METROLOGY WITH AUTOCOLLIMATORSMETROLOGY WITH AUTOCOLLIMATORS K. J. Hume B.Sc., M.L.Mech.E., M.I.Prod.E. Reader in Production Engineering Longhboroigh Unis of Teco HILGER & WATTS LTD LONDONger & Watts Led, 1965 Published by HILGER & WATTS LTD ‘08 ST PANCRAS WAY, LONDON, NW PREFACE In May 1961, the late Victor Towns, then Technical Director of Hilger & Watts Ltd, first suggested that I should write a book on autocollimators. He felt that there were still many precision engineers, inspectors and technologists who did not fally appreciate the potential value of these instruments. In the three years and a half or so since then, a good deal of develop- ment work has taken place, particularly in photoelectric autocollimators, which has improved accuracy of measure- ment and made operation and observation simpler. Further developments in the automatic recording and computation of instrument readings are likely to bring greater accuracy and eed. "PNo book of this nature can deal solely with principles of operation and methods of tabulation and computation without reference to equipment in current use. I believe that, to be convincing and authoritative, an author must write mainly from his own experience and from authentic information which he can receive first hand, It is for this reason, and the fact that Hilger & Watts Ltd are the only manufacturers of a comprehensive range of autocollimators, that their instru- ments figure largely in this book. My grateful thanks are due to my friends, both at Hilger & Watts and at the National Physical Laboratory, for their help and advice, without which this book would scarcely have got off the typewriter, KH December 1964ACKNOWLEDGEMENTS. Plates 2(a), 14(6) and 19(2) are Crown Copyright and have been reproduced by kind permission of the Director of the National Physical Laboratory. Plates 9(8), 13(a), 17(4) and 18(a) have been reproduced by kind permission of Coventry Gauge & Tool Company Ltd. Plate 15(6) has been reproduced by kind permission of the Engis Equipment Company, U.S.A. CONTENTS Development of autocollimators Optical principles ‘Typical instruments Associated equipment Angular measurement Circular division Calibration of polygons Alignment testing Further test and equipment Bibliography Index 126 139 141CHAPTER ONE Development of Autocollimators Tue autocollimator, or, to give it its precise title, the auto- collimating telescope, is an instrument of high precision that has gained an important place in engineering and technology. It probably first came into use in the works of optical instrument manufacturers for checking parallelism and squareness of optical and mechanical components in instruments. In such places, and in many other optical applications, the collimator has long been used for the setting and alignment of telescopes on spectrometers, theodolites, and similar instruments. “Collimate’ is derived from Latin roots and means to bring into line. In the optical sense, it means to bring rays of light into a parallel beam. Optical principles and theory are dealt with in the next chapter and it is sufficient to say here that, if a point source of light or an illuminated object is placed at the principal focus on the axis of a convex lens or lens system, the rays of light emerging from the lens will be in the form of a beam parallel to the axis. Light received by a telescope from a distant object is also in the form of a parallel beam or family of parallel beams if the source is extended. ‘These beams are brought to a focus in the focal plane of the objective lens where an image of the distant object is produced. A collimator provides an artificial object at infinity and is thus particularly useful for setting and adjusting telescopes within a limited space. Plate 1 shows the test room of an instrument manufacturer where several collimators are placed around the walls in care- fully calibrated positions for the final checking and adjustment of surveying instruments. From this type of application it is ust one step further to illuminate a graticule in the telescope and thus project, as well as receive, a parallel beam. A plane reflector set up at some point in front of the telescope would then reflect the projected parallel beam back into the instrument objective, From general considerations it is fairly obvious that any small angular deflection of the mirror will deflect the image seen in the telescope and thus provide means of measuring2 Metrology With Autocollimators small angular differences or movements at some distance from. the observational instrument. Furthermore, as is demon- strated in Chapter 2, the image in the telescope appears stationary even if the reflector is moved backwards or forwards, provided its reflecting surface is always parallel to the first position. ‘This is a most useful property of the autocollimator, Instrument makers used the instrument to check parallelism between surfaces of an instrument under construction and later, autocollimators were used for similar purposes in preci- sion engineering not necessarily connected with the optical instrument industry. In his book, Gauges and Fine Measurements, Vol. Il, F. H. Role gives an example of the use of an auto- collimator for testing the flatness of a surface by what is now known as the ‘inclination’ method of traversing a small carriage along the surface and observing the reflected beam from a plane reflector mounted on the carriage. Rolt describes this method in detail. He also gives references to articles on autocollimators which have appeared from 1g20 onwards; thesc are probably the earliest references to engineering applications. The carly autocollimators were not complete instruments in themselves. They were built up from a collimator, illumi nator, cover-glass reflector and micrometer eyepiece or microscope, all mounted on a base. An instrument of this type is illustrated in Plate 2, Since the 19208, demands for increasing accuracies in manufacture were met by improved methods of measurement and the autocollimator was deyloped as a commercial instrument for use in standards rooms and inspection departments as well as for alignment of machine tools, large jigs and fixtures. Today, its use has been so extended. that many instruments are sometimes used permanently set ‘up on one structure, particularly in the U.S.A. where there are many applications in missile construction and launching programmes. ‘The autocollimator has from the first been a highly-sensitive instrument, enabling readings to be taken direct to a fraction of a second of arc. An instrument of low sensitivity was also developed many years ago by Adam Hilger Ltd for their own use. This was called the Angle Dekkor and was a good deal simpler in construction than the more sensitive instrument. It was, in fact, more like a simple telescope, with objective lens and eyepiece, and it enabled readings to be taken direct to one minute and closer by estimation. Development Of Autocollimators 3 Plate 2 shows an early model of the Angle Dekkor. A feature, which is still retained in the modern design, is that the projected object is an illuminated scale, its reflected image being super- imposed on another scale at right angles to it and permanently visible in the eyepiece. This system enables readings to be taken in two directions at right angles and thus, by compound- ing the two readings, angular variations can be measured in any direction. Illustrations of the field of view in the eyepiece and more detailed descriptions of construction and function are given in Chapter 3, Because of its lower sensitivity, and to enable angles to be measured in various positions, the Angle Dekkor can be somewhat less rigidly mounted than the more sensitive instrument. In the majority of work involving measurement of angles on gauges and tools, accuracies of a few tenths of a minute are adequate. Returning to the sensitive autocollimator, the first com- mercial instrument of this type in England was made by E, R. Watts & Son Ltd and was known as the Microptic autocollimator. It was basically made to the pattern of the instrument designed by the National Physical Laboratory. ‘This design was continued with minor modifications over a number of years and has now given rise to several variations which will be described in later chapters. A significant advance was made when a photoelectric reading microscope was fitted. This gave a greatly increased sensitivity but, at the same time, showec up very obviously the undesirable effects of temperature variations, disturbing both the air in front of the instrument and the mechanical stability of the instrument itself. ‘Another sensitive autocollimator was made for many years by Taylor, Taylor & Hobson Ltd. This was somewhat different in design from the Watts instrument but operated in a very similar manner. The American Davidson Optronics Company also manufacture autocollimators and the German Zeiss organi- zation did so until recently. _ The use of autocollimators is by no means restricted to instruments which are sold as such ‘ in their own right’ so to speak. Many optical measuring and other instruments incorporate autocollimating systems, often without this being realized by the purchaser or user. A typical example of this is optical comparator of the type originally made by Zeiss ind now also made in England by Optical Measuring Tools ‘d, Precision Grinding Ltd, and possibly other manufacturers.4 Metrology With Autocollimators ‘The N.P.L.-Hilger gauge interferometer and the N.P.L. design of a flatness interferometer, also made by Hilger & Watts Ltd, incorporate autocollimating systems as an essential part of their designs The following chapters aim at providing information of fa theoretical and practical nature for the user of instruments, for those concerned with their application and for those who teach or instruct in the technologies with which autocolli- mators are or may be associated. Chapter 2 deals with optical principles and provides enough information for a reasonable understanding of the design and function of autocollimators without concerning the reader with more advanced optical theory which lies more within the province of the designer of ‘optical systems. In this direction it is sufficient to say that the art and science of lens design (for both art and science are necessary and complementary) have advanced rapidly in the last twenty years or so. Much of optical design work consists of ray tracing, the calculation of paths of rays through a lens which will be made up of at least two and often more elements. Electronic computers have eliminated much of the sheer hard work of calculation, doing in a fraction of a second, or a few seconds, arithmetic which could take minutes or hours, even with the help of desk calculators. ‘The lens elements in autocollimators are, however, not complicated compared with, say, high-power microscope objectives or wide-aperture camera lenses. Nevertheless, improvements in production techniques have benefited even the simpler optical systems. In autocollimators, mechanical precision and alignment in the construction of the instrument are of great importance and it is in these directions that improvements in manufacture have improved accuracy. As in most other branches of science, technology and engineering, developments in electronics have revolutionized measurement and control. The introduction of transistors alone has made practicable many refinements which, while they had been technically possible for a long time, were not very convenient when bulky equipment had to be used and often carried around, ‘The photoelectric microscope applied to the auto- collimator has produced a significant step forward in accuracy of measurement, particularly as the associated electronic gear is housed in a convenient portable case and can be run from batteries if necessary. Deoelopment Of Autocllimators 5 Basically, the autocollimator is simply an instrument which will measure quite small angular differences or variations. Highly-sensitive instruments have a range of only about ten minutes of arc and the coarser ones cover one degree. From this, it might be thought that applications would be severely restricted and confined to the actual measurement or com parison of angles, but this is very far from being the case. It is true that many of the most important and useful appli- cations are concerned with angular measurement but, in other measurements where linear dimensions are concerned, these instruments can be particularly useful. Such applications include the checking of flatness and squareness of precision surfaces and the amplification of small linear movements which can be converted to angular deflections. ‘Much of the usefulness of the autocollimator in these applications depends on various accessories and pieces of auxiliary equipment which can be used with it. The first requirement is, of course, a plane reflector ; it could be said to be an essential part of the instrument itself, except that it can take many forms, from the surface of a slip gauge to highly- reflective surfaces, specially prepared for a particular purpose. Reflectors mounted on carriages for flatness measurement, precision polygons for circular division, optical squares for accurate right-angle settings and measurements, Porro prisms for restricting effects of deflections to a chosen plane, and many other specially designed accessories give the autocollimator a versatility possessed by few other measuring instruments. The precision and versatility of the autocollimator are largely due to its physical separation from the object being measured. While it is true that there must be a rigid and stable link, such as that provided by a surface-table, the autocollimator differs from instruments such as dial gauges and comparators in not requiring contact of its measuring elements with the object being measured, Its measuring element is, in fact, a beam of light which needs only an uninterrupted path and lom from optical disturbances as may be caused by temperature variations in the intervening air. This makes Possible the use of a reflector whose distance from the instru- Rent may vary without affecting readings, an essential pute, in_measuring surface alignment or comparing the tive angles of two separated surfaces.onarren Two Optical Principles ‘Ture are two fundamental optical principles on which the operation of any autocollimator is based. These are the collimation of a beam of light emerging from a point source at the principal focus of a converging lens and the deflection of a beam of light caused by the tilt of a mirror in which it is reflected. ‘The first principle is illustrated in Fig, 2.1 where the source of light or illuminated object O is situated at the principal focus of the converging lens. It is fundamental in geometrical Fic. 21. Optical principle of collimation ‘optics that rays of light entering the lens, having passed through the principal focus, emerge from the lens as a beam parallel to the principal axis. Within certain limitations, light emanating from a point anywhere on the plane through the principal focus, the focal plane of the lens, is rendered parallel on emerging from the lens. In this case, the beam is parallel to an axis drawn through the point source and the optical centre of the lens. These conditions hold true if the langle between this axis and the principal axis is reasonably small, but effects, known as aberrations of the lens, introduce distortions for points which lie an appreciable distance off the principal axis. Rays from points between the lens and its principal focus produce a divergent beam and rays from points outside the principal focus produce a convergent beam. The essential feature of the autocollimator is the parallel beam produced from points lying in the focal plane. 6 Optical Principles 7 The second principle, illustrated in Fig. 2.2, is one of the first learnt by the student of elementary optics. Itis that a ray of light, incident on a plane reflector making an angle 9 with the normal to the surface, will be reflected on the opposite side of the normal, also at angle 6. The special case of this is that rays incident normal to the surface will be reflected back Fic. 2.2. Optical principle of reflection along their own paths. It will be seen that the angle between the incident and the reflected ray is 20, hence, if the mirror is inclined by the angle 3, the angle between the incident ray and the reflected ray is increased by 25. COLLIMATOR AND TELESCOPE ‘An instrument based on the principle shown in Fig. 2.1 is called a collimator and usually consists of an illuminated graticule placed in the focal plane of an objective lens. A telescope is virtually the same instrument in reverse, receiving rays which are parallel, or nearly so, and bringing them to a focus in the focal plane or in a plane close to it. For the present Purpose we are concerned with a telescope which is receiving Parallel light from an object at infinite distance and which will therefore form an image in the principal focal plane of its objective lens. _A combination of a collimator and telescope is shown in Fig. 2.g. The instruments are shown with their optical axes in line and it will be seen that rays emanating from an illuminated object O, are rendered parallel by the collimator objective, travel to the telescope objective and are then Tr Nght 0 a focus on the optical axis in the principal plane at plane Tatly, rays from another point Oz, also in the focal are rendered parallel at a different angle and are aught to a focus at I, in the telescope. The ratio of the rents (O,0;)/(I,1,) is equal to the ratio of the focal '/fz. Tt will be obvious from the diagram that the pi8 Metrology With Autocoltimators position of image I, relative to its objective is quite independent of the distance travelled by the parallel rays between the collimator and telescope objectives. It is also true, although perhaps not quite so obvious, that the position of image I, is quite independent of the distance between the two objectives. ‘This is because the position of the image formed from a parallel beam entering the objective is governed solely by the angle of that beam relative to the axis of the lens and not in any way by the distance the parallel beam has travelled before it has entered the lens. In the case of image I, there is a limiting factor, however, and this will be apparent from the diagram. Fic. 23. Combination of collimator and telescope If the telescope is moved further and further away, it will reach a point where none of the rays emanating from O, will enter the telescope objective and hence image T, will not be formed. The further O, is from the axis the shorter will be the separation of the objectives before image I, disappears, but theoretically the image I, of p still be formed at infinite separation of the two instruments, It follows therefore that a graticule of finite size, placed in the focal plane of the collimator, will produce an image in the focal plane of the telescope but, as the separation of the instruments is increased, there will come a point where the proportion of the graticule of which an image is formed will be reduced. It must be emphasized, however, that the size of the image is not reduced in any way, this size being solely a function of the relative focal lengths of the collimator and telescope objectives. If these focal lengths are identical the magnification will be unity. It is therefore only the field area which is reduced so that at large separations only the central area of the graticule image will be seen and this will finally disappear to a single point on the axis. These conditions will again be varied if the ‘two axes are not co-incident and also if they are not parallel. nt O, on the axis will An instrument manufacturers test rm Paar 1Piste Optical Principles 9 AUTOCOLLIMATOR From the foregoing it will be scen that the collimator and telescope systems are mirror images of each other, except that the rays from points not on the axis give an image on the ‘opposite side of the axis. If now the system is folded over, as, it were, about a line normal to the axis mid-way between the two objectives and a mirror placed on this line, we shall get the condition shown in Fig. 2.4. Assuming first that the reflector is normal to the axis of the system, it is clear that rays emanating from an illuminated Fic. 25. Deflection of image duc to tit of reflector ‘object O, on the axis will come from the lens as a parallel beam and will be reflected back along their own paths, forming an image at the same position at O, on the axis, that is to say at the principal focus of the lens. If now the mirror is tilted through a small angle 8 (Fig. 2.5), as we have already seen in Fig. 2,2, the reflected rays will move through an angle 28 and will form an image, still in the focal plane of the objective, at a position 1;. As seen in Fig. 2.3, the displacement of T, will be independent of the distance travelled by the parallel ays before entering the objective, and therefore the distance of the reflector from the objective does not affect either the size or displacement of image ;. 210 ‘Metrology With Autocllimators ‘This displacement is directly calculable from the rays passing through the centre of the objective and the distance 1,, 1; is therefore equal to 2f8,f being the focal length of the objective. Although the illuminated object O, has been shown on the axis, it need not be in this position ; the same principles apply even if it is to one side of the axis, Naturally the position of the image will be affected by this, but its deflection caused by tilt of the mirror will be exactly the same as before, provided the angles are relatively small. ‘Such an instrument, having a suitably illuminated object in the focal plane of the objective and some means of measuring any displacement of the image, also in the focal plane, is there- fore a combined collimator and telescope and is called an autocollimating telescope or autocollimator. In all that follows in this book these same basic principles apply. The instruments themselves may be more complicated by having micrometer microscopes to measure image displacement, by having prisms or reflectors to turn the beams through angles to suit certain applications, by having photoelectric devices to measure the position of the image with greater sensitivity, but, if the foregoing principles are fully understood, there should be no difficulty in understanding the general function of any instruments of this type. It will be observed that quite a number of optical instruments which are not themselves con- cerned with measuring angles, incorporate autocollimating systems. Such applications will be found in comparators for Inear measurement, flatness interferometers, length inter~ ferometers and various other measuring instruments. Tt should always be remembered that an initial displacement of the image from the object position is of litle consequence. ‘Although for convenience the object has been shown on the optical axis and the position of the image indicated asa displace- ment from the object position, there is never, or very seldom, any virtue in measuring this displacement. What is required of the instrument is a measurement of the image movement from one position to another consequent on changes of angle of the external reflector. Thus it will be appreciated that the autocollimator is a comparator of angular positions of an ‘external reflector and is not in itself a measure of the absolute position of that reflector unless comparison is made between the Teadings obtained from two different reflecting surfaces. Such an arrangement can be obtained by having two reflectors, Optical Principles n which may be at different separations from the objective, an these will produce two separate and distinct images in the focal plane of the objective, Such reflectors can be arranged so that tach covers only part of the aperture of the objective; alter- natively, one or both reflectors can be transparent, Quite good images can be obtained from plane transparent reflectors > although the intensity is naturally somewhat diminished. The principle of this is illustrated in Fig. 2.6 where two reflectors R, and R, produce the two images I, and I,. Se re pF abs I. Fic. 26. Two reflectors producing two images PRACTICAL ARRANGEMENTS So far, all that has been considered has been the formation of an image by the reflection of beams emanating from an illuminated object in the focal plane of an objective lens. In practice, however, it is necessary to provide an object and laminate it, and also to provide some meant of observing and measuring movement of the image. It is in the various systems and methods of doing this that particular instruments differ quite considerably. Generally speaking, there are two categories of instrument. In the first, the object graticule may take the form of fine cross-wires centred on or near the axis of the objective lens, together with a microscope system with Imicrometer eyepiece for magnifying and measuring the image GaPiacement. In the second type, the illuminated object takes the form of a small scale to one side of the axis, the reflected image being formed against another scale or index line in the eroraie) 7 a eee it is usual for the magnification a single eyepics ent being “iors fic fl c eyepiece, measurement being made ese two arrangements are shown diagrammatically in gs. 2.7 and 28 respectively. In’ Fig, 7, showing. an12 Metrology With Autocolimators instrument of high magnification, the primary graticule is illuminated by a small lamp and condensing lens at the side of the optical axis, the light being projected along the axis to the graticule by a 45° transparent reflector. The returning rays forming the image in the focal plane are observed by a Fic. 2.7. Optical system of the Microptic autocolimator so Femme Fi, 28. Optical system of the Angle Dekkor micrometer microscope through the same 45° reflector. Natur- ally, a good deal of light is lost at the reflection in the 45 reflector and a smaller amount is again lost by transmission through the reflector to the microscope. The micrometer eyepiece of the microscope measures the second image at the magnification of the microscope objective. In the instrument of lower sensitivity, illustrated in Fig. 2.8, the image is observed directly by a Ramsden eyepiece and a lower overall magnifi- cation is obtained. Optical Principles 13 2.9 shows an alternative arrangement of the instrument 2.7. Here, the primary graticule is placed to one side of the axis and illuminated at right angles, rays from the graticule being deflected along the axis by a 45° reflector. The reflected image is formed on the axis and is observed directly by the microscope as before. It will be obvious that another image is, also formed by further reflection in the 45° reflector and this, image will be in a plane through the primary graticule, parallel to the axis, but is not of course observed. ‘An advantage of this system over the first is that the primary graticule is not seen directly in the eyepiece. This enables the Qo Es a Ont ht T= Ohm ee Sd Fic. 2.9. Optical system of the Universal Microptic autocollimator primary graticule centre and its image to be superimposed, optically speaking. In the first instrament the primary graticule would obscure its image if both were superimposed. From the earlier discussion of optical principles, it will be realized that by working exactly on the optical axis, the reflector may be used at a much larger range. In such an instrument, the positions of the primary graticule and illuminating system can be interchanged with the microscope. _ In the foregoing explanations of the two main types of instrument no attempt has been made to go into constructional details of particular instruments made commercially; this will be done in the next chapter. It is far better for the user or student of any instrument to understand, if at all possible, the principles underlying the construction and operation of the instrument without being distracted in any way by specific details. It is apparent, from many answers to examination