Chapter 4b

From: Subject: Chapter 4b Date: Tue, 22 May 2007 22:04:40 +0200 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C79CBD.31D0D4B0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3028 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C79CBD.31D0D4B0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://alice.as.arizona.edu/~rogerc/chapters/Chapter%204b.html Chapter 4b Chapter 4b. Survey of Apochromats (Triplet=20 Systems).

Triplets form the mainstay of present = day=20 apochromatic designs. This is because by adding a third element it = becomes=20 much easier to manufacture high-performance lenses cost-effectively; and = more=20 combinations of glasses are available to do the job. Yet even here = there=20 are limits as one pushes for faster and faster focal ratios. If=20 diffraction limited performance and exquisite color correction are = demanded at=20 f/7 for a 150mm lens, then it may be necessary to add a fourth=20 element. Or a radical departure from the closely = spaced lens=20 arrangements which we have seen so far may also be contemplated. = The=20 Petzval lens in which there are two widely separated doublets may prove = helpful=20 (cf. Chapter 5). Of the rich variety possible in three-element = lens=20 combinations, we will survey a sampling in the present = chapter.

Harold=20 Dennis Taylor developed and patented the first practical triplet in 1892 = [British Patent no. 17994; cf. S. Czapski & O. Eppenstein,=20 Grundz=FCge der Theorie der optischen Instrumente nach = Abbe, 3rd ed.=20 (Verlag J.A. Barth, 1924), p. 567; H. Chr=E9tien, Calcul des = combinaisons=20 optiques, 4th ed. (Paris, 1958), pp. 261-267; and G.R. Nankivell, = "The Cooke=20 Photovisual Objective and the 22.9cm Refractor at the Carter = Observatory, New=20 Zealand," Journal of the Antique Telescope Society 24 (2002), pp. = 4-8].=20 He seems to have been alerted to the possibility of making a = triplet=20 through the published writings of Abbe and Hastings [cf. H.D. Taylor,=20 Adjustment and Testing of Telescope Objectives, 5th ed. (Adam = Hilger,=20 1983), pp. 78-87, especially p. 79; and C.S Hastings, "On Triple = Objectives with=20 complete Color Correction," The American Journal of Science and = Arts,=20 3rd series, vol. 18 (1879), pp. 429-435]. In 1894, Taylor = published a=20 detailed description of his triplet, specifying the glass types, their = order in=20 the construction, and the relationships of their surface curves. = He also=20 illustrated his lens with a layout [cf. H.D. Taylor, "Description of a = Perfectly=20 Achromatic Refractor," Monthly Notices of the Royal Astronomical = Society=20 54.5 (1894), pp. 328-337; reprinted in Adjustment and = Testing,=20 pp. 78-87, especially pp. 82-83].

The glass types in = question were=20 all "ordentlich" or "regular" types produced at the time by Schott. = Facing=20 the sky came a light barium flint (O.543); in the middle a borosilicate = "short=20 flint" (O.164); and on bottom a light silicate crown (O.374). = O.164 was a=20 replacement for O.658, an earlier borosilicate short-flint which Taylor = had=20 specified in his patent. O.164 allowed somewhat better correction = than=20 O.658. Henri Chr=E9tien, the French optical designer, studied = Taylor's=20 objective and has left an interesting discussion about it [cf. = Chr=E9tien, p.=20 262ff.; cf. also H. Hovestadt, Jena Glass and its Scientific and = Industrial=20 Applications (London,1902), pp. 134-137]. James R. Lynch has = fitted=20 the indices from the 1902 Schott catalog to Buchdahl's 5-term dispersion = formula. Using Lynch's results and Taylor's illustration and = description,=20 we can form a convincing approximation of Taylor's second form of = objective=20 (employing O.164) in ZEMAX. This allows a direct comparison with = the=20 layout specified in Taylor's article.

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	1069.14	15	O.543	160	0
2	Standard	-371.47	0.1		160	0
3	Standard	-371.47	3	O.164	160	0
4	Standard	279.24	3.167		160	0
5	Standard	279.24	15	O.374	160	0
6	Standard	8325.07	2683.23		160	0
7	Standard	Infinity	0.230		47.162	0
Image	Standard	-914.04			47.156	0

Table 1: = 150mm f/18=20 Cooke-Type "Photo-visual" Triplet

Next comes = the=20 layout:

1. 150mm f/18 Cooke-Type "Photo-visual" Triplet=20

The thinness of = the convex=20 central element is intentional, since Taylor's illustrations as well as=20 surviving Photo-visuals show that he purposely employed thin glass [cf. = Taylor,=20 Monthly Notices, p. 332; Adjustment and Testing, p. 82; = and=20 Nankivell, pp. 4-8]. The ray fan plots and spots come next. = Since=20 this and all subsequent designs are aplanatic, I do not give ran fan = plots for=20 the off-axis images:

Figure 1: Axial Ray Fan Plot for a 150mm f/18 = Cooke-Type=20 "Photo-visual" Triplet

Figure 2: Spot diagrams for a 150mm = f/18=20 Cooke-Type "Photo-visual" Triplet

Optically, the design is=20 excellent for a lens not employing fluorite or fluor-crown. Notice = the=20 enlarged airgap between the second and third elements, meant to suppress = spherochromatism. The residual 5th order spherical aberration in = not=20 important at the present focal ratio, but would need to be removed = through=20 aspherizing if the lens were built at a faster speed.

Cooke and = Sons=20 began selling Taylor's Photo-visuals by the mid-1890s, and Taylor = himself=20 presented the design in April 1894 to the Royal Astronomical Society = [cf.=20 Observatory 213 (April, 1894), pp.132-134]. Two of the = largest=20 lenses were constructed almost immediately: a 9-inch in 1896 for = Edward=20 Crossley, a wealthy English amateur, and a 12.5-inch at about the same = time for=20 Cambridge University [cf. Nankivell, p. 5; and D.W. Dewhirst, "A Cooke=20 Photovisual Lens in a Compensated Cell," Sky and Telescope 49.1 = (1975),=20 pp. 24-25]. They also made a number of other Photo-visuals by 1905 = [cf.=20 W.J.S. Lockyer, "Note on the Permanency of some Photo-visual Lenses," = Monthly=20 Notices of the Royal Astronomical Society 68 (1908), pp.=20 19-29].

Unfortunately, all these lenses began to degrade soon = after=20 completion. Indeed, Sir Howard Grubb and A.C. Ranyard had both = expressed=20 concern regarding the permanency of their glasses at the April 1894 = meeting.=20 But Taylor and his employers defended the lenses and expected no = decay=20 [cf. Observatory 213 (April, 1894), pp. 147-148]. Yet by = 1908 there=20 was ample evidence of glass degradation [cf. Lockyer, "Note on the=20 Permanency..," pp. 19-29]. Ironically, whereas Taylor had most = been at=20 pains to allay concerns about the permanency of the borosilicate = short-flint, it=20 was the inner surface of the light silicate crown at the rear of the = lens which=20 was most affected, and to a lesser extent the inner surface of the front = light=20 barium flint [cf. Taylor, Monthly Notices, pp. 333-334; = Adjustment and=20 Testing, pp. 83-84; and Lockyer, "Note on the Permanency..," pp. = 22ff.].=20 Yet the middle short-flint also decayed with the passage of time; = and like=20 many other short-flint glasses, if actual droplets of water ever sat on = its=20 surface for a length of time, deep corrosion ensued. Recently, the = 9-inch=20 Crossley lens was destroyed in this way after 100 years of service [cf.=20 Nankivell, pp. 6-7]. It is a danger facing many short-flint = apochromats.=20 Even if nothing catastrophic occurred, owners of the early Cooke = lenses=20 could expect them to need repolishing every 25 years or so [cf. = Dewhirst, p.=20 25].

The optical success of Taylor's lens spurred Cooke and Sons = to=20 search for more stable glasses. They had already replaced O.658 = with=20 O.164. Next they replaced the ordinary crown O.374 with O.599 [cf. = Taylor's reply to Lockyer in Lockyer, p. 29]. Schott too = recognized the=20 problem and by 1902 had removed O.374 from the market [cf. H. Hovestadt, = Jena=20 Glass and its Scientific and Industrial Applications (McMillan, = 1902), pp.=20 388-393]. For its part, Zeiss recognized the value of Taylor's = design and=20 quickly marketed their own similar triplet, called the "B" objective, = designed=20 by Albert K=F6nig [cf. A. Sonnefeld, "Der K=F6ngische Apochromat B," = Zeitschrift=20 f=FCr Instrumentenkunde 61 (1941), pp. 261-264; R. Riekher, = Fernrohre und=20 ihre Meister, 2nd. ed. (Verlag Technik, 1990), p. 214]. Since = Zeiss=20 had such close ties to Schott, they were apparently able from the outset = to=20 choose better, more stable glasses than Taylor had used. Even so, = old=20 Zeiss B lenses can show fungal growths [Wolfgang Busch per email=20 communication and photographs a)= and b)=20 ].

K=F6nig's student, Horst K=F6hler, has indicated the modern = Schott glass=20 types and geometry of the "B" objective, as well as radii of curvature = and=20 spacings for a small version. From this information it is possible = to=20 produce an approximation of the B at 150mm f/18, in order to show how = the lens=20 would compare to Taylor's [cf. A. K=F6nig and H. K=F6hler, Fernrohre = und=20 Entfernungsmesser, 3rd ed. (Springer Verlag, 1959), p.134, nr. = 9]:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	683.456	18	BaLF4	160	0
2	Standard	-276.868	0.1		160	0
3	Standard	-276.284	7	KzF2	160	0
4	Standard	188.838	7.258		160	0
5	Standard	195.389	18	K7	160	0
6	Standard	1006.367	2666.608		160	0
7	Standard	Infinity	-0.074		47.138	0
Image	Standard	-683.119			47.139	0

Table 2: = 150mm f/18=20 "Zeiss B"-Type Triplet

The layout looks like so::

2. 150mm f/18
"Zeiss B"-Type=20 Triplet

The ray fan = plots and=20 spot diagrams come next:

Figure 3: Axial Ray Fan Plots for 150mm f/18 = "Zeiss B"-Type=20 Triplet

3D"Zeiss

Figure 4: Spot Diagrams for 150mm f/18 "Zeiss = B"-Type=20 Triplet

The color correction is not quite as good as in = Taylor's=20 objective, even apart from the performance at 0.436 micron. On the = other=20 hand, the "Zeiss B"-type has almost no spherochromatism, and only a = small amount=20 of zonal spherical aberration, which itself could be removed with = suitable=20 aspheric figuring in the outer zones. Therefore, the lens could be = built=20 at a faster focal ratio, f/15 being the target at which Zeiss = aimed. =20 Incidentally, this is one of the few apochromatic designs which actually = fulfills Abbe's criteria for a true apochromat as discussed in the last=20 chapter.

The main problem with the "B" and the Cooke = "Photo-visual"=20 objectives--in addition to possible glass deterioration--is the strongly = curved=20 interior surfaces and the large airgap between the middle short-flint = element=20 and the final crown. These features made the lenses very sensitive = to=20 errors in the tilt and centration of the elements relative to one = another, as=20 well as to temperature changes. Even small alignment errors would = produce=20 strong coma in the image. Taylor and Zeiss recognized this and = made=20 provision for it in the design of their lens cells, introducing = carefully made=20 spacers and retaining rings which expanded and contracted with = temperature in=20 such a way as to keep the lens elements properly oriented with respect = to one=20 another [cf. Taylor, "The Cooke Photo-Visual Objective," in The = Adjustment=20 and Testing of Telescope Objectives, 5th ed. (Adam Hilger, 1983), = pp. 54-57,=20 especially p. 55; Sonnefeld, pp. 262-263; J.G. Baker, "Planetary = Telescopes,"=20 Applied Optics 2.2 (1963), pp. 111-129, especially p. 118; = and=20 Dewhirst, pp. 24-25]. August Sonnefeld, the designer of the Zeiss = AS=20 objective, in his discussion of the B-type said that "One must...expect = from the=20 user that he value the B-objective like a highly sensitive physical = measuring=20 instrument...and treat it accordingly."

Nevertheless, = Zeiss=20 occassionally produced this objective type at a much faster focal = ratio. =20 Michael Kiessling in Germany owns a 130mm f/8.5 [cf.=20 www.achromat.de/html/frameset_tele.html; Carl Zeiss; B130/1110], made in = the=20 1920s for terrestrial observation. This objective contains a = two-part cell=20 housing in the front sub-cell the first two glass elements, and in the = rear=20 sub-cell the separated third element. The two sub-cells can be = fully=20 adusted relative to one another, and then the lens cell as a whole can = be=20 adjusted with respect to the tube. Kiessling reports that the = objective=20 when used on the sky produces very good images with little outstanding=20 color. And I myself, having recently tested the objective (while = on a=20 visit to Germany) in autocollimation using both a Ronchi and a = knife-edge test,=20 can corroborate the goodness of the color correction and figure. = The=20 objective gave surprisingly good performance!

Now, the reason for = the=20 steep curves in these triplets is because the dispersions of the glasses = do not=20 differ sufficiently from one another. We saw the same problem in = Chapter=20 4a especially in regard to the "Zeiss A"-type and the SSKN8/KzFSN4 = doublets.=20 In part to overcome this problem, Zeiss later developed the "F" or = "dense=20 flint" objective. This became possible during the middle of the = 20th=20 century with the advent of extra dense flint glasses which displayed = abnormal=20 dispersions. One such abnormal dispersion flint is called SF11. = The=20 "SF" abbreviation stands for "Schwerflint," that is, "dense flint" in = German.=20

SF11 can be combined with another dense flint such as SF1, SF4, = SF9,=20 etc. and a dense phosphate crown of much lower dispersion, such as PSK3 = or one=20 of the "BaK" or "SK" barium crowns. Zeiss's "F" objective = contained the=20 glasses PSK3, SF4, and SF11, according to H. K=F6hler who developed it = along with=20 R. Conradi [cf. K=F6nig and K=F6hler, p. 61; p. 135, nr. 12; and p. = 139]. We=20 can form an approximation of the "F" at 150mm and f/15 as follows:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	14223	16	PSK3	160	0
2	Standard	-461.190	0.1		160	0
3	Standard	-461.190	10	SF4	160	0
4	Standard	302.368	0.914		160	0
5	Standard	305.400	18	SF11	160	0
6	Standard	-1032.53	2267.513		160	0
7	Standard	Infinity	-.085		39.356	0
Image	Standard	-830.316			39.372	0

Table 3: = 150mm f/15=20 "Zeiss F"-Type Triplet

The layout looks like so::

3. 150mm f/15
"Zeiss F"-Type=20 Triplet

Clearly the interior curves are much weaker than in = the "B"=20 objective and the airgap between the middle and rear elements is far = smaller.=20 Its performance at f/15 is good, though not excellent:

Figure 5: Ray Fan Plots for 150mm f/15 "Zeiss = F"-type=20 Triplet

Figure 6: Spot Diagrams for 150mm f/15 = "Zeiss=20 F"-Type Triplet

Although the color correction seen here is not as = good as in=20 a Taylor or "Zeiss B"-type of apochromat, it is still respectable in = comparison=20 to an achromat. Since the interior curves of the "F" are weaker = than those=20 of a Taylor or Zeiss B, it is possible to build the system even faster, = as Zeiss=20 did, producing the "F" as a half-apochromat down to about f/11 [cf. = K=F6nig and=20 K=F6hler, p. 61; p. 135, nr. 12; and p. 139]. Other combinations = of dense=20 flints and crowns can give better color correction, but the present set = has the=20 advantage of significantly weakening the curves, which eases = fabrication,=20 mounting, and sensitivity to tilts and decenters of the elements [cf. = Baker, p.=20 119 on the possibility of a superachromatic dense flint = triplet].

The=20 next step forward in the design of practical apochromatic triplets for = amateur=20 astronomy came when it was realized that although cementing large lens = elements=20 was not possible, filling the gaps between them with a very thin layer = of oil=20 (or special index matching gel), and sealing the edges of the lens was = feasible.=20 I do not know when this realization occurred. Certainly, = James G.=20 Baker, the famous American optical designer, understood it by 1963, when = he=20 suggested building various large half- and full-apochromatic objectives = cemented=20 together with "liquid cements...now available" [cf. Baker, p. 125ff.].=20 Probably the realization occurred to various people independently = of one=20 another.

At present, a common method of sealing the edges of = oil-spaced=20 lenses is by means of polyimide pressure-senstive tape, which goes by = the=20 tradename of "Kapton." This tape is very effective at sticking to = the=20 glass despite the oil, and forms a durable long-term barrier against = leakage.=20 As for spacing oils, many different types can work (including = plain=20 cooking oil!), but ideally one would like an oil or gel which matches = the index=20 of the glasses izona.edu/%7Erogerc/chapters/suw-1977-10-p.340.jpg"> = 1)=20 & 2)=20 ; for an English translation, cf. 3) ].=20 In it he described how to make a short-flint triplet easily from=20 prefabricated sets of lens blanks which he in conjunction with H. = Reichmann=20 Precision Optics of Brokdorf, Germany, were selling as kits [cf. W. = Busch,=20 "Herstellen eines fast apochromatischen Fernrohr-Objectivs aus = vorgefertigten=20 Teilen," in the "Tips f=FCr die Astropraxis" department of = Sterne und=20 Weltraum 16 (1977), pp. 338-341; also cf. "20 Jahre Kompaktobjektive = mit=20 =D6lf=FCgung," parts 1 & 2, in Sternkieker (nos. 1 & 2, = 1995), pp.=20 18-19; 77-78]. Accompanying the article was an advertisement from = the=20 Reichmann company offering kits for two apertures, 130mm and 150mm both = at about=20 f/15. Since Busch's work has been so little known in the English = speaking=20 world, in what follows I offer more extended coverage of it than of = other,=20 better known designers or lens types.
Busch considered his design to = be an=20 improved type of half-apochromat, though in practice with nearly full=20 apochromatic performance. His kits and procedures for producing = the=20 objectives were ingenious, and it is unfortunate this his contribution = to the=20 wide-spread dissemination of apochromatic objectives among amateur = astronomers=20 in recent decades has been so little known outside = Germany.

Busch's=20 optical design was broadly as follows: his lens consisted of = sandwiching a=20 piece of Schott KzFN2, a slightly abormal-dispersion short-flint, = between two=20 pieces of Schott B270, a type of crown glass not normally used in high = precision=20 optics, but similar to the ordinary K-type Schott crown glasses. = Such a=20 sandwiching arrangement of one type of glass between two specimens of = another=20 glass will be seen later in this chapter (cf. Table 9) when we consider = the high=20 performance triplet ED apochromats. In principle, the color = correction and=20 performance of Busch's lens should be similar to the short-flint = doublets we saw=20 in Chapter 4a, since the same types of glasses are involved. But = Busch had=20 two cards up his sleeve which altered that performance fundamentally for = the=20 better. The first and most important was the oil-spacing. By = filling=20 the gaps between the glasses with oil, he essentially nullified the = interior=20 surfaces' contribution to the lenses' wavefront errors, a feature we = have=20 discussed previously. Then too, the oil film automatically = regulates the=20 spacing and tilt between the individual lenses, largely removing the = causes of=20 coma in the air-spaced Taylor and Zeiss B objectives. =20

Busch's second card was to split up, as it were, the crown = element=20 of a standard short-flint doublet into two pieces, placing them one in = front and=20 one in the rear, and dividing the optical power between them. By = doing so,=20 he could achieve weaker curves on all the lens elements and diminish the = monochromatic aberrations associated with strong curves, especially the=20 spherochromatism. He could also in this way have enough degrees of = optical=20 freedom to correct coma, and fully protect his short-flint element from=20 weathering, since it would be sandwiched between two weather-resistent = exterior=20 crown elements, and excluded from humidty and chemical attack by the oil = layer.=20 Indeed, Busch left his protype triplet outside in the weather of = Hamburg,=20 Germany for two years before exhibiting it at a meeting in Cologne in = 1976 [cf.=20 "Herstellen...," p. 338]. The weather-resistence was further = enhanced by=20 Busch's choice of glasses, since his short-flint was one of the most = chemically=20 stable which Schott made, and the crown glass is nearly = inert.

But=20 Busch's great merit is shown in how he developed his design into a lens = which=20 could actually be made by an ordinary ATM without any more equipment = than is=20 needed to make a Newtonian mirror. Part of the driving force = behind his=20 choice of glasses was the realization that if the difference in the = index of=20 refraction from crown to flint was sufficiently small, it would be fully = possible to leave all four interior surfaces of the lens combination = fine=20 ground, but unpolished. The oil film would fill in the = grinding=20 pits and no reflection would be seen between adjacent interior surfaces. = The fine ground surfaces would look entirely transparent to the = naked eye!=20

To demonstrate this astounding fact, the editors of = Sterne und=20 Weltraum magazine displayed on the first page of Busch's article a=20 photograph of a finished objective left with fine-ground interior = surfaces.=20 Below the lens lies a sheet of music, partly covered by the lens = and=20 partly left uncovered. Close observation of the photo shows that = the lens=20 has just been oiled and that the oil is still spreading between the = elements.=20 At center the lens appears beautifully transparent where the oil = film=20 lies. But then comes a larger annulus of glass which the oil has = not yet=20 reached. This area appears fine ground and matte. =

Moreover,=20 three years later in 1980, B. Wedel of the Wilhelm Foerster Observatory = in=20 Berlin published an independent appraisal of a 150mm f/15 Busch = objective [cf.=20 "Ein Vergleichstest: "Immersionsobjektiv" von Wolfgang Busch--Zeiss-B = Objektiv,"=20 Sterne und Weltraum 19 (1980), pp. 422-423]. Wedel noted = that=20 everyone's scepticism concerning transparency vanished as soon as the = objective=20 was actually seen, and that some experienced planetary observers = actually felt=20 that the Busch objective slightly outperformed a 150mm f/15 Zeiss B, = brought in=20 to allow direct comparison with an apochromat of known high-performance = [cf.=20 also W. Rohr, "Erfahrungen mit einem Immersions-Objektiv HAB 130/1900,"=20 Sterne und Weltraum 18 (1979), pp. 313-314].

According to = Wedel,=20 comparative photographs of M3 taken through both telescopes showed the = same=20 limiting magnitude, although the Busch objective gave a somewhat darker=20 background. On the other hand, the Zeiss B showed slightly sharper = images=20 when the photographs were examined under a microscope. Despite = shining a=20 laser through the Busch objective, Wedel could see no more scatter from = the=20 unpolished interior surfaces than from the polished exterior ones.=20 Whereas, photoelectric measurements demonstrated the theoretically = superior color correction of the Zeiss B. Visual assessment, = however,=20 failed to detect any practical difference in performance.

Thus, = it was a=20 draw. Wedel and his observers gave high marks to the Busch = objective,=20 comparing it favorably to the Zeiss lens. Since according to Busch = himself, one could build his objectives from the kit for about 1/3 the = price of=20 a comparable finished lens, clearly this type of objective represented a = very=20 good value to the enterprising ATM.

I can myself = corroborate much=20 of this from personal experience, having built and used three Busch = objectives.=20 The oil films render them completely transparent. No = scattered light=20 is visible during a star test, lunar or planetary observation, or when = examining=20 a bright light bulb directly through the objective. The interior = glass=20 surfaces appear as if completely polished, and the objectives performed=20 magnificently.

But Busch offered still more. One of the = most=20 formidable obstacles to amateur construction of refractors is certainly = the need=20 for a carefully made lens cell. But a complete cell in metal was = offered=20 as part of the kit. Another obstacle is the need to "dewedge" the = lens=20 elements. "Wedge" consists in the non-uniformity of thickness as = one=20 proceeds around the periphery of a lens. In other words, at 12 = o'clock=20 (say) on the lens as you face it, you have a thickness of "x," whereas = at 6=20 o'clock you have some other thickness. Hence, the lens as a whole = has a=20 slight "wedge" component to its shape, rather like a prism. This = error, if=20 left uncorrected, will stretch a star image into a short spectrum, just = as a=20 real prism will. The spectrum is, of course, the aberration called = "lateral color" which we studied in Chapter 2.

Normally an = optician will=20 grind away the wedge-error, but an ATM familiar only with mirror-making = will not=20 possess the know-how or have the proper equipment to measure and verify = the=20 result. Hence, the ATM's objective lens may show lateral color. = But=20 lateral color can also arise from decentration of the lens elements with = respect=20 to one another. Busch overcame both these problems by making his = KzFN2=20 element somewhat smaller in diameter than the B270 elements which = surrounded it=20 and by providing four plastic centering screws built into the lens cell. = The centering screws pressed lightly against the KzFN2 and allowed = the=20 user purposely to change its centration, thereby also changing the = amount of=20 lateral color produced by the objective. This meant that even if = the lens=20 elements had some wedge, the user could compensate by adjusting the = centration=20 of the middle element. Thus, the user could remove any lateral = color,=20 arising from fabrication errors, during use at the telescope. Even = more=20 ingeniously, the user could compensate for atmospheric dispersion in = stellar or=20 planetary images by similarly adjusting the lens. I have myself = performed=20 such adjustments on Busch objectives and they work = perfectly.

Busch's HAB=20 ["Halbapochromat Bausatz"] system was therefore extremely practical and = really=20 did put a high-quality half-apochromat within reach of a mirror maker, = without=20 the need for additional know-how or fabrication equipment. The kit = itself=20 came with a set of excellent instructions by Busch, which I have seen = courtesy=20 of H.C. Schr=F6der, an engineer in Germany who also supplied me with a = detailed=20 prescription for the 130mm f/15 objective, as well as with an = engineering=20 drawing and list of the kit's contents as supplied by Reichmann = Precision=20 Optics. According to Reichmann, the kit contained the following: = 3=20 lens elements, bevelled, edged round and curve generated; 1 lens cell, = threaded=20 with a retainer ring and black anodized; 4 plastic centering screws; 4 = different=20 glass filters for checking the color correction; 1 unit of special oil = for=20 contacting the lenses; grit, polishing compound and pitch; detailed = working=20 instructions; and 1 grinding tool for working the exterior lens=20 surfaces.

The instructions from Busch told in some detail how to = grind=20 the interior lens surfaces together, as well as how to use the grinding = tool on=20 the outside surfaces, and when to stop. The level of detail and = various=20 reminders are appropriate to the needs of someone who has successfully = finished=20 one or two paraboloidal mirrors. Much more interesting, however, = are the=20 instructions concerning oiling, polishing, figuring, and testing. = Busch=20 recommends using a slight amount of oil, just enough so that after a = number of=20 hours, the oil layer will finally expand to reach the outer edge of the = lens.=20 No taping is required or indeed possible because of the centering=20 screws.

After oiling, the assembled objective is inserted into = its cell,=20 and then polished and figured on its exterior surfaces. The very = valid=20 reason for doing this is to avoid flexure of the lens elements, if they = are=20 polished individually on the usual grinding stand or machine. This = could=20 introduce zonal errors or astigmatism, especially in the hands of an=20 inexperienced lens maker. With the whole objective assembled in = the cell,=20 the exterior lens surfaces become in effect far stiffer and more = resistent to=20 flexure since the exterior lenses rest on those below them. The = total=20 stack up of glass is quite stiff and the oil layer (properly applied) is = incompressible.

Now the one real difficulty with Busch's lens (a=20 prescription for which will be given in a moment) is that it requires a = somewhat=20 aspheric exterior front surface. But in a stroke of genius, Busch = tells=20 how to produce the required asphere almost automatically. He = describes how=20 to cut a paper ring, place it between the first and second lenses = resting on the=20 oily layer between, and then how to polish the outer surface of the = first lens=20 with somewhat more force than usual. Because the paper ring only = the=20 supports part of the front lens (its outer periphery), and leaves the = rest=20 (midsection) unsupported, more polishing action will occur over the ring = and in=20 its vacinity. Less polishing will occur in proportion as one moves = toward=20 the center of the lens. Thus gradually with persistence an oblate=20 ellipsoidal surface will arise, which is exactly what is needed.=20

For testing, Busch suggests using the Foucault or Ronchi = test with=20 a slit source. He outlines four test methods: autocollimation = against a=20 flat mirror; use of a Newtonian telescope to create a collimated beam = feeding=20 the objective under fabrication; use of a finished Fraunhofer achromat = for the=20 same purpose; and barring those methods, use of a bare slit placed at a = large=20 distance and nulling the objective for blue light. All these = methods=20 should be valid, and armed with them the ATM has everything necessary to = make a=20 finished lens. No wedge testing, no spherometry is necessary; one = does not=20 even need to polish four of the six surfaces! It was a marvelous = kit and a=20 clever plan! Alas, it was little known outside of Germany. = But=20 certainly Wolfgang Busch's name and achievement deserve to be known by = lovers of=20 fine apochromatic lenses. Perhaps never before had anyone marketed = a=20 refractor kit of any kind that was so wholly practical, so clearly and=20 completely thought out and described.

A Busch-type lens may be = formed as=20 follows:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	1081.885	19	B270	160	0.449
2	Standard	-405.421	6	KzFN2	160	0
3	Standard	268.536	18	B270	160	0
4	Standard	Infinity	2220.457		160	0
5	Standard	Infinity	-0.064		39.407	0
Image	Standard	-846.714			39.421	0

Table 4: = 150mm f/15=20 "HAB"-Type Semi-Apochromat

The layout = of the=20 lens looks as follows:

4. 150mm f/15 "HAB"-Type
Semi-Apochromat=20

The ray fans come = next:

Figure 7: Ray Fans for 150mm f/15 =
HAB"-Type=20 Semi-Apochromat

And the spot diagrams, in which I have omitted deep = red=20 (0.707 micron) and violet (0.436 micron) in order to make the Airy disk = more=20 clearly visible:

Figure 8: Spot Diagrams for 150mm f/15 "Busch = System"-Type Triplet

Obviously, the performance is not as good as that = given by=20 the Taylor or Zeiss types of apochromats, but it is still respectable = and far=20 better than an achromat. The red rays just fill the Airy disk, = while the=20 blue form a disk no more than twice as large. Violet is not well=20 controlled, but since it is so faint this hardly matters for visual = observing.=20 There is a small amount of coma, but its magnitude is trivial and = could=20 not be seen in practice. Overall, the Busch objective has achieved = an=20 outstanding balance between performance and practicality. The kits = are no=20 longer available, and KzFN2 has gone out of production. But = similar and=20 better corrected lenses can be formed from KzFSN4 and the ED=20 glasses.

After Busch came Roland Christen in the early 1980s who=20 revolutionized amateur interest in high-performance lenses [cf. R. = Christen, "An=20 Apochromatic Triplet Objective," Sky and Telescope (Oct., 1981), = pp.=20 376-380; "Revised Triplet Design," Sky and Telescope (April, = 1982), pp.=20 411-412; and "Design and Construction of a Super Planetary Telescope = Objective,"=20 Telescope Making 28 (Fall, 1986), pp. 20-23]. Christen's = original=20 lens designs were essentially oil-spaced versions of Taylor's, using = three=20 different glass types to achieve better color correction. Like = Busch,=20 Christen noted in his published articles that the oiled interior = surfaces of=20 such lenses need not be figured accurately, since they contribute = essentially=20 nothing to the wavefront errors [cf. Sky and Telescope (April, = 1982), pp.=20 411-412]. Moreover, oiling makes the tilt and decenter problems of = the old=20 Cooke and Zeiss triplets completely disappear. Thus it becomes=20 comparatively easy to fabricate high-performance apochromats, especially = in the=20 small sizes popular today.

I myself have built a number of = these=20 short-flint, as well as ED oiled triplets and found them among the = easiest=20 optics to make accurately. In many instances it was not necessary = to do=20 any figuring at all: the lenses were complete as soon as they had = been=20 carefully polished out. The first of these lenses, a 90mm f/12 = short-flint=20 triplet won a merit award for optical excellence at the 2002 RTMC = Astronomy=20 Expo; and the second, a 140mm f/12 ED triplet is equally good in color=20 correction and figure. Both have smooth wavefronts of 1/8th wave = pv (at=20 532nm) or better. Nothing more than the simplest lens cells has = been=20 necessary for either of the lenses. More recently I have completed = a 140mm=20 f/9 ED triplet, like that shown in Table 7 below, and a 175mm f/12 ED = triplet of=20 a different design. All were comparatively easy to make and=20 figure.

What follows is a short-flint triplet closely modeled on = those=20 published by Christen in the above-mentioned articles:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	1862.235	18	BK7	160	0
2	Standard	-365.407	6	KzFS1	160	0
3	Standard	365.407	18	BaFN10	160	0
4	Standard	-1342.645	1492.275		160	0
5	Standard	Infinity	0.023		26.241	0
Image	Standard	-582.177			26.251	0

Table 5: = 150mm=20 f/10 KzFS1 Oil-Spaced Triplet

5. 150mm f/10 KzFS1 Oil-Spaced Triplet = =

This is an elegant symmetrical design, much faster = in focal=20 ratio than any of the preceding lenses. It proved possible to = increase the=20 speed because the design uses a short-flint (KzFS1) of more abnormal = dispersion=20 than those seen above. Indeed, Christen stated at the time he was = building=20 his first lenses that his batch of KzFS1 was even better in its partial=20 dispersions than the catalog values [cf. Sky and Telescope (Oct., = 1981),=20 p. 378]. So, the ray fan plots and spot diagrams given below are = no doubt=20 worse than what he actually achieved. Yet they give an idea of the = excellence of the corrections:

Figure 9: Axial Ray Fan Plots for a 150mm = f/10 KzFS1=20 Oil-Spaced Triplet

3D'Spot

Figure 10: Spot Diagrams for a 150mm = f/10 KzFS1=20 Oil-Spaced Triplet

This design is excellent for f/10 and can provide = very=20 satisfying views. One must remember, of course, that the human eye = has=20 only a slight sensitivity to 0.436 micron, so that only a very faint = violet halo=20 would be visible around the brightest white stars in a dark sky.=20 Otherwise, even at high powers stars in this type of lens would = look sharp=20 and completely free of false color [cf. Christen, Telescope Making = 28=20 (Fall, 1986), pp. 23]. The lens's chromatic focal shift diagram = gives the=20 classic flattened "S" shape of a short-flint triplet apochromat, = comparable to=20 the color curves published by Czapski, Wolf, Steinheil and others = starting in=20 the 1880s:

Figure 11: Chromatic Focal Shift for 150mm = f/10 KzFS1=20 Oil-Spaced Triplet

Alas, KzFS1 is no longer made. The = related=20 short flint, KzFSN4, on the other hand is a standard Schott glass. = It can=20 be teamed with the slightly abnormal fluor-crown N-FK5 and the ordinary = barium=20 flint N-BaF51 to make an essentially identical type of triplet:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	2017.256	18	N-FK5	160	0
2	Standard	-341.788	5	KzFSN4	160	0
3	Standard	304.103	20	N-BaF51	160	0
4	Standard	-978.561	1496.236	<>	21.268	0

Table 6: = 150mm f/10=20 KzFSN4 Oil-Spaced Triplet

The geometry of this lens is very similar to the = KzFS1=20 triplet shown above. Therefore I omit a layout. The = performance is=20 as follows:

Figure 12: Ray Fan Plots for 150mm f/10 KzFSN4 = Oil-Spaced=20 Triplet

3D"Spot

Figure 13: Spot Diagrams for 150mm f/10 = KzFSN4=20 Oil-Spaced Triplet

The color residual is somewhat worse, though in = practice one=20 would probably see no difference between the present lens and the=20 preceding.

These two oil-spaced lenses represent the = approximate limit=20 of what can be achieved with a safe oil-spaced short-flint design. = One=20 must understand that many of the short-flints are sensitive to water and = will be=20 etched by it, if it is allowed to stand on their surfaces for more than = a few=20 minutes. Even long-term exposure to atmospheric humidity may = degrade them.=20 Therefore, sealing these glasses inside a layer of oil is a good=20 conservation measure. Anti-reflection coatings can also help, and = if they=20 are used, it is indeed possible to add airspaces between the three lens = elements=20 and vary all six radii of curvature, in order to improve the = spherochromatism=20 and basic color correction. But then we may again encounter the = centration=20 problems of the old Zeiss B and Taylor objectives. Therefore, it = is=20 probably not useful to push the short-flint design any further.

A = better=20 plan is to switch to an oil-spaced fluor-crown triplet, as commercial = telescope=20 makers have done. By employing Ohara FPL53 in combination with = ZKN7 we=20 can decrease the focal ratio to f/9 as follows:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	580.789	10	ZKN7	160	0
2	Standard	304.444	20	FPL53	160	0
3	Standard	-688.687	10	ZKN7	160	0
4	Standard	-2590.862	1325.095		160	0
5	Standard	Infinity	-.063		23.601	0
Image	Standard	-499.454			23.575	0

Table 7: = 150mm f/9=20 ZKN7/FPL53/ZKN7
Oil-Spaced Triplet = Apochromat

It will be seen here that (as in the Busch = objective) we have=20 a sandwich construction: the central element of FPL53 is = surrounded by two=20 elements of ZKN7. This is a very effective arrangement leading to = smaller=20 spherochromatism than we saw in the doublet made of these two glasses in = Chapter=20 4a (cf. Table 9), and more importantly to a far easier construction. = Since=20 the two interior spaces are filled with oil, the four interior lens = surfaces=20 cannot readily distort the wavefront. Figuring this lens is now = relatively=20 easy.

The layout is as follows:

6. 150mm f/9 ZKN7/FPL53/
ZKN7 = Oil-Spaced=20 Triplet = Apochromat

The ray fan=20 plot and spot diagrams come next:

Figure 14: Axial Ray Fan Plot for 150mm f/9 = ZKN7/FPL53/ZKN7=20
Oil-Spaced Triplet Apochromat

Figure 15: Spot Diagrams for 150mm f/9=20 ZKN7/FPL53/ZKN7
Oil-Spaced Triplet Apochromat

The = color=20 correction is excellent and the spherochromatism is under control. = The=20 small 5th order residual of spherical aberration seen in green light is = of=20 little significance. An examination of the chromatic focal shift = diagram=20 shows a notable improvement over that for a short-flint = design:

Figure 16: Chromatic Focal Shift Diagram for = 150mm f/9=20 ZKN7/FPL53/ZKN7 Triplet

Comparing the maximum focal shift = to the=20 diffraction limited range shows for the first time that former is now = much=20 smaller than the latter, which is another sign that our lens possesses = excellent=20 color correction. Many vertical slices through the graph will = intersect=20 three widely separated wavelengths of light. Figure 15 shows = excellent=20 correction for coma, only a small amount of chromatic astigmatism being = clearly=20 displayed. While Figure 14 shows good spherical correction for the = e-line.=20 Thus, here we have achieved an excellent practical lens worthy of = the name=20 apochromatic.

I have built a 140mm f/9 version of the above lens = and it=20 performs admirably. Only the merest hint of color can be seen in = the=20 Fresnel rings as you rack through focus, even when observing Vega. = At=20 focus, the Airy disk and ring system look absolutely free of false = color.=20

It is, of course, also possible to use fluorite for the = abnormal=20 dispersion middle element, as was done in the Zeiss APQ objective, built = at=20 100mm aperture and 1000mm focal length (f/10). Such a lens would = no doubt=20 give superb results [cf. A. Karnapp & J. Pudenz, "The 100/1000mm APQ = objective--a new level of quality in astronomical optics," Jenaer=20 Rundschau 31.3 (1986), pp. 140-141; and U. Laux, Astrooptik, = 2nd ed.=20 ( Sterne und Weltraum, 1999), pp. 51-53].

Now, if one must = push=20 for still faster focal ratios, then it is possible to use the oiled = combination=20 of ZKN7 and FPL53 down to about f/7 in a 150mm diameter lens or f/6 in a = 125mm=20 lens. Color correction remains acceptable. Below f/7 or f/6, = spherochromatism will degrade the performance so that color will = reappear in the=20 image. Certainly the one commercial 125mm f/6 ED triplet which I = have=20 closely examined, showed signs of being near the limit. At focus = no=20 outstanding color was seen; but on racking through focus plenty of color = was=20 evident in the Frenel rings, showing the barely contained = spherochromatism at=20 work. So here lies a fundamental limit in oil-spaced triplet = design.=20 The residual 5th order spherical aberration component best seen in = green=20 light will also grow, although with suitable aspheric figuring that = could be=20 removed.

Another way to improve the performance of fast = apos is by=20 adding a fourth lens element [cf. U. Laux, Astrooptik, 2nd = ed.=20 (Sterne und Weltraum, 1999), p. 47]. Combined with one = narrow=20 airgap, this easily results in greatly improved performance. The = following=20 is a such design for a 150mm f/7 four-element = apochromat:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Standard	433.00	8	BK7	160	0
2	Standard	226.55	27	FPL53	160	0
3	Standard	-460.68	0.042		160	0
4	Standard	-474.59	12	F2	160	0
5	Standard	-245.25	10	BaF4	160	0
6	Standard	-1507.04	1018.98		160	0
7	Standard	Infinity	-0.056		18.356	0
Image	Standard	-391.08			18.329	0

Table 8: = 150mm f/7 FPL53=20 Four-element Apochromat

The layout for this lens is as follows:

7. 150mm f/7 Four-
Element=20 Apochromat

The lens can be thought of as a Fraunhofer-type = objective=20 with crown and flint elements both composites of two lenses each. = By=20 forming each composite element from two different glasses, it is easily = possible=20 to fine tune the partial dispersions which results in almost no = outstanding=20 color. Moreover, spherochromatism can be almost completely=20 suppressed.

The performance is as follows:

Figure 17: Ray Fan Plots for 150mm f/7 = Four-element=20 Apochromat

3D"Ray

Figure 18: Spot Diagrams for 150mm f/7 = Four-element=20 Apochromat

These are the best spot diagrams we have seen so = far. =20 Even down to a wavelength of 1.000 micron (not illustrated) the color = blurs stay=20 much smaller than the Airy disk. The ray fan plot shows only a = small=20 spherochromatism. The 5th order spherical residual common to all = the=20 wavelengths could be removed through figuring. The main problem = with this=20 lens is its great thickness (57mm), which will slow down thermal = equilibration=20 and promote spherical aberration in the image.

Despite the = advantages of=20 oil-spacing, recently the major manufacturers of commercial apochromats = haved=20 shifted back to air-spacing. The reason seems to be twofold: = first,=20 the demand for improved color correction at both short and long = wavelengths for=20 astrophotography (CCD detectors are much more sensitive to deep red and = violet=20 than is the human eye); and second, the needs of apertures in excess of = 150mm=20 diameter.

By dispensing with the oil, four more air-glass = surfaces=20 become available for variation as degrees of freedom. This allows = the=20 interior surfaces of the objective to be played off against one another = for the=20 purpose of cancellling 3rd order spherical aberration, while at the same = time=20 the lens powers can be refined for better nullifying of the color error = and=20 spherochromatism. To show an example of what is possible, below I = give a=20 design for a 155mm f/7 air-spaced triplet apochromat:

Surface	Type	Radius	Thickness	Glass	Diameter	Conic
Object	Standard	Infinity	Infinity		0	0
Stop	Even Asphere	507.156	7.75	SK2	160	0
2	Standard	290.991	0.104		160	0
3	Standard	276.892	24.2	FPL53	160	0
4	Standard	-393.550	0.473		160	0
5	Standard	-376.823	9.7	FK5	160	0
6	Standard	-1197.50	1061.469		160	0
7	Standard	Infinity	0.015		9.471	0
Image	Standard	-395.529			9.469	0

Table 9: = 155mm f/7=20 Air-Spaced Triplet Apochromat

The = layout=20 is as follows:

8. 155mm f/7 Air-Spaced =
Triplet=20 = Apochromat

Since = this=20 objective is fast and designed with the needs of astrophotography in = mind, a=20 more through evaluation of its performance across a broader spectral = range will=20 prove instructive. Moreover, we can compare the results with those = published for a similar type of objective actually produced and sold by = a=20 commercial manufacturer. I must stress yet again, however, that my = design=20 is not an attempt to "reverse engineer" a commercial lens. I have = no=20 knowledge whatever of the actual prescription of any commercial = optics. =20 This website exists merely as a teaching tool, not an equipment=20 review.

Let us first look at the longitudinal aberration graph = for the=20 above lens. This graph shows for various colors the distance along = the=20 optical axis (abscissa) at which rays striking the entrance pupil at = various=20 pupil heights (ordinate) will intersect the optical axis:

Figure=20 19: Longitudinal Aberration Graph for 155mm f/7
Air-spaced = Apochromat=20 listed in Table 9

Notice first that more wavelengths = have been=20 specified than usual (0.406, 1.0154 and 0.589 micron) in order to extend = the=20 spectral coverage. In addition, one should note that the objective = is=20 nulled for 0.546 micron to give a flat vertical line, indicating zero = spherical=20 aberration. All other wavelengths end up either overcorrected or=20 undercorrected; that is, the lens shows spherochromatism of the usual = sort seen=20 in almost all refractor objectives.

Compare this to the following = graph=20 derived from the manufacturer's literature:

Figure=20 20: Manufacturer's Longitudinal Error Graph for
Commercial = 155mm f/7=20 Air-spaced Triplet Apochromat

A careful comparison of the = two=20 graphs will show that my lens's performance closely replicates the = commercial=20 lens, although its spherochromatism is somewhat larger. One should = keep=20 that replication in mind when examining the next figure, which shows the = polychromatic Strehl ratio graph for my lens given above in Table = 9:

Figure 21: Polychromatic Strehl = Ratio=20 Graph for Lens listed in Table 9 above.

On first inspection = one may=20 recoil from the graph in Figure 21 since over such a large spectral = bandwidth=20 the objective looks terrible, being far from diffraction limited. = But the=20 close similarity of the graphs in Figures 19 and 20 precludes any large=20 error. The commercial lens--if indeed it performs as indicated in = Figure=20 20--will give a better polychromatic Strehl ratio graph, but not=20 drastically. Rather, since the public has demanded zero visible color error and a very short = focal=20 ratio from the commercial makers of apochromats, compromises have had to = be=20 made. But notice that the spectral regions over which performance = falls to=20 less than a Strehl ratio of 50% are quite small and would be invisible = to the=20 human eye. Moreover, the Airy disk pattern for an optic showing a = 50%=20 Strehl ratio will look a good deal like that of a perfect optic, except = that the=20 diffraction rings around the Airy disk will appear brighter and more = extensive=20 than they should be. There will not be a large patch of unfocused = light=20 like the blue halo which one sees around stars in an achromat. = Over the=20 bandwidth from the C- to the F-line, one would have the following=20 performance:

Figure 22: Polychromatic = Strehl Ratio=20 Graph from C to F in Table 9 Lens

If one compares this = graph to=20 Figure 10 of Chapter 3a, showing the equivalent information for a 200mm = f/15=20 achromat, it is easy to see how much better the color performance is in = the=20 present lens. Since the manufacturer claimed an even smaller = longitudinal=20 error (Figure 20), it might well be that from C to F the commercial lens = still=20 will show a Strehl ratio of 80% or better. In other words, at C = and F the=20 lens would still be diffraction limited, showing no more than about 1/4 = wave=20 peak-to-valley of spherical aberration. At the e-line (0.546 = micron) the=20 theoretical Strehl ratio would be nearly 100%.

The chromatic = focal shift=20 diagram ("color curve") for the lens in Table 9 is as follows:

Figure=20 23: Chromatic Focal Shift Diagram for 155mm f/7 Lens of Table = 9

One can see that we have here a true = apochromat=20 with three color crossings (found as before by taking a vertical slice = through=20 the graph) which are widely separated as they should = be.

A=20 second manufacturer has recently stated that: "...any lens...[which] has = a peak=20 visual null (~5550A - the green-yellow) with a Strehl ratio of .95 or = better,=20 [is] coma corrected and is diffraction limited from C (red) to F (blue) = with 1/4=20 wave OPD spherical or better, has good control of the violet g = wavelength with=20 no more than 1/2 wave OPD P-V spherical and optical spot sizes that = concentrate=20 the maximum amount of photons within the diffraction limit...will = satisfy the=20 modern definition of 'Apochromatism.'" This manufacturer also = notes that=20 such a lens should display three widely separated color = crossings.

Now,=20 what the second manufacturer wishes to do is to give a modernised = version of=20 Abbe's 19th century definition of apochromatism [cf. Chapter 4a for a = discussion=20 of that] with a view to functionality and what will make a good lens in=20 practice. We have already seen in the last chapter that in = practice=20 virtually no triplet apochromatic telescope objective--even one using=20 fluor-crown glass--can meet Abbe's definition in the strict sense. = So=20 instead, the manufacturer gives a practical definition tailored to what = he finds=20 feasible and satisfactory for current lenses. It will be seen that = the=20 objective presented in Table 9--despite the unpleasant looking = polychromatic=20 Strehl ratio graph of Figure 21--essentially meets this definition of=20 "apochromatism." There are three widely spaced color crossings, = the lens=20 is coma corrected, it shows a Strehl ratio of better uto;" border=3D"1"=20 cellpadding=3D"0" cellspacing=3D"0">

Figure=20 24: Chromatic Focal Shift Diagram for Commercial 160mm = f/7.5
Air-Spaced=20 Triplet Apochromat

The correction in this case = extends=20 from 0.405 to 0.707micron. A revision of the lens given in Table 9 = above=20 yields the following chromatic focal shift diagram:

Figure=20 25: Chromatic Focal Shift Diagram for 160mm f/7.5
Air-Spaced = Triplet=20 Apochromat given in Table 10 (below)

As can be seen, the curves in Figures = 24 and 25=20 are very similar to one another, and the maximum focal shift = range/diffraction=20 limited range numbers are nearly identical. The prescription for = my=20 revised lens is as follows:

Surface

Type

Radius

Thickness

Glass

Diameter
Conic

Object

Standard

Infinity

0
0

Stop

Even Asphere
805.108

SK2
165
0

Standard

312.720

0.050

165
0
3
Standard
280.023
25
FPL53
165
0
4
Standard
-459.535
2.230

165
0
5
Standard
-359.426
10
FK5
165
0
6
Standard
-593.217
1183.379

165
0
7
Standard
Infinity
0.015

10.494
0

Image

Standard

-435.044

10.476
0

Table 10: = 160mm f/7.5=20 Air-Spaced Triplet Apochromat

Its polychromatic Strehl ratio = diagram=20 comes next:

Figure=20 26: Polychromatic Strehl Ratio Diagram for Lens in Table = 10

This objective shows improvement at = the longer=20 wavelengths, and certainly meets the functional "revised" definition of = an=20 apochromat. Between C and F it shows diffraction limited = performance and=20 is probably similar in design and performance with what is currently on = the=20 market at 160mm and f/7.5. The design can also be scaled up to = 250mm=20 f/9. When that is done, the whole spectral bandwidth from g- to r- = (0.436=20 to 0.707micron) performs better than the diffraction limit. =

I have=20 seen one 10" f/9 triplet from a commercial maker and it showed no = visible color=20 error. That is not to say, however, that the telescope gave a = stellar=20 performance. On the contrary, by introducing airgaps back into=20 apochromatic lenses--which inevitably show strong internal curves--we = bring back=20 the old problems of the Zeiss B and Taylor triplets, namely their great=20 sensitivity to temperature and to internal alignment. I was rather = aghast=20 to see the severe spherical aberration in the 10" lens, due to the = falling=20 temperature that night. Because of the great thickness and mass of = the=20 lens, as well as the fluor-crown's very high coefficient of thermal = expansion=20 and its insulted position in the middle of the lens, this $40,000US = extravagent=20 objective never performed as well that night as a decent 10" Newtonian=20 would. My impression is that the owner found this true on other = nights as=20 well and lamented that the lens could not keep up with the falling=20 temperature. Other examples of this type of instrument also show = the same=20 problem I am told by my optical acquaintances. So while the = smaller lenses=20 of this type in the 160mm range may be fine, it would appear to me that = the=20 makers of the larger lenses have overreached the limits of what triplet = apos are=20 capable of--at least the air-spaced variety. It is a shame that = oiling,=20 the revolutionary technical advance introduced by Wolfgang Busch and = Roland=20 Christen almost 30 years ago, has been abandoned. Oiled lenses = even of=20 rather large thickness show much more moderate variation of spherical = aberration=20 during cool-down in my experience. Perhaps the large air-spaced = beasts=20 will work well on tropical islands where the diurnal temperature = variation is=20 minimal. But people who live in temperate climates may wish to be = careful=20 of large air-spaced ED lenses.

That concludes = our=20 survey of apochromatic objectives. Several special refinements = will be=20 found in the last two chapters. In Chapter 5 we will examine the=20 so-called "Petzval" telescope and sub-aperture color correctors. = In=20 Chapter 6 we look at two completely different forms of refractor: = Ludwig=20 Schumann's "Medial" and "Brachymedial"=20 telescopes.

Ch= apter=20 5

Back to=20 Table of Contents

the barely contained spherochromatism at work. 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