An Improvement in Photographic Lenses, also applicable to Mioroscope and Lantern Objectives
Year: 1893

page_text: Date of Application, 30th Jan., 1893
Complete Specification Left, 30th Oct., 1893-Accepted, 30th Jan., 1894
PROVISIONAL SPECIFICATION.
An Improvement in Photographic Lenses, also applicable to
Mioroscope and Lantern Objectives.
" I, HAROLD DENNIS TAYLOR, of 20 Bootham Terrace, York, Optical Manager
to Messrs. T. Cooke & Sons, Buckingham Works, York, Opticians and
Engineers &c., do hereby declare the nature of this invention to be as follows:-
It consists of a peculiar combination of three separate achromatic & approxi-
mately aplanatic lenses, in virtue of which the image thrown by the whole triple
' lens is rendered perfectly flat and also free from marginal astigmatism, even when
a very wide angle of view is included.
Moreover, these advantages are secured consistently with the use of a much
larger working aperture than has hitherto been possible, except for narrow angles
of view. Thus the rapidity of the lens for ordinary subjects, such as landscapes,
may be increased to a very great extent, moving objects &c. receiving a full
exposure in (say) half a second where otherwise perhaps two to four seconds or
more would be required to make the same impression on the sensitive plate, owing
to the lenses of ordinary type requiring to be stopped down considerably in order
to eliminate the effects of curvature of field & marginal astigmatism.
In order to fully explain the nature of my invention & its essential novelty &
thus possibly obviate dispute which might arise owing to the superficial likenesses,
which some one or two photographic lenses bear to the one of my invention, being
erroneously mistaken for essential identity, it will be necessary for me to enter at
considerable length into the theory of photographic lenses & explain the real
nature of the corrections hitherto more or less relied upon for attaining flatness of
field & the best possible marginal definition.
It must first be premised that all lenses herein referred to are supposed to bé
achromatic, or to refract the brightest visual rays and the most active blue photo-
graphic rays to the same fodus, at any rate on the optic axis, and also that they are
corrected for spherical aberration more or less accurately, that is, the edge rays of
au axial pencil or bundle of rays are refracted to the same focus as those ravš
which pass through the lens at or near its centre, supposing that the said lens is
used in its proper manner & position. Nearly all the separate lenses used in
photographic combinations of the best quality are in themselves compounded of
tivo or more lenses of different sorts of glass cemented together, whereby the above
conditions of achromatiam & freedom from spherical aberration (or, shortly,
aplanatism) are more or less closely fulfilled.
I shall also premise, for the sake of simplicity, that all rays impinging upon the
front of the combination are proceeding from very distant points and may therefore
be considered parallel.
"Now let a pencil of such raya passing obliquely through such a lens be
considered. Such pencils or bundles of rays, emanating respectively from separate
points of the subject to be photographed, are refracted obliquely through the lens &
go to form, however, imperfectly, the marginal image.
In Fig. 1. L is a lens. Let it be supposed that rays R-R from a very distant
point on the optic axis A-A are refracted to the focus F, which is therefore the
principal focus. Let P-P be a plane perpendicular to the optic axis and passing
through the principal focus F. Let this plane be called, throughout this Speci
fication, the principal focal plane. Now the parallel but oblique rays - coming
from a very distant point and forming a considerable angle with the axis A-A, do
- not come to a focus upon the plane P-P. but somewhere between the points ƒ and o
•

page_text: much nearer to the lens. Thus the image has a very considerable curvature. Not
only so, but the image at ƒ and g is a very astigmatio, which is the term used to
describe the following state of things.
Let two rays in the plane of the paper be considered, or any pairs of rays
which may be situated or contained in any planes which pass approximately
through the point g and cut the aperture of the lens along chords which are parallel
to the plane of the paper. All such planes are herein referred to as primary
planes.
Let it be understood also that each pair of rays r―r in its own plane, as above
defined, is symmetrically situated with regard to a line perpendicular to the plane
of the paper and passing through the centre of the lens, or in other words, that the
two-rays r-r of each pair strike the lens at equal distancos from, and on each side
of, the aforesaid perpendicular. Then all such symmetrical pairs of raya situated
in primary planes come to focus at about the same perpendicular.distance f―k from
the plane P-P and more or less close to the point f.
Such points fare situated, according to the obliquity, along a curve Fƒ which
may approximately be described as a circle of a radius generally equal to about Åths
or scarcely more than one quarter of the principal focal length.
And now let planes perpendicular to the paper but all approximately passing
through the primary focus be considered. Such planes are herein termed secondary
planes. And, as before, let any two parallel rays in such planes be considered, one
ray of each pair being above the paper plane and the other below it. Then all auch
pairs of raya in secondary planes come to a focus not at or near f, but more or less
near a point g which is much nearer the plane P-P than the point fis; in fact the
distance from g to the plane P-P is generally less than one half of the distance
from to the plane P➡P but seldom so little as one third of that distance. The
curve F-g, along which rays in secondary planes come to a focus according to the
degree of obliquity may approximately be described as a circle whose radius is
generally about the of the principal focal length. The best possible focus for the
oblique beam or pencil. of rays we are considering is found at a point about half
way between & g, or in other words, half way between the focus for primary
rays & the focus g for secondary rays. And these points of best possible focus are
ranged along an intermediate curve F-m, according to the obliquity, which may
again be approximately described as a circle whose radius is generally about tbs
of the principal focal length.
So far I have been dealing with the case of symmetrical pairs of rays in
primary planes; rays striking the lens at equal distances on each side of the
perpendicular drawn through the centre of the lens.
It is now necessary to consider the same meniscus like lens with regard to its
action upon any two rays in primary planes which do not impinge upon it at equal
distances from the perpendicular through the centre of the lens, but at more or less
unequal distances from the same; two rays such as a and b, or d & à (Fig. 2) for
instance.
Just as before, it can be shown that the symmetrical pairs of rays such as a & à,
b&b, d&d, each respectively intercross or have their focal points at about equal
distances short of the plane P-P. But such points are not coincident in a direction
perpendicular to the optic axis, but are arranged along a short line C-D, which, it
should be pointed out, is purposely much oxaggerated in Fig. 2.
Two symmetrical rays passing through the lens very near its centre and on each
side of that ray c-c which passes through without deviation, may be said to come
to a focus at c upon the contral oblique ray c-c. But the symmetrical pair of
rays a & a intercross at the point A, the pair 6 & 6 intercross at the point B while
the pair d & à intercross at the point D, considerably to one side of the oblique
central ray c-c. Now the necessary consequence of this peculiar arrangement is
that the intersecting points or foci for any eccentric pairs of rays such as ò & à,b & a,

page_text: •
d&c, a & b, &c. are thrown either much nearer to the lons or else much further off
the lens than the line C-D. Thus d & b intercross at the point marked d + b,
a&e focus at a + c, à & c nt à + c & so on. Now let it be supposed that the
oblique rays striking the lens in Fig. 2 are proceeding from a distant but bright
point of light & that a piece of ground glass is placed in the position g-g to receive
the image, which is viewed from behind. It will be found impossible to get a clear
focus. For the rays d & 6 from the upper side of the lens are all out of focus on
the soreen while rays such as b & à from the other aide of the lens are equally out
of focus. Thus rays proceeding from parts of the lens more or less near its two
margins form a diffused halo upon the screen, while the only rays coming to
anything like a focus upon it are those proceeding from the centre of the lens &
which focus about C. Therefore the image takes the form of the balloon shaped
penumbra shown in Fig. 3 where the small & bright end è corresponds to the focus
at C & the outlying & least bright portion D corresponds to the point D on which
5 impinge the much out of focus & therefore diffused rays from both margins & & & of
the lens.
.
Now this curious eccentric balloon shaped penumbra, growing less & less bright
from C to D, is characteristic of a lens which gives what I herein call unsymmetrical
oblique refraction.
The amount & nature of this eccentric penumbra depends both upon the form
of the lens and the state of divergence, parallelism or convergence of the oblique
pencils of light impinging upon the lens, considered in relation to the lens. It is
sufficient, however, to point out that the state of things illustrated in Fig. 2 is
oharacteristic of a lens which is of the meniscus form or else approaching to that,
5 when the rays impinging upon its convex surface are either parallel or divergent.
On the other hand, if rays either parallel or convergent impinge upon an inverse
meniscus like Fig. 4 or a lens more or less approaching that form, then the points
at which symmetrical pairs of rays intercross are situated upon a line C₁-D, which
extends away from the oblique axis c-c, in a direction opposite to the case shown
in Fig. 2, while eccentric pairs of rays such as i & à, passing through the lower
margin of the lens, focus very short as at + & rays such as &
through the upper margin of the lens focus very long as at the point i + k.
On introducing a screen ground glass at g-g, as before, it will be found that
there is an eccentric penumbra (Fig. 5.) formed at the focus as in the previous case,
only the larger & less bright bulk of it is turned away from the optic axis A-A
instead of towards it as in the case of Fig. 2.
"
passing
And now the effect of introducing an opaque stop or diaphragm (with an aperture
in it smaller than the lens) behind the lens in Fig. 2 is at once apparent. As
shown in Fig. 2, the stop only allows to pass the eccentric rays à & à & those
included between them. But a &'d come to a focus, as we have seen, at the
point a + which is either much nearer the plane P-P or even beyond it. Thus
the effect of the stop is to only allow those eccentric oblique rays to pass which
come to a focus at the greatest distances from the lens, & thus the image is very
considerably flattened.
The same effect is produced in the case of Fig. 4 by placing the stop in front of
the lens, in which case the effect is to only allow those eccentric rays, such as c & k
(& those included) to pass, whose focus is situated about c + much nearer to the
plane PP. In this case also the field of view is very much finttened.
So far I have only illustrated the selecting effect of a stop upon the foci of
oblique rays situated in the plane of the paper or, in other words, in primary
planes.
It would be extremely difficult to illustrate the effect of the same stop upon the fooi
of the same pencils considered in secondary planes. But it can be mathematically

page_text: .
demonstrated, by a process far too long & complex for reproduction here, that
any correction in the way of either shortening or extending the focal distances
of rays in primary planes by means of a diaphragm or stop, is invariably accom-
panied by a corresponding shortening or extension of the focal distances for rays in
secondary planes which is always just one third of the primary correction and is of
the same tendency. In other words, any diaphragm correction for rays in primary
planes is always three times the corresponding correction for the same pencils
considered in secondary planes. The mathematical demonstration of this can not be
directly applied to large obliquities or to cases where the aperture of the lens is
very large compared to the focal length, but oven in these cases practico seems to 1
point to the general truth of the above theorem. For upon this theorem, depends
the truth of that fact so thoroughly demonstrated in practice, viz. that it is
absolutely impossible to so correct a photographic lens made of ordinary glasses by
means of stops or diaphragms as to rendor the image or field of view quite flat for
rays in primary planes and for rays in secondary planes simultaneously.
For, have pointed out above (see Fig. 1.) that the deviation- from the
focal plane P-P of the focus for the oblique symmetrical rays - passing
through the lens at open aperture and considered in primary planes, is almost
invariably 2} times the deviation g-k of the focus for the same pencil of raya
considered in secondary planes. Hence no diaphragm corrections due to the a
prefence of a stop can ever noutralise both these errors or deviations —k & g—k
simultaneously.
Hence if, by means of diaphragms, the field of view or imago is rendered
perfectly flat for rays in primary planes, yet the deviations from a flat image for
rays in secondary plaues will not be fully corrected and there will still remain such
ap amount of curvature of image for rays in secondary planes ns will render a
- distinct image impossible towards the edge of the field of view, unless the lens is.
used at a very small aperture.
It is this condition of things which is responsible for the so called astigmatism
which is invariably present at the fooi for pencils of rays which are refracted at
considerable.obliquity through photographic lenses made of ordinary glasses &
correated in the usual way so as to give as flat a field as is consistent with fair:
marginal definition.
There is only one, condition which renders it possible, by means of diaphragms,
..to produce an'iinage quite flat for rays in primary planes & for rays in secondary
planes simultaneously, or in other words, to produce an imago quite flat and
at the same time free from marginal astigmatism. It is this. If
"
"
= the index of refraction for the positive lens of an approximately
achromatin lens.
M= the index of refraction for the negative lens combined with.the above.
D=
the ratio which the focal length of the negative lens bears to that of
the positive lens. If the lens is achromatic, D then is equal to the
dispersive ratio between the two lenses.
I
Then the following relation must exist ciz. M=f, which implies that the
index of refraction for the negative or concave lens must bear the same ratio
to the index for the positive or convex lens as the focal length of the positive
lens bears to the focal length of the negative lens.
This very exceptional condition, only rendered possible since 1886 by the
production of some entirely new sorts of glass, is attained very closely in Schroeder
& Stuart's Pateut Concentric Lens, in which the positive lens has an index of
refraction as high as about 161 & the negative lens an index of only 1·51 or so.
The focal length of the negative lens is consequently only about times or
1:066 times the focal length of the positive lens. They are thus so nearly of the
"same focal length that the resulting focal length of the two combined is very long
'1·61
1-51

page_text: in proportion to the diameter of the lens, & therefore it is impossible to work such
a lens with anything but a small relative aperture.
Thus it will be seen that photographic lonses of large aperture in proportion
to their focal length (& therefore possessing the important quality of great rapidity
5 of action) and at the same time having a flat field, free from marginal astigmatism,
are not to be attained by means of those diaphragm corrections which have hitherto
been relied upon for correcting the errors of such lenses.
For this reason I have, in my invention, mado use of a method of correction
which, as applied by me, is ontirely now. It may be explained as follows:-
Returning again to Fig. 2 & 4 it will be noticed that the unsymmetrical oblique
refraction & the consequent focal penumbra is of a contrary character in the
two cases. In Fig. 2. the rays refracted through the upper parts of the lens such
ns & bare brought to the shortest focus, while in Fig. 4 the rays from the lower
parts of the lens, such as i &, pass to the shortest focus.
In the case of Fig. 2. the bright small end of the penumbra (Fig. 3.) is turned
away from the optic axis A-A, while in the case of Fig. 4 the bright small end
of the penumbra (Fig. 5) is turned towards the optic axis A-A. It is obvious
then, that a form of lens somewhere intermediate between the forms of Figs. 2 & 4
is possible, which will be free from this unsymmetrical oblique refraction. This is
the case in actual fact. In Fig. 6 is shown roughly a form of lens, made of
ordinary crown & flint glasses, which has the property of what I call symmetrical
oblique refraction.
:
It will be found that any two rays - whatever, whether they impinge upon
the lens at equal distances on either side of its central perpendicular or not, are
refracted to one & the same focal point p situated upon the oblique axis ce
I am here speaking of rays in primary planes. Supposing, as before, a white
screen or ground glass to be placed at g-g to receive the focus of rays from
some distant luminous point, & moved to & fro towards the lens, between the
positions p&s, the appearances seen are as follows.
When the screen cuts through the focus » for rays in primary planes, the
appearance on the screen is a luminous line Fig. 7, a. perpendicular to the plane
of the paper. Moving the screen further away from the lens, the focal line (a)
changes into the vertical oval b; when the screen is about half way between the
primary & secondary foci, the appearance is approximately a luminous circle o
on moving still further out the appearance is the horizontal oral d, while, when the
screen cuts through the secondary focus at a, the appearance is approximately the
horizontal luminous line e, situated in the plane of the paper.
1
If the curves of the lens are nicely adjusted, these focal formations are as nearly
as possible symmetrical even when the rays forming them are refracted through the
lons at great obliquity.
The eccentric balloon shaped- appearances shown in Figs. 3 & 5 are no longer
visible.
Now, if Fig. 6 is carefully considered, it will be rendily seen that the presence
of a stop or diaphragm, whether in front of or behind the lens, cannot possibly
bring about any appreciable focal corrections. Wherever it may be placed, the
focal point for rays in primary planes will still be at p and therefore no alteration
in the amount of curvature of the image will be produced.
Thus a lens giving symmetrical refraction for oblique rays may be said to have
its diaphragm corrections eliminated or reduced to zero.
Given the optical properties of any two or more glasses composing a lens
and the circumstances in which it may be used, the forms which must be given to
such leases in order to eliminate the diaphragm corrections & consequently ensure
the property of symmetrical oblique refraction, can always be calculated by means
of formula which it is scarcely necessary for me to specify here.
So far as I am aware, lenses having this property of symmetrical oblique refraction.
have never been deliberately used in compound photographic camera lenses, at

page_text: any rate with any. CODscious aim or appreciation of the possibilities opened out
by proper combinations of positive & negative lenses of this type.
For I will now show that a combination of such lenses may have the errors of
curvature of image & marginal astigmatism yielded by the individual lenses,
simultaneously corrected or neutralized with a very near approach to perfection
at any rate, while a reasonably short focal length relatively to aporture may
result from the whole combination.
Fig. 8 serves to illustrate the principle of correction on which my invention is
founded. L represents a positive lens giving symmetrical oblique refraction for
rays proceeding. from very distant points. Let P-P be, as before, the principle
focal plane for this lens L.
Then Pis the curve along which the foci for oblique rays in primary planes
are arranged. Let p be one of these foci for a pencil of rays passing through the
lens and inclined at an angle to the optic axis A-A. Now the deviation of p
from the plane P-P is usually and conveniently expressed as a correction to the
reciprocal of the focal length L-P, or in other words, as a correction to the focal
power of the lens L. Let the point p be referred to the optic axis by drawing the
line p-p perpendicular to A-A.
Then
=
F
tan¹
(2n) (34+1), where F stands for the principle focal
μ
length of the lens L & µ stands for a sort of mean for the indices of refraction for
the glasses of which the lens is composed. Now let N be a negative lons of much
the same materials & of the same focal length or focal power as L, and also (for
reasons yet to be assigned) possessing the property of symmetrical oblique refrac-
tion. Let this lens be placed somewhere between L & its foous P. It can bo
proved, that wherever N may be placed between L & P, it will correct the
curvature and astigmatism of the image yielded by L & thus throw a flat & very
perfect image upon the plane Q—Q.
"
For the angle under which the point p is viewed from the centre of the lens N,
distance L-P
is and tan is evidently equal to tan × distance N—P
& therefore tan³ 0 =
tan'
'
But it can also be shown that the curvature correction for the
point p, when referred to the point N, is equal to (the curvature correction for
point p as viewed from L) x (✓✓P). That is, as viewed from N, and apart
from the increase in angle of obliquity, the curvature correction is approximately

page_text: {r("+)} (LP)' for positive lens as
'tan'
- {'' (P)'} ("±³) for
viewed from N.
for neg. lens,
and these errors also neutralise one another, & therefore the resulting image
at Q-Q is both flat and free from astigmatism.
Now it would be impossible to achieve this result if the lens L gave unsymme-
trical oblique refraction, for it is obvious that the aperture of the negative lens N
forms a diaphragm with respect to the lens L & therefore more or less serious.
diaphragm corrections would be introduced and the conjunction of a flat image
with freedom from inarginal astigmatism more or less rendered impossible.
The equivalent focal length of the whole combination is expressed by
where F = the principal focal length of lens Ļ
-
"
"
"
"
of lens N
& d = the distance between the nearest focal centres of L & N
•
The combination in this form boars some resemblance to the old orthoscopic lens
& has the same fault of giving an unsightly amount of negative distortion.
Now the way in which I completely get rid of this grave defect of distortion is by
dividing the positive element of the combination into two parts & placing the
negativo lens in a certain position between. I claim no originality for this device,
which was long ago carried out in Dallmeyers triplet lens among others. Fig. 9
is a diagram showing one form of my triplet lens. B & F are the two positive
lenses and C the negative correcting lens. If F and B are equal in focal length
or in focal power, then O is about half way between; it is more powerful
than B then C is placed rather nearer to F than to B and vice versa.
All three lenses are designed to give symmetrical oblique refraction as nearly as
possible or to have their diaphragm corrections eliminated. The stop or diaphragm
which regulates the aperture is most conveniently placed close to C.
By far the most convenient method of combining the triplet is to adapt the
lens C is such a manner that an axial pencil of rays proceeding from a very
distant point & converged by F shall be rendered parallel again between C & B,
for then the distance between C and B can be regulated so as to entirely free the
combination from distortion, without materially disturbing any other corrections.
When this condition is attained the distance d'is equal to the difference between
the focal lengths of F & C respectively.
Fig. 10 shows a still more convenient form of the lens, which is better adapted
for a wide angle with a large aperturo.
In this case the flint lens of the frout Jens F is placed outside, consistently with
the condition of symmetrical oblique refraction, while the lens B may be arranged
with a slightly flatter front surface.
If f =
f₁ =
the principal focal length of C
of F

page_text: The most rapid combination is obtained when F & B are equal in focal length.
The angle of view embraced is then a medium one.
A wide angle lens of considerable rapidity is obtained when the focal length of
B is double or three times the focal length of F.
There is now another matter in connection with my combination which should be d
pointed out.
I have shown that a positive lens giving symmetrical oblique refraction may have
its errors of curvature of field and astigmatism corrected by a negative lens with
the same properties & of the same materials & focal length placed behind it.
But the formule only apply when the obliquity is not great. On looking into l
the matter more closely it can be shown, that when the rays considered are entering
the lens at great obliquity, then the negative lens need not be quite so powerful
as was concluded above. In fact the negative lens may have a focal length
of upwards of thirty per cent. greater than the equivalent focal length of the
positive lenses combined, or, in other words, its power may be upwards of 1
25 per cent. less than that of the two positive lenses combined. The degree of this
disparity depends upon the relations between the focal lengths of the two positive.
leuses & the separations between them. This fact is of great advantage in my
invention as it enables me to obtain more rapidity & a greater angle of view than I
could otherwise obtain. I explain this disparity, or inequality between the focal 2
power of the negative lens and the sum of the focal powers of the two positive
lenses, by attributing it to what I call parallax, which may be understood by
referring to Fig. 11. where F is a positive lens & C a negative correoting lens.
Let it be supposed that C is placed exactly half way between F & its axial focus P.
The image thrown by F is formed along the curve P-p, for rays in primary planes.. 2
The image of a point only a little way off the axis is formed at h (for instance)
only slightly short of the plane P-P. Then it is evident that tan 6 is almost
exactly double tan & the relations I above pointed out hold good. But the
image of a very obliquely situated object is formed up at p, on the curve P-p.
Now if this same inage were formed upon the plane P-P at the point, then
again tangent would be exactly double tangent x. But it is evident from mere
inspection, that tan (the angle under which p is really viewed from the centre of
the lens C) is more than double tan x & therefore the lens C will exert more power
than is necessary in correcting the errors of curvature and astigmatism of the
lateral portions of the field, and therefore a lens of rather less power than F will a
best correct the field considered generally.
This explanation is equally applicable to the case of a triple combination and
certainly seems to be confirmed in practice, although I am by no means sure that
this is the whole explanation of the fact that I can get the field of view singularily
flat throughout its extent by using a correcting lens of a power equal to little more
than three quarters of the focal powers of the two positive lenses combined, that is
when the two latter are of equal focal lengths. If the focal length of B is twice
that of F, then, or the focal power of the negative lens, need only be about
-85
G
+
And now I will explain why not only the two positive lenses but also the 4
negative correcting lens should have the property of symmetrical oblique
not en much to christe the PARANAA of any diaphragm

page_text: Otherwise, instead of the focus of the oblique pencil being practically a point, it
will more or less have an eccentric balloon-shaped appearance very like Fig. 3. or
Fig. 4. This is also the appearance seen at thn focus, for rays of even very small
obliquity, of telescope object glasses of ordinary type, its presence at the focus
being an infallible symptom of the object-glass being "out of square" or having a
slight tilt. It is well known to most opticians that this eccentric flare at the focus.
is absolutely inconsistent with good definition, & here it cannot be too strongly
emphasised that a photographio lens may have all the errors of curvature of field
& marginal astigmatism perfectly corrected, & yet fail to give good definition
towards the margins of the field owing simply to the fact that the lens as a whole
is not designed to give symmetrical oblique refraction. This is a grave matter
which has not always received the attention from opticians which it merited.
Therefore, in, my combination, I make it a point that the negative correcting
lens, as well as the two positive lonses, shall be as free as possible from the property
of unsymmetrical oblique refraction, so that rays passing through at considerable
obliquity shall be refracted to symmetrical foci as far as it is possible to securo such
a condition throughout a large field of view when the aperture is relatively largo.
As to the materials of which the lenses should be composed, since it is important
that the curves shall be kept as flat as possible, seeing that so much of the power
of the positive lenses is neutralized by the negative lens, it is requisite that crown
glasses of the lowest possible dispersive power should be utilised in conjunction
with flint glasses of ordinary type, otherwise the denser fint would have to be
used, which are objectionable in photographic leuses owing to their comparative
opacity to the violet & ultra violet chemical rays.
Thus without resorting to a denser flint glass than ordinary dense flint having an
index of refraction for yellow light of 1-60 to 1-62, I can secure a ratio of dis-
persive powers between the lightest crown glass & the said flint of upwards of 2.
Now the then achromatised lenses of my combination have cach to fulfil
simultaneously these four conditions, among others :-
1. Each lens must be achromatic in the sense of refracting the yellow D ray of
the spectrum to the same focus as the photographically most active blue ray G.
2. Each lens must be rondered free from sphorical aberration as far as is possible
with the large apertures required.
3. Each must fulfil, as perfectly as is possible throughout a large field, the
essential condition of giving symmetrical refraction to oblique rays, or, in other
words, each lens must have its diaphragm corrections reduced to zero.
4. The inner or adjacent surfaces of each lens must have the same radius of
ourvature, one surface fitting the other, so that the two lenses may be cemented
together, a condition, which although not essential, is nevertheless highly desirable
& conducive to the rapidity of the whole combination.
The best possible achievement of all the above conditious requires a geat deal of
calculation supplemented by much experiment & it is for that reason that I reserve
the more exact statemont of the curves & materials required & other working
directions, in order that they may be supplied in my Complete Specification.
I would point out that so far as I know, the only other photographic lenses
likely to be confused with my invention, are Petzval's orthoscopic & Dallmeyers
triplet, in both of which a negative lens is used for flattening the field. But in
neither of them are the conditions essential to my invention fulfilled. The negative
correcting lens is not nearly powerful enough, in either of those lenses while in both
of them, it can be shown that very considerable diaphragm corrections of the
ordinary character prevail, the lenses not being of a form calculated to give
symmetrical oblique refraction or oven a near approach to it.
In conclusion I would point out that my invention is equally applicable for
lantern projecting lenses, the chief modification required for fitting it better for
that purpose, consisting in correcting the achromatism to suit visual purposes, when,
as is well known, the lenses would be over-corrected for photographic purposes.
My leus is also applicable when made on a sufficiently small scale & corrected

page_text: for visual purposes, for microscope objectives of low or comparatively low powers,
when a very large, flat & uniform field of view is required and when a larger
angular aperture than about 18° is not of so much consequence.
In adapting my combination for unusually largo apertures, I may find it conducive
to success to make one or more of the lenses of three separate lenses cemented
together instead of two, consistently with the conditions of aplanatism, achromatism
& symmetrical oblique rofraction being simultaneously attained.
Dated this 28th day of January 1893.
COMPLETE SPECIFICATION.
An Improvement in Photographic Lenses, also applicable to
Microscope and Lantern Objectives.
I, HAROLD DENNIS TAYLOR, of 20 Bootham Terrace, York, Optical Manager
to Messrs. T. Cooke & Sons, Buckingham Works, York, Opticians and Engineers
&c., do hereby declare the nature of this invention and in what manner tho samo
is to be performed, to be particularly described and ascertained in and by the
following statement :-
It consists of a peculiar combination of three separate achromatic & approxi-
mately aplanatic lenses, in virtue of which the image thrown by the whole triple
lens is rendered perfectly flat and also free from marginal astigmatism, even when a
wide angle of view is included.
Moreover these advantages are secured consistently with the use of a much-
larger working aperture than has hitherto been possible, except for narrow angles
of view. Thus the rapidity of the lens for ordinary subjects, such as landscapes,
may be increased to a very great extent, moving objects receiving a full exposure
in, (say) hulf a second, where otherwise perhaps two to four seconds or more would
be required to make the same impression on the sensitive plate, owing to the lenses
of ordinary type requiring to be stopped down considerably in order to reduce the
effects of curvature of field & marginal astigmatism.
In order to fully explain the nature of my invention and its essential novelty as
well as possibly obviate dispute which might arise owing to the superficial likenesses,
which some one or two photographic lenses bear to the one of my invention, being
erroneously mistaken for essential identity, it will be necessary for me to enter at
considerable length into the theory of photographic lenses, & explain the real
nature of the corrections hitherto more or less relied upon for attaining flatness of
field & the best possible marginal definition.
It must first be premised that all lenses herein referred to are supposed to be
achromatic or to refract the brightest visual rays and the most active blue
photographic rays to the same focus, at any rate approximately, and also that they
are corrected for spherical aberration more or less accurately, that is, the edgo
rays of an axial pencil or bundle of raya are refracted to approximately the same
focus as those rays which pass through the lens at, or near its centre, supposing
that the said lens is used in its proper manner and position. Nearly all the
separate lenses used in photographic combinations of the best quality are in them-
selves compounded of two or more lenses of different sorts of glass cemented
together, whereby the above conditions of achromatism and freedom from spherical
aberration (or shortly aplanatism) are more or less closely fulfilled.
I shall also premise, for the sake of simplicity, that rays infringing upon the
front of the combination are proceeding from very distant points and may therefore
be considered parallel.
Let a pencil of such rays passing obliquely through such a lens be considered.
Such pencils or bundles of rays, emanating respectively from separate points of the
subject to be photographed, are refracted obliquely through the lens, and gọ to
form, however imperfectly, the marginal image.

page_text: In Fig. 1 (see drawing of my Provisional Specification) L is a lens. Let it be
supposed that rays R-R from a very distant point on the optic axis A—A_are
refracted to the focus F, which is therefore the principal foous. Let P-P ben
plane perpendicular to the optic axis and passing through the principal focus F.
Let this plane be called, throughout this Specification, the principal focal plane.
Now the parallel but oblique rays - coming from a very distant point and
forming a considerable angle with the axis A-A do not come to a focus upon the
plane P-P but somewhere between the pointef & g, much nearer to the lens-
thus the image has a very considerable curvature-not only so, but the image
at&g is very astigmatic, which is the term used to describe the following state of
things.
Let two rays r in the plane of the paper be considered, or any pairs of rays
which may bo situated or contained in any planes which pass approximatoly
through the point 7 and cut the aperture of the lens along chords which are
parallel to the plane of the paper. All such planes are heroin referred to as
primary planes. Let it be understood also that each pair of rays - in its own
plane, as above defined, is symmetrically situated with regard to a line perpendicular
to the plane of the paper and passing through the centre of the lens, or in other
words, that the two rays of each pair strike the lens at equal distances from,
and on each side of, the aforesaid perpendicular. Then all such symmetrical
pairs of rays situated in primary planes come to a focus, or cross one another, at
about the same perpendicular distance -k, from the plane P-P and more or less
close to the point. Such points fare situated, according to the obliquity, along
a curve - which may approximately be described as a circle of a radius
generally equal to about ths or scarcely more than one quarter of the principal
focal length.
And now let planes perpendicular to the paper, but all approximately passing
through the primary focus f, be considered. Such planes are herein termed
secondary planes. And, as before, let any two parallel rays in such planes be
considered, one ray of each pair being above the paper plane and the other below
it. Then all such pairs of rays in secondary planes come to a focus not at or
Dear, but more or less near a point g which is much nearer the plane P-P than
the point is; in fact the distance from g to the plane P-P is generally less than
one half of the distance from to the plane 1-P, but seldom so little as one third
of that distance. The curve F-g along which rays in secondary planes come to a
focus according to the degree of obliquity, may approximatoly be described as a
circle whose radius is generally about ths of the principal focal length. The best
possible focus for the oblique beam or pencil of rays we are considering is found at
a point about half way between ƒ & g, or in other words, half way between the
focus for rays in primary planes and the focus g for rays in secondary planes.
And these points of best possible foci are arranged along an intermediate
curve F-m according to the obliquity, which may again be approximately
described as a circle whose radius is generally about ths of the principal focal
length. This difference of focus for the same pencil of rays in primary planes
and in secondary planes constitutes the so called astigmatism. So far I have
been dealing with the case of symmetrical pairs of rays in primary planes;
rays striking the lens at equal distances on each side of the perpendicular
to the paper drawn through the centre of the lens. The above astigmatism is
totally independent of the form of the lens, if not inordinately thick. It is now
necessary to consider the meniscus-like lens Fig. 2. with regard to its action upon
any two rays in primary planes, which do not impinge upon it at equal distances
from the perpendicular to the paper drawn through the centre of the lens, but at
more or less unequal distances from the same: two rays such as a &b or d & à
Fig. 2. for instance.
Just as before it can be shown that the symmetrical pairs of rays such
as a & à, b & b, d & à each respectively intercross or have their focal points at
•

page_text: .
-
about equal distances short of the plane P-P. But such points are not coincident
in a direction perpendicular to the optic axis, but are arranged along a short
liue C-D, which, it should be pointed out, is purposely much oxaggerated
in Fig. 2. Two symmetrical rays passing through the lens very near its centre and
on each side of that ray c-a which passes through without deviation, may be said
But the
to come to a focus at c almost upon the central oblique ray c—c.
symmetrical pair of rays a & à intercross at the point A, the pair b&b intercross
at the point B while the pair d & à intercross at the point D, considerably to one
side of the oblique central ray cc. Now the necessary consequence of this.
peculiar arrangement is, that the intersecting points or foci for any eccentrio paira
of rays, such as & à, b & a, d & oa & &c. are thrown either much nearer to
the lens or else much further from the lens than the line C-D. Thus & & & inter-
cross at the point marked d + b, a & a focus at a + e, a & cat a + c and so on.
Now let it be supposed that the oblique rays striking the lens on Fig. 2 are
proceeding from a distant but bright point of light and that a piece of ground
glass is placed in the position g-g to receive the image, which is viewed from
behind. It will be found impossible to get a clear focus. For the rays d & b from
the upper side of the lens are all out of focus on the screen while rays such
as band from the other side of the lens are equally out of focus. These rays
therefore form a diffused halo upon the screen, while the only rays coming to
anything like a compact focus upon it are those proceeding from the centre of the
lens and which focus about C. Therefore the image takes the form of the balloon
shaped penumbra shown in Fig. 3. where the small & bright-end C corresponds to
the focus at C. and the outlying and least bright portion D corresponds to the
point D on which impinge the much-out of focus and therefore diffused rays from
each margin d & à of the lens. Mixed up with these appearances are the effects of
astigmatism as shown in Fig. 1ª, or Fig. 7.
Now this curious eccentric balloon shaped penumbra, or "coma," growing less
& less bright from C to D, is characteristic of a lens which gives, what I herein
call, unsymmetrical oblique refraction.
The amount and nature of this eccentric penumbra depends both upon the form
of the lens and the state of divergence, parallelism or convergence of the oblique
pencils of light impinging upon the lens, considered in relation to the lens.
It is sufficient, however, to point out that the state of things illustrated in Fig. 2.
is characteristic of a lens which is of the meniscus form or else approaching to that,
when the rays impinging upon its convex surface are either parallel or divergent.
On the other hand, if rays either parallel or convergent impinge upon au inverse
meniscus like Fig. 4. or a lens more or less approaching that form, then the points,
at which symmetrical pairs of rays intercross, are situated upon a line C-D₁ which
extends away from the oblique axis C-C, in a direction opposite to the case
shown in Fig. 2. while eccentric pairs of rays, such as & , passing through the
lower margin of the lens, focus very short, as at it and rays such as i & k
passing through the upper margin of tho lens focus very long as at the
point i+k.
+
On introducing a screen of ground glass at g-g as before it will be found that
there is an eccentric penumbra or "coma "Fig. 5 formed at the focus as in the
previous case, only the larger & less bright bulk of it is turned away from the optio
axis A-A instead of towards it as in the case of Fig. 2.
And now the effect of introducing an opaque stop or diaphragm, (with an
aperture in it smaller than the lens) behind the lens in Fig. 2 is at once apparent.
As shown in Fig. 2, the stop only allows to pass the eccentric rays à & d and
those included between them.
But a &d come to a focus, as we have seen, at the point à + à which is either

page_text: much nearer the plane P-P or even beyond it. Thus the effect of the stop is, to
only allow those eccentric-oblique rays to pass which come to a focus, or intercross,
at the greatest distance from the lens, and thus the image formed by rays in primary
planes is very considerably flattened, or completely so.
The same effect is produced in the case of Fig. 4. by placing the stop in front of
the lens, in which case the effect is to only allow those eccentric rays, such
as && (& those included) to pass, whose focus is situated about c + k much
nearer to or upon the plane P-P. In this case also the field of view is very much
flattened, or completely so.
So far I have only illustrated the selecting effect of a stop upon the foci of
oblique rays situated in the plane of the paper, or, in other words, in primary
planes. It would be extremely difficult to illustrate the effect of the same stop
upon the fooi of the same pencils considered in secondary planes. But it can be
mathematically demonstrated by a process far too long & complex for reproduction
here, that any correction in the way of either shortening or extending the focal
distances of rays in primary planes by means of a diaphragm or stop, is invariably
accompanied by a corresponding shortening or extension of the focal distances for
rays in secondary planes, which is always just one third of the primary correction
and is of the same tendency. In other words, any diaphragm correction for rays in
primary planes is always three times the corresponding simultaneous correction for
the same pencils considered in secondary planes.
The mathematical demonstration of this can not be directly applied to large
obliquities or to cases where the aperture of the lens is very large compared to the
focal length, but even in these cases practice seems to point to the general truth of
the above theorem. For upon this theorem depends the truth of that fact, so
thoroughly demonstrated in practice, viz., that it is absolutely impossible to so
correct a photographic lens, made of ordinary glasses, by means of stops or
diaphragms, as to render the image or field of view quite flat for rays in primary
planes and for rays in secondary planes simultaneously.
For I have pointed out above (Fig. 1) that the deviation - from the focal
plane P-P of the focus for the oblique symmetrical rays r- passing through tho
lens at open aperture and considered in primary planes, is almost invariably
24th times the deviation g-k of the focus for the same pencil of rays considered
in secondary planes. Hence no diaphragm corrections due to the presence of a
stop, placed behind, in front of, or between such lenses, can ever neutralise both
these errors or deviations fk and g--k simultaneously. Hence, if by menus of
diaphragms the field of view or image is rendered perfectly flat for rays in primary
planes, yet the deviation from a flat image for rays in secondary planes will not be
fully corrected and there will still remain such an amount of curvature of image
for rays in secondary planes as will rendor a distinct image impossible towards the
edge of the field of view, unless the lens is used at a very small aperture. Wherens
if the astigmatism is perfectly corrected, then the image will remain curved, and to
a radius generally equal to 13 times the principal focal length. It is this condition
of things which is responsible for the astigmatism which is invariably present at
the foci for pencils of rays which are refracted at considerable obliquity through
photographic lenses made of ordinary glasses and corrected in the usual way, so as
to give as flat a field as is consistent with fair marginal definition. There is only
one condition which renders it possible, by means of diaphragms, to produce an
image quite flat for rays in primary planes and for rays in secondary planes
simultaneously, or in other words, to produce an image quite flat and at the same
time free from marginal astigmatism.
If д =
D
the index of refraction for the positive lens of an approximately
achromatic lens.
M = the index of refraction for the negative lens combined with the above.
===== the ratio which the focal length of the negative lens bears to that of
the positive lens. If the lens is achromatic, D then is equal to the
disnersive ratio batween the two olarCOR.

page_text: •
M =
which implies that the index of refraction for the negative or concave
lens must bear the same ratio to the index for the positive or convex lens as the
focal length of the positive lens bears to the focal length of the negative lens.
This very exceptional condition, only rendered possible since 1886 by the
production of some entirely new sorts of glass, is attained very closely in
Schroeder & Stuarts patent concentric lens, in which the positivo lens has an indox
of refraction as high as about 1-61 and the negative lens an index of only 1.51 or
1-61
so. The focal length of the negative lens should consequently be only about 1.51
times, or 1066 times the focal length of the positive lens. They are thus so nearly
of the same focal length that the resulting focal length of the two combined is very
long in proportion to the diameter of the lens, and therefore it is impossible, for
that reason alone, apart from other considerations, to work such a lens with anything
but a sinal relative aperture.
Thus it will be seen that photographic lenses of large aperture in proportion to
focal length (and therefore possessing the important quality of great rapidity of
action) and at the same time having a flat field, free from inarginal astigmatism,
are not to be attained by means of those diaphragm corrections which have hitherto
been relied upon for correcting the errors of such lenses.
For this reason I have, in my invention, made use of a method of correction
which, as applied by me, is entirely new. It may be explained as follows.
Returning again to Figs. 2 & 4 it will be noticed that the unsymmetrical oblique
refraction and the consequent focal penumbra is of a contrary character in the two
cases. In Fig. 2. the rays refracted through the upper parts of the lens, such
as d & bare brought to the shortest focus, while in Fig. 4. the rays from the lower
parts of the lens, such as & pass to the shortest focus.
In the case of Fig. 2. the bright small end of the coma or penumbra (Fig. 3) is
turned away from the optic axis A-A, while in the case of Fig. 4. the bright small
end of the coma or penumbra (Fig. 5.) is turned towards the optic axis A-A.
It is obvious then, that a form of lens somewhere intermediate between the forms
of Figs. 2 & 4 is possible, which will be free from this unsyinmetrical oblique
refraction. This is the case in actual fact. In Fig. 6 is shown roughly a form of
lens made of ordinary crown or flint glasses, which has the property of what I call
symmetrical oblique refraction.
It will be found that any two rays - whatever, whether they impinge upon
the lens at equal distances on either side of its central perpendicular or not, are
refracted to one and the same focal point p, situated upon the oblique axis C-C.
I am here speaking of rays in primary planes. Supposing, as before, a white
screen or ground glass to be placed at g-g to receive the focus of rays from some
distant luminous point and moved to & fro towards the lens, between the
positions p&s, the appearances scen are as follows.
When the screen cuts through the focus p. for rays in primary planes, the
appearance on the screen is a luminous line Fig. 7. (a) perpendicular to the plane of
the paper. Moving the screen further away from the lens, the focal line (a) changes
into the vertical oval b; when the screen is about half way between the primary
and secondary foci, the appearance is approximately a luminous circle (c); on
moving still further out the appearance is the horizontal oval (d) while, when the
screen cuts through the secondary focus at S, the appearance is approximately the
horizontal luminous line (e) situated in the plane of the paper. If the curves of
the lens are nicely adjusted, these focal formations are as nearly as possible sym-
metrical, even when the rays forming them are refracted through the lens at great
obliquity.
The eccentric balloon shaped appearances shown in Figs. 3 & 5 are no longer

page_text: Now if Fig. 6 is carefully considered it will be readily seen, that the presenco
of a stop or diaphragm, whether in front of, or behind the lens cannot possibly
bring about any appreciable focal corrections. Wherever it may be placed, the
focal point for rays in primary planes, will still be at p. and therefore no alteration
in the amount of curvature of the image will be produced.
Thus, an aplanatic lens giving symmetrical refraction for oblique rays, may be
said to have its diaphragm corrections eliminated or reduced to zero.
Given the optical properties of any two or more glasses composing a lens, and
the circuinstances in which it must be used, the forms which must be given to
such lenses in order to eliminate the diaphragm corrections and consequently
secure the property of symmetrical obliquo refraction can always be calculated by
means of formula which it is scarcely necessary for me to specify hore.
So far as I am aware, lenses having this property of symmetrical oblique
refraction have never been deliberately used in compound photographic camera
lenses, at any rate with any conscious aim or appreciation of the possibilities
opened out by proper combinations of positive & negative leases of this type.
For I will now show that a combination of such lenses, may have the errors of
curvature of image and marginal astigmatism incidental to the individual lenses,
simultaneously corrected or neutralized with a very near approach to perfection at
any rate, while a reasonably short focal length relatively to aperture may result
from the whole combination.
Fig. 8. serves to illustrate the principle of correction on which my invention is
founded. L represents a positive lons giving symmetrical oblique refraction for
rays proceeding from very distant points. Let P-P. be, as before, the principal
focal plano for the lens L.
Then P-p is the curve along which the foci for oblique rays in primary planca
are arranged. Let p. be one of these foci for a pencil of rays passing through the
lons and inclined at an angle to the optic axis A-A.
Now the deviation of p. from the plane P-P. is usually and conveniently
expressed as a correction to the reciprocal of the focal length L-P., or in other
words, as a correction to the focal power of the lens L. Let the point p. be referred
to the optic axis by drawing the line p-p perpendicular to A—A.
Then
=
F
+
tan' (3+) where F stands for the principal focal
μ
length of the lens L and stands for a sort of mean (for simplicities sake) for tho
indices of refraction of the glasses of which the lens is composed. Now let N be
a negative lens made of much the same materials and of the samo focal length
or focal power as L, and also (for reasons yet to be assigned,) possessing the
property of symmetrical oblique refraction. Let this lens be placed somewhere
between Land its focus P. It can be proved, that wherever N may be placed
between L&P. it will correct the curvature and astigmatism of the imago
yielded by L & thus throw a flat and very good image upon the plane Q-Q.
For the angle under which the point p. is viewed from the centre of the lens N.
distance L-P
is 0, & tan 8 is evidently equal to tan ✈ ×
and therefore tan³ 0 =
tan' (=)
distance N-P
But it can also be shown that the curvature correction for the
point p. when referred to the point N, is equal to (the curvature correction for
point p as viewed from L) x
that is, as viewed from N, and apart from
the increase in angle of obliquity, the curvature correction is approximately
expressed by

page_text: But the correction for curvature of field yielded by the negative lens N is
of an opposite character or sign to that yielded by the positive lens and is
expressed by
tan¹
-
tan³ A
12/17 (3) 4 + 1); but
μ
tan² 0
is, as I have shown, equal to
(✓✓-1). Therefore the resulting correction for curvature, after refraction
These curvature errors also neutralise one another, and therefore the resulting
image at Q-Q is both flat and free from astigmatism.
Now it would be impossible to achieve this result if the lens L gave unsym-
metrical oblique refraction, for it is obvious that the aperture of the negative
lens N forms a diaphragm with respect to the lens L and therefore, more or less
serious diaphragm corrections would be introduced and the conjunction of a flat
image with freedom from marginal astigmatism, more or less rendered impossible.
T
where F
=
F
=
and d
=
the principal focal length of lens L
"
"
of lens N
"9
the distance between the centres of L & N.
The combination in this form bears resemblance to the old orthoscopic lens and
has the same fault of giving an unsightly amount of negative distortion.
Now the way in which I completely get rid of this grave defect of distortion_ia 2
by dividing the positive element of the combination into two parts and placing the
negative lens in a certain position between.
I claim no originality for this device which was long ago carried out in Dallmeyers
triplet lens among others.
Moreover, although a doublet might be made on this principle, formed of a
positive lens with a negative lens behind it, which would give a very flat & good
image of a distant subject (if we leave the distortion out of consideration) yet it
can be shown that such a doublet would be comparatively useless when it came to
be used for near subjects or for copying.
For this reason alone, the doublet form is very much inferior to the triplet form
of my lens, which I shall shortly proceed to particulary describe.
But first there is another matter in connection with my combination which should
'be pointed out.
I have shown that a positive lens giving symmetrical oblique refraction, may
have its errors of curvature of field and astigmatism corrected by a negative lens

page_text: having the same properties, and of much the same materials and focal length,
placed behind it.
But the formule only apply when the obliquity is not very great. As a matter
of fact, I find that in the lens Fig. 12. which I have worked out, the focal
power (✓✓) of the negative lens is actually only ·85
(+33) when the field of
view is flat, or only 85 per cent. of the united focal powers of the front & back
lenses. These focal powers, however, are the theoretical focal powers, calculated
on the supposition that the lenses are very thin.
1
Doubtless this apparent difference or disparity between ✓ and (½ + ½³) is
B
largely due to the comparatively large thicknesses involved, as well as to the fact
that the formula for oblique pencils are scarcely so applicable to great obliquities
and large relative apertures.
In my Provisional Specification I put forward another explanation of the above
disparity, which, however, I have since found reason to discard altogether.
And now I will explain why not only the two positive lenses, but also the
negative correcting lens, should have the property of symmetrical oblique refraction.
It is not so much to obviate the presence of any diaphragm corrections, for such
corrections, so long as the stops for regulating the aperture of the lens are placed
close to the negative lens, would not be very serious. But let it be supposed, that
a pencil of rays of considerable obliquity passes through the whole combination
and is brought to a focus without any astigmatism at a point in a perfectly plane
image. It is refracted symmetrically by the two positive lenses, & therefore, if its
final focus is to be symmetrical it must also meet with symmetrical oblique
refraction in passing through the negative lens; otherwise, instead of the final
focus of the oblique pencil being practically a point, it will more or less have an
eccentric balloon shaped appearauce very like Fig. 3 or Fig. 4. This is also the
appearance seen at the focus, for rays of even very small obliquity; of telescope
object glasses of ordinary type, its presence at the focus being an infallible
symptom of the object glass being "out of square" or having a slight tilt. It is
well known to most opticians that the eccentric flare at the focus is absolutely
inconsistent with good definition, & here it cannot be too strongly emphasised that
a photographic lens may have all the errors of curvature of field and marginal
astigmatism perfectly corrected, and yet' fail to give good definition towards the
margins of the field, owing simply to the fact that the lens as a whole is not
designed to give symmetrical oblique refraction.
In the accompanying drawing Sheet 2 Fig. 12 is shown a longitudinal section
through the one form of my lens which I have been able to work out completely.
F. is the front combination, which is exposed to the subject to be photographed ;
N is the negative combination and B is the back combination.
The glasses of which the lenses are composed have the following optical properties
and designations.
First lens L, and last lens L, are made of a rather light silicate flint glass with
the following optical properties

page_text: 2nd lens L, 4th lens L, & 5th lens L, are made of light phosphate crown having
the following optical properties
Refractive index for
the D ray
Difference between the indices
of refrn. for D & Ġ raya
Reciprocal of dis-
persive power

page_text: B.
Clear aperture of last surface r,= "194
Central thickness = -008
Diameter somewhat larger than aperture.
The central thicknesses, as given above, should be as closely followed out as
possible; for instance, the rather large contral thicknesses of L. & L. are necessary
in order to ensure that the field of view shall be flat for actinic and visual rays
simultaneously and also ensure a larger field of good definition in other ways.
Of course the diameters of the necessary wheels and gauges will be obtained by
doubling the above radii.
This combination is a moderately wide angle lens. Its nodal point or the point
from which its equivalent focal length is to be measured, is at the point marked n
just in front of the apex of front lens. It is intended to fully cover a plate whose
length is equal to the equivalent focal length, with the hitherto thought impossible
aperture of. This it does and with oven illumination up to the sides of the field
of view.
F
For instance a lens of 7 inches equivalent focal length_should cover a
F
7 × 5 plate with reasonable sharpness up to the corners with and almost the
8'
full aperture of the lens should be visible when the eye is placed near one end of
the opening in the frame carrying the ground glass screen.
F
The diaphragma or stops regulating the aperture are placed as closely as possible
behind the lens N, as shown in Fig. 12. The cloar aperture of the stop
necessary for the aperture is equal to the equivalent focal length x '098 or
almost oth of the focal length.
It should be borne in mind that the parallel beam of light which strikes the first
F
is condensed to the breadth about when it enters
ΤΟ
8
F
lens with a breadth equal to
the stop. The other stops for
F F F
11-3' 16' 32
&o. of course have their diameters
settled by reference to the standard aperture for
F
If desired an iris diaphragm may be fixed behind the lens N and the size of the
tube made to accommodate it.
WORKING INSTRUCTIONS.
The quickest way of roughing out the front lane L. is to chuck the glass block in a
0
WORKING INSTRUCTIONS.
The quickest way of roughing out the front lane T, is to chuck the glass block in a
lathe and turn out the hollow surface with a hardened steel tool or still better a
diamond, keeping the glass all the time moistened with turpentine. Of course the
same method may be applied to all the deeper curved surfaces, if found more
expeditious than the ordinary methods of grinding in tools with coarse emery.
5 The light phosphate crown glass will be found softer in grinding than ordinary

page_text: crown, more brittle and more apt to fly if incautiously heated. The polishing
methods in which the optician is most skilled and finds most successful for deep curves
may be used. So far I have found wax polishes the best for the deeper curves.
The lenses with the shallower curves may be worked up in blocks of three or
upwards and polished oither by a dry (for shallow curves) or a wet process (for
deop curves). The phosphate crown polishes very rapidly, but the worker, if
using a wet polishing process for this glass, should be carefully cautioned against
letting any of the wet rouge or putty powder dry upon its surface when finishing, or
it cannot be got off again; and all trace of wet polishing material should be wiped
off while kept moist by breathing, or dipping into water.
After being polished, each lons should be most carefully and exactly centred
down and fitted into its cell or counter-gell, as the case may be.
This operation should be done in a dioptric centering lathe, that is, a lathe in
which the lens is made to run perfectly truo by observation of the transmitted
image, as well as by the reflected image, which latter test is not sufficiently roliable
in its nature, especially as the reflections from both surfaces aro not always clearly.
recognisable.
The fit of the lenses in their cells should admit of no perceptible shake, but they
should be able to just freely rotate. The form of brass mounting which I have
drawn to scale in Fig. 12 should be carried out with great truth; the threads
should, for ordinary sizes, be about 50 to the inch and should not be chased up by
hand, but by means of a screw cutting lathe or a lathe with a traversing mandril.
It is a most excellent precaution to reserve the final ont to be taken off the interiors
of all the flanges or rings, which confine the lenses, to the very last. Thus, if the
whole mounting is truly chucked by the cap flange C, then all the interior flanges
which confine the lenses may be trued up together, first by turning up the interiors
of the back cell of lens B, which may then, if necessary, be unscrewed without
disturbing the chucking; then the inside of the interior cell which is to carry
lens N may be trued up, after which the body tube carrying this may be unscrewed
and a final cut taken off the interiors of the front cell, which remains in the chuck.
This if carefully done ensures great truth in the alignment of the three leus
combinations, on which the success of the whole lens very seriously depends.
After being properly centered and fitted into their respective cells, the back &
front combinations may be finally cemented together with balsam.
After baking & cooling they should be carefully cleaned, then warmed again and
placed in their proper cells, which also should be warmed!
While all warm together the counter rings of the cells should be screwed down
sufficiently to just confine the lenses, so that they may be just rotated in their cell
"between the fingers but without shake. This operation secures the correct centering
. of one lens over. its fellow.
:
When cold again the counter rings should be adjusted. That is the edge of the
main cell should be rubbed down until the counter ring cau be screwed home tight
up to its shoulder without causing the lens to be at all nipped.
The lens should then be capable of a slight amount of rotation but without
shake.
The negative lens L should be temporarily put together with some thin new
balsam and then be pushed home in its cell. Its sticky edges should be sufficient
to hold it there while the whole combination is being tested, for the purpose of
seeing whether the negative lens N requires a slight alteration or not. For, owing
to inevitablo variations in the optical properties of the several glasses or in the
curvatures, slight alterations of the negative lens will, as often as not, be necessary,
if the lens is to be made as porfect as it is possible to make it.
The lens should be mounted temporarily in a trial camera carrying a ground
glass screen rather larger than the plate which the lens is intended to cover, for
instance, a lens'of 74 inches equiv. focal length is best tried with a whole plate
screen. This camera should have facilities for easy focussing and its soreen should
be most accurately square to the optic axis of the lens, The first thing necessary

page_text: is to properly adjust the distance between the front lens F and the neg. lens N.
The back lens B being taken out the other two should be aimed axially at a very
distant object such as a weathercock. Then a small telescope of a foot focal length
or so should first be focussed upon the distant weathercock, and then it should be
placed behind the lens N so as to view the distant weathercock through both
lenses F & N. If now the distance between F & N is about right then no very
material alteration in the length of the telescope should be necessary in order to
see the weathercook distinctly. In other words the light should emerge in a
parallel beam after traversing both lenses F & N, or, if not quite parallel then
preferably slightly divergent. Of course shortening the main tube of the mount
allows the cell carrying the lens F to be screwed nearer to N.
The lens should now be tried with its back lens B in position. It should first be
roughly examined for distortion. A vertically stretched thick. wire is the best
object to focus upon. Some accurately straight lines should be always ruled upon
the focussing screen more or less near its margin, for comparison with the image of
the wire. If any material amount of distortion of the type shown in Fig. 13 in
visible then the main tube of the lens must be shortened so as to allow the lens B
to approach nearer to lens N until the distortion is quite removed. That being
done the lens should next be tested for correct centering &c. An artificial point of
light at the end of a long darkened room is the best for this purpose. Rack
somewhat within focus so as to cause the image to show a disc of light about both of
an inch diameter on the centre of the soreon. The corrections for spherical
aberration may now be advantageously examined, or any zones of bad figuring
detected, if there are such.
If the centering of the lenses and mount is all right, then on rotating the
camera from side to side and up & down &c. the disc or oval of light projected on
the screen should look precisely the same in size and slinpe, and show precisely the
same changes, if any, along whichever radius, drawn from the contre of the screen,
it may be caused to travel. If along any meridian the image at (say) 3 inches from
the centre, differs materially from what it is at 3 inches from the centre in the
opposite direction, then there is something at fault.
may, as easily as not be caused by the negative lens not being pushed perfectly
home in its cell, or there being a little looseness of fit in it.
After correct centering has been assured, the lens should be tested for flatness of
field, by carefully focussing the distant weathercock on the centre of the screen
and then rotating the camera so as to bring the image first near one margin of the
screen and then near the other; when, if the field is perfectly flat, the image
should remain very well defined up to the margins of the screen without any
alteration of focussing being required.
If bowever, the best possible Intoral image of the weathercock is obtained only
by causing the lens to approach more to the screen, then the field of view is proved
to be round, or concave towards the lens. If the best marginal image is obtained
by causing the lens to recede more from the screen, then the field of view is proved
to be hollow, or convex towards the lens.
Obviously to correct a round field the negative lens must be deepened or made
stronger either on one side or the other, while to correct a hollow field, the negative
lens must be weakened by flatteuing either one side or the other.
For instance, in the case of a 7+ inch lens, where, in order to accurately focus the
weathercock at a point 3 inches from the centre of the screen, the distance between
the lous & screen has to be lessened by 'th inch. The first surface of the
negative lens will be about 3-20 inches radius, and to correct the above amount of
rounduess of field this radius of 3.20 should be altered to about 3-15. A few
extra tools, differing slightly in curve, for altering the outside surfaces of the
negative lens should generally be available. Very small alterations in these curves
can be performed by manipulating with a polisher in the lathe. Supposing an
alteration in the negative lens to be required, the next thing is to find which side
of the negative lens it is requisite to alter. This is determined by the presence

page_text: "
of "coma," if there is any. The lens must be again tried in the distant artificial
star and the character of the ", coma nbserved, should there be any. Fig. 14
represents the focussing soreen; the slightly out of focus imagos shown at A, B, C
& D represent a case of inward " coma or coma in which the side flare or wing
of light is directed towards the centre of the screen. While a, b, c & d represent
a case of outward "coma or coma in which the side flare or wing of light is
directed away from the centre of the plate. Now the lens will never perform at
its best, even if the field is flat, so long as any serious amount of "coma
" exists
and it must always be eliminated consistently with the other corrections being
attained. Now the rules to be observed are as follows-
"
coma.
"
"
"
Deepening the back curve r, of the negative lens produces outward “coma.
Deepening the front curve of the negative lens produces inward "coma.'
Flattening the back curve rg produces inward “
Flattening the front curver, produces outward "coma.'
Therefore, to cure a round field when the lens also shows outward “ coma
deepen r..
"
"
To cure a round field when the lens also shows inward coma, deepen . To
cure a hollow field when the lens also shows outward coma, flatten r, and to curo a
hollow field when the lens also shows inward coma flatten r
But if the field is about perfectly flat, while the lens shows outward coms, then
deepen r, & flatten r, the two alterations being such as to neutralize one another
as regards effect upon the focal power of N. If the field is about perfectly flat,
while the lens shows inward coma then flatten r, and deepen, keeping the foonl
power of N the same.
Finally should the field not be flat while the lens shows no 66 coma "then both
sides of the neg. lens should be either deepened or flattened simultaneously, as the
case may be.
The lens will be found to perform the best, all things considered, when the image
is perfectly free from coma at a distance from the centre of the screen, equal to
half the equivalent fecal length. It will then be found to give a slight amount of
inward coma when tho image falls half way between the aforesaid position and the
centre.
It should be remarked that owing to the small dispersive power of the
phosphate crown glasses and the presence of the positive lens L, of highly
dispersive extra dense flint glass, the amount of secondary spectrum present at the
focus of this lens is very considerably less than that present at the focus of any
photographic lens made of ordinary glasses, and therefore when the optician is
testing this lens for colour correction he must expect, when the lens is properly
corrected so as to refract the D & G rays to the same focus, to see considerably
less red fringe inside focus and less green fringe outside focus, than he has been
accustomed to.
It should also be remarked that the front combination F cannot be made truly
aplanatic, for even when the curves are truly spherical, a well pronounced zonal
aberration will be noticeable, the zone of rays which pass through at about ths of
the semi-aperture from the centre are refracted to the shortest foons. But when
the whole triplet lons is tried with stop no serious zonal aberration should be
noticeable if all the figuring is properly carried out.
F
After the negative lens has been properly corrected, it should then be finally
cemented together and fixed in its cell. It is decidedly preferable not to burnish it
in, but to cement it in its cell by a mixture of rather stiff Canada balsam, made
black by admixture with lamp black. The whole triplet should then be tried again
for symmetry of centering, for it may be found necessary to warm the mount again
for the purpose of settling the negative lens more home into its cell by judicious
pressure. Often a one sided pressure will cure a slight fault of this sort, which
may easily arise if the layer of balsam between the two lenses is thicker on one

page_text: side than the other. When cold the triplet may be tried again until finally
approved.
This objective will answer porfectly well for lantern projection, if the bighost
illuminating power is not exacted and especially if the space is confined. While,
if made on a very small scale, it will answer tolerably well for a microscope
projecting lens.
But I have not yet been able to work out the forms which will give as great an
illuminating or light grasping power as is often required for both the above
purposes as well as for camera work. I can only skotch out one or two useful
forms of my invention which I shall doubtless perfect before long.
For instance Fig. 15 shows a more rapid form of my lens on the same lines exactly
as the one which I have particularly described, only the back lens B is here more
powerful relatively to the front lens F and the whole lens is meant to cover a plate
F
whose length is about 3rds of the equivalent focal length, with an aperture of
5.65
and very nearly even illumination. Fig. 16. is a sketch of a symmetrical form of
lens which embodies the principle of my invention. In the cases of the lenses
represented in Figs. 12 & 15 1 linve supposed the rays first incident upon the lens
to be parallel as when coming from a distant object. And the curves of all three
combinations are so arranged that each combination F, N, & B gives symmetrical
oblique refraction or has its diaphragm corrections eliminated as nearly as
practicable for the rays passing through it, on the condition that the rays, when
firat incident, are parallel.
But I must point out what happens when the rays first incident become divergent,
as when coming from a very near object. Lens F no longer gives symmetrical
oblique refraction in that case and diaphragm corrections now arise whose tendency
is to make the field of view hollow (in the sense defined above). Moreover the
back lens B which is now also receiving divergent rays, no longer gives symmetrical
oblique rofraction, but it can be shown that the tendency of the consequent
diaphragm corrections of lens B is to make the field of view round and this tendency is
of the opposite character to that exerted by lens F. And it can be shown that not
only are these two tendencies opposite in character but that they are equal or very
nearly equal in amount, so that the field of view still remains flat (if the original
object is flat).
This is tantamount to the following very important general proposition relating
to this triplet, viz., that if the two positive lenses F & B are simultaneously and
individually free from diaphragm corrections or each have the property of
symmetrical oblique refraction, when the first incident rays have a certain degree
of divergence or are parallel, then the triplet as a whole will remain free from
diaphragm corrections, for any other likely degree of divergence of the first
incident rays. Therefore the triplets shown in Figs. 12 & 15, although initially
designed for yielding a perfect image of a distant subject, with the form of each
lens calculated accordingly, are, as a matter of fact, about equally good in their
performanco when used for copying equal size; when of course the incident rays
are very divergent.
Thus the principle of my invention, that the whole burden of rendering the
field of view flat shall devolve upon the negative lens, and that diaphragm
corrections, being eliminated, shall contribute practically nothing to that end, still
holds good. Therefore the form of lens sketched in Fig. 16 naturally suggests
itself. There the whole lens is initially calculated with a view to copying a flat
object to equal size. Therefore the two positive lenses should be exactly alike in
form and power, but turned opposite ways, and with the negative lens placed half
way between them, and both individually designed to give symmetrical oblique
refraction or to be free from, diaphragm corrections when the incident rays are
diverging as much as the emergent rays are converging, as shown in Fig. 16. Should
such a combination as this be used on distant subjects, then the consequent diaphragm

page_text: corrections of lens F, tending to round the field of view, will. be almost_perfectly
neutralized by the consequent simultaneous diaphragm corrections in leus B, tending
to hollow the field of view. Thus, under all oircumstances likely to happen in
practice, the flat image yielded by my lenses is brought about by the power of a
negative lens only, and is in no appreciable degree due to those diaphragm
corrections which are more or less relied upon for flattening the field of view in
all photographic lenses hitherto made; the employment of which diaphragm
corrections, as I have before pointed out, renders it impossible to obtain a flat field
of view, which shall at the same time be free from astigmatism, excepting under
those exceptional conditions carried out in Dr. Schroeder & Stuarts concentric lens,
which conditions howover preclude any large aperture being attainable.
The rapidity of the symmetrical triplet shown in Fig. 16 depends upon the
relative separation between the two positive lenses. Calling the focal length of
the negative lens N, 1 or unity and the focal length of cach positiva lens 2 or
thereabouts. Then the maximum rapidity or shortest equivalent focal length is
obtained when the separation between F & N and between N & B is equal to 1.
As this distance is reduced, while keeping the focal lengths of all three lenses
about the same, so will the equivalent focal length increase and the rapidity
decrease. The equivalent focal length of any triplet whatever may be approxi-
mately obtained by the following formula :-
.
In the above formula, expressing the equivalent focal length,
=
=
the principal focal length of the neg. lens N
ditto
do.
ditto
do.
of the front lens F
of the back lens B
the distance or separation between the front lens F & the negative lons N.
the separation between the negative lens N & the back leus B.
But each distance found requisite for certain convenient degrees of rapidity, requires
a different form to be given to the two positivo lenses, in order to ensure the
elimination of diaphragm corrections in each lens, when the whole triplet is being
used for copying equal size, which condition implies the elimination of the
diaphragm corrections of the whole triplet under any other conditions under which
it is likely to be used. But throughout these modifications, the form of the
negative lens obviously need not be materially altered, since, when the triplet is
being used for copying equal size, the rays traversing lens N are invariably
converging to & diverging from two points situated at equal distances from the
the negative lens, but on opposite sides of it, as shown in Fig. 16.
This symmetrical form of my triplet certainly promises many practical advan-
tages in manufacture, when the curves are once determined; but it presents more
theoretical & practical difficulties in working out than the forms which I have
shown in Figs. 12 & 15 and particularly described above in the case of Fig. 12.
Having now particularly described & ascertained the nature of my said inven-
tion & in what manner the same is to be performed, I declare that what I
claim is :-
•
•
A photographic triplet lens, lantern or microscopic projecting lens, composed of
two substantially achromatic and aplanatic positive lenses and a substantially
achromatic & aplanatic negative lens placed between the two positive lenses; all
three lenses being severally so designed as to simultaneously have the herein
defined property of symmetrical oblique refraction, or have their diaphragm
corrections eliminated as completely as possible when the rays first incident on the

page_text: front lens are either parallel or have a certain assigned degree of divergence;
- while the focal power of the negative lens is made as nearly equal to the combined
focal powers of the two positive lenses as is found necessary to the complete
flattening of the image or field of view; the whole burden of correcting the oblique
5 pencils against curvature of field & astigmatism, thus falling entirely upon the
negative lens; by which device a flat image combined with general freedom from
astigmatism is secured.
Dated this 25th day of October 1893.