator remark), and only then adjust the L2-PR distance. If by accident we lose the fringe pattern by large misalignment, it is not advisable to search for the diffraction disks at the interferometer exit, but rather start again from the beginning of this paragraph. Fringe pattern Let us assume the test object is a perfectly spherical mirror. In this case with the interferometer at the centre of curvature the fringe pattern shows an evenly bright (exit A1) or dark (A2) surface. If we now move P1 or P2 sideways or in height (translator remark: X,Y coordinates,), straight, parallel and structure-less fringes appear (see also the numbered front cover pictures) regardless of their orientation. If the test specimen has surface defects it clearly shows in the fringes (Picture 1 and 2). Pictures 1 and 2 We have to examine these interferences in greater detail because we want to know if maybe the usable field of view is smaller than P1-P2, and what defects the test specimen shows for on axis and tilted rays. The interferograms are so manifold, that we can only deal with spherical aberration, astigmatism and coma here, and have to restrict ourselves in most cases to the optical axis. Irregular variations of the wavefront are reflected by irregular variations in fringe width and directions. We see an example in picture 2, the interferogram of a Fraunhofer objective of unknown origin. It shows 1 lambda aberration for single pass (see pictures 3 and 4). Pictures 3 and 4 The maximum aberration following picture 1 is lambda/15. Of special interest to us is of course the interferogram of the spherical aberration for the central rays, the paraxial focus (picture 3) and next to it (picture 4 and also picture 2). Additional parts of the article mostly dealing with fringe analysis are omitted here because electronic data reduction has now taken the place of visual geometric analysis. Appropriate and powerful software is available today at: /index.php?title=Interferogram_ Analysis. Two final remarks on fringe photography. To avoid vignetting a small Kepler telescope with a power of 2 to 4 between the interferometer and the camera is advisable. Further the camera has to be focused onto the rim of the mirror under test, otherwise the fringes get frayed out at their ends. Literature [1] K.-L. Bath, Ein einfaches Common Path Interferometer, Optik 36 (172) 349. [2] Original article in Sterne und Weltraum, 1973/6, Translation from German by Andreas Derwahl with kind permission of Sterne und Weltraum, Heidelberg.

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