Reflective Telescopes

• Nicolas Zucchi [132, 170] made the first attempt to build a reflecting telescope in 1616, i.e. soon after Galileo developed the refractor. He states that he procured a bronze concave mirror "executed by an experienced and careful artist in the trade" and used it directly with a Galilean eyepiece. In order to avoid obstruction by the observer's head, his design introduced a significant beam deviation at the mirror, similarly to the front-view type later introduced by W. Herschel. Depending on the mirror f-ratio (which is not known), the coma and astigmatism due to this deviation may have partly deteriorated the image quality. The attempt failed; however it is generally assumed that in fact the mirror figuring was of poor quality.

5 Unfortunately in his analysis Szulc did not take the correct Kerber's value for the zonal ray height ratio hK/hmax. However, Szulc's comments leading to the non-Gaussian achromatism condition, K1/V1 + K2/V2 = Sz/f'2, are of great historical interest.

Reflective Optics
Fig. 1.6 Afocal two-mirror telescopes by Mersenne in L'Harmonie Universelle [108]. Forms 1 and 2 are the Cassegrain and Gregory afocal limit forms (facsimile in Danjon & Couder [44])

• Marin Mersenne (1588-1648) published L'Harmonie Universelle [108] in 1636, in which he introduced the afocal forms of two-mirror reflectors (Fig. 1.6). As noted by Wilson [170], "the full significance of novel and remarkable features presented in Mersenne's works - although often referred to - certainly could not be fully appreciated by Mersenne and his contemporaries." His confocal paraboloid concept may today be described by the following features:

(a) This is the first telescope proposed combining two mirrors.

(b) It includes forms later introduced by Gregory and Cassegrain as afocal limit forms.

(c) It includes two other afocal forms which are retro-reflective (cf. Sect. 2.3).

(d) With enough beam compression, and similarly to the Galileo refractive form, the Cassegrain and Gregory designs are directly usable for observing a small field of view.

(e) The Cassegrain afocal form, as well as its focal form which can be immediately derived from it, appears to provide a larger telephoto effect than the Gregory, i.e. the resulting focal length is larger compared to the instrument length. This is a fundamental feature in the development of large and compact reflectors. However, its importance was not emphasized by Descartes, nor by Newton.

(f) In forms 1 and 2, the paraboloid confocal pair provide aberration corrections other than just spherical aberration only: third-order coma and astigmatism are also corrected.

For these features, Mersenne must be credited for inventing the basic geometrical form of the modern telescope [170]. It was demonstrated in the mid-twentieth century - i.e. more than 300 years later - from on-axis and field aberration analysis, that Mersenne's forms 1 and 2 are aplanats but also anastigmats, i.e."quasi-perfect" optical systems (cf. Sect. 2.3). These remarkable properties escaped Schwarzschild who in 1905 elaborated the two-mirror telescope theory, Chretien who investigated two-mirror aplanatic systems, and also escaped Paul with his three-mirror theory.

Although potentially included in these theories, quite surprisingly none of these authors derived the specific properties of Mersenne afocal systems.

• James Gregory (1638-1675) proposed a two-mirror reflector in his Optica Promota (1663): a paraboloidal concave mirror provides a primary focus which is re-imaged by an ellipsoidal concave mirror located after this focus. The resulting focus - the ellipsoid conjugate focus - is formed back towards the paraboloid mirror where a hole in this mirror allows the light to emerge for using an eyepiece [85]. As mentioned above, the stigmatic property of a parabola was demonstrated by the Greek geometer Diocles. However, in the case of finite conjugates, it remains unclear whether the stigmatic properties for the ellipse and hyperbola were known by his successors of the second Alexandrian school such as Pappus (290-350) or the first known female mathematician Hypatia (~370-415). Gregory sub-contracted the figuring of a low f-ratio mirror - which would not require any aspherization - but his attempt ended with useless results.

• Isaac Newton (1643-1727) presented his second reflector to the Royal Society in 1672 (Fig. 1.7): The beam reflected from a concave paraboloid mirror is focused

Fig. 1.7 Newton's reflecting telescope with the original mirror and eyepiece (The Royal Society, from King [85])

at the side on the tube side via a small flat mirror before the focus inclined at 45°. The concave mirror, 34 mm in diameter, was used with a 25 mm clear aperture; its 175 mm focal length - f/7 reflected beam - did not require any aspherization. A positive-lens eyepiece of 5 mm focal length provided a magnification of 35. Newton succeeded in polishing a sufficiently good spherical surface by himself. He explains his choice of speculum metal for the mirrors (bell-metal or CuSn25 alloy i.e bronze [115]), and proposed adding arsenic for a better polish. In 1704, he wrote that he used pitch polishers [85]; this appears to be the first written mention of pitch polishers for metal mirrors. Although Newton's two telescopes remained demonstration models only, his selective process leading to the speculum metal marked an unrivalled progress in mirror figuring technology.

• Laurent Cassegrain (1629-1693) proposed a more compact form of two-mirror reflector: A convex mirror is located before the focus of the beam reflected by a concave mirror. The resulting focus - the hyperboloid conjugate focus - is formed back towards the concave mirror through a hole which allows the light to emerge for using an eyepiece (Fig. 1.8). He confided a resume of the principle to de Berce who described it to the French Academy in 1672. The description of the telescope published in Journal des Scavans [27] was de Berce's, who introduced it as "plus spirituel" (more astute) than Newton's reflector. Subsequently, Newton (and also Huygens) criticized Cassegrain's proposal with a list of disadvantages compared to his own design or Gregory's; he did not see that Cassegrain's more compact design could be a fundamental advantage - providing a larger telephoto effect - in the development of large reflectors. Added to the context was the fact that Descartes favored the development of lenses. Under these circumstances Cassegrain never attempted

Elaboration Spherical Mirror
Fig. 1.8 Gregory, Newton, and Cassegrain forms of two-mirror telescopes. P: paraboloid, E: ellipsoid, H: hyperboloid

to build his reflector. The first historical account on Cassegrain has been recently given by A. Baranne and F. Launay [10].

The whole basic framework - theory as well as speculum mirror surfacing techniques - for the development of two-mirror metal reflectors was completely established by these four latter scientists. In 1674, Robert Hooke built with some success a 180 mm aperture Gregorian with an output beam at f/15. In 1721, John Hadley realized a 150 mm aperture Newtonian at f/10 and also built several small Cassegrain and Gregorian reflectors. Around 1740, James Short became a renowned reflector maker in London allowing him to progressively develop an industry which built more than a thousand reflectors. Up to 1768, he proposed in his catalog [85] 12 differing aperture diameters from 28 to 450 mm, primary mirror f-ratios from f/3 to f/8, and eyepieces magnifying from 18 to 1,000 times. Short was involved in metallurgy in order to cast fine speculum mirror blanks; he also developed accurate mechanical systems to keep the Gregorian mirrors aligned when focusing. ClaudeSimeon Passement, Engineer of King Louis XV and scientific instrument maker, built microscopes and many Gregorian telescopes in the period 1730-1769.

Now, it must be noted that the early success of the Gregorian form is due to the fact that an erect image is viewed - instead of an inverted image as in the Newton or Cassegrain forms -, which better satisfied the public demand for terrestrial observing.

• William Herschel (1738-1822), after concluding in 1773 that available telescopes were not convenient enough for astronomical observations, invested himself in the design and construction of reflectors. He patiently and accurately ground various concave speculum mirrors of 220 mm aperture, from f/7 to f/15, using convex metal tools, starting with emery, and ending with pitch polishers. After succeeding in casting large speculum disks and building a polishing machine, Herschel completed his 1.22 m - f/10 aperture reflector (40-foot telescope) in 1789, which was last used in 1815. That same year (1789) he completed the construction of the famous 0.47 m - f/13 aperture reflector (20-foot telescope), which he observed with until 1826 and which was later used by his son John Herschel in South Africa (1834-1838). Having low f-ratios, most of Herschel's reflectors used a direct "frontview" vision at the upper end of the tube (Figs. 1.9 and 1.10): the focal surface was set near the tube wall by a convenient mirror tilt. H. Draper later commented on Herschel front-view telescopes that his mirrors showed astigmatism from figuring so that he compensated or at least minimized the astigmatism of all tilted beams by choosing the best azimuth position of the mirror. Assuming that the mirror perfectly corrected the front-view astigmatism by a toroid deformation, his 40- and 20-foot reflectors gave, at the eyepiece center, a coma of 5.9 and 3.1 arcsec rms, respectively.

• Lord Rosse i.e. William Parsons (1800-1867), after constructing several telescopes, undertook the development of larger size reflectors. He erected a foundry, workshops and a polishing machine that was powered by a steam engine. In 1839, he completed a reflector with a 0.91 m - f/13 aperture spherical mirror in a CuSn32 speculum alloy. The next year he undertook the construction of a 1.83 m - f/10

Lord Rosse Teliscope
Fig. 1.9 (Right) W. Herschel 40-foot focal length telescope (from King [85]). (Left) Lord Rosse's 6-foot or 1.83-m aperture telescope (from Imago Mundi)

aperture Newtonian reflector which was put into service in 1847 (Fig. 1.9). Because the mirror tarnished rapidly in the air, it had to be repolished every six months; thus two mirrors were built so that one could be used while the other was being repolished. This reflector was also used by many other scientists and operated until 1878. Although the Irish sky allows only a few observable nights, Lord Rosse obtained excellent images of nebulae and spiral galaxies. He discovered an extended ring object he named the Crab Nebula, and the spiral structure of galaxies, detecting the Whirlpool Galaxy M51 and many others he drew with fine details closely resembling photographs.

• William Lassel (1799-1880), in 1859, completed a 1.22 m - f/9.5 aperture Newtonian reflector with an equatorial mount which was used in Malta until 1865. In order to minimize the deformation due to gravity, he invented for it the astatic levers mirror support system - replacing the system by stacked triangles or whiffletrees -where each weight on a lever generates an amplified force proportional to the cosine of zenith angle. His system came into general use for all large reflectors with passive support.

Active Optical System Astronomy
Fig. 1.10 Optical arrangement of Herschel front-view telescope. Cassegrain telescope with Nas-myth foci/

• James Nasmyth (1808-1890), in 1845, designed and built a 0.51m aperture f/9 - f/25 modified-Cassegrain reflector with an alt-az mount and with a third plane mirror giving a 90° deviation. This tertiary mirror, located at the node of the axes, provided horizontal focused beams he observed in a fixed position through the hollow altitude axis while seated on the rotating azimuth platform. This was the first large telescope of Cassegrain form. From the point of view of residual aberrations, if one assumes that his primary and secondary mirrors were both spherical, it provided paraxial images of 1.7 arcsec in diameter. His three-mirror concept - providing the now-called Nasmyth foci (Figs. 1.10 and 1.11) - always associates an alt-az mount and has now become of general use for all large reflectors over 5 m aperture.

From the focal ratios of the above constructed reflectors, it can be seen that the size of axial image residuals are in accordance with an atmospheric seeing limitation of 2-3 arcsec for mirrors simply requiring an accurate spherical polishing. Considering a conicoid mirror (Sect. 1.7), the theoretical asphericity correction of fourth degree - i.e. when unbalanced with a curvature term - can be expressed by

where Q = f /D and k are the f-ratio and conic constant (cf. Sect. 1.7).

For all reflectors by Short, the 1.22 m - f/10 by Herschel and the 1.83 m - f/10 by Rosse, this asphericity amplitude zmax is smaller than 1 - 1.5 ¡m. Aspheriz-ing these mirrors would not have significantly improved the 1.5-2 arcsec image

Bedford Planetarium

Fig. 1.11 (Left) Nasmyth's 20-inch aperture telescope (from King [85]). aperture telescope (Marseille Observatory)

(Right) Foucault's 0.8-m

Fig. 1.11 (Left) Nasmyth's 20-inch aperture telescope (from King [85]). aperture telescope (Marseille Observatory)

(Right) Foucault's 0.8-m quality because of the seeing limitation. In a Cassegrain form with spherical mirrors, the spherical aberration of the primary is partly compensated by the secondary. Because of the lack of accurate testing methods and the necessity to frequently re-polish speculum mirrors because of tarnishing, spherical figuring was the only way to promptly overcome those difficulties. For a long time, the surfacing problem of mirrors has not been the inability of executing a correct aspherization, but the inability to execute a sphere:

^ The period of reflectors with "spherical or quasi-spherical mirrors" ended around I860 when Foucault obtained accurate paraboloids by introducing the powerful knife-edge optical test.

• Leon Foucault (1819-1868) applied Drayton's chemical process of cold silvering on Saint-Gobain glass disks polished by Secretan-Eichens and concluded that the method could be easily repeated on similar glass mirrors because glass is chemically neutral. The silver is deposited from a solution of silver nitrate and ammoniac when reduced by glucose [60, 160]. Steinheil, in Munich, had previously obtained silver-on-glass mirrors using Liebig's process; however, this was by hot silvering i.e. requiring the risky use of a boiling solution. Compared to the tarnishing of speculum mirrors, silver-on-glass mirrors eliminated the repol-ishing problem; chemical removal of the tarnished silver layer conserves the original polished shape of the glass even after many repeated re-silverings. In 1858, at the suggestion of Moigno, Foucault examined the shape of a 36 cm aperture mirror reputed to be spherical. With the sensitive optical knife-edge test he had just invented, he found an axisymmetric center-edge defect. Instead of re-figuring the entire mirror surface as was the usual practice, Foucault proceeded by local retouches and in a few hours obtained a perfectly spherical mirror; he states that "local retouch method [is] ... an established fact" [160]. A basic quantitative Foucault test uses a multi-aperture screen placed in front of the mirror; the screen defines radial and concentric aperture zones with radial widths set narrower from center to edge. The mirror is illuminated by a source-slit and some reflected beams can be intersected by a mobile knife-edge when observing through an eyepiece. Assuming that the slit and knife-edge are maintained on a same line and that the aperture zones expand in a perpendicular direction to it, appropriate axial and lateral displacements of the knife-edge allow one to observe the simultaneous auto-collimation of two symmetric given zones. The correct set up of the axial position of a focused zone is obtained if the light vanishes totally in a tiny movement of the knife. The table of successive axial positions of the auto-collimated knife-edge with respect to corresponding aperture-zone radii allows determining the mirror shape in one direction. Foucault thus obtained an accurate quantitative tool for aspherization control. In collaboration with Secretan and Eichens, a 40-cm aperture silver-on-glass reflector was completed in 1858 and presented before the French Academy [59]. This collaboration continued with an 80-cm aperture-f/5.7 reflector; the Saint-Gobain glass disk, twice as thick at center as at edge, was retouched by Foucault to a quite exact paraboloid shape - i.e. a 4.3 ¡im asphericity in r4. The telescope focus was located inside

(or near) a total reflection prism at the head-ring center; an f/5.7-f/20 focal expander re-imaged the focus which then was observed at the side of the tube (Fig. 1.11).6

• George Airy (1801-1892) showed, in 1835 [2], that with perfect seeing conditions, such as close to vacuum conditions, a circular mirror (or a lens) cannot provide an infinitely small image of a point. The observed image at the Gaussian focus is an interference pattern formed of a bright central peak surrounded by concentric rings. Airy calculated the intensity distribution at the diffracted image. Considering a mirror of diameter D, used at wavelength X, which provides perfect spherical wavefronts converging to a Gaussian focus, the maximum resolution of diffraction limited images (cf. Sect. 1.11) is the angle

For instance, a 27-cm aperture telescope used at 0.55-nm wavelength with perfect images just resolves two stars separated of 0.5 arcsec.

• William Rowan Hamilton (1805-1865) published, in 1833 [71, 170], the first and famous analysis of the geometrical theory of aberrations by introducing characteristic functions. In the case of centered optical systems, he deduced the general form of the aberration function in terms of a power series using three fundamental parameters: the aperture radius, the field radius, and the azimuth angle.

• Joseph Petzval (1807-1891) investigated with considerable success the third-order aberrations for the new task of designing large aperture and wide field objectives for photography. Unfortunately, his extensive manuscript on the subject was destroyed by thieves and he never rewrote it; he demonstrated the practical value of his analysis by constructing, around 1840 [17], an unrivaled "portrait lens." Petzval was probably the first to have derived the two coupled coefficients which simultaneously define primary astigmatism and field curvature. In anastigmatic systems, the field curvature is often called Petzval's curvature.

• Ludwig von Seidel (1821-1896), in 1856 [144], elaborated the first formal analysis of the five monochromatic third-order aberrations by explicitly expressing their amounts introduced by a given surface. Thus, summing them independently through the system, the Seidel sums allows deriving its general properties.

6 The telescope life extended from 1864-1965 in the Marseille Observatory with research on nebulae, galaxies, and double stars. Stephan did the first trials to measure stellar diameters from modified fringe patterns as predicted by Fizeau; unfortunately, the two-aperture base allowed by the mirror was too small, and he concluded in 1874 that stellar diameters must be smaller than 0.16 arcsec (Stephan [148]) (the first stellar diameters were resolved in 1922 by Michelson with the Hooker telescope and enlarging base). Later, the first astrophysical images with narrow-band etalons were obtained by Fabry, Perot, and Buisson. In both Foucault's 40- and 80-cm reflectors, the mirror was supported by an inflatable cushion in which the observer blew in or let out some air until obtaining a satisfactory image. This supporting concept was next used by Henry Draper in the USA [48].

• Ernst Abbe (1840-1905), in 1873 [1], discovered the condition for a system to satisfy both the correction of primary spherical aberration - stigmatism - and primary coma, thus providing aplanatism. Using large aperture microscopes, the botanist J. Lister had previously noticed their unexpected image quality and concluded that more than the spherical aberration was corrected. The Abbe sine condition is an important theorem in optical design. Considering the axial beam, this can be stated as follows: if the surface generated by the locus of the intersection points of incident rays and emergent conjigates is a sphere, then the system is aplanatic.

• Lord Rayleigh (1842-1919) showed, in 1879 [123], that if tolerating a 20% light decrease in the intensity at the central peak, then the corresponding departure from the Gaussian reference sphere amounts to a quarter of a wavelength in terms of primary spherical aberration. It was further shown that for primary coma and astigmatism, the peak intensity is less affected by such a quarter wave deformation. Hence, this result became known as Rayleigh's quarter wave criterion, one of the simplest and most useful rules among the various tolerance criteria which have been formulated [17]).

• Georges Ritchey (1864-1945) was an uncontested expert in optical polishing, in the design and construction of surfacing machines, and in the development and practice of accurate optical testing. He had a remarkable ability to achieve the important features making new giant reflectors a complete success. After completing the optics of the 60-inch reflector for Mount Wilson, he succeeded with those of the 100-inch Hooker Reflector in 1917. His deep understanding and interest in the advantages of aplanatic systems, and his encouragement of Chretien, led to the Ritchey-Chretien form, whose second prototype was a 1-m aperture reflector (Fig. 1.12).

• Karl Schwarzschild (1873-1916), known for his first-rank achievements in several fields of physics, formulated the complete third-order theory of one- and two-mirror systems in 1905 [142]. His eikonal method allowed him to determine the amount of each third-order aberration in a given point of the field. From his general formulation, he derived the two-mirror cases for an object at infinity. He discovered that for any two-mirror anastigmat telescope, the axial separation of the mirrors must be twice the system focal length. Most of these anastigmatic systems are described in Sect. 4.1.

• Henri Chretien (1879-1956) elaborated the complete theory of two-mirror telescopes satisfying the sine condition, thus corrected from all-order spherical aberration and all-order linear coma. Apparently before 1910, he derived the theoretical shape of the mirrors by integrations of differential equations including this condition. This led him to formalize the so-called mirror parametric equations. From these results, he derived the third- and fifth-order theory for the Cassegrain and Schwarzschild forms. In the Cassegrain aplanatic telescope - known as the Ritchey-Chretien telescope - Chretien derived accurate representations of the primary and secondary mirrors as hyperboloids. These studies were published in two articles in 1922 [30]. Aware of all sorts of optical systems and of their key points for aberration correction, Chretien also invented spectacular anamorphotic systems known

1910 Binoculars

Fig. 1.12 The 1-m Ritchey-Chretien Reflector, primary mirror f/4, Cassegrain focal ratio f/7.3, focal plane scale 28arcsec/mm. Designed by George W. Ritchey, and completed in 1934, it was originally installed at the US Naval Observatory in Washington D.C. and then relocated to Flagstaff in 1955 (after Chretien [29])

Fig. 1.12 The 1-m Ritchey-Chretien Reflector, primary mirror f/4, Cassegrain focal ratio f/7.3, focal plane scale 28arcsec/mm. Designed by George W. Ritchey, and completed in 1934, it was originally installed at the US Naval Observatory in Washington D.C. and then relocated to Flagstaff in 1955 (after Chretien [29])

as Cinemascope for movie panoramic recording and projection. His famous "Calcul des Combinaisons Optiques" [29], reissued several times, is a brilliant and profound exposition of all useful properties of optical systems; it also contains many invaluable historical notes. Chretien is a co-founder of the Institute of Optics which was created in 1920 in Paris.

• Bernhard V. Schmidt (1879-1935) invented, in 1929, a new class of reflector called wide field telescopes or wide field cameras. In Hamburg he built the first such reflector using a 36 cm aperture aspherical corrector plate and obtained perfect image quality on curved photographic films over an entire 7.5° field of the sky. Schmidt telescopes quickly became of primordial use to establish complete cartographies of the sky. Associated with the Palomar 5-m telescope, the Palomar 1.2 m aperture Schmidt was built for this complementary task with 5° field surveys (cf. Chaps. 4 and 5). The situation changed with large-format CCDs which require a flat field of view. FOV of 1.5 or 2° can be provided by a Ritchey-Cretien telescope with two mirrors of the same curvature, equipped with a Gascoigne two-plate astigmatism corrector. With such a 2.5 m telescope, the Sloan Digital Sky Survey (Sdss) uses time-delay-and-integrate imaging - or drift scan imaging as is also used by liquid mirror telescopes (Lmts) - and produces multi-passband surveys and fiber-fed spectrograms. All-reflective Schmidt systems bring an efficient solution for a telescope dedicated to wide-field spectroscopic surveys with 4,000 optical fibers motorized on a 5° FOV, Lamost is the telescope showing the largest optical etendue (cf. Sect. 1.9.3 and Chaps. 4 and 5).

The reflector projects with 1-1.5 m diameter glass mirrors undertaken in France after Foucault and up to 1907 ended in fiascos. Finally, the glass mirror concept was scaled up in the USA for successive 1.5 and 2.5 m reflectors at Mount Wilson using Saint-Gobain blanks. Pyrex glass material was developed for the Palomar 5-m and Caucasus 6-m, and Zerodur vitroceram for the Vlt's four 8.2-m blanks. Some historical telescopes built in the period 1900-2008 are listed in Table 1.1.

• Fritz Zernike (1888-1966) initially developed, in 1934 [178], the phase-contrast method in order to improve the Foucault test. His important contribution to diffraction theory led him to the invention of the phase-contrast microscope for which he received the Nobel prize. Zernike also invented the orthogonal polynomials for representing wavefront surfaces now in general use in optical testing.

• Maurice Paul (1890-1981), a pupil of Chretien, published, in 1935 [170, 178], a general analysis of three-mirror telescopes. He investigated such anastigmatic systems and critically analyzed the cases of aspheric plates and lenses for field correction.

• Albert Bouwers (1893-1972) introduced, in 1948 [19], a concentric meniscus lens for wide-field catadioptric cameras using a spherical concave mirror. These systems were used in astronomy for panoramic imaging and spectrograph cameras.

• Dimitri Maksutov (1896-1964) invented, in 1944 [100], independently of Bouwers, catadioptric cameras using a null power lens for correcting the spherical aberration of a concave mirror. His system was widely built for astronomical purposes.

• Andre Couder (1897-1979) invented a two-mirror anastigmat telescope with a concave secondary: Couder's telescope (cf. Sect. 4.1) is an outgrowth of the Schwarzschild theory of two-mirror telescopes. Inventing the null test method for large mirrors (1927), he made many contributions to the development of reflectors, such as proposing the Couder law for mirror support systems and advocating vase form metal mirrors plated with enamel (cf. Sects. 7.2 and 8.2).

• Cecil R. Burch (1901-1983) described a two-mirror Schwarzschild design which led to the development of reflective microscope objectives. In 1943, Burch published a powerful method for treating the Seidel aberrations of an optical system that he called a "see-saw diagram" [23] or diagram of Schmidt plates. Burch's method has been and is still used for searching for aplanatic or anastigmatic solutions.

Table 1.1 Some historical reflectors built in the period 1900-2008

Year

Apert.[m]

Name, Location

Type

f-ratio

Mount

Focus

+1 0

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  • sante
    How to make concave surface from hyperboloid in mirrors?
    2 years ago

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