Editing Fresnel lens (section)

=== 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.