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Dr E.H.Linfoot had two distinguished careers of which only the second, in astronomical optics, is generally known to astronomers and must perforce be the chief subject of the present notice. His earlier equally outstanding career in pure mathematics must, however, be touched upon, for its intrinsic merit and because the optical work grew out of it; a fuller account is to appear shortly in the Bulletin of the London Mathematical Society.
Edward Hubert Linfoot was born in Sheffield on 1905 June 8 into a musical and mathematical family. He was the eldest child and only son of George Edward Linfoot and his wife Laura, née Clayton. His father had been a boy violinist, and afterwards a mathematics teacher before returning to music as Director of Music for the Sheffield LEA. The son displayed his inheritance of these gifts not only in his mathematical career but also in remaining all his life extremely sensitive to music, particularly J.S.Bach, which he would play on the piano for solace.
Linfoot attended the King Edward VII School in Sheffield where his abilities resulted in him taking the old Higher Certificate three times (obtaining distinctions in all his subjects of Mathematics, Additional Mathematics, Chemistry and German). He had won a Balliol scholarship at the age of 16 but did not matriculate until two years later in 1923. He graduated in 1926 with First Class Honours, and was awarded the degree of DPhil only two years later for a dissertation on almost periodic functions. His Goldsmith Senior Scholarship was then extended to enable him to spend 1928-29 in Göttingen where his already excellent German became fluent. This was followed by the award of a Jane Eliza Procter Fellowship at Princeton University 1929-31, after which he returned to Balliol as a Supervisor until his appointment in 1932 as Assistant Lecturer, and then Lecturer, in Mathematics at the University of Bristol. In 1935 he married Joyce Dancer, herself a distinguished mathematician, whose devoted support was evident to all and for which he expressed deep gratitude. They had a daughter and son born respectively in 1945 and 1947.
One of Linfoot's teachers had been G.H.Hardy, and it is no surprise that his mathematical publications, the first of which appeared when he was still an undergraduate, are in the field of classical analysis, number theory, Fourier transforms and probability. His interests were however extremely wide, extending to mathematical logic, dimension theory and the foundations of quantum mechanics. While an undergraduate, he had developed an individual technique of preparing exemplary notebooks based on lectures, tutorials and his own researches. These notebooks provide one of the best written records of the mathematics of the time, and happily it has been stated that they are to be preserved in the Archives of the London Mathematical Society. Linfoot had been naturally left-handed, but had schooled himself to write with his right hand, and a curiosity of his manuscripts is that he usually used the right hand when using a pen, and the left for pencil.
During the late 1930s, Linfoot's attention gradually switched to optics. The reasons for this are complex. Inspired, as so many proto-astronomers have been, by Albert G.Ingalls' Amateur Telescope Making he had in his teens constructed a small telescope for lunar observations, and this early interest had remained with him. He also foresaw the European conflict to come, and rightly believed that optics would play an important part in it. In addition, his own testimony is that he had come to question his continued creativity in pure mathematics, and it is a tribute to his modesty and courage that he wished others to know how he had recovered from this period of self-doubt, and be encouraged by it. Dr C.R.Burch, who was himself an essentially physical thinker and who had long wished to strengthen the mathematical side of his optics group, encouraged Linfoot's interest and with the approval of Professor Tyndall the facilities of the Physics Department, H.H.Wills Laboratory, were placed at his disposal initially to make a telescope for himself. What had in this way begun as a hobby, happily blossomed into his second professional career. At first, however, he meticulously set about learning the practical skills of figuring optical components, which he found both interesting and restful and only later began to use his mathematical knowledge in the service of practical optics. Linfoot said of this transition that in pure mathematics he needed to learn to think with complete accuracy, whereas in optics he had to learn to think with controlled inaccuracy, and he found this the more difficult of the two.
He was particularly concerned to liberate optics from the historical restriction to spherical surfaces by the introduction of aspheric figurings. One of the first fruits was a pair of aspheric microscopes exhibited at the Physical Society in 1939, and now in the Whipple Science Museum. After the outbreak of war, he worked for the Ministry of Aircraft Production on optical systems for air reconnaissance and other projects. After the war, in addition to theoretical researches, he was concerned with the wide-field wide-aperture meteor cameras then being constructed at Bristol.
In 1948 February, the University of Oxford awarded Linfoot the degree of ScD for his mathematical researches. Shortly after this, 1948 June 1, he was appointed Assistant Director of the Observatories, Madingley Road, Cambridge, and John Couch Adams Astronomer, in succession to Dr H.A.Brück who had resigned to take up the Directorship of the Royal Observatory, Edinburgh. Linfoot remained at Cambridge for the next 22 years until his retirement on 1970 September 30.
Even in pure mathematics, where generality is of the essence, Linfoot was not fully satisfied until he had pursued generalities down to specific cases, and this attitude was invaluable in meeting the needs of practical optics. It also caused him to take a special interest in the application of electronic digital computers, then quite new, to practical problems, and the power and elegance of the programs he wrote for the EDSAC I machine were noteworthy.
Any summary of his rich contribution to astronomical optics must necessarily be over-simplified, but the main elements may perhaps be characterized as synthesis, error-balancing, assessment and testing. The optical designer has so many choices open to him that he is unlikely to chance upon a new and improved configuration unless he is guided by deep theoretical principles, of which that of the Petzval sum leading to the Taylor triplet is an historical example. One of Linfoot's major contributions to synthesis was to apply his formidable analytic ability to the physical concept of the optical plate-diagram of Burch; this led, for example, to much of his work on Schmidt-Cassegrain and related systems. Apart from a few classical cases, moreover, optical systems are always imperfect, and successful design depends on an optimal compromise in balancing the inevitable errors. This in turn requires precise definitions of what is 'best', or in other words a mathematical theory of optical assessment. Linfoot welcomed enthusiastically the ideas of communication and information theory which were particularly current following the publication of C.E.Shannon's Mathematical Theory of Communication in 1948. He was able to unify ray-theoretic and wave-theoretic methods of assessment, and to show that the principal traditional measures of image-quality were all included as linear combinations of only two measures, depending on the extent to which asymmetry of the image was to be penalized. Finally, a theoretical design is of no value unless the optical system can be successfully fabricated. This requires iterative reduction of errors of figure, which in turn is dependent on methods of optical testing. Here again, Linfoot was concerned to provide a soundly-based theoretical approach to the circumstances in which a ray-theoretic approximation could safely be used, and how diffraction effects could be allowed for in other cases. He also placed great emphasis on the need to define adequately the centre of figure of an optical surface, the alignment of complex optical systems such as astronomical telescopes, and similar matters of crucial practical importance.
Fortunately he retained the habit of keeping detailed notebooks, which provide a complete record of his 30 years of work in optics, apart from two volumes relating to the 1950s which are missing. His collaborators during this period included G.Black, P.B.Fellgett, D.G.Hawkins, P.A. Wayman, R.C. Witcomb and E.Wolf. With the encouragement of Professor R.O.Redman, the Director of the Observatories at the time, he studied the diffraction structure of star images in the presence of instrumental aberration and atmospheric seeing, and the effects of asymmetric aberrations in astrometric photography.
Linfoot was elected a Fellow of our Society on 1940 June 12. He served on the Council 1946-50, on the Library Committee 1949-56, and on the Photographic Instrument Committee 1952-56. He was a consultant for the St Andrew's Telescope, the Isaac Newton Telescope, and the Anglo-Australian Telescope, as well as being a consultant to NASA. He was elected Fellow of Wolfson College (then called University College) in 1966. In addition to his numerous publications in the learned literature, he published two books; Recent Advances in Optics in 1955, and Fourier Methods in Optical Image Evaluation in 1964.
Linfoot's health was never robust. His need to reserve his effort for what was of greatest importance could give the impression of a more retiring disposition than he in fact possessed, and this contributed to the sense of intellectual loneliness that he undoubtedly felt even in a great university, particularly among astronomers who in the days before radio astronomy and space research tended towards conservatism of outlook. In his work he was energetic and forthcoming, particularly with his own students whom he treated with courtesy, and a respect which he expected them to reciprocate. His interest in particular cases meant that students and colleagues had the benefit not merely of general precepts but also of being shown how these needed to be applied in detail, both in the scientific work itself and in its presentation for publication. He had no time for what was careless or imprecise. This included what he saw as the falsely egalitarian theories, then gaining currency in education, which he saw as opposed to true equality of opportunity, particularly for the gifted person of humble origins. His theoretical achievements are matters of public record, but only those who were privileged to know him personally can testify to the immense delicacy and practical skill which he brought to the problems of figuring optical surfaces, either working purely by hand or using the various polishing machines he had brought from Bristol, including the famous Hindle machine. He had cultivated tastes not only in music but also in literature and art (he suspected the van Meegeren 'Christ and his Disciples at Emmaus' from the first), and was a connoisseur of chess and of go (wei ch'i). He always retained a certain aura of the worldly-wise urbanity of post 1914-18 Oxford, and it was somehow characteristic of him that when he found his barrel of optical pitch was stove in, but that the pitch flowed out of the hole at about the rate he used it, he let well alone and made no attempt to find another container. His patriotism, already evident in his transfer to optics at Bristol, emerged also after the war when a German optician was visiting the Observatories. Linfoot confided that he judged the visitor to be a Nazi, and would therefore refuse to speak to him in German. However when his master flat was in danger of being scratched by the visitor's attempt to obtain optical contact, an even stronger priority led to an anguished cry of 'Nicht schlieren!'.
Dr E.H.Linfoot died on 1982 October 14 aged 77 years. His contributions to knowledge have already become stepping stones to further advances, and his teaching lives on in pupils who owe much to him and remember him with affection and gratitude.
Any Fellow having any knowledge of Dr Linfoot's missing notebooks is requested to inform the Society. The writer of the above notice gratefully acknowledges the help of information received from Dr J.Bell, Dr D.W.Dewhirst, Mr P.D. Hingley and Mrs J.Linfoot.
P.B.FELLGETT
Edward Hubert Linfoot was born in Sheffield on 1905 June 8 into a musical and mathematical family. He was the eldest child and only son of George Edward Linfoot and his wife Laura, née Clayton. His father had been a boy violinist, and afterwards a mathematics teacher before returning to music as Director of Music for the Sheffield LEA. The son displayed his inheritance of these gifts not only in his mathematical career but also in remaining all his life extremely sensitive to music, particularly J.S.Bach, which he would play on the piano for solace.
Linfoot attended the King Edward VII School in Sheffield where his abilities resulted in him taking the old Higher Certificate three times (obtaining distinctions in all his subjects of Mathematics, Additional Mathematics, Chemistry and German). He had won a Balliol scholarship at the age of 16 but did not matriculate until two years later in 1923. He graduated in 1926 with First Class Honours, and was awarded the degree of DPhil only two years later for a dissertation on almost periodic functions. His Goldsmith Senior Scholarship was then extended to enable him to spend 1928-29 in Göttingen where his already excellent German became fluent. This was followed by the award of a Jane Eliza Procter Fellowship at Princeton University 1929-31, after which he returned to Balliol as a Supervisor until his appointment in 1932 as Assistant Lecturer, and then Lecturer, in Mathematics at the University of Bristol. In 1935 he married Joyce Dancer, herself a distinguished mathematician, whose devoted support was evident to all and for which he expressed deep gratitude. They had a daughter and son born respectively in 1945 and 1947.
One of Linfoot's teachers had been G.H.Hardy, and it is no surprise that his mathematical publications, the first of which appeared when he was still an undergraduate, are in the field of classical analysis, number theory, Fourier transforms and probability. His interests were however extremely wide, extending to mathematical logic, dimension theory and the foundations of quantum mechanics. While an undergraduate, he had developed an individual technique of preparing exemplary notebooks based on lectures, tutorials and his own researches. These notebooks provide one of the best written records of the mathematics of the time, and happily it has been stated that they are to be preserved in the Archives of the London Mathematical Society. Linfoot had been naturally left-handed, but had schooled himself to write with his right hand, and a curiosity of his manuscripts is that he usually used the right hand when using a pen, and the left for pencil.
During the late 1930s, Linfoot's attention gradually switched to optics. The reasons for this are complex. Inspired, as so many proto-astronomers have been, by Albert G.Ingalls' Amateur Telescope Making he had in his teens constructed a small telescope for lunar observations, and this early interest had remained with him. He also foresaw the European conflict to come, and rightly believed that optics would play an important part in it. In addition, his own testimony is that he had come to question his continued creativity in pure mathematics, and it is a tribute to his modesty and courage that he wished others to know how he had recovered from this period of self-doubt, and be encouraged by it. Dr C.R.Burch, who was himself an essentially physical thinker and who had long wished to strengthen the mathematical side of his optics group, encouraged Linfoot's interest and with the approval of Professor Tyndall the facilities of the Physics Department, H.H.Wills Laboratory, were placed at his disposal initially to make a telescope for himself. What had in this way begun as a hobby, happily blossomed into his second professional career. At first, however, he meticulously set about learning the practical skills of figuring optical components, which he found both interesting and restful and only later began to use his mathematical knowledge in the service of practical optics. Linfoot said of this transition that in pure mathematics he needed to learn to think with complete accuracy, whereas in optics he had to learn to think with controlled inaccuracy, and he found this the more difficult of the two.
He was particularly concerned to liberate optics from the historical restriction to spherical surfaces by the introduction of aspheric figurings. One of the first fruits was a pair of aspheric microscopes exhibited at the Physical Society in 1939, and now in the Whipple Science Museum. After the outbreak of war, he worked for the Ministry of Aircraft Production on optical systems for air reconnaissance and other projects. After the war, in addition to theoretical researches, he was concerned with the wide-field wide-aperture meteor cameras then being constructed at Bristol.
In 1948 February, the University of Oxford awarded Linfoot the degree of ScD for his mathematical researches. Shortly after this, 1948 June 1, he was appointed Assistant Director of the Observatories, Madingley Road, Cambridge, and John Couch Adams Astronomer, in succession to Dr H.A.Brück who had resigned to take up the Directorship of the Royal Observatory, Edinburgh. Linfoot remained at Cambridge for the next 22 years until his retirement on 1970 September 30.
Even in pure mathematics, where generality is of the essence, Linfoot was not fully satisfied until he had pursued generalities down to specific cases, and this attitude was invaluable in meeting the needs of practical optics. It also caused him to take a special interest in the application of electronic digital computers, then quite new, to practical problems, and the power and elegance of the programs he wrote for the EDSAC I machine were noteworthy.
Any summary of his rich contribution to astronomical optics must necessarily be over-simplified, but the main elements may perhaps be characterized as synthesis, error-balancing, assessment and testing. The optical designer has so many choices open to him that he is unlikely to chance upon a new and improved configuration unless he is guided by deep theoretical principles, of which that of the Petzval sum leading to the Taylor triplet is an historical example. One of Linfoot's major contributions to synthesis was to apply his formidable analytic ability to the physical concept of the optical plate-diagram of Burch; this led, for example, to much of his work on Schmidt-Cassegrain and related systems. Apart from a few classical cases, moreover, optical systems are always imperfect, and successful design depends on an optimal compromise in balancing the inevitable errors. This in turn requires precise definitions of what is 'best', or in other words a mathematical theory of optical assessment. Linfoot welcomed enthusiastically the ideas of communication and information theory which were particularly current following the publication of C.E.Shannon's Mathematical Theory of Communication in 1948. He was able to unify ray-theoretic and wave-theoretic methods of assessment, and to show that the principal traditional measures of image-quality were all included as linear combinations of only two measures, depending on the extent to which asymmetry of the image was to be penalized. Finally, a theoretical design is of no value unless the optical system can be successfully fabricated. This requires iterative reduction of errors of figure, which in turn is dependent on methods of optical testing. Here again, Linfoot was concerned to provide a soundly-based theoretical approach to the circumstances in which a ray-theoretic approximation could safely be used, and how diffraction effects could be allowed for in other cases. He also placed great emphasis on the need to define adequately the centre of figure of an optical surface, the alignment of complex optical systems such as astronomical telescopes, and similar matters of crucial practical importance.
Fortunately he retained the habit of keeping detailed notebooks, which provide a complete record of his 30 years of work in optics, apart from two volumes relating to the 1950s which are missing. His collaborators during this period included G.Black, P.B.Fellgett, D.G.Hawkins, P.A. Wayman, R.C. Witcomb and E.Wolf. With the encouragement of Professor R.O.Redman, the Director of the Observatories at the time, he studied the diffraction structure of star images in the presence of instrumental aberration and atmospheric seeing, and the effects of asymmetric aberrations in astrometric photography.
Linfoot was elected a Fellow of our Society on 1940 June 12. He served on the Council 1946-50, on the Library Committee 1949-56, and on the Photographic Instrument Committee 1952-56. He was a consultant for the St Andrew's Telescope, the Isaac Newton Telescope, and the Anglo-Australian Telescope, as well as being a consultant to NASA. He was elected Fellow of Wolfson College (then called University College) in 1966. In addition to his numerous publications in the learned literature, he published two books; Recent Advances in Optics in 1955, and Fourier Methods in Optical Image Evaluation in 1964.
Linfoot's health was never robust. His need to reserve his effort for what was of greatest importance could give the impression of a more retiring disposition than he in fact possessed, and this contributed to the sense of intellectual loneliness that he undoubtedly felt even in a great university, particularly among astronomers who in the days before radio astronomy and space research tended towards conservatism of outlook. In his work he was energetic and forthcoming, particularly with his own students whom he treated with courtesy, and a respect which he expected them to reciprocate. His interest in particular cases meant that students and colleagues had the benefit not merely of general precepts but also of being shown how these needed to be applied in detail, both in the scientific work itself and in its presentation for publication. He had no time for what was careless or imprecise. This included what he saw as the falsely egalitarian theories, then gaining currency in education, which he saw as opposed to true equality of opportunity, particularly for the gifted person of humble origins. His theoretical achievements are matters of public record, but only those who were privileged to know him personally can testify to the immense delicacy and practical skill which he brought to the problems of figuring optical surfaces, either working purely by hand or using the various polishing machines he had brought from Bristol, including the famous Hindle machine. He had cultivated tastes not only in music but also in literature and art (he suspected the van Meegeren 'Christ and his Disciples at Emmaus' from the first), and was a connoisseur of chess and of go (wei ch'i). He always retained a certain aura of the worldly-wise urbanity of post 1914-18 Oxford, and it was somehow characteristic of him that when he found his barrel of optical pitch was stove in, but that the pitch flowed out of the hole at about the rate he used it, he let well alone and made no attempt to find another container. His patriotism, already evident in his transfer to optics at Bristol, emerged also after the war when a German optician was visiting the Observatories. Linfoot confided that he judged the visitor to be a Nazi, and would therefore refuse to speak to him in German. However when his master flat was in danger of being scratched by the visitor's attempt to obtain optical contact, an even stronger priority led to an anguished cry of 'Nicht schlieren!'.
Dr E.H.Linfoot died on 1982 October 14 aged 77 years. His contributions to knowledge have already become stepping stones to further advances, and his teaching lives on in pupils who owe much to him and remember him with affection and gratitude.
Any Fellow having any knowledge of Dr Linfoot's missing notebooks is requested to inform the Society. The writer of the above notice gratefully acknowledges the help of information received from Dr J.Bell, Dr D.W.Dewhirst, Mr P.D. Hingley and Mrs J.Linfoot.
P.B.FELLGETT
Edward Hubert Linfoot's obituary appeared in Journal of the Royal Astronomical Society 25:2 (1984), 219-222.