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<BODY><BIG>Chapter 4b. &nbsp;Survey of Apochromats (Triplet=20
Systems).<B><BR><BR></B></BIG>
<DIV align=3Djustify><BIG><SMALL>Triplets form the mainstay of present =
day=20
apochromatic designs. &nbsp;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. &nbsp;Yet even here =
there=20
are limits as one pushes for faster and faster focal ratios. &nbsp;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.</SMALL></BIG>&nbsp; Or a radical departure from the closely =
spaced lens=20
arrangements which we have seen so far may also be contemplated. =
&nbsp;The=20
Petzval lens in which there are two widely separated doublets may prove =
helpful=20
(cf. Chapter 5). &nbsp;Of the rich variety possible in three-element =
lens=20
combinations, we will survey a sampling in the present =
chapter.<BR><BR>Harold=20
Dennis Taylor developed and patented the first practical triplet in 1892 =

[British Patent no. 17994; cf. S. Czapski &amp; O. Eppenstein,=20
<I>Grundz=FC</I><I>ge der Theorie der optischen Instrumente nach =
Abbe</I>, 3rd ed.=20
(Verlag J.A. Barth, 1924), p. 567; H. Chr=E9tien, <I>Calcul des =
combinaisons=20
optiques</I>, 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," <I>Journal of the Antique Telescope Society</I> 24 (2002), pp. =
4-8].=20
&nbsp;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
<I>Adjustment and Testing of Telescope Objectives</I>, 5th ed. (Adam =
Hilger,=20
1983), pp. 78-87, especially p. 79; and C.S Hastings, "On Triple =
Objectives with=20
complete Color Correction," <I>The American Journal of Science and =
Arts</I>,<I>=20
</I>3rd series, vol. 18 (1879), pp. 429-435]. &nbsp;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. =
&nbsp;He also=20
illustrated his lens with a layout [cf. H.D. Taylor, "Description of a =
Perfectly=20
Achromatic Refractor," <I>Monthly Notices of the Royal Astronomical =
Society=20
</I>54.5&nbsp; (1894), pp. 328-337; reprinted in <I>Adjustment and =
Testing</I>,=20
pp. 78-87, especially pp. 82-83]. &nbsp;<BR><BR>The glass types in =
question were=20
all "ordentlich" or "regular" types produced at the time by Schott. =
&nbsp;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). =
&nbsp;O.164 was a=20
replacement for O.658, an earlier borosilicate short-flint which Taylor =
had=20
specified in his patent. &nbsp;O.164 allowed somewhat better correction =
than=20
O.658. &nbsp;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, <I>Jena Glass and its Scientific and =
Industrial=20
Applications</I> (London,1902), pp. 134-137]. &nbsp;James R. Lynch has =
fitted=20
the indices from the 1902 Schott catalog to Buchdahl's 5-term dispersion =

formula. &nbsp;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. &nbsp;This allows a direct comparison with =
the=20
layout specified in Taylor's article.&nbsp; <BR><BR>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>1069.14<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>15<BR></DIV></TD>
    <TD vAlign=3Dtop>O.543<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-371.47<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>0.1<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-371.47<BR></TD>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>O.164<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>279.24<BR></TD>
    <TD vAlign=3Dtop>3.167<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>279.24<BR></TD>
    <TD vAlign=3Dtop>15<BR></TD>
    <TD vAlign=3Dtop>O.374<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>8325.07<BR></TD>
    <TD vAlign=3Dtop>2683.23<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>0.230<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>47.162<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-914.04<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>47.156<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 1: =
&nbsp;150mm f/18=20
Cooke-Type "Photo-visual" Triplet</DIV></DIV></DIV><BR></DIV>Next comes =
the=20
layout:<BR><BR>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"25%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter><IMG height=3D304 alt=3D"Taylor Triplet"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Cookelayout=
.JPG"=20
      width=3D121> <BR>1. 150mm f/18 Cooke-Type "Photo-visual" Triplet=20
    <BR></DIV></TD></TR></TBODY></TABLE></DIV><BR><BR>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
<I>Monthly Notices</I>, p. 332; <I>Adjustment and Testing</I>, p. 82; =
and=20
Nankivell, pp. 4-8]. &nbsp;The ray fan plots and spots come next. =
&nbsp;Since=20
this and all subsequent designs are aplanatic, I do not give ran fan =
plots for=20
the off-axis images:<BR><BR><BR>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"Cooke Photo-visual Ray Fan =
Plot"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Cookerayfan=
.JPG"=20
width=3D442> <BR>Figure 1: &nbsp;Axial Ray Fan Plot for a 150mm f/18 =
Cooke-Type=20
"Photo-visual" Triplet<BR><BR></DIV><BR>
<DIV align=3Dcenter><IMG height=3D442 alt=3D"Cooke Photo-Visual Spots"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Cookespot.J=
PG"=20
width=3D592> <BR>&nbsp; <BR>Figure 2: &nbsp;Spot diagrams for a 150mm =
f/18=20
Cooke-Type "Photo-visual" Triplet<BR></DIV><BR>Optically, the design is=20
excellent for a lens not employing fluorite or fluor-crown. &nbsp;Notice =
the=20
enlarged airgap between the second and third elements, meant to suppress =

spherochromatism. &nbsp;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.<BR><BR>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
<I>Observatory</I> 213 (April, 1894), pp.132-134]. &nbsp;Two of the =
largest=20
lenses were constructed almost immediately: &nbsp;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," <I>Sky and Telescope</I> 49.1 =
(1975),=20
pp. 24-25]. &nbsp;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," =
<I>Monthly=20
Notices of the Royal Astronomical Society</I> 68 (1908), pp.=20
19-29].<BR><BR>Unfortunately, all these lenses began to degrade soon =
after=20
completion. &nbsp;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
&nbsp;But Taylor and his employers defended the lenses and expected no =
decay=20
[cf. <I>Observatory</I> 213 (April, 1894), pp. 147-148]. &nbsp;Yet by =
1908 there=20
was ample evidence of glass degradation [cf. Lockyer, "Note on the=20
Permanency..," pp. 19-29]. &nbsp;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, <I>Monthly Notices</I>, pp. 333-334; =
<I>Adjustment and=20
Testing</I>, pp. 83-84; and Lockyer, "Note on the Permanency..," pp. =
22ff.].=20
&nbsp;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. &nbsp;Recently, the =
9-inch=20
Crossley lens was destroyed in this way after 100 years of service [cf.=20
Nankivell, pp. 6-7].&nbsp; It is a danger facing many short-flint =
apochromats.=20
&nbsp;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].<BR><BR>The optical success of Taylor's lens spurred Cooke and Sons =
to=20
search for more stable glasses. &nbsp;They had already replaced O.658 =
with=20
O.164. &nbsp;Next they replaced the ordinary crown O.374 with O.599 [cf. =

Taylor's reply to Lockyer in Lockyer, p. 29]. &nbsp;Schott too =
recognized the=20
problem and by 1902 had removed O.374 from the market [cf. H. Hovestadt, =
<I>Jena=20
Glass and its Scientific and Industrial Applications</I> (McMillan, =
1902), pp.=20
388-393]. &nbsp;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," =
<I>Zeitschrift=20
f=FCr Instrumentenkunde</I> 61 (1941), pp. 261-264; R. Riekher, =
<I>Fernrohre und=20
ihre Meister</I>, 2nd. ed. (Verlag Technik, 1990), p. 214]. &nbsp;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. &nbsp;Even so, =
old=20
Zeiss B lenses can show fungal growths [Wolfgang Busch <I>per </I>email=20
communication and photographs <A=20
href=3D"http://alice.as.arizona.edu/~rogerc/photos/B_130-1940.jpg">a)</A>=
 and <A=20
href=3D"http://alice.as.arizona.edu/~rogerc/photos/B_Fungus.jpg">b)</A>=20
].<BR><BR>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. &nbsp;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, <I>Fernrohre =
und=20
Entfernungsmesser</I>, 3rd ed. (Springer Verlag, 1959), p.134, nr. =
9]:<BR>
<DIV align=3Dcenter><BR>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>683.456<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>18<BR></DIV></TD>
    <TD vAlign=3Dtop>BaLF4<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-276.868<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>0.1<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-276.284<BR></TD>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD vAlign=3Dtop>KzF2<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>188.838<BR></TD>
    <TD vAlign=3Dtop>7.258<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>195.389<BR></TD>
    <TD vAlign=3Dtop>18<BR></TD>
    <TD vAlign=3Dtop>K7<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD vAlign=3Dtop>Standard</TD>
    <TD vAlign=3Dtop>1006.367<BR></TD>
    <TD vAlign=3Dtop>2666.608<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>-0.074<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>47.138<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-683.119<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>47.139<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 2: =
&nbsp;150mm f/18=20
"Zeiss B"-Type Triplet</DIV></DIV></DIV><BR></DIV>
<DIV align=3Djustify>The layout looks like so::<BR></DIV>
<DIV align=3Dcenter><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"25%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter><IMG height=3D304 alt=3D"Zeiss Type B Layout"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissBlayou=
t.JPG"=20
      width=3D123> <BR>2. 150mm f/18 <BR>"Zeiss B"-Type=20
  Triplet<BR></DIV></TD></TR></TBODY></TABLE><BR></DIV></DIV>The ray fan =
plots and=20
spot diagrams come next:<BR><BR>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"Ray Fan Diagram for Zeiss =
Type B"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissBrayfa=
n.JPG"=20
width=3D442> <BR>Figure 3: &nbsp;Axial Ray Fan Plots for 150mm f/18 =
"Zeiss B"-Type=20
Triplet<BR><BR><BR><IMG height=3D442 alt=3D"Zeiss B-Type Spots"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissBspot.=
JPG"=20
width=3D592> <BR>&nbsp; <BR></DIV>
<DIV align=3Dcenter>Figure 4: &nbsp;Spot Diagrams for 150mm f/18 "Zeiss =
B"-Type=20
Triplet<BR></DIV><BR>The color correction is not quite as good as in =
Taylor's=20
objective, even apart from the performance at 0.436 micron. &nbsp;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. &nbsp;Therefore, the lens could be =
built=20
at a faster focal ratio, f/15 being the target at which Zeiss =
aimed.&nbsp;=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.<BR><BR>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. &nbsp;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. &nbsp;Even small alignment errors would =
produce=20
strong coma in the image. &nbsp;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 <I>The =
Adjustment=20
and Testing of Telescope Objectives</I>, 5th ed. (Adam Hilger, 1983), =
pp. 54-57,=20
especially p. 55; Sonnefeld, pp. 262-263; J.G. Baker, "Planetary =
Telescopes,"=20
<I>Applied Optics</I> 2.2 (1963), pp. 111-129, especially&nbsp; p. 118; =
and=20
Dewhirst, pp. 24-25]. &nbsp;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."&nbsp; <BR><BR>Nevertheless, =
Zeiss=20
occassionally produced this objective type at a much faster focal =
ratio.&nbsp;=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.&nbsp; 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.&nbsp; 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.&nbsp; Kiessling reports that the =
objective=20
when used on the sky produces very good images with little outstanding=20
color.&nbsp; 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.&nbsp; =
The=20
objective gave surprisingly good performance!<BR><BR>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. &nbsp;We saw the same problem in =
Chapter=20
4a especially in regard to the "Zeiss A"-type and the SSKN8/KzFSN4 =
doublets.=20
&nbsp;In part to overcome this problem, Zeiss later developed the "F" or =
"dense=20
flint" objective. &nbsp;This became possible during the middle of the =
20th=20
century with the advent of extra dense flint glasses which displayed =
abnormal=20
dispersions. &nbsp;One such abnormal dispersion flint is called SF11. =
&nbsp;The=20
"SF" abbreviation stands for "Schwerflint," that is, "dense flint" in =
German.=20
<BR><BR>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. &nbsp;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]. &nbsp;We=20
can form an approximation of the "F" at 150mm and f/15 as follows:<BR>
<DIV align=3Dcenter><BR>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>14223<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>16<BR></DIV></TD>
    <TD vAlign=3Dtop>PSK3<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-461.190<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>0.1<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-461.190<BR></TD>
    <TD vAlign=3Dtop>10<BR></TD>
    <TD vAlign=3Dtop>SF4<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>302.368<BR></TD>
    <TD vAlign=3Dtop>0.914<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>305.400<BR></TD>
    <TD vAlign=3Dtop>18<BR></TD>
    <TD vAlign=3Dtop>SF11<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD vAlign=3Dtop>Standard</TD>
    <TD vAlign=3Dtop>-1032.53<BR></TD>
    <TD vAlign=3Dtop>2267.513<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>-.085<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>39.356<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-830.316<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>39.372<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 3: =
&nbsp;150mm f/15=20
"Zeiss F"-Type Triplet</DIV></DIV></DIV><BR></DIV>
<DIV align=3Djustify>The layout looks like so::<BR></DIV><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"25%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter>
      <DIV align=3Dcenter><IMG height=3D301 alt=3D"Zeiss F Objective"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissFlayou=
t.JPG"=20
      width=3D124> <BR></DIV>3. 150mm f/15 <BR>"Zeiss F"-Type=20
  Triplet<BR></DIV></TD></TR></TBODY></TABLE><BR></DIV>
<DIV align=3Dcenter>
<DIV align=3Djustify>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
&nbsp;Its performance at f/15 is good, though not excellent:<BR><BR>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"Zeiss F Ray Fan"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissFrayfa=
n.JPG"=20
width=3D442> <BR></DIV>
<DIV align=3Dcenter>Figure 5: &nbsp;Ray Fan Plots for 150mm f/15 "Zeiss =
F"-type=20
Triplet<BR></DIV></DIV><BR><BR><IMG height=3D442 alt=3D"Zeiss F-Type =
Spots"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/ZeissFspot.=
JPG"=20
width=3D592> <BR>&nbsp; <BR>Figure 6: &nbsp;Spot Diagrams for 150mm f/15 =
"Zeiss=20
F"-Type Triplet<BR></DIV></DIV><BR>
<DIV align=3Djustify>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. &nbsp;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]. &nbsp;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].<BR><BR>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
&nbsp;I do not know when this realization occurred. &nbsp;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
&nbsp;Probably the realization occurred to various people independently =
of one=20
another.<BR><BR>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." &nbsp;This tape is very effective at sticking to =
the=20
glass despite the oil, and forms a durable long-term barrier against =
leakage.=20
&nbsp;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"&gt; =
1)</A>=20
&amp; <A=20
href=3D"http://alice.as.arizona.edu/~rogerc/chapters/suw-1977-10-p.341.jp=
g">2)</A>=20
; for an English translation, cf. <A=20
href=3D"http://alice.as.arizona.edu/~rogerc/chapters/SuW%201977.doc">3)</=
A> ].=20
&nbsp;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&nbsp;"Tips f=FCr die Astropraxis" department of =
<I>Sterne und=20
Weltraum</I> 16 (1977), pp. 338-341; also cf. "20 Jahre Kompaktobjektive =
mit=20
=D6lf=FCgung," parts 1 &amp; 2, in <I>Sternkieker</I> (nos. 1 &amp; 2, =
1995), pp.=20
18-19; 77-78]. &nbsp;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. &nbsp;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. <BR>Busch considered his design to =
be an=20
improved type of half-apochromat, though in practice with nearly full=20
apochromatic performance. &nbsp;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.<BR><BR>Busch's=20
optical design was broadly as follows: &nbsp;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. =
&nbsp;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. &nbsp;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. &nbsp;But =
Busch had=20
two cards up his sleeve which altered that performance fundamentally for =
the=20
better. &nbsp;The first and most important was the oil-spacing. &nbsp;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. &nbsp;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. &nbsp;=20
&nbsp;<BR><BR>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. &nbsp;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. &nbsp;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
&nbsp;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]. &nbsp;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.<BR><BR>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. &nbsp;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, <I>but unpolished</I>. &nbsp;The oil film would fill in the =
grinding=20
pits and no reflection would be seen between adjacent interior surfaces. =

&nbsp;The fine ground surfaces would look entirely transparent to the =
naked eye!=20
&nbsp;<BR><BR>To demonstrate this astounding fact, the editors of =
<I>Sterne und=20
Weltraum</I> magazine displayed on the first page of Busch's article a=20
photograph of a finished objective left with fine-ground interior =
surfaces.=20
&nbsp;Below the lens lies a sheet of music, partly covered by the lens =
and=20
partly left uncovered. &nbsp;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
&nbsp;At center the lens appears beautifully transparent where the oil =
film=20
lies. &nbsp;But then comes a larger annulus of glass which the oil has =
not yet=20
reached. &nbsp;This area appears fine ground and matte. =
&nbsp;<BR><BR>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
<I>Sterne und Weltraum</I> 19 (1980), pp. 422-423]. &nbsp;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
<I>Sterne und Weltraum</I> 18 (1979), pp. 313-314]. <BR><BR>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. &nbsp;On the other hand, the Zeiss B showed slightly sharper =
images=20
when the photographs were examined under a microscope. &nbsp;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
&nbsp;Whereas, photoelectric measurements demonstrated the theoretically =

superior color correction of the Zeiss B. &nbsp;Visual assessment, =
however,=20
failed to detect any practical difference in performance.<BR><BR>Thus, =
it was a=20
draw. &nbsp;Wedel and his observers gave high marks to the Busch =
objective,=20
comparing it favorably to the Zeiss lens. &nbsp;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. &nbsp;<BR><BR>I can myself =
corroborate much=20
of this from personal experience, having built and used three Busch =
objectives.=20
&nbsp;The oil films render them completely transparent. &nbsp;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. &nbsp;The interior =
glass=20
surfaces appear as if completely polished, and the objectives performed=20
magnificently.<BR><BR>But Busch offered still more. &nbsp;One of the =
most=20
formidable obstacles to amateur construction of refractors is certainly =
the need=20
for a carefully made lens cell. &nbsp;But a complete cell in metal was =
offered=20
as part of the kit. &nbsp;Another obstacle is the need to "dewedge" the =
lens=20
elements. &nbsp;"Wedge" consists in the non-uniformity of thickness as =
one=20
proceeds around the periphery of a lens. &nbsp;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. &nbsp;Hence, the lens as a whole =
has a=20
slight "wedge" component to its shape, rather like a prism. &nbsp;This =
error, if=20
left uncorrected, will stretch a star image into a short spectrum, just =
as a=20
real prism will. &nbsp;The spectrum is, of course, the aberration called =

"lateral color" which we studied in Chapter 2.<BR><BR>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. &nbsp;Hence, the ATM's objective lens may show lateral color. =
&nbsp;But=20
lateral color can also arise from decentration of the lens elements with =
respect=20
to one another. &nbsp;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. =

&nbsp;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. &nbsp;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. &nbsp;Thus, the user could remove any lateral =
color,=20
arising from fabrication errors, during use at the telescope. &nbsp;Even =
more=20
ingeniously, the user could compensate for atmospheric dispersion in =
stellar or=20
planetary images by similarly adjusting the lens. &nbsp;I have myself =
performed=20
such adjustments on Busch objectives and they work =
perfectly.<BR><BR>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. &nbsp;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. &nbsp;According to Reichmann, the kit contained the following: =
&nbsp;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.<BR><BR>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. &nbsp;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. &nbsp;Much more interesting, however, =
are the=20
instructions concerning oiling, polishing, figuring, and testing. =
&nbsp;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
&nbsp;No taping is required or indeed possible because of the centering=20
screws.<BR><BR>After oiling, the assembled objective is inserted into =
its cell,=20
and then polished and figured on its exterior surfaces. &nbsp;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. &nbsp;This =
could=20
introduce zonal errors or astigmatism, especially in the hands of an=20
inexperienced lens maker. &nbsp;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. &nbsp;The =
total=20
stack up of glass is quite stiff and the oil layer (properly applied) is =

incompressible.<BR><BR>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. &nbsp;But in a stroke of genius, Busch =
tells=20
how to produce the required asphere almost automatically. &nbsp;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. &nbsp;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. &nbsp;Less polishing will occur in proportion as one moves =
toward=20
the center of the lens. &nbsp;Thus gradually with persistence an oblate=20
ellipsoidal surface will arise, which is exactly what is needed.=20
&nbsp;<BR><BR>For testing, Busch suggests using the Foucault or Ronchi =
test with=20
a slit source. &nbsp;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. &nbsp;All these =
methods=20
should be valid, and armed with them the ATM has everything necessary to =
make a=20
finished lens. &nbsp;No wedge testing, no spherometry is necessary; one =
does not=20
even need to polish four of the six surfaces! &nbsp;It was a marvelous =
kit and a=20
clever plan! &nbsp;Alas, it was little known outside of Germany. =
&nbsp;But=20
certainly Wolfgang Busch's name and achievement deserve to be known by =
lovers of=20
fine apochromatic lenses. &nbsp;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.<BR><BR>A Busch-type lens may be =
formed as=20
follows:<BR></DIV>
<DIV align=3Dcenter><BR>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>1081.885<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>19<BR></DIV></TD>
    <TD vAlign=3Dtop>B270<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0.449<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-405.421<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>6<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>KzFN2<BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>268.536<BR></TD>
    <TD vAlign=3Dtop>18<BR></TD>
    <TD vAlign=3Dtop>B270<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>2220.457<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>-0.064<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>39.407<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-846.714<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>39.421<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 4: =
&nbsp;150mm f/15=20
"HAB"-Type Semi-Apochromat<BR></DIV></DIV></DIV><BR><BR></DIV>The layout =
of the=20
lens looks as follows:<BR><BR>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"30%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter><IMG height=3D328=20
      alt=3D"Busch System 150mm f/15 Semi-apochromat"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Buschlayout=
.JPG"=20
      width=3D195> <BR>4. 150mm f/15 "HAB"-Type <BR>Semi-Apochromat=20
  </DIV></TD></TR></TBODY></TABLE><BR></DIV>The ray fans come =
next:<BR><BR>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"150mm f/15 Busch Rayfan"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Buschrayfan=
.JPG"=20
width=3D442> &nbsp; <BR>Figure 7: &nbsp;Ray Fans for 150mm f/15 =
<BR>HAB"-Type=20
Semi-Apochromat<BR><BR><BR>
<DIV align=3Djustify>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:<BR></DIV><BR><IMG height=3D442=20
alt=3D"150mm f/15 Busch Spot Diagrams"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Buschspot.J=
PG"=20
width=3D592> <BR><BR>Figure 8: &nbsp;Spot Diagrams for 150mm f/15 "Busch =

System"-Type Triplet<BR></DIV><BR>
<DIV align=3Djustify>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. &nbsp;The red rays just fill the Airy disk, =
while the=20
blue form a disk no more than twice as large. &nbsp;Violet is not well=20
controlled, but since it is so faint this hardly matters for visual =
observing.=20
&nbsp;There is a small amount of coma, but its magnitude is trivial and =
could=20
not be seen in practice. &nbsp;Overall, the Busch objective has achieved =
an=20
outstanding balance between performance and practicality. &nbsp;The kits =
are no=20
longer available, and KzFN2 has gone out of production. &nbsp;But =
similar and=20
better corrected lenses can be formed from KzFSN4 and the ED=20
glasses.<BR><BR>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," <I>Sky and Telescope</I> (Oct., 1981), =
pp.=20
376-380; "Revised Triplet Design," <I>Sky and Telescope</I> (April, =
1982), pp.=20
411-412; and "Design and Construction of a Super Planetary Telescope =
Objective,"=20
<I>Telescope Making</I> 28 (Fall, 1986), pp. 20-23]. &nbsp;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. &nbsp;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. <I>Sky and Telescope</I> (April, =
1982), pp.=20
411-412]. &nbsp;Moreover, oiling makes the tilt and decenter problems of =
the old=20
Cooke and Zeiss triplets completely disappear.&nbsp; Thus it becomes=20
comparatively easy to fabricate high-performance apochromats, especially =
in the=20
small sizes popular today. &nbsp;<BR><BR>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. &nbsp;In many instances it was not necessary =
to do=20
any figuring at all: &nbsp;the lenses were complete as soon as they had =
been=20
carefully polished out. &nbsp;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. &nbsp;Both have smooth wavefronts of 1/8th wave =
pv (at=20
532nm) or better. &nbsp;Nothing more than the simplest lens cells has =
been=20
necessary for either of the lenses. &nbsp;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. &nbsp;All were comparatively easy to make and=20
figure.<BR><BR>What follows is a short-flint triplet closely modeled on =
those=20
published by Christen in the above-mentioned articles:<BR></DIV>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>1862.235<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>18<BR></DIV></TD>
    <TD vAlign=3Dtop>BK7<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-365.407<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>6<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>KzFS1<BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>365.407<BR></TD>
    <TD vAlign=3Dtop>18<BR></TD>
    <TD vAlign=3Dtop>BaFN10<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-1342.645<BR></TD>
    <TD vAlign=3Dtop>1492.275<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>0.023<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>26.241<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-582.177<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>26.251<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 5: =
&nbsp;150mm=20
f/10&nbsp;KzFS1 Oil-Spaced Triplet<BR><BR><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"25%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter><IMG height=3D241 alt=3D"Christen 1 Layout"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Christenlay=
out.JPG"=20
      width=3D100> <BR>5.&nbsp; 150mm f/10&nbsp;KzFS1 Oil-Spaced Triplet =

    =
<BR></DIV></TD></TR></TBODY></TABLE><BR></DIV></DIV></DIV></DIV></DIV>
<DIV align=3Djustify>This is an elegant symmetrical design, much faster =
in focal=20
ratio than any of the preceding lenses. &nbsp;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. &nbsp;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. <I>Sky and Telescope</I> (Oct., =
1981),=20
p. 378]. &nbsp;So, the ray fan plots and spot diagrams given below are =
no doubt=20
worse than what he actually achieved. &nbsp;Yet they give an idea of the =

excellence of the corrections:<BR><BR><BR>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"Christen Ray Fan Plot"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Christenray=
fan.JPG"=20
width=3D442> <BR>Figure 9: &nbsp;Axial Ray Fan Plots for a 150mm =
f/10&nbsp;KzFS1=20
Oil-Spaced Triplet<BR><BR><BR><IMG height=3D442=20
alt=3D'Spot Diagrams for "Christen"-Type Triplet'=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Christenspo=
t.JPG"=20
width=3D592> <BR><BR>Figure 10: &nbsp;Spot Diagrams for a 150mm =
f/10&nbsp;KzFS1=20
Oil-Spaced Triplet<BR><BR>
<DIV align=3Djustify>This design is excellent for f/10 and can provide =
very=20
satisfying views. &nbsp;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
&nbsp;Otherwise, even at high powers stars in this type of lens would =
look sharp=20
and completely free of false color [cf. Christen, <I>Telescope Making =
</I>28=20
(Fall, 1986), pp. 23]. &nbsp;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:<BR><BR>
<DIV align=3Dcenter><IMG height=3D442=20
alt=3D"Chromatic Focal Shift for Christen-type Lens"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/Christenchr=
omfocshift.JPG"=20
width=3D592> <BR><BR>Figure 11: &nbsp;Chromatic Focal Shift for 150mm =
f/10 KzFS1=20
Oil-Spaced Triplet<BR></DIV><BR>Alas, KzFS1 is no longer made.&nbsp; The =
related=20
short flint, KzFSN4, on the other hand is a standard Schott glass. =
&nbsp;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:<BR>
<DIV align=3Dcenter><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>2017.256<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>18<BR></DIV></TD>
    <TD vAlign=3Dtop>N-FK5<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>-341.788<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>5<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>KzFSN4<BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>304.103<BR></TD>
    <TD vAlign=3Dtop>20<BR></TD>
    <TD vAlign=3Dtop>N-BaF51<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-978.561<BR></TD>
    <TD vAlign=3Dtop>1496.236<BR></TD>
    <TD vAlign=3Dtop>&lt;&gt; </TD>
    <TD vAlign=3Dtop>21.268<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 6: =
&nbsp;150mm f/10=20
KzFSN4 Oil-Spaced Triplet</DIV>
<DIV align=3Dcenter><BR>
<DIV align=3Djustify>The geometry of this lens is very similar to the =
KzFS1=20
triplet shown above. &nbsp;Therefore I omit a layout. &nbsp;The =
performance is=20
as follows:<BR><BR></DIV><IMG height=3D342=20
alt=3D"Ray Fan for KzFSN4 Oil-Spaced Triplet"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/KzFSN4rayfa=
n.JPG"=20
width=3D442> <BR>Figure 12: &nbsp;Ray Fan Plots for 150mm f/10 KzFSN4 =
Oil-Spaced=20
Triplet<BR><BR><BR><IMG height=3D442=20
alt=3D"Spot Diagrams for KzFSN4 Oil-Spaced Triplet"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/KzFSN4spot.=
JPG"=20
width=3D592> <BR><BR>Figure 13: &nbsp;Spot Diagrams for 150mm f/10 =
KzFSN4=20
Oil-Spaced Triplet &nbsp;<BR></DIV><BR>
<DIV align=3Dcenter>
<DIV align=3Djustify>The color residual is somewhat worse, though in =
practice one=20
would probably see no difference between the present lens and the=20
preceding.<BR>&nbsp;&nbsp;</DIV>
<DIV align=3Dcenter>
<DIV align=3Djustify>These two oil-spaced lenses represent the =
approximate limit=20
of what can be achieved with a safe oil-spaced short-flint design. =
&nbsp;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. &nbsp;Even long-term exposure to atmospheric humidity may =
degrade them.=20
&nbsp;Therefore, sealing these glasses inside a layer of oil is a good=20
conservation measure.&nbsp; 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. &nbsp;But then we may again encounter the =
centration=20
problems of the old Zeiss B and Taylor objectives. &nbsp;Therefore, it =
is=20
probably not useful to push the short-flint design any further.<BR><BR>A =
better=20
plan is to switch to an oil-spaced fluor-crown triplet, as commercial =
telescope=20
makers have done. &nbsp; By employing Ohara FPL53 in combination with =
ZKN7 we=20
can decrease the focal ratio to f/9 as follows:<BR>
<DIV align=3Dcenter><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></TD>
    <TD vAlign=3Dtop>580.789<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>10<BR></DIV></TD>
    <TD vAlign=3Dtop>ZKN7<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>304.444<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>20<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>FPL53<BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-688.687<BR></TD>
    <TD vAlign=3Dtop>10<BR></TD>
    <TD vAlign=3Dtop>ZKN7<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-2590.862<BR></TD>
    <TD vAlign=3Dtop>1325.095<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>-.063<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>23.601<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-499.454<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>23.575<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 7: =
&nbsp;150mm f/9=20
ZKN7/FPL53/ZKN7 <BR>Oil-Spaced Triplet =
Apochromat<BR></DIV><BR></DIV></DIV>
<DIV align=3Dcenter>
<DIV align=3Djustify>It will be seen here that (as in the Busch =
objective) we have=20
a sandwich construction: &nbsp;the central element of FPL53 is =
surrounded by two=20
elements of ZKN7. &nbsp;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. =
&nbsp;Since=20
the two interior spaces are filled with oil, the four interior lens =
surfaces=20
cannot readily distort the wavefront. &nbsp;Figuring this lens is now =
relatively=20
easy. &nbsp;<BR><BR>The layout is as follows:<BR></DIV>
<DIV align=3Djustify>
<DIV align=3Dcenter><BR>
<TABLE style=3D"WIDTH: 30%" cellSpacing=3D0 cellPadding=3D0 border=3D1>
  <TBODY>
  <TR>
    <TD style=3D"VERTICAL-ALIGN: top">
      <DIV align=3Dcenter><IMG height=3D306 alt=3D"Layout for FPL53/ZKN7 =
Triplet"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/FPL53f9layo=
ut.JPG"=20
      width=3D140> &nbsp; <BR>6. &nbsp;150mm f/9 ZKN7/FPL53/<BR>ZKN7 =
Oil-Spaced=20
      Triplet =
Apochromat<BR></DIV></TD></TR></TBODY></TABLE><BR></DIV><BR>The ray fan=20
plot and spot diagrams come next:<BR>
<DIV align=3Dcenter><BR></DIV>
<DIV align=3Dcenter><IMG height=3D342 alt=3D"Ray Fan for FPL53 f/9 Lens" =

src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/FPL53f9rayf=
an.JPG"=20
width=3D442> <BR>Figure 14: &nbsp;Axial Ray Fan Plot for 150mm f/9 =
ZKN7/FPL53/ZKN7=20
<BR>Oil-Spaced Triplet Apochromat<BR></DIV><BR><BR>
<DIV align=3Dcenter><IMG height=3D442 alt=3D"Spot Diagrams for FPL53 f/9 =
Lens"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/FPL53f9spot=
.JPG"=20
width=3D592> <BR></DIV>
<DIV align=3Dcenter><BR>Figure 15: &nbsp;Spot Diagrams for 150mm f/9=20
ZKN7/FPL53/ZKN7 <BR>Oil-Spaced Triplet Apochromat<BR><BR><BR></DIV>The =
color=20
correction is excellent and the spherochromatism is under control. =
&nbsp;The=20
small 5th order residual of spherical aberration seen in green light is =
of=20
little significance. &nbsp;An examination of the chromatic focal shift =
diagram=20
shows a notable improvement over that for a short-flint =
design:<BR><BR><BR>
<DIV align=3Dcenter><IMG height=3D442=20
alt=3D"Chromatic Focal Shift Diagram for FPL53 Lens"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/FPL53f9chro=
mfocshift.JPG"=20
width=3D592> <BR><BR>Figure 16: &nbsp;Chromatic Focal Shift Diagram for =
150mm f/9=20
ZKN7/FPL53/ZKN7 Triplet<BR></DIV><BR>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. &nbsp;Many vertical slices through the graph will =
intersect=20
three widely separated wavelengths of light. &nbsp;Figure 15 shows =
excellent=20
correction for coma, only a small amount of chromatic astigmatism being =
clearly=20
displayed.&nbsp; While Figure 14 shows good spherical correction for the =
e-line.=20
&nbsp;Thus, here we have achieved an excellent practical lens worthy of =
the name=20
apochromatic.<BR><BR>I have built a 140mm f/9 version of the above lens =
and it=20
performs admirably. &nbsp;Only the merest hint of color can be seen in =
the=20
Fresnel rings as you rack through focus, even when observing Vega. =
&nbsp;At=20
focus, the Airy disk and ring system look absolutely free of false =
color.=20
&nbsp;<BR><BR>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). &nbsp;Such a lens would =
no doubt=20
give superb results [cf. A. Karnapp &amp; J. Pudenz, "The 100/1000mm APQ =

objective--a new level of quality in astronomical optics," <I>Jenaer=20
Rundschau</I> 31.3 (1986), pp. 140-141; and U. Laux, <I>Astrooptik</I>, =
2nd ed.=20
(<I> Sterne und Weltraum</I>, 1999), pp. 51-53].<BR><BR>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. &nbsp;Color correction remains acceptable. &nbsp;Below f/7 or f/6, =

spherochromatism will degrade the performance so that color will =
reappear in the=20
image. &nbsp;Certainly the one commercial 125mm f/6 ED triplet which I =
have=20
closely examined, showed signs of being near the limit. &nbsp;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. &nbsp;So here lies a fundamental limit in oil-spaced triplet =
design.=20
&nbsp;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.&nbsp;<BR>
<DIV align=3Djustify><BR>Another way to improve the performance of fast =
apos is by=20
adding a fourth lens element&nbsp;[cf. U. Laux, <I>Astrooptik</I>, 2nd =
ed.=20
(<I>Sterne und Weltraum</I>, 1999), p. 47]. &nbsp;Combined with one =
narrow=20
airgap, this easily results in greatly improved performance. &nbsp;The =
following=20
is a such design for a 150mm f/7 four-element =
apochromat:<BR></DIV></DIV>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter><BR>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"75%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>433.00<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>8<BR></DIV></TD>
    <TD vAlign=3Dtop>BK7<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>226.55<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>27<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>FPL53<BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-460.68<BR></TD>
    <TD vAlign=3Dtop>0.042<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-474.59<BR></TD>
    <TD vAlign=3Dtop>12<BR></TD>
    <TD vAlign=3Dtop>F2<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-245.25<BR></TD>
    <TD vAlign=3Dtop>10<BR></TD>
    <TD vAlign=3Dtop>BaF4<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-1507.04<BR></TD>
    <TD vAlign=3Dtop>1018.98<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>-0.056<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>18.356<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-391.08<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>18.329<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 8: =
&nbsp;150mm f/7 FPL53=20
Four-element Apochromat</DIV></DIV></DIV></DIV></DIV><BR><BR>
<DIV align=3Dcenter>
<DIV align=3Djustify>The layout for this lens is as follows:<BR>
<DIV align=3Dcenter>
<TABLE cellSpacing=3D0 cellPadding=3D0 width=3D"25%" border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dcenter><IMG height=3D331 alt=3DLayout=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/4elmf7layou=
t.JPG"=20
      width=3D160> <BR>7. 150mm f/7 Four-<BR>Element=20
  Apochromat<BR></DIV></TD></TR></TBODY></TABLE><BR></DIV></DIV>
<DIV align=3Djustify>The lens can be thought of as a Fraunhofer-type =
objective=20
with crown and flint elements both composites of two lenses each. =
&nbsp;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. &nbsp;Moreover, spherochromatism can be almost completely=20
suppressed.<BR><BR>The performance is as follows:<BR><BR>
<DIV align=3Dcenter><IMG height=3D342=20
alt=3D"Ray Fan Plot for 150mm f/7 Four-element Apochromat"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/4elmf7rayfa=
n.JPG"=20
width=3D442> <BR>Figure 17: &nbsp;Ray Fan Plots for 150mm f/7 =
Four-element=20
Apochromat<BR><BR><BR><IMG height=3D442=20
alt=3D"Ray Fan Plot for 4-Element f/7 Design"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/4elmf7spot.=
JPG"=20
width=3D592> &nbsp; <BR>Figure 18: &nbsp;Spot Diagrams for 150mm f/7 =
Four-element=20
Apochromat<BR><BR>
<DIV align=3Djustify>These are the best spot diagrams we have seen so =
far.&nbsp;=20
Even down to a wavelength of 1.000 micron (not illustrated) the color =
blurs stay=20
much smaller than the Airy disk. &nbsp;The ray fan plot shows only a =
small=20
spherochromatism. &nbsp;The 5th order spherical residual common to all =
the=20
wavelengths could be removed through figuring.&nbsp; 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.<BR><BR>Despite the =
advantages of=20
oil-spacing, recently the major manufacturers of commercial apochromats =
haved=20
shifted back to air-spacing.&nbsp; The reason seems to be twofold:&nbsp; =
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.&nbsp; <BR><BR>By dispensing with the oil, four more air-glass =
surfaces=20
become available for variation as degrees of freedom.&nbsp; 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.&nbsp; To show an example of what is possible, below I =
give a=20
design for a 155mm f/7 air-spaced triplet apochromat:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center">
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter>
<DIV align=3Dcenter><BR>
<TABLE style=3D"WIDTH: 75%" cellSpacing=3D0 cellPadding=3D0 border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Even Asphere<BR></TD>
    <TD vAlign=3Dtop>507.156<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>7.75<BR></DIV></TD>
    <TD vAlign=3Dtop>SK2<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>290.991<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>0.104<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>276.892<BR></TD>
    <TD vAlign=3Dtop>24.2<BR></TD>
    <TD vAlign=3Dtop>FPL53<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-393.550<BR></TD>
    <TD vAlign=3Dtop>0.473<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-376.823<BR></TD>
    <TD vAlign=3Dtop>9.7<BR></TD>
    <TD vAlign=3Dtop>FK5<BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-1197.50<BR></TD>
    <TD vAlign=3Dtop>1061.469<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>160<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>0.015<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>9.471<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-395.529<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>9.469<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 9: =
&nbsp;155mm f/7=20
Air-Spaced Triplet Apochromat</DIV></DIV></DIV></DIV></DIV></DIV><BR>The =
layout=20
is as follows:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center">
<TABLE=20
style=3D"MARGIN-LEFT: auto; WIDTH: 20%; MARGIN-RIGHT: auto; TEXT-ALIGN: =
left"=20
cellSpacing=3D0 cellPadding=3D0 border=3D1>
  <TBODY>
  <TR>
    <TD style=3D"VERTICAL-ALIGN: top">
      <DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 124px; =
HEIGHT: 328px"=20
      alt=3D"155mm f/7 Layout"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155f7layout=
.JPG"><BR></DIV>
      <DIV style=3D"TEXT-ALIGN: center">8. 155mm f/7 Air-Spaced =
<BR>Triplet=20
      =
Apochromat<BR></DIV><BR></TD></TR></TBODY></TABLE><BR></DIV><BR>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.&nbsp; Moreover, we can compare the results with those =

published for a similar type of objective actually produced and sold by =
a=20
commercial manufacturer.&nbsp; I must stress yet again, however, that my =
design=20
is not an attempt to "reverse engineer" a commercial lens.&nbsp; I have =
no=20
knowledge whatever of the actual prescription of any commercial =
optics.&nbsp;=20
This website exists merely as a teaching tool, not an equipment=20
review.<BR><BR>Let us first look at the longitudinal aberration graph =
for the=20
above lens.&nbsp; 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:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"155mm f/7 Longitudinal Error Graph"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155f7longit=
udinal.JPG"><BR><BR>Figure=20
19:&nbsp; Longitudinal Aberration Graph for 155mm f/7 <BR>Air-spaced =
Apochromat=20
listed in Table 9<BR></DIV><BR><BR>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.&nbsp; 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.&nbsp; 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.<BR><BR>Compare this to the following =
graph=20
derived from the manufacturer's literature:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><BR>
<TABLE=20
style=3D"MARGIN-LEFT: auto; WIDTH: 30%; MARGIN-RIGHT: auto; TEXT-ALIGN: =
left"=20
cellSpacing=3D0 cellPadding=3D0 border=3D1 frame=3Dborder>
  <TBODY>
  <TR>
    <TD style=3D"VERTICAL-ALIGN: top"><IMG style=3D"WIDTH: 467px; =
HEIGHT: 616px"=20
      alt=3D"Manufacturerer's Longitudinal Error Graph"=20
      =
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155colorcur=
ve.jpg"></TD></TR></TBODY></TABLE><BR>Figure=20
20:&nbsp; Manufacturer's Longitudinal Error Graph for<BR>Commercial =
155mm f/7=20
Air-spaced Triplet Apochromat<BR></DIV><BR>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.&nbsp; 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:<BR><BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"155mm f/7 Strehl Ratio Graph"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155f7Strehl=
.JPG"><BR></DIV><BR>
<DIV style=3D"TEXT-ALIGN: center">Figure 21:&nbsp; Polychromatic Strehl =
Ratio=20
Graph for Lens listed in Table 9 above.<BR></DIV><BR>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.&nbsp; =
But the=20
close similarity of the graphs in Figures 19 and 20 precludes any large=20
error.&nbsp; 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.&nbsp; Rather, since the public has demanded zero <SPAN=20
style=3D"FONT-STYLE: italic">visible</SPAN> color error and a very short =
focal=20
ratio from the commercial makers of apochromats, compromises have had to =
be=20
made.&nbsp; 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.&nbsp; 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.&nbsp; There will not be a large patch of unfocused =
light=20
like the blue halo which one sees around stars in an achromat.&nbsp; =
Over the=20
bandwidth from the C- to the F-line, one would have the following=20
performance:<BR><BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"Strehl from C to F"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155f7Strehl=
CF.JPG"><BR></DIV>
<DIV style=3D"TEXT-ALIGN: center"><BR>Figure 22:&nbsp; Polychromatic =
Strehl Ratio=20
Graph from C to F in Table 9 Lens<BR><BR><BR></DIV>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.&nbsp; 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.&nbsp; 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.&nbsp; At the e-line (0.546 =
micron) the=20
theoretical Strehl ratio would be nearly 100%.<BR><BR>The chromatic =
focal shift=20
diagram ("color curve") for the lens in Table 9 is as follows:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"Chromatic Focal Shift for 155 f/7 Air-spaced Triplet"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/155f7colorc=
urve.JPG"><BR><BR>Figure=20
23:&nbsp; Chromatic Focal Shift Diagram for 155mm f/7 Lens of Table =
9<BR><BR>
<DIV style=3D"TEXT-ALIGN: justify">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.<BR></DIV></DIV><BR>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.'"&nbsp; This manufacturer also =
notes that=20
such a lens should display three widely separated color =
crossings.<BR><BR>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.&nbsp; 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.&nbsp; =
So=20
instead, the manufacturer gives a practical definition tailored to what =
he finds=20
feasible and satisfactory for current lenses.&nbsp; 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."&nbsp; 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"&gt; <TBODY><TR><TD=20
style=3D"VERTICAL-ALIGN: top"><IMG style=3D"WIDTH: 445px; HEIGHT: 422px" =

alt=3D"160mm f/7.5 air-spaced triplet"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/160colorcur=
ve.jpg"><BR></TD></TR></TBODY></TABLE><BR>Figure=20
24:&nbsp; Chromatic Focal Shift Diagram for Commercial 160mm =
f/7.5<BR>Air-Spaced=20
Triplet Apochromat<BR><BR></DIV>
<DIV style=3D"TEXT-ALIGN: center"><BR></DIV>The correction in this case =
extends=20
from 0.405 to 0.707micron.&nbsp; A revision of the lens given in Table 9 =
above=20
yields the following chromatic focal shift diagram:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"160mm f/7.5 Color Curve"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/160f7colorc=
urve.JPG"><BR><BR>Figure=20
25:&nbsp; Chromatic Focal Shift Diagram for 160mm f/7.5 <BR>Air-Spaced =
Triplet=20
Apochromat given in Table 10 (below)<BR><BR>
<DIV style=3D"TEXT-ALIGN: justify">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.&nbsp; The prescription for =
my=20
revised lens is as follows:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><BR>
<TABLE=20
style=3D"MARGIN-LEFT: auto; WIDTH: 75%; MARGIN-RIGHT: auto; TEXT-ALIGN: =
left"=20
cellSpacing=3D0 cellPadding=3D0 border=3D1>
  <TBODY>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Surface<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>Type<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Radius<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Thickness<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Glass<BR></DIV></TD>
    <TD vAlign=3Dtop>Diameter<BR></TD>
    <TD vAlign=3Dtop>Conic<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Object<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>Standard<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Infinity<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>0<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Stop<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Even Asphere<BR></TD>
    <TD vAlign=3Dtop>805.108<BR></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>8<BR></DIV></TD>
    <TD vAlign=3Dtop>SK2<BR></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>2<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>312.720 </TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>0.050<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>3<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>280.023<BR></TD>
    <TD vAlign=3Dtop>25<BR></TD>
    <TD vAlign=3Dtop>FPL53<BR></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>4<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-459.535<BR></TD>
    <TD vAlign=3Dtop>2.230<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>5<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-359.426<BR></TD>
    <TD vAlign=3Dtop>10<BR></TD>
    <TD vAlign=3Dtop>FK5<BR></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>6<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>-593.217<BR></TD>
    <TD vAlign=3Dtop>1183.379<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>165<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>7<BR></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>Standard<BR></TD>
    <TD vAlign=3Dtop>Infinity<BR></TD>
    <TD vAlign=3Dtop>0.015<BR></TD>
    <TD vAlign=3Dtop><BR></TD>
    <TD vAlign=3Dtop>10.494<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR>
  <TR>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>Image<BR></DIV></TD>
    <TD style=3D"WIDTH: 15%" vAlign=3Dtop>
      <DIV align=3Dleft>
      <DIV align=3Dleft>
      <DIV align=3Dleft>Standard<BR></DIV></DIV></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft>-435.044<BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>
      <DIV align=3Dleft><BR></DIV></TD>
    <TD vAlign=3Dtop>10.476<BR></TD>
    <TD vAlign=3Dtop>0<BR></TD></TR></TBODY></TABLE><BR>Table 10: =
&nbsp;160mm f/7.5=20
Air-Spaced Triplet Apochromat</DIV></DIV><BR></DIV>
<DIV style=3D"TEXT-ALIGN: justify"><BR>Its polychromatic Strehl ratio =
diagram=20
comes next:<BR><BR>
<DIV style=3D"TEXT-ALIGN: center"><IMG style=3D"WIDTH: 592px; HEIGHT: =
442px"=20
alt=3D"160mm f/7.5 Polychromatic Strehl"=20
src=3D"http://alice.as.arizona.edu/~rogerc/images/apotriplets/160f7Strehl=
.JPG"><BR><BR>Figure=20
26:&nbsp; Polychromatic Strehl Ratio Diagram for Lens in Table =
10<BR><BR>
<DIV style=3D"TEXT-ALIGN: justify">This objective shows improvement at =
the longer=20
wavelengths, and certainly meets the functional "revised" definition of =
an=20
apochromat.&nbsp; 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.&nbsp; The design can also be scaled up to =
250mm=20
f/9.&nbsp; When that is done, the whole spectral bandwidth from g- to r- =
(0.436=20
to 0.707micron) performs better than the diffraction limit.&nbsp; =
<BR><BR>I have=20
seen one 10" f/9 triplet from a commercial maker and it showed no =
visible color=20
error.&nbsp; That is not to say, however, that the telescope gave a =
stellar=20
performance.&nbsp; 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.&nbsp; I was rather =
aghast=20
to see the severe spherical aberration in the 10" lens, due to the =
falling=20
temperature that night.&nbsp; 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.&nbsp; 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.&nbsp; Other examples of this type of instrument also show =
the same=20
problem I am told by my optical acquaintances.&nbsp; 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.&nbsp; 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.&nbsp; Oiled lenses =
even of=20
rather large thickness show much more moderate variation of spherical =
aberration=20
during cool-down in my experience.&nbsp; Perhaps the large air-spaced =
beasts=20
will work well on tropical islands where the diurnal temperature =
variation is=20
minimal.&nbsp; But people who live in temperate climates may wish to be =
careful=20
of large air-spaced ED lenses.<BR><BR><SPAN=20
style=3D"FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman'">That concludes =
our=20
survey of apochromatic objectives. &nbsp;Several special refinements =
will be=20
found in the last two chapters. &nbsp; In Chapter 5 we will examine the=20
so-called "Petzval" telescope and sub-aperture color correctors. =
&nbsp;In=20
Chapter 6 we look at two completely different forms of refractor: =
&nbsp;Ludwig=20
Schumann's "Medial" and "Brachymedial"=20
telescopes.<BR></SPAN></DIV></DIV></DIV></DIV><BIG><B><BR></B></BIG>
<DIV align=3Dcenter><BIG><B><A=20
href=3D"http://alice.as.arizona.edu/~rogerc/chapters/Chapter%205.html">Ch=
apter=20
5</A> </B></BIG></DIV></DIV>
<DIV align=3Dcenter><BR><A =
href=3D"http://alice.as.arizona.edu/~rogerc">Back to=20
Table of Contents</A> </DIV></DIV></DIV></DIV></DIV></DIV></DIV>
<DIV></DIV>the barely contained spherochromatism at work. &nbsp;So here=20
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