Editing Fresnel lens (section)

== History ==

=== Forerunners ===

The first person to focus a lighthouse beam using a lens was apparently the London glass-cutter Thomas Rogers, who proposed the idea to [[Trinity House]] in 1788.{{r|tag-prior}} The first Rogers lenses, 53{{nbsp}}cm in diameter and 14{{nbsp}}cm thick at the center, were installed at the [[Old Lower Lighthouse]] at [[Portland Bill]] in 1789. Behind each lamp was a back-coated spherical glass mirror, which reflected rear radiation back through the lamp and into the lens. Further samples were installed at [[Baily Lighthouse|Howth Baily]], [[North Foreland]], and at least four other locations by 1804. But much of the light was wasted by absorption in the glass.{{r|tag-prior}}<ref>Levitt, 2013, p.{{nbsp}}57.</ref>

In 1748, [[Georges-Louis Leclerc, Comte de Buffon]] was the first to replace a convex lens with a series of concentric [[Annulus (mathematics)|annular]] prisms, ground as steps in a single piece of glass,{{r|chisholm-1911-lighthouse}}to reduce weight and absorption. In 1790{{r|condorcet-1790}} (although secondary sources give the date as 1773{{r|appleton-1861|p=609}} or 1788{{r|tag-2017}}), the [[Marquis de Condorcet]] suggested that it would be easier to make the annular sections separately and assemble them on a frame; but even that was impractical at the time.{{r|tag-fres}}<ref name=levitt-p71>Levitt, 2013, p.{{nbsp}}71.</ref> These designs were intended not for lighthouses,{{r|chisholm-1911-lighthouse}} but for [[burning glass]]es.{{r|appleton-1861|p=609}} [[David Brewster]], however, proposed a system similar to Condorcet's in 1811,{{r|chisholm-1911-lighthouse|tag-2017|ripley-dana-1879}} and by 1820 was advocating its use in British lighthouses.{{r|chisholm-1911-brewster}}

=== Publication and refinement ===
[[File:Fresnel lighthouse lens diagram.png|thumb|Cross-section of a first-generation Fresnel lighthouse lens, with sloping mirrors&nbsp;''m,{{hsp}}n'' above and below the refractive panel&nbsp;''RC'' (with central segment&nbsp;''A''). The design was later improved by replacing the mirrors with reflective prisms to reduce losses. If the cross-section in every vertical plane through the lamp&nbsp;''L'' is the same (cylindrical symmetry), the light is spread evenly around the horizon.]]

The French {{ill|Commission des Phares|FR|Commission des phares (France)}} (Commission of Lighthouses) was established by Napoleon in 1811, and placed under the authority of French physicist [[Augustin-Jean Fresnel]]'s employer, the Corps of Bridges and Roads. As the members of the commission were otherwise occupied, it achieved little in its early years.<ref>Levitt, 2013, pp.&nbsp;49–50.</ref> However, on 21&nbsp;June 1819—three months after winning the physics {{lang|fr|Grand Prix}} of the Academy of Sciences for his celebrated memoir on [[diffraction]]—Fresnel was "temporarily" seconded to the commission on the recommendation of [[François Arago]] (a member since 1813), to review possible improvements in lighthouse illumination.{{r|tag-fres}}<ref>Levitt, 2013, pp.&nbsp;51, 53; Elton, 2009, p.{{nbsp}}190; Fresnel, 1866–70, vol.&nbsp;1, p.{{nbsp}}xcvii, and vol.&nbsp;3, p.{{nbsp}}xxiv. ("July 21" in Levitt, 2013, p.{{nbsp}}240, is a transcription error, inconsistent with the primary source cited.)</ref>

By the end of August 1819, unaware of the Buffon-Condorcet-Brewster proposal,{{r|tag-fres|ripley-dana-1879}} Fresnel made his first presentation to the commission,<ref>Fresnel, 1866–70, vol.&nbsp;3, pp.&nbsp;5–14; on the date, see p.{{nbsp}}6n. Levitt (2013, p.{{nbsp}}58) gives the date only as August 1819.</ref> recommending what he called {{lang|fr|lentilles à échelons}} ('lenses by steps') to replace the reflectors then in use, which reflected only about half of the incident light.<ref>Levitt, 2013, pp.&nbsp;56, 58.</ref> Another report by Fresnel, dated 29 August 1819 (Fresnel, 1866–70, vol.&nbsp;3, pp.&nbsp;15–21), concerns tests on reflectors, and does not mention stepped lenses except in an unrelated sketch on the last page of the manuscript. The minutes of the meetings of the Commission go back only to 1824, when Fresnel himself took over as Secretary.<ref>Fresnel, 1866–70, vol.&nbsp;3, p.{{nbsp}}6n.</ref> Thus the exact date on which Fresnel formally recommended {{lang|fr|lentilles à échelons}} is unknown.{{citation needed|date=April 2023}} Much to Fresnel's embarrassment, one of the assembled commissioners, [[Jacques Charles]], recalled Buffon's suggestion.<ref name=levitt-p59 /> However, whereas Buffon's version was [[Lens (optics)#Types of simple lenses|biconvex]] and in one piece,<ref>Levitt, 2013, p.{{nbsp}}59. The biconvex shape may be inferred from Buffon's description, quoted in Fresnel, 1822, tr.&nbsp;Tag, at p.{{nbsp}}4.</ref> Fresnel's was [[Lens (optics)#Types of simple lenses|plano-convex]] and made of multiple prisms for easier construction.

With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, found a way to remove defects by reheating and remolding the glass. Arago assisted Fresnel with the design of a modified [[Argand lamp]] with concentric wicks (a concept that Fresnel attributed to [[Benjamin Thompson|Count Rumford]]<ref>Fresnel, 1822, tr.&nbsp;Tag, p.{{nbsp}}11.</ref>), and accidentally discovered that [[fish glue]] was heat-resistant, making it suitable for use in the lens. The prototype, finished in March 1820, had a square lens panel 55{{nbsp}}cm on a side, containing 97 polygonal (not annular) prisms—and so impressed the Commission that Fresnel was asked for a full eight-panel version. This model, completed a year later in spite of insufficient funding, had panels 76{{nbsp}}cm square. In a public spectacle on the evening of 13&nbsp;April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.<ref>Levitt, 2013, pp.&nbsp;59–66. Levitt gives the size of the eight-panel version as {{convert|28+1/3|inch|mm|order=flip|abbr=on}}. Elton (2009, p.{{nbsp}}193) gives it as 76{{nbsp}}cm and indicates that the first panel was tested on 31 October 1820; cf. Fresnel, 1866–70, vol.&nbsp;3, pp.&nbsp;xxxii & xxxiv, and Fresnel, 1822, tr.&nbsp;Tag, p.{{nbsp}}7.</ref>

Soon after this demonstration, Fresnel published the idea that light, including apparently [[polarization (waves)|unpolarized]] light, consists exclusively of [[transverse wave]]s, and went on to consider the implications for [[birefringence|double refraction]] and partial reflection.<ref>A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et&nbsp;seq., ''Annales de Chimie et de Physique'', Ser.{{nbsp}}2, vol.&nbsp;17, pp.&nbsp;102–111 (May 1821), 167–196 (June 1821), 312–315 ("Postscript", July 1821); reprinted in Fresnel, 1866–1870, vol.&nbsp;1, pp.&nbsp;609–648; translated as "On the calculation of the tints that polarization develops in crystalline plates, &amp;&nbsp;postscript", {{Zenodo|4058004}} / {{doi|10.5281/zenodo.4058004}}, 2021.</ref>

Fresnel acknowledged the British lenses and Buffon's invention in a memoir read on 29&nbsp;July 1822 and printed in the same year.<ref>Fresnel, 1822, tr.&nbsp;Tag, pp.&nbsp;2–4.</ref> The date of that memoir may be the source of the claim that Fresnel's lighthouse advocacy began two years later than Brewster's;{{r|chisholm-1911-brewster}} but the text makes it clear that Fresnel's involvement began no later than 1819.<ref>Fresnel, 1822, tr.&nbsp;Tag, p.{{nbsp}}1.</ref>

Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by [[Saint-Gobain]],<ref name=levitt-p71 /> giving eight rotating beams—to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements.{{r|gombert-2017}} This refracted the light to a sloping plane mirror, which then reflected it horizontally, 7&nbsp;degrees ahead of the main beam, increasing the duration of the flash.<ref>Fresnel, 1822, tr.&nbsp;Tag, pp.&nbsp;13, 25.</ref> Below the main panels were 128 small mirrors arranged in four rings, stacked like the slats of a [[louver]] or [[Venetian blind]]. Each ring, shaped like a [[frustum]] of a [[cone]], reflected the light to the horizon, giving a fainter steady light between the flashes. The official test, conducted on the unfinished {{lang|fr|[[Arc de Triomphe]]|italic=no}} on 20 August 1822, was witnessed by the Commission—and by [[Louis XVIII]] and his entourage—from {{convert|20|mi|km|order=flip}} away. The apparatus was stored at [[Bordeaux]] for the winter, and then reassembled at [[Cordouan Lighthouse]] under Fresnel's supervision—in part by Fresnel's own hands. On 25&nbsp;July 1823, the world's first lighthouse Fresnel lens was lit.<ref>Elton, 2009, p.{{nbsp}}195; Levitt, 2013, pp.&nbsp;72–76.</ref> As expected, the light was visible to the horizon, more than {{convert|20|mi|km|order=flip}} out.{{r|watson-1999}}

The day before the test of the Cordouan lens in Paris, a committee of the Academy of Sciences reported on Fresnel's memoir and supplements on double refraction—which, although less well known to modern readers than his earlier work on diffraction, struck a more decisive blow for the wave theory of light.<ref>Buchwald, 1989, pp.&nbsp;260, 288–290, 297; cf.&nbsp;Born & Wolf, 1999, p.{{nbsp}}xxviii.</ref> Between the test and the reassembly at Cordouan, Fresnel submitted his papers on [[photoelasticity]] (16&nbsp;September 1822), [[elliptical polarization|elliptical]] and [[circular polarization]] and [[optical rotation]] (9&nbsp;December), and partial reflection and [[total internal reflection]] (7&nbsp;January 1823),<ref>Fresnel, 1866–1870, vol.&nbsp;1, pp.&nbsp;713–718, 731–751, 767–799.</ref> essentially completing his reconstruction of [[physical optics]] on the [[transverse wave]] hypothesis. Shortly after the Cordouan lens was lit, Fresnel started coughing up blood.<ref name=levitt-p97>Levitt, 2013, p.{{nbsp}}97.</ref>

In May 1824,{{r|ripley-dana-1879}} Fresnel was promoted to Secretary of the {{lang|fr|Commission des Phares}}, becoming the first member of that body to draw a salary,<ref>Levitt, 2013, p.{{nbsp}}82.</ref> albeit in the concurrent role of Engineer-in-Chief.<ref>Elton, 2009, p.{{nbsp}}190.</ref> Late that year, being increasingly ill, he curtailed his fundamental research and resigned his seasonal job as an examiner at the {{lang|fr|[[École Polytechnique]]|italic=no}}, in order to save his remaining time and energy for his lighthouse work.{{r|brock-1909}}<ref>Young, 1855, p.{{nbsp}}399; Boutry, 1948, pp.&nbsp;601–602.</ref>

In the same year he designed the first ''fixed'' lens—for spreading light evenly around the horizon while minimizing waste above or below.{{r|tag-fres}} Ideally the curved refracting surfaces would be segments of [[toroid]]s about a common vertical axis, so that the dioptric panel would look like a cylindrical drum. If this was supplemented by reflecting ([[catoptrics|catoptric]]) rings above and below the refracting (dioptric) parts, the entire apparatus would look like a beehive.<ref>Cf. Elton, 2009, p.{{nbsp}}198, Figure&nbsp;12.</ref> The second Fresnel lens to enter service was indeed a fixed lens, of third order, installed at Dunkirk by 1 February 1825.<ref>Levitt, 2013, p.{{nbsp}}84.</ref> However, due to the difficulty of fabricating large toroidal prisms, this apparatus had a 16-sided polygonal plan.<ref>Elton, 2009, pp.&nbsp;197–198.</ref>

In 1825 Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.{{r|tag-fres}}<ref>Elton, 2009, pp.&nbsp;198–199.</ref>

Also in 1825, Fresnel unveiled the {{lang|fr|Carte des Phares}} ('lighthouse map'), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes called "orders" (the first being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (16 panels).<ref>Levitt, 2013, pp.&nbsp;82–84.</ref>

In late 1825,<ref>Elton, 2009, p.{{nbsp}}200.</ref> to reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a catadioptric prism, through which the light would travel by refraction through the first surface, then [[total internal reflection]] off the second surface, then refraction through the third surface.<ref>Levitt, 2013, pp.&nbsp;79–80.</ref> The result was the lighthouse lens as we now know it. In&nbsp;1826 he assembled a small model for use on the {{lang|fr|[[Canal Saint-Martin]]|italic=no}},{{r|musee}} but he did not live to see a full-sized version: he died on 14&nbsp;July 1827, at the age of 39.

=== After Fresnel ===

The first stage of the development of lighthouse lenses after the death of Augustin Fresnel consisted in the implementation of his designs. This was driven in part by his younger brother Léonor—who, like Augustin, was trained as a civil engineer but, unlike Augustin, had a strong aptitude for management. Léonor entered the service of the Lighthouse Commission in 1825, and went on to succeed Augustin as Secretary.<ref>Levitt, 2013, pp.&nbsp;28, 72, 99.<!-- Elton, (2009, p.190) says Leonor became Secretary in "1837", which is either a mistyping of "1827" or a misreading of the primary source cited. --></ref>

The first fixed lens to be constructed with toroidal prisms was a first-order apparatus designed by the Scottish engineer [[Alan Stevenson]] under the guidance of Léonor Fresnel, and fabricated by Isaac Cookson & Co. using French glass; it entered service at the [[Isle of May]], Scotland, on 22 September 1836.<ref>Elton, 2009, pp.&nbsp;199, 200, 202; Levitt, 2013, pp.&nbsp;104–105.</ref> The first large catadioptric lenses were made in 1842 for the lighthouses at Gravelines and [[Île Vierge]], France; these were fixed third-order lenses whose catadioptric rings (made in segments) were one metre in diameter. Stevenson's first-order [[Skerryvore]] lens, lit in 1844, was only partly catadioptric; it was similar to the Cordouan lens except that the lower slats were replaced by French-made catadioptric prisms, while mirrors were retained at the top. The first ''fully'' catadioptric first-order lens, installed at Pointe d'Ailly in 1852, also gave eight rotating beams plus a fixed light at the bottom; but its top section had eight catadioptric panels focusing the light about 4&nbsp;degrees ahead of the main beams, in order to lengthen the flashes. The first fully catadioptric lens with ''purely revolving'' beams—also of first order—was installed at [[Saint-Clément-des-Baleines]] in 1854, and marked the completion of Augustin Fresnel's original ''Carte des Phares''.<ref>Levitt, 2013, pp.&nbsp;108–110, 113–116, 122–123. Elton (2009, p.{{nbsp}}208) notes that although the Skerryvore lens was lit on 1&nbsp;February 1844, the catadioptric portion was yet to be added.</ref>

[[Thomas Stevenson]] (younger brother of Alan) went a step beyond Fresnel with his "holophotal" lens, which focused the light radiated by the lamp in nearly all directions, forward or backward, into a single beam.<ref>Elton, 2009, pp.&nbsp;209–210, 238.</ref> The first version, described in 1849, consisted of a standard Fresnel bull's-eye lens, a paraboloidal reflector, and a rear hemispherical reflector (functionally equivalent to the Rogers mirror of 60&nbsp;years earlier, except that it subtended a whole hemisphere). Light radiated into the forward hemisphere but missing the bull's-eye lens was deflected by the paraboloid into a parallel beam surrounding the bull's-eye lens, while light radiated into the backward hemisphere was reflected back through the lamp by the spherical reflector (as in Rogers' arrangement), to be collected by the forward components. The first unit was installed at North Harbour, [[Peterhead]], in August 1849. Stevenson called this version a "catadioptric holophote", although each of its elements was either purely reflective or purely refractive. In the second version of the holophote concept, the bull's-eye lens and paraboloidal reflector were replaced by a catadioptric Fresnel lens—as conceived by Fresnel, but expanded to cover the whole forward hemisphere. The third version, which Stevenson confusingly called a "dioptric holophote", was more innovative: it retained the catadioptric Fresnel lens for the front hemisphere, but replaced the rear hemispherical reflector with a hemispherical array of annular prisms, each of which used ''two'' total internal reflections to turn light diverging from the center of the hemisphere back toward the center. The result was an all-glass holophote, with no losses from metallic reflections.<ref>Elton, 2009, pp.&nbsp;210–213.</ref>

[[James Timmins Chance]] modified Thomas Stevenson's all-glass holophotal design by arranging the double-reflecting prisms about a vertical axis. The prototype was shown at the [[1862 International Exhibition]] in London. Later, to ease manufacturing, Chance divided the prisms into segments, and arranged them in a cylindrical form while retaining the property of reflecting light from a single point back to that point. Reflectors of this form, paradoxically called "dioptric mirrors", proved particularly useful for returning light from the landward side of the lamp to the seaward side.<ref>Elton, 2009, pp.&nbsp;221–223.</ref>

[[File:Fresnel Lens at Point Arena Lighthouse Museum.jpg|thumb|First-order group-flashing Fresnel lens, on display at the Point Arena Lighthouse Museum, [[Point Arena Light]]house, [[Mendocino County, California]]. The three dioptric panels (inside the brass rings) and three catadioptric panels (outside) are partly split in two, giving three double-flashes per rotation.]]

As lighthouses proliferated, they became harder to distinguish from each other, leading to the use of colored filters, which wasted light. In 1884, [[John Hopkinson]] eliminated the need for filters by inventing the "group-flashing" lens, in which the dioptric and/or the catadioptric panels were split so as to give multiple flashes—allowing lighthouses to be identified not only by frequency of flashes, but also by multiplicity of flashes. Double-flashing lenses were installed at Tampico (Mexico) and [[Little Basses Reef Lighthouse|Little Basses]] (Sri&nbsp;Lanka) in 1875, and a triple-flashing lens at [[Casquets lighthouses|Casquets Lighthouse]] ([[Channel Islands]]) in 1876.<ref>Elton, 2009, pp.&nbsp;227–230; Levitt, 2013, p.{{nbsp}}219.</ref> The example shown (right) is the double-flashing lens of the [[Point Arena Light]], which was in service from 1908 to 1977.<ref>Point Arena Lighthouse Keepers, Inc., [https://www.pointarenalighthouse.com/about/lighthouse-history/ "Lighthouse History"] {{Webarchive|url=https://web.archive.org/web/20210119171021/https://www.pointarenalighthouse.com/about/lighthouse-history/ |date=19 January 2021 }}, accessed 1&nbsp;March 2021.</ref>

The development of hyper-radial lenses was driven in part by the need for larger light sources, such as gas lights with multiple jets, which required a longer focal length for a given beam-width, hence a larger lens to collect a given fraction of the generated light. The first hyper-radial lens was built for the Stevensons in 1885 by [[Barbier, Benard, et Turenne|F.&nbsp;Barbier & Cie]] of France, and tested at [[South Foreland Lighthouse]] with various light sources. [[Chance Brothers]] (Hopkinson's employers) then began constructing hyper-radials, installing their first at [[Bishop Rock, Isles of Scilly|Bishop Rock]] Lighthouse in 1887.<ref>Elton, 2009, p.{{nbsp}}233; Levitt, 2013, pp.&nbsp;222–224.</ref> In the same year, Barbier installed a hyper-radial at [[Tory&nbsp;Island]]. But only about 30 hyper-radials went into service{{r|tag-hyper}} before the development of more compact bright lamps rendered such large optics unnecessary (see ''[[Hyperradiant Fresnel lens]]'').

Production of one-piece stepped dioptric lenses—roughly as envisaged by Buffon—became feasible in 1852, when John L. Gilliland of the [[Corning Inc.|Brooklyn Flint-Glass Company]] patented a method of making lenses from pressed and molded glass. The company made small bull's-eye lenses for use on railroads, steamboats, and docks;{{r|tag-us}} such lenses were common in the United States by the 1870s.{{r|ripley-dana-1879|p=488}} In 1858 the company produced "a&nbsp;very small number of pressed flint-glass sixth-order lenses" for use in lighthouses—the first Fresnel lighthouse lenses made in America.{{r|tag-us}} By the 1950s, the substitution of plastic for glass made it economic to use Fresnel lenses as condensers in overhead projectors.<ref>A. Finstad, "New developments in audio-visual materials", ''Higher Education'', vol.&nbsp;8, no.{{nbsp}}15 (1&nbsp;April 1952), pp.&nbsp;176–178, at p.{{nbsp}}176.</ref>