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The Development of the Photographic Objective

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Abstract and Figures

Photographic objectives are one of the most popular imaging devices worldwide. Using the optical design software Zemax, the aberrations affecting the photographic objectives from the simplest Wollaston meniscus to the more sophisticated double-Gauss lenses are here investigated.
shows a simulation of the focal shift due to longitudinal chromatic aberrations in the visible spectrum. The plot was made for an ordinary achromatic doublet of aperture f/15 and focal length 54 mm. As illustrated, the focal shift experiences a parabolic trend which reduces the value to roughly 48 µm. This represents a huge improvement compared to the previous Wollaston meniscus. In addition, Chevalier noticed experimentally that field curvature could be partially removed by turning around his doublet [4], as shown in Figure 3.5. Following this way, he obtained a flat field for even more than 20° from the axis. Nevertheless, this operation involved the appearance of a large amount of coma. Indeed, as shown in Fig. 2.5 (b), the dashed rays passing through the lower side of the lens were sharply bent upwards resulting in a position above the focal point D. However, by means of a suitable choice of the aperture distance from the doublet it was possible to 'hide' this effect and obtain images with reasonable resolution. During the 1860s different attempts to improve the Landscape lens were made without a significant success. For instance, T. Grubb made a lens in 1857 called " Aplanat " because of the low spherical aberration. This was made placing the crown element in front of the meniscus flint element (Figure 3.6 (a)). Although the apparent improvement, the absence of spherical aberrations turned out to be a disadvantage as it could not allow the correction of coma by a suitable choice of the aperturelens distance. Further designs were made some years later by Dallmeyer who released two similar triplets consisting of three elements: the " Rapid Landscape " and the " Rectilinear Landscape " lens shown in Figure 3.6. With these lenses Dallmeyer managed to cover a total angular field of 74° which represented the limit of these simple landscape lenses.
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The$Development$of$the$Photographic$Objective!!! ! !!MSc!Optics!&!Photonics!
Giuseppe!Antonacci!! ! ! Imperial!College!London!
1!
Self Study Project
The Development of the Photographic Objective
Giuseppe Antonacci
Imperial College London, 24th March 2010, Prof. R. Smith
Abstract
Photographic objectives are one of the most popular imaging devices worldwide. Their historical
development has been retraced from the simplest Landscape lenses. Thanks to the Petzval lens, the
aperture has risen to f/3.6. Furthermore, the design of symmetrical systems allowed the straight
correction of coma, distortion and transverse chromatic aberration. Basing on this principle, a
wide range of Anastigmats and Double-Gauss lenses have been designed. Both Telephoto and
Reverse Telephoto lenses have been investigated through their basic optical principles.
1. Introduction
Photographic objectives have represented a wide field of research for optical designers since the
first half of the 19th century. They can be arranged with one or more groups of lenses made of
glasses of different refractive index. Moreover, the shape, the distance and the dimension of each
component rigorously establish the objective performance. This survey is addressed to give an
historical view on their development following the reasons which led designers to adopt different
types of systems. The production of new photographic lenses was indeed guided by the period
requirements in terms of their aperture size and the total angular field enabled to cover. These two
parameters, as well as the focal length, define uniquely the nature of a photographic objective.
The starting point of this survey was the simple “Pinhole Camera”. This was firstly investigated in
order to understand the reasons behind the requirement of lenses. Curiously, the first photographic
objective was realised before the invention of photography, in 1812. This was a simple meniscus
lens corrected from astigmatism by means of a suitable distance from the stop position. In 1821
Chevalier designed his “Landscape” lens composed of an achromatic doublet made of a crown and
a flint component of opposite power. This covered a total field of roughly 40° but had a limited
aperture of f/15 due to the big coma. The general request of a faster objective was promptly fulfilled
by the mathematician Petzval. He designed a lens composed of a cemented doublet as the front
component and a separated doublet on the rear. The lens achieved good results for an aperture of
The$Development$of$the$Photographic$Objective!!! ! !!MSc!Optics!&!Photonics!
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f/3.6 and a maximum field of 30°. Thanks to the advent of symmetrical systems, in the 1850s,
coma, distortion and transverse chromatic aberration could be automatically removed. The “Rapid
Rectilinear” was one of the most successful early symmetrical objectives made of two inverted
achromatic doublets with respect to a central stop. Double-Gauss systems relied on the advantage of
symmetry as well. Their arrangement is still considered as a model by lens designers for the
production of ordinary objectives. A wide range of Anastigmat lenses have been also investigated
until the advent of the famous Rudolph’s Tessar. Furthermore, both Telephoto and Reverse
Telephoto systems have been treated on their basic optical principles.
2. The Pinhole Camera
The simplest and oldest imaging device is the so-called “Pinhole Camera”. This consists of a
camera obscura provided of a pinhole on one side. The optical principles behind this camera date up
to the fifth century BC where light had been newly found to travel in straight lines. The Chinese
philosopher Mo Ti was the first who noticed the composition of an inverted image on the rear plane
of a pinhole. He understood the principle for which the light reflected through the top of an object
will form the bottom side of the resulting image after passing through a hole of small dimension.
Pinhole camera is a lensless device that allows the formation of almost ‘perfect’ images. Indeed,
apart from small chromatic aberrations, this is not affected by any other kind of defections such as
field curvature or distortion. As a consequence, images from even wide-angular fields remain
perfectly rectilinear and, in addition, they were provided of an infinite depth of field. The Physics
Nobel price Lord Rayleight worked on the optical principles of pinhole cameras towards the end of
the 19th century. He found an expression for the best image distance d as a function of the pinhole
radius r
(2.1)
where λ is the wavelength [1]. Of course, the smaller the pinhole size, the sharper is the image.
Nevertheless, the biggest limitation of pinhole cameras is the extremely long time of exposure
necessary to make pictures. Indeed, even in bright days they might require more than one-hour
exposure to acquire enough light. Therefore, it is straightforward to understand how the requirement
of lenses was inevitable with the advent of photography. Although the higher amount of light
collected into the camera, lenses opened a new field of research addressed to control the aberrations
introduced by them.
3. The Landscape Lens
Curiously, the first photographic lens was designed roughly 25 years before the invention of
photography. Previously, lenses were used for a small range of practical applications, such as for
the design of telescopes and microscopes objectives. The invention of the camera obscura created
indeed a new field of application for lenses which has broadened massively in the last two century.
d=2r2
λ
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3.1 The Wollaston simple meniscus
The first lens mounted on a camera obscura was a biconvex
crown-glass lens that allowed good definition on the centre of
the image but experienced an overall degradation after few
field angles. In 1812 the English scientist W. H. Wollaston
made a considerable improvement replacing the simple
biconvex lens with a meniscus-shaped model. This has been
mounted with its concave side in front of the stop, as shown
in Figure 3.1. Wollaston managed to correct astigmatism
empirically by means of a suitable distance from the aperture
[2]. Indeed, with the release of the Seidel coefficients for the low-order aberration terms about 60
years later, astigmatism was found to be dependent on both the stop position and the lens shape, as
illustrated by the expression
(3.1)
where SI, SII and SIII are the Seidel coefficients for spherical aberration, coma and astigmatism
respectively, H is the Lagrange invariant and E is the eccentricity parameter. Indeed, by a suitable
choice of spherical aberration and coma (both dependent on the bending parameter B) and the stop
position, astigmatism could be removed from the system, as shown in Figure 3.2.
Nevertheless, the simple meniscus could not control field curvature as it required the employment
of further elements. As a consequence, objects were imaged on a curved surface, namely the “Petzal
curve”, instead of an ideal plane. This problem was partially hidden by using small apertures that
allowed a reasonable definition over the whole field. Moreover, huge amounts of chromatic
aberrations affected the Wollaston’s lens performance. A plot of the focal shift due to longitudinal
!
Figure 3.1 | The simple Wollaston’s
Landscape lens!
!
SIII
*=SIII +(HE)2SI+2HESII
Figure 3.2 | Field curvature and distortion plots
for a typical meniscus lens designed with a field
angle of 35
°
. For a stop-lens distance of roughly
7 mm the T and S curves are superimposed, i.e.
there is not astigmatism.!
!
!
Figure 3.3 | Focal shift plot for a typical
meniscus. The total focal shift due to longitudinal
chromatic aberrations is approximately 2.6 mm
in the visible light.!
!
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chromatic aberrations for a typical meniscus lens in the visible spectrum is shown in Figure 3.3.
Furthermore, this lens suffered also from spherical aberrations, coma and distortion and its defects
became visible only after the discovery of photography in 1839.
The Wollaston’s meniscus, also known as the “Periscopic” lens, produced good images in the
range between f/16 and f/8 apertures with a sharp definition until 25° from the axis. Although its
considerable defects, this lens remained very commonly used in photography for almost 50 years.
3.2 The Achromatic Landscape Lens
The first attempt to improve the Wollaston’s singlet was made in 1821 by C. Chevalier, a notable
telescopes and microscopes designer. He produced a doublet composed of a positive biconvex
crown of low refractive index (nA~1.52; VA~64) and a negative plano-vex flint of higher refractive
index (nB~1.62; VB~36) cemented together. Thanks to this combination of glasses (the only
available in that period), Chevalier managed to design empirically a lens almost free from
chromatic aberration. Indeed, the two conditions required to remove longitudinal chromatic
aberrations [3] can be expressed by
(3.2)
where KA and KB are the powers of the two elements respectively and K is the total power of the
doublet. Since VA and VB are both positive, these conditions lead to the necessity of two lenses of
opposite powers. Using the glass specifications expressed above, from equations (3.2) it is also
possible to find the relationship
(3.3)
which is sufficiently satisfied by the Chevalier lens.
Figure 3.4 | Focal shift plot for a Chevalier doublet. Thanks to the parabolic
trend, the total shift amounts to roughly 48
µ
m in the visible spectrum.
KA=VA
VAVB
K KB=VB
VAVB
K
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!
Figure 3.5 | Chevalier’s Landscape lens. Field
curvature and coma are partially removed by placing
the flint component at a certain distance from the
aperture (b).
Figure 3.4 shows a simulation of the focal shift due to longitudinal chromatic aberrations in the
visible spectrum. The plot was made for an ordinary achromatic doublet of aperture f/15 and focal
length 54 mm. As illustrated, the focal shift experiences a parabolic trend which reduces the value
to roughly 48 µm. This represents a huge improvement compared to the previous Wollaston
meniscus.
In addition, Chevalier noticed experimentally that field curvature could be partially removed by
turning around his doublet [4], as shown in Figure 3.5. Following this way, he obtained a flat field
for even more than 20° from the axis.
Nevertheless, this operation involved the
appearance of a large amount of coma. Indeed,
as shown in Fig. 2.5 (b), the dashed rays
passing through the lower side of the lens
were sharply bent upwards resulting in a
position above the focal point D. However, by
means of a suitable choice of the aperture
distance from the doublet it was possible to
‘hide’ this effect and obtain images with
reasonable resolution.
During the 1860s different attempts to
improve the Landscape lens were made
without a significant success. For instance, T.
Grubb made a lens in 1857 called “Aplanat”
because of the low spherical aberration. This
was made placing the crown element in front
of the meniscus flint element (Figure 3.6 (a)).
Although the apparent improvement, the
absence of spherical aberrations turned out to
be a disadvantage as it could not allow the correction of coma by a suitable choice of the aperture-
lens distance. Further designs were made some years later by Dallmeyer who released two similar
triplets consisting of three elements: the “Rapid Landscape” and the “Rectilinear Landscape” lens
shown in Figure 3.6. With these lenses Dallmeyer managed to cover a total angular field of 74°
which represented the limit of these simple landscape lenses.
!! ! !!!!! !!!!!!!!!!!!!!! !
Figure 3.6 | From left to right, the Grubb Aplanat lens (a), the Dallmeyer’s
Rapid Landscape (b) and the Dallmeyer’s Rectilinear Landscape lens (c).
(a)
(b)
(c)
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!
Figure 4.1 | The Petzval’s Portrait lens, f/3.6
4. The Petzval Portrait Lens
With the birth of photography in 1939 the only lens available in that period was the Chevalier’
achromatic doublet. However, the former had an aperture of f/15 that limited the time of exposure
to almost 30 minutes even in bright sunlight. Of course, a faster objective was strongly required to
make simple portraits even in slightly darker environments.
The first real attempt was made by the 32-year-old Hungarian mathematician Joseph Petzal in
1940. He was stimulated by his colleague A. F. Von Ettinghausen, a professor of physics in Vienna,
because of the award being offered by the Society for the Encouragement of National Industry for a
faster lens. In six months Petzal managed to design a new lens capable to achieve an aperture of
only f/3.6 with a focal length of 150 mm.
Starting with a cemented doublet corrected from spherical and chromatic aberrations, he placed a
stop behind in order to correct astigmatism with the same principle adopted by Wollaston. Then, a
separated pair was also placed behind the stop at an apposite distance to equally correct its
astigmatism (Figure 4.1). Likewise to the doublet, the pair of lenses employed was corrected from
both spherical and chromatic aberrations. Moreover, this presented an equal amount of coma but of
opposite sign to that introduced by the front doublet. Since coma is linearly dependent on the
bending parameter (SII
B), this condition was achieved by setting appropriate values for the lens
curvatures. The Petzal’s lens finally resulted to be corrected for spherical and chromatic aberrations,
astigmatism and coma. Nevertheless, this still suffered field curvature and this limited the image
definition until an angular field of approximately 28°. For this reason, the former was used mainly
for ordinary portraitures. Furthermore, since antireflection coatings have been not available until the
1940s, the air separation between two elements was faced as a serious problem. Indeed,
approximately 5% of the total light caught by the objective was back-reflected by each glass-air
interface thus affecting the image brightness. Moreover, second air-glass reflections could
dramatically deteriorate the images quality. In fact, ghost reflections could result in the formation of
further images such as distant objects or diaphragms.
Thanks to the high aperture, the Petzal’s objective achieved a much smaller exposure time and this
allowed even indoor photographs. Moreover, this lens was widely used for almost one century and
it was considered the fastest lens until 1910 when anastigmats of bigger aperture have been
produced.
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5. Symmetrical Lenses
Towards the end of the 1850s, the great advantages of symmetrical systems about a central stop
began to be realized by optical designers. Indeed, an objective made of whatever lens components
placed exactly symmetrical about a central stop can automatically be corrected from all orders of
coma (
SII =0
), distortion (
SV=0
) and transverse chromatic aberration (
CII =0
). This is
due to the opposite ray heights with respect to the optical axis from one side to the other. In other
words, the aberrations affecting the front and the rear components cancel each other as they have
equal values but with opposite sign due to the system symmetry. In order to appreciate this
discovery we firstly have to comprehend the relevance of distortion in a period when photography
was fresh-invented. Until the daguerreotype process, indeed, only extremely slow lenses were
available that could allow pictures only on static objects because of the long time of exposure.
Therefore, large architectonical structures such as building or walls have been taken as the main
subjects for photographers. These objects required a reasonable wide-angle for been captured and
thus, distortion was found to be the main source of degradation for the resulting pictures. It is then
straightforward to understand how the advent of symmetrical objectives was highly appreciated by
both photographers and lens designers. Nevertheless, in order to be completely corrected from these
three aberrations, these systems required a unit magnification which was considerably difficult and
even not of great utility to produce. However, it was realised that even non-perfect symmetrical
designs could strongly reduce coma, distortion and transverse chromatic aberration to almost
negligible values. On the other hand, spherical aberration, astigmatism, field curvature and
longitudinal chromatic aberration were still affecting these systems and therefore small apertures
had to be employed for the earliest objectives.
5.1 Wide-angle Lenses
As mentioned before, the period between 1860 and 1870 was characterised by a strong interest on
making lenses with extremely large angular fields. One of the earliest wide-angle lens was designed
by Sutton in 1859. He created the water-filled “Panoramic” ball lens whose structure relied on the
symmetry about a single point in the middle of the lens. The Sutton Panoramic lens achieved a wide
angular field limited by vignetting to roughly 120º. Nevertheless, a small aperture of f/30 has been
required because of the consistent presence of both spherical and chromatic aberrations. In 1860 C.
Harrison and J. Schnitzer made one of most famous wide-angle symmetrical lenses. This was called
the “Globe Lens” because the front and the rear element formed part of the same sphere (Figure 5.1
(a)). This particular shape allowed a field angle of almost 80º for an aperture of f/30. A reasonable
improvement was made by E. Bush in 1865 with the “Pantoskop Lens” whose surfaces were made
more deeply curved than in the Globe Lens, as illustrated in Figure 5.1 (b). This lens was
completely corrected for spherical aberrations until a total field angle of 80º at f/25. In the same
year, C. Steinheil designed the “Periskop” consisting of two simple Wollaston’s meniscus mounted
symmetrically with respect the central stop (Figure 5.1 (c)). The lens obtained good result until an
aperture of f/15. The limit on this series of wide-angle lenses was reached in 1900 with the release
of the Goerz “Hypergon” made of two strongly curved meniscus lenses symmetrical respect to the
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central stop, as shown in Figure 5.1 (d). The lens covered a flat anastigmatic field until 134º with an
aperture of f/20.
Although these lenses have taken advantage from their symmetrical structure, all of them still
suffered from some other kind of aberrations such as spherical and longitudinal chromatic
aberrations. For this reason, they faced the necessity of having small apertures and consequently a
long time of exposure for making pictures.
5.2 The Rapid Rectilinear
By far one of the most successful photographic objectives ever made was the “Rapid Rectilinear”
designed simultaneously and independently by Dallmeyer and Steinheil in 1866. This was produced
between the invention of photography in 1839 and the release of the Anastigmat in 1890 when the
only available lenses were the simple Wollaston meniscus lens, the Petzval portrait lens and the
wide-angle Globe lens. It was then logical the strong request of an intermediate lens that could
cover an angular field of about ±24º for a reasonable aperture of approximately f/7. The idea was to
employ a lens similar to the Grubb achromatic landscape whose main feature was the low presence
of spherical aberration. Recalling equation (3.1), it is possible to notice that although the small
value of SI, astigmatism can be still controlled by a suitable choice of the stop-lens distance.
However, this implies the requirement of a certain amount of coma. By placing an equal inverted
component behind the central stop, any amount of coma could be automatically removed from the
system thanks to the symmetry.
! !!!! !!!! !!!! !
Figure 5.1 | From left to right, the Harrison Globe lens (a), the Bush
Pantaskop (b), the Steinheil Periskop (c) and the Goerz Hypergon lens (d).
!
Figure 5.2 | The Rapid Rectilinear, f/7
!
!
(a)
(b)
)
(c)
(d)
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More in details, the Rapid Rectilinear (Figure 5.2) resulted almost free from both spherical and
longitudinal chromatic aberration thanks to the shape of each surface and the combination of
glasses employed. In addition, a certain quantity of coma was used to control astigmatism through a
suitable stop distance. The former was then removed together with distortion and transverse
chromatic aberration by means of the system symmetry. On the other hand, this arrangement
implied also a unit magnification of the conjugates and therefore, for very long distant objects, the
lens started to face its own limitations.
The Rapid Rectilinear achieved a great performance until a total angular field of 50º for an
aperture between f/8 and f/7. Furthermore, this was considered the most common lens employed by
cameras manufacturers for almost 60 years.
6. The Anastigmats Lens
In 1886 a new series of barium crown glasses of higher refractive index was produced by Abbe
and Schott. The reason behind this important release follows from the analysis of the Petzval
Theorem. If a system is free from spherical aberration, coma and astigmatism then a sharp image is
formed on a surface of radius RS=RT=R. More in details, the radius of the Sagittal curvature RS and
that of the Tangential curvature RT introduced by astigmatism will be equal to the Petzval radius R
defined by the summation [5]
(6.1)
where ri and ni are the radius of curvature and the refractive index of the i-th surface respectively,
and na is the refractive index of the last medium for the general case of i=0,..,N surfaces. Equation
(6.1) is known as the Petzval Theorem and it gives the necessary condition for the flatness of the
field, i.e. for R→∞. Moreover, it has to be noticed that the Petzval curvature is independent from
the surfaces thickness, the objects distances and the stop position. In the case of a single lens, the
Petzval condition reduces to r1=r2. Thus, in order to be positive such a lens should be thick and of
meniscus shape. This also explains the common employment of meniscus lenses in photographic
objectives. Furthermore, for a cemented doublet, the condition for a flat field becomes [6]
(6.2)
where a and b refer to the crown and the flint lenses respectively and V is the usual V-value. This
condition tells us that V and n should rise and fall together, in contradiction with the ordinary ‘old’
type of existing glasses. Abbe and Schott focused their research on this purpose since 1880. They
tried to produce a glass of high refractive index and high V-value such that this could be combined
with a flint of low refractive index and relatively low V-value. Their aim was achieved in 1886 with
the release of the new barium crown glasses that allowed the design of a new-achromat doublet well
corrected from both astigmatism and field curvature. Table 6.1 wants to compare the ‘old’ glasses
specifications with the new set.
1
R
=na
1
r
i
1
ni
1
ni1
i
V
n
a
=V
n
b
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Old-achromat
New-achromat
Glass
n
V
V/ n
n
V
V/ n
Crown
1.5290
51.60
33.8
1.6234
56.3
34.7
Flint
1.5632
42.9
27.4
1.5427
47.5
30.8
Table 6.1 | Specification and comparison of the old and the new set of glasses
6.1 The Rudolph Anastigmats
The Ross designer H. Schroeder was the first who effectively employed the new Schott glasses for
the design of a new flat field lens. He replaced the new achromat doublet in both components of the
previous Rapid Rectilinear. However, this lens, known as ‘Concentric’ was limited by the presence
of spherical aberrations that enabled an aperture of just f/20 for a field angle of 60°.
In 1895 Paul Rudolph of Zeiss released the first ‘Anastigmat’ lens, after recalled ‘Protar’, based on
a non-symmetrical Rapid Rectilinear design. This was composed of a cemented doublet made by
old glasses on the front, and a new-achromat behind the stop. In order to correct the system from
spherical aberrations and other important defects, Rudolph made the front doublet of very low
power. In fact, the minimum value of SI for a thin lens approximation is [7]
(6.3)
where h is the ray height at the lens surface, K is the power of the lens and C is the conjugate
parameter. This expression follows from the condition
(6.4)
where B is the bending parameter which, as mentioned before, defines the shape of the lens.
Equation (6.3) shows the strong dependence of spherical aberrations on the lens power (K3).
Hence, besides an appropriate choice of the surfaces curvature, Rudolph made additionally the front
component extremely weak. Furthermore, the lens was designed such as the astigmatism and field
curvature introduced by the first component could be removed by the new-achromat [8]. The
original Rudolph’s Protar, shown in Figure 6.1, was released by Zeiss with an aperture of f/4.5. This
achieved a reasonable performance until 40°.
Figure 6.1 | The Rudolph’s Protar, f/4.5
(SI)min =h4K3
4
n
n1
2
n
n+2
C2
B=
2n21
( )
n+2
C
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As explained before, in the Rudolph’s Protar the front element was imposed to be of very low
power in order to control spherical aberrations whilst the rear component carrying most of the
system power compensated astigmatism and field curvature. In 1899 Rudolph tried to separate both
components with narrow airspaces for the final design of the so-called ‘Unar’ lens. The advantage
of the air separations between the elements was to correct spherical aberration without the necessity
of strong dispersive cemented interfaces. Although the Unar lens (Figure 6.2 (a)) produced good
results, Rudolph quickly understood the advantage of having a strong cemented doublet behind the
stop, and thus he created in 1902 the ‘Tessar’ lens. This had still two separated element made by
two similar dense crown as the front component and a new-achromat cemented doublet of high
power on the rear (Figure 6.2 (b)).
Figure 6.2 | The Rudolph’s Unar (a) and Tessar (b). The first has separated doublets
in both sides whilst the second has a strong cemented doublet as the rear component.
Thanks to the rear cemented doublet, the Rudolph’s Tessar lens achieved a great performance with
an almost flat field until an aperture of f/4.5. Furthermore, this was released in 1903 and conferred
to the Zeiss Company the commercial monopoly of photographic objectives until the end of World
War I.
6.2 Symmetrical Anastigmats
The outcome of the first Zeiss Anastigmat Protar led the mathematician E. von Höegh in the
design of a triplet corrected from spherical aberrations, astigmatism, field curvature and chromatic
aberrations. Since the triplet still suffered from coma, a symmetrical component was placed in the
rear of the stop for the final design of the symmetrical “Dagor” lens, produced by the Goerz
Company in 1892. Von Höegh made his cemented triplet such as the refractive index from the stop
onwards slightly increased [8]. By a suitable choice of the surfaces radii of curvature and thickness,
the focal length and the Petzval sum have been controlled. Moreover, the two cemented interfaces
were used to correct spherical aberrations and field curvature. Hence, thanks to the symmetry of the
system the other transverse aberration (i.e. coma, distortion and transverse chromatic aberration)
were automatically removed. The considerable flat field and the overall good performance allowed
the Dagor lens to operate at f/4.5.
(a)
(b)
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Figure 6.3 | The von Höegh’s Dagor (a) and Celor (b). Both lenses were
commercially released by the Goerz Company in 1890s.
Some years later, von Höegh decided to replace the two symmetrical cemented triplets with two
separated doublets. The idea was to arrange the two components in a symmetrical configuration
about the central stop, as he did in his previous Dragon lens. Therefore, having automatically
corrected the three transverse aberrations with the symmetry, von Höegh had five degrees of
freedom in both components to control spherical aberrations, astigmatism, field curvature and
longitudinal chromatic aberrations. These five parameters were the two lens powers, the two
bendings and the airspace separation namely.
As mentioned for the Rapid Rectilinear lens, even though the symmetrical arrangement is very
powerful, this is also limited by the requirement of a unit magnification for an ideal operation.
However, the von Höegh’s lens has been assessed to achieve a great performance even for very
distant objectives for which the three transverse aberrations were still controlled. A small amount of
coma sometimes appeared leading to a slight modification of the symmetrical configuration.
The lens designed by von Höegh made of a new barium crown and a light flint element, was
released by Goerz Company in 1899 under the name of ‘Celor’ (Figure 6.3 (b)). Many similar
productions were made with a range of apertures between f/4.5 and f/6.3. These lenses were labelled
as “Dialype” because of the airspace separations adopted.
6.3 The Cooke Triplet
In 1893 the English designer H. Taylor of Cooke Company produced a revolutionary photographic
objective composed of a separated triplet. The foundation of Taylor’s argument was initially to
employ a positive and a negative component having equal power and refractive index. Following
this way, Taylor arrived analytically to the conclusion that the Petzval Sum reduces automatically to
zero. Additionally, this arrangement would allow any desired power just by a suitable separation
between the two components. On the other hand, the asymmetrical configuration would have
involved enormous amount of other types of aberration, such as transverse chromatic aberration and
distortion. Therefore, the positive element has been split in two components and the negative one
has been mounted between them. This final configuration (Figure 6.4) strongly influenced Rudolph
in the design of his Tessar lens. A deep mathematical analysis was made by Taylor addressed to
figure out a suitable setting of the system parameters that allowed the best performance for his lens.
Indeed, with a triplet we have a total of 8 degrees of freedom to use for the correction of
aberrations. The three powers and the two lenses separations were generally used to control the
effective focal length of the system, field curvature, distortion and the two chromatic aberrations.
(b)
(a)
The$Development$of$the$Photographic$Objective!!! ! !!MSc!Optics!&!Photonics!
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Moreover, the remaining degrees of freedom, i.e the three bending parameters, were used for the
correction of spherical aberration, coma and astigmatism.
Figure 6.4 | The Cooke Triplet, f/3
The first triplet released by Cooke had an aperture of f/3 for a total field angle of roughly 44° and
was thus mainly used for portrait pictures. This was made of ‘old’ crown and flint glasses with an
almost equal distance from each component. In 1895 a similar triplet was designed with a narrow
separation between the first components and a longer one for the rear half. Furthermore, using two
high-index barium glasses and a flint, Taylor managed to achieve a lens of f/7.7 aperture and a total
field of almost 60°. It has to be noticed that due to the asymmetry of the system, these kind of
lenses strongly relied on their own degrees of freedom and therefore the manufacturing process
required to be extremely accurate for a faithful reproduction of the desired parameters.
7. The Double-Gauss lenses
Nowadays, Double-Gauss lenses still represent a model for the design of high-aperture
photographic objectives. Their invention date up in the early 1817 when the famous German
mathematician C. F. Gauss released a work regarding the potential improvements for the old
Fraunhofer Telescope made by a single meniscus. The argument of Gauss was to place a second
negative meniscus behind the original positive component. Following this way, the German
mathematician obtained the correction of spherochromatism. The Gauss telescope remained a
theoretical model as it was never produced and used in astronomy. However, in 1888 G. Clark had
the insight of using the two menisci elements for the design of a photographic objective by placing
an equal pair inverted about the central stop. This symmetrical arrangement, shown in Figure 7.1, is
known as the famous ‘Double-Gauss’ lens in honour of his original creator.
Figure 7.1 | The Clarck’s Double-Gauss lens
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Similar early lenses of the Clark’s model were released some years later by Baush & Lomb
Company with aperture f/8, f/12 and f/35. However, these lenses had not particular successful
especially because of the huge vignetting experienced.
7.1 The Zeiss Planar Lens
After the release of the first astigmatic lens in 1985, Rudolph decided to modify his Protar
adopting the Double-Gauss prototype. This conferred to the designer the advantages of the
symmetry for which the three transverse aberrations were automatically removed. However, the
Clark’s lens was affected by a considerable amount of spherical aberrations, astigmatism and field
curvature due to the large separation between the two thin menisci. These defects were visible even
for small apertures. By increasing the thickness of the negative components and shortening the
airspace separation between the two elements, Rudolph steeply reduced these aberrations. Indeed,
the power of a thick lens of refractive index n is given by [7]
(7.1)
where d is the axial thickness. Therefore, by suitable values of c1 and c2 it was possible to control
the Petzval sum and, at the same time, the lens power. Furthermore, in order to achromatise the
lens, Rudolph had the great idea of placing a “ghost” surface into the thick central components. The
former was a cemented interface that was used to separate two glasses of same refractive index but
different dispersions. As a consequence, since the change in refractive index with the wavelength
δ
n could not be equal across the ghost surface, the cemented interface introduced some longitudinal
and transverse chromatic aberrations. These extra contributions, whose values relied on the
interface curvature, were used to correct the total chromatic aberrations of the system. For this
purpose, Rudolph employed two glasses of 1.57 refractive index.
The new Rudolph’s lens was commercially released by Zeiss Company under the name of ‘Planar’
in 1897. This achieved an excellent performance for an f/4.5 aperture. Figure 7.2 shows its ultimate
configuration.
Figure 7.2 | The Rudolph’s Planar, f/4.5
The Double-Gauss lens modified by Rudolph has been reproduced in innumerable versions. The
most notable were the H. W. Lee’s ‘Opic’ of Taylor-Hobson Company (Figure 7.3 (a)) made in
K=(n1) c1c2+(n1)
n
c1c2d
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L
F
min
=1+1
4
K2
K1
1920 with an aperture of f/2 and the seven-element Kodak Aero Ektar (Figure 7.3 (b)) in 1941
which achieved an aperture of f/0.95. Moreover, in 1944 the Schneider Company realised the five-
element ‘Xenotar’ lens (Figure 7.3 (c)) where the rear positive element was removed and the
negative rear was split in two parts for a total aperture of f/2.8.
Figure 7.3 | The Opic lens (a), the Kodak Aero Ektar (b) and the Xenor lens (c)
Over 300 Double-Gauss lenses have been manufactured by many photographic companies during
the second half of the 20th century. Even today they represent the basic model for the design of
high-aperture photographic objectives.
8. The Telephoto Lenses
Telephoto lenses have been widely used in photography as they provide magnifications of the
objects. These optical systems have the main feature of a focal length greater than the total length of
the system, i.e. the length between the first element and the focal plane. As a consequence,
telephoto objectives are typically shorter compared to the ordinary photographic lenses investigated
so far. The basic arrangement of these systems is composed of a positive achromatic doublet as the
front component and a negative achromatic doublet behind. An important parameter characterising
the telephoto lenses is the ratio between the length of the system L and the focal length F. This is
known as the ‘Telephoto Ratio’ and is given by [7]
(8.1)
where h1 and h2 are the ray heights at the front and the rear component respectively, and K1 and K2
the lens powers. Differentiating equation (8.1) with respect to h2 it has been found that the
minimum ratio occurs when h2/h1=1/2, i.e. when
(8.2)
L
F
=1+h2
h1
h2
2
h1
2
K2
K1
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Figure 8.1 | The Dallmeyer’s Telephoto lens
!
Moreover, the condition for the zero field curvature
SIV =0
( )
imposes
K1=K2
!corresponding
to a minimum telephoto ratio of
L/F
( )
min =0.75
. Indeed, this value was satisfied by the majority
of these lenses even though sometimes it was also reduced to roughly 0.6.
The first concrete application of the Telephoto system was made by T. R. Dallmeyer, the son of J.
H. Dallmeyer, in 1891. He placed an achromatic doublet in the front component and a cemented
triplet behind (Figure 8.1). Furthermore, the lens was designed to provide a variable focal length
thanks to a translational mechanism that allowed to change the separation between the two
components. The lens aperture also varied in accordance to this separation. The variable-focal-
length property was immediately appreciated by both designers and photographers as images of
different magnifications could be easily obtained. In addition, long focal lengths could be provided
without the necessity of long objective extensions.
Similar lenses have been made after the Dellmeyer type. However, the early telephoto objectives
faced the common problem of having large amounts of aberrations. Indeed, the front achromatic
doublets were typically well-corrected from aberrations whilst the rear component still suffered lots
of defects. In addition, the latter had also the disadvantage of magnifying the residual aberrations
introduced by the front doublet [4]. These problems have been partially compensated by the
employment of further elements and fixing the separation of the two components. An example of
such arrangement was the Zeiss ‘Tele-Tubus’, released in 1901 where the first component was a
cemented quadruplet designed by Rudolph, and the rear was composed of a negative cemented
triplet (Figure 8.2).
Figure 8.2 | The Zeiss Tele-Tubus
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In the 20th century many companies manufactured long-focus lenses. These provided
magnifications between 2X and 8X. After this range, distortion strongly limited their performance.
7.1 Reversed Telephoto Lens
Particular relevance throughout the history of photographic lenses has been also covered by the so-
called “Reversed Telephoto” lenses. Such systems have the negative component in front of the
positive one, i.e. exactly the inverse structure compared to the usual Telephoto objective. The
advantages of this arrangement are mainly the shorter total focal length and the longer back focal
length. Furthermore, they allowed high apertures and wide-angle fields. These lenses have been
frequently manufactured after the advent of the 35 mm camera in the 1950s. A typical Reverse
Telephoto lens released in that period is the wide-angle 18.5 mm made by Spiratone (Figure 8.3).
The latter covered a total field of roughly 100° for an aperture of f/3.5.
Figure 8.3 | The Spiratone wide-angle 18.5 mm lens
Reverse Telephoto lenses were widely employed in projector designers. However, they had limited
applications in photography because of the expensive manufacturing costs due to the big size of the
front components. In addition, distortion was a serious problem faced by these lenses due to the
extreme asymmetry of their structure.
9. Conclusions
Photographic objectives have been investigated through their historical development. The latter
was strongly influenced by the period requirements. The time of exposure related to the aperture
size as well as the angular field have been the main parameters characterising the nature of a
photographic lens.
The earliest and simplest imaging device was the Pinhole Camera. This had the problem of the
extreme long time of exposure that led to the requirements of lenses. The first photographic
objective was the Wollaston’s meniscus which was quickly replaced by the Chavelier’s achromatic
doublet. These two lenses were mainly used for landscape pictures because of the long time of
exposure required. A huge improvement was made by Petval with the design of his Portrait lens.
The latter achieved an aperture of f/3.6 but was limited over 30° of total field because of the
presence of field curvature. Around the middle of the 19th century, designers discovered the great
The$Development$of$the$Photographic$Objective!!! ! !!MSc!Optics!&!Photonics!
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18!
advantages of symmetrical systems. Indeed, they allowed the straight correction of coma, distortion
and transverse chromatic aberrations. Lots of lenses have been designed following this
arrangement. The first was the Rapid Rectilinear composed of two inverted achromatic doublets
with respect to a central stop. The period between the 1890 and 1930 has seen the development of
many Anastigmat lenses. The one that achieved most success was the Rudolph’s Tessar composed
of a separated doublet of low power on the front, and a strong cemented achromatic doublet on the
rear. The same designer realised in 1896 the Planar lens whose arrangement relied on the basic
structure of a Double-Gauss lens. The great innovation introduced by Rudolph was the addition of a
“ghost” surface which enabled the control of chromatic aberration. The optical principles of both
the Telephoto and the Reverse Telephoto lenses have been also investigated. The first enabled
magnified images thanks to the long focal length, whilst the second were able to cover wide-angle
fields.
Nowadays, photographic objectives still rely on the basic principles investigated so far. For
instance, the Double-Gauss arrangement is still considered a model for ordinary lenses. Telephoto
systems are also widely employed for a large variety of applications.
References
[1] G. GBUR, E. WOLF; The Rayleigh range of Gaussian Schell-model beams; Journal of Modern
Optics, 2001, vol. 48, no. 11, 1735 – 1741
[2] W. TAYLOR, H. W. LEE; The development of the photographic lens, Proceedings of the Physical
Society, Volume 47, Issue 3, pp. 502-518 (1935).
[3] J. SMITH; Modern Lens Design; Genesee Optics Software, INC., Rochester, 1992, pag. 63
[4] R. KINGSLAKE; A History of the Photographic Lens; Academic Press, 1989
[5] BORNE, WOLF; Principles of Optics; 7th ed., Cambridge University Press (1999), pag. 273
[6] R. KINGSLAKE; The Development of the Photographic Objective; JOSA (1934), Vol. 24, Issue 3,
pp. 73-84
[7] R. SMITH; Optical Design; Imperial College London, Jan. 2010
[8] R. KINGSLAKE; Lens Design Fundamentals; Academic Press, New York, 1978
ResearchGate has not been able to resolve any citations for this publication.
Article
The concept of the Rayleigh range, well known in the theory of coherent beams, is generalized to a class of partially coherent beams. Curves are presented which show the dependence of the Rayleigh range on the spot size of the beam and on the spectral degree of coherence of the light in the plane of the waist.
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This book provides the skills and knowledge to develop practical lenses needed for the ever emerging variety of 21st-century applications. Continuing to focus on fundamental methods and procedures of lens design, this revision of a classic modernizes symbology and nomenclature, expands the aberration study to include the transverse and wave forms, enlarges the discussion of three-mirror tilted and decentered systems, and explores modulation transfer function and diffraction-based aberrations in the optimization process. As computer-based optical design is the rule today, this edition provides practical guidance on how to use a lens design program in general, without tying to a particular software package. This book is ideal as a textbook for advanced undergraduate or graduate course in lens design principles and as a self-learning tutorial and reference for the practitioner. * Many new lens design examples - ranging from the simple lenses to complex zoom lenses and mirror systems - give insight for both the newcomer and specialist to the field. * New chapter on techniques to select a starting lens configuration. * Two new chapters explain how to effectively select and use lens design software, and to carry out optimization techniques and performance analysis.* Problems are included at the end of chapters.
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Citation R. Kingslake, "Development of the photographic objective," J. Opt. Soc. Am. 24, 73- (1934) http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-24-3-73
Article
The concept of the Rayleigh range, well known in the theory of coherent beams, is generalized to a class of partially coherent beams. Curves are presented which show the dependence of the Rayleigh range on the spot size of the beam and on the spectral degree of coherence of the light in the plane of the waist.
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Principles of Optics is one of the classic science books of the twentieth century, and probably the most influential book in optics published in the past forty years. This edition has been thoroughly revised and updated, with new material covering the CAT scan, interference with broad-band light and the so-called Rayleigh-Sommerfeld diffraction theory. This edition also details scattering from inhomogeneous media and presents an account of the principles of diffraction tomography to which Emil Wolf has made a basic contribution. Several new appendices are also included. This new edition will be invaluable to advanced undergraduates, graduate students and researchers working in most areas of optics.