THE THEORY AND APPLICATION
OF THE '
CONCAVE DIFFRACTION GRATING

Thesis for the Degree of M. S.

C Fred Clarke
1935

llll"Hill"lllllllflllllllll”lllfllllllllllIIHHIHHIHM

 

301701 0947

 

(W& 1&5 r.

PLACE IN REFURN BOX to re
TO AVOID FINE ret
MAY BE RECALLED w

move this checkout from your record.
urn on or before date due.
ith earlier due date if requested.

 

./,// l, 1”
»r V /I/ / Wab/

L"

of the

CIT CAVE DIE 1* LIACTICN GFJLT I'TG

Thesis for Degree of M. S.
“\-
wt"

\

C: Fred Cla ke

1935

IE APPLECIATION

I wish to excress my apcreciation to Dr. C. D. Hausa who
suggested this Problem and who has guided thro :hout; to
Prof. C. W. Chapman for his cooperation in furnishing the
necessary equipment; to George L. Chapman for his guidance in

the mechanical construction, and to the physics staff for the

gany helpful suggestions and encouragements.

10384.3

TABLE OF CONTEUT

I General Introduction _

II Theoretical Considerations

III Details of XeCthical Construction

IV Adjustment and Oeeration

V Limitations, Aberrations, and Resolving Power

of this Grating
VI Conclusion

VI I E ibl iO graffihy

LIST OF ILLUSTRATIQHS

Plate E0.

I Plan and Elevation of the Spectrcgruph
II Plan and Section of fine Grating Carriage
III Two Sections of the Camera.and Carriage‘
IV Details of the Slit Carriage

V Views of the Apparatus

VI The Completed Spectrograph

VII The Calibration Curve

VIII Various Spectra

Page

10
12
in
16
19
20

23

INTRODUCTION

The purpose of this paper is to explain the construction and
operation of a smell grating spectrograph.

In order to accomplish this, it will be necessary;

1) to review briefly the theory of the grating, 2) to give the
mechanical details of the necessary construction of the spectrograph,
3) to consider in detail the difficulties and limitations arising in
the adjustment and Operation of the apparatus, and M) to compare its
resolving power with the equipment available in this labratory.

The grating is a Wallace Heolica of a Michelson concave
diffraction grating. It has 25,110 lines per inch and a focal length
of 1060 mm. To meet the above objectives it was necessary to provide
a mounting for this grating which would; 1) be flexible, 2) provide
easy adjustment from one setting to another, and 3) give accurate re-

setting to any desired region of the spectrum.

(1)

(1)

THEORETICAL CCNSIDERATIODS

An Optical grating consists of a piece of glass or speculum
metal which has been ruled with from 3000 to 30,000 lines to the inch.
The glass allows the light to pass between each ruled line but the
ruled line is practically opaque. The speculum metal acts as a
mirror each groove acting as a small reflector. The ruling of these
gratings is a delicate, expensive, and slow task. There has been
develOped, by T. Thorp, R. J. Wallace, and others, a method of re—
producing these gratings by making a collodion or pyroxilin cast of
the original, and mounting this case on some suitable foundation.‘
Rowland discovered that if a grating were ruled on a concave mirror
the grating would produce sharp images, itself, without any lens
system being necessary.

The concave grating used in this problem is a Wallace replica
of a grating ruled on Hichelson's engine at the University of Chicago.
The cast is mounted on a silvered glass mirror, which in turn is
mounted h.a block of plaster of paris, This grating has 25,110 lines
to the inch, and a.focal length of 106.0 cm. The lines are 3 cm.
long and the ruling extends for 5 cm.

From the elementary theory of the diffraction grating the re-
lation between the angle of the incident ray (9, , the angle of the
diffracted ray 6%., and the wavelength 3X , for any plans grating,

*#
is given by the equation

711= 169w 9,-f-3Lru92)

(2)
* Chas. F. Meyer--The Diffraction of Light,ep. 130 ~59. 182

I""‘Chas. F. heyer-—The Diffraction of Light-~p. 116

where n is the spectral order observed and a is the grating
spacing vis., the distance from a.point in one ruled line to a
correSponding point in the adjacent line, or simply, the recipro-
cal of the number of lines per unit length in the grating. This
elementany theory is applicable to any plane transmission or re-
flection grating. If this equation is applied to each element of a
concave reflection grating an expression should be found which would
determine the focal relation.

In the development of this focal relation for the concave
grating, the grating space . a is considered constant along the
arc. In practice a grating is ruled with the spacing constant along
the chord. However, since the aperture of a grating is small, the
spacing along the are or chord will not differ anpreciably. (It
can be shown that this constant spacing along the chord instead of
along the arc is essential in the perfection of the image.)"l

In figure 1 let 0 be the source and its image I formed by
the grating KM'. With DI, the radius of curvature of the grating,
as a diameter draw a circle tangent to the grating at its center.
Consider the two rays from 0, CM and OM' incident on the grating.
Let 9 represent the snall element of the grating between M and
M'. The angles 9! and 9, 449, , and 9; andfidoiekare the

angles of incidence and diffraction respectively since any line

( 3 )
*Chas. r. lieyer-—The Diffraction of Light-1). LI30.

(2)

 

7
1

Figure 1

dun 1): nae-.9, +3c. 9.1)]

from D is normal to the
gret ing surface.

..In order to form a
diffracted image in a
given order of a partic-
ular wavelength it is
necessary that H)
remain constant over
the surface of the grat-
ing. This condition may
be exnressed by differentiat—
ing the grating equation
with respect to 9 and
setting this equal to zero.
The correct focal relation
will then be that which

satisfi as this equation.

Since a is a constant for any particular grating this equation re—

duces to

6010,10, + (161613490120 .

In order to have an image, 9, and 523‘ must compensate for each

other to satisfy equation (2).

(1+)

*Chas. F. Mayer--The Diffraction of Light-page 155

(3)

(1+)

Letting R represent the radius of curvature of the grating,
r1 the distance OLE, and re the distance IL: in figure 1, by geometry;r

(F. +19! 7‘ HUI ‘1 W1." 62/ +A‘9/ .

0r ‘
0m, :4’,-g :i,%

V:
by using radian measure to represent the angles if, and W1 .
j: e cos 9/ since for small arcs the arc may be substituted for its
chord or the chord for the arc, (the error introduced being small) and

the element of the grating surface is small.

Therefore 4 9 __ ۤ:g<_1:&/ ___ e,
I ”‘ r I?
I

. e 9 a
written 4 (9.3.. 3 _@___2; - ~—

3 H

Substituting these values in equation (2) gives

CM9___§_ _§.Qzefli..§— _-—_
“Qt—7.4 R}*‘”’”‘%[ a K O

and similarly A79; may be

If rl :: R cos 9, and r2 2 R cos 93‘ eqwtion (1+) is satisfied.
This condition exists when 0 and I both lie on the circle having DL as
a diameter. Other conditions may satisfy this equation but this one is
of particular significance. This circle is commonly called the Rowland
circle and is understood to he the circle tangent to the center of the
grating using the radius of curvature as its diameter.

In general practice a narrow slit is used as the source 0 . It
follows from equation 0+) that if the slit is placed any where on the
Rowland circle, its image will be in focus on this circle also, and for
any given 9/ its position will depend upon )1 and R of equation (1).

( 5 )

t
Figure 2 is a.sketch of die Eagle mounting. Light enters

the slit S and is reflected to the grating G where it is diffracted
to the plate P. Here the various wavelengths are separated over the
plate. Optically the slit S is ,just above or below the center of the
plate P. Since it is necessary that the grating and plate remain on
the Rowland circle as they are rotated, the corresponding change in
the chord is made, as illustrated in figure 3. The center of the
Rowland circle moves along the normal to the line PG as the machine

is adjusted to the various snectral orders. From figure 2 it is

evident that the angle of incidence 9, and the angle of diffraction

96?. are identical. Therefore equation (1) reduces to
7, ;, _-_-. a. 6K. 44;» 9

for the Eagle type of mounting. It is also evident from equation (14»)
that if all points on the plate P are to be in focus at the same

setting it must have the curvature of the Rowland circle.

 

 

Figure 2

To definitely illustrate these positions, take the iron line
A -‘—"- 148559.757 A. and calculcate the required positions with
equation (5). This particular grating has 25110 lines per inch,

(6)

or 9885.8 lines per cm. Therefore a ;: 10115.h i . R==106.0 cm.

From equation (5) is obtained

*-

(6) 9=W§£— ciz/aé.aao

2

 

P
' l '-“- 4859.757 a =lOllS,/!,3.f
N e g; 1-; l '1,-
150 341 li..;-,C,14 7.5 5.5,

 

H

2 28°43' 92.96 15.9 6.2

 

46’6.5' 73.49 25.6 14.3

 

.p.

 

73'55' 29.36 41.2 513.9

 

 

 

 

 

 

 

 

Table I

 

Figure 3

Figure 3 gives graphically the relative positions of the camera
and grating for the orders as shown in table 1. As the length of the
chord is changed, the grating and plateholder must rotate equal amounts
in opposite directions in order to remain tangent to the Rowland circle.

It is clear from equation (6) that in the same position in which the
first order diffracted image of R = 14859.75 A is obtained, will occur
the second order of A: 21429.87 A . and the third order A:1619.75 A .
Neglecting, of course, the probability of absorption of these shorter

wavel eng ths.

( 7 )

COI-ISTRUCTIUN

There are four main parts to a grating spectrograph, l) the
grating support, 2) the camera or plate holder, 3) the slit arfl
mounting, N) the general support for these three arranged in a
manner which will provide the necessary adjustment.

In the Eagle mounting* it is necessary to have the slit and
center of the plate Optically coincident. This is impossible
mechanically. However, a very close approximation to this ideal
may be had by lifting the plate Just above the plane of the Rowland
circle which includes the Optical axis of the grating, and then
placing the slit Just below this circle, both coincident with a
line through the circle perpendicular to the plane of the circle.

Actually this last may be accomplished in two ways. The
slit may be mounted directly beneath the plate holder. (The die-
advantage being that only one exposure may be obtained on any given
plate as there is no opportunity to move the plate into successive
positions without covering up the slit with the phate holder.) Or
the slit may be mounted perpendicular to this Optical path and just
below the plane of the Rowland circle with a 15° totally reflecting
prism at the foot of the perpendicular, and the optical path adjusted
until it is the same length as in the previous condition. This is
shnilar to the mounting used in.the litrow type of prism spectrographs.

The distance between the grating and the plate holder'must be
capable of a wide range of literal adjustment and must be capaflie of
reset positions quickly and.easily. The maximum length.must be the

(8)
*E. C. Baly-Spectroscony Vol. 1-dpp. 205-212

focal length of the grating, in this instance 1% cm. The minimum
length will depend on the spectral order possible with the grating at
hand. This one was constructed with a range of ME" to 16" from grating
to plate. This adjustment is the length of the chord O the Rowland
circle.

As the chord is changed in the Rowland circle the grating must
remain tangent to the d.rcle and the curve of the plate holder must
always coincide with this circle. Therefore, rotational motion must
be given to change from one part Of the spectrmn to another and from
one order to another. This will amount to a right handed motion of
one and a corresponding left handed motion of the other, of equal
amounts.

The simplest support seened to be a lathe bed, although a
U beam or, even a flat plate could be machined as a track for the
lateral movement of the grating carriage. This one is a wood turnp
ing, lathe bed in 5 3/16" long by 6 5/16" wide. The camera, slit,
and grating are mounted on carriages machined to the ways of the
lathe bed. The camera carriage is mounted permanently on one end
of the bed since it receives the greatest mechanical strains during
Operation. The slit carriage clamps to the bed and may be changed at
will by loosening two clamping screws. This carriage also supports
the totally reflecting prism. The grating carriage is free to move
laterally on the ways and is controlled by a screw'the length of
the bed with a pitch of 1/10 of an inch. The plan, elevation, and

also a section are shown in Plate I.

(9)

 

 

9:20: p» .P

 

 

 

 

 

 

 

 

 

 

 

I’D

 

 

 

 

 

 

 

 

 

TILE. I-I vhf...

 

 

 

 

 

 

mwmb mum 598.305 0% gm memoduomnmdw

 

I

17‘
d

FLnT.

(lo)

The grating carriage, the details of which are sham“. in Plate II,
is of 3/8" rolled brass stock 5;" x 12". The V ways are cut length-
wise. In the upper side a circular recess is turned n.8968 inches in
diameter in which the worm.gear rests. The center of this is cut and
threaded for a B/M" mounting stud. 4A recess is cut on one side for
the mm. Cone bearings on either end of this worm hold it in
position against the worm gear. .A square shaft through the wonn
allows the longitudinal motion of the carriage. Thistsorm.and gear
have a nitch of 1/13" R. H.

The diameter of the circular plate, 14.89", is such that 200
threads are cut in its perishery. Thus one comnlete revolution of
the worm moves the worm gear If/lOO radians, which is one division
on the calibrated dial mounted Just above the nlate. The worm gear
was cut with a standard 13 thread tan by constnicting a jig to fit
into the tool post of the lathe to carmy the gear level with the
centers and allow free rotation of the gear. The tap in the lathe
will automatically feed the circular plate as it cuts the gear.

Just above this worm.gear and supported by it is the circular

scale 6"

in diameter. Above this is the grating mounting, surported
by three leveling screws, and held in place by a coil spring. The
grating is capable of being tilted either forward and backward or to
either side and its heighth is also controlled by these leveling
screws. It may be given a slight rotational motion by two screws
at the tOp of the mounting.

The carriage is connected to the screw by a four inch cast
babbit nut linked with a flat spring. This suffices for the reset

purposes required of this anoaratus; but if direct measurements are

necessary, a direct mounting should be used such as is used on com-

'parator screws. Then by dividing the dial in 100 parts the move-

(11)

 

 

 

 

 

 

 

 

 

 

 

 

;' . '9
‘ O
I
\
S> 0
a:
1 .-
1 69 °
i
J
A 1
!v 44f
O
T L

Plan at B

 

 

 

 

 

 

 

 

 

 

 

5¢ction It 3

 

 

Plan and Section of the Grating Carriage

:5 ATE II

(12)

 

ment could be read directlv to 1/1000 of an inch.

The details of the camera and its carriage are shown in Plate III.
The carriage is wade from a rolled iron plate 3/M" thick, 6" x 8". A
circular recess is also tirned in this flats of the same diameter as
that in the grating carriage, n.89 inches. V ways are cut Length—
wise of this plate. Both are cut deeper to compensate for its added
thickness. The circular plate is cut to a worm gear the same as for
the grating except that a left hand tap is used. This worm.gear is
held in place by a 3/M" stud screw into the iron plate. .A steel
ball in the center of this stud carries a brass bolt which supports
the camera.mounting plates. The lower plate is clamped to thevvonn
gear by four studs, giving opportunity to level in either direction.
The upper plate is fastened to the lower plate by means of the brass
bolt supporting the camera and two circulai'ways bolted near either
end of the lower plate with corresponding ways in the upper plate.
These allow rotation of one plate with respect to the other which
gives Opportunity to correct for errors in the worm gears. Between
these plates and fastened to the lower one is a 6" calibrated and
verniered dial identical to the one used in the grating;mounting.
The upper plate is rotated over the lower one by means of’a worm
meshing in a rack near one end of these plates. The amount of
rotation is read from the circular scale.

0n the'upper plate is mortised a 3/3" brass plate 12" wide
and 9 In/lé" high. This is so placed that the emulsion of the
photographic plate in the plate holder is directly above the center
of the two supporting bolts. This places the center of the photo—

graphic plate coincident with the center of the rotation of the camera.

(13)

 

mmerHwo mp.“ was $886.0 9% mo macapoem

 

 

U a. 3.300....

 

 

 

 

 

 

 

 

 

p i a o. a 3 coda.
A...- .. “I
., uh .I. .u.s L
n V v .Qh- ‘5'. a I “Or-p t ‘ l-
...H .t‘
.... l r
' 1.. n D. .
0 ~ \ ‘ «my»: s r
.AL\
.h .

 

 

 

 

 

 

 

 

 

L01~0£0~lt :9 ‘3) Q _vI 30:00“ 72.03::

 

 

 

 

 

 

 

 

 

. t on
xvloaouct \. c.3900

 

lo

 

II

 

 

 

 

 

III

ATE

PL.”

(114)

any r tation of the camera alone should in nowise alter the

(D
(_.

Henc
focus at the center of the plate.

On this Vertical plate in vertical ways, see section 0 Plate III
is a carriage which supnorts the plate holder. This carriage is free
fo move through a vertical distance of 6 n. and is controlled by a
screw at the top. These wove are also high enough so that they give
covering to the ends of the plate holder and with the upeerzand
lower clamps furnish a complete light seal be ween the plate holder
and its carriage.

The back of this carriage, except a small distance on each
side which is left as a bearing surface is aach'ned down about .008"

to permit these surfaces to be painted a dull black which furnishes

a Very useable light seal. On the back of'the craera a Z bar was

formed into a Square box 11;" x 6' over which the light tight cloth
hood is fastened. This frame also contains ways whereby a mask can
be lowered. This mask is suitably cut with horizontal slots of
varying width which allow different widths to be exposed on the
plate.

The slit mounting, details of Which are sh wn in plate IV,
consists of an iron bar 3/u" x 2" x 8" in which ways are milled
so that it will fit rigidly on the lathe bed. One end extends
5%" from the center of the bed. It is held in place by a clamping
;;late directl beneath the ways of the bed, and secured by means
(bf two clamping screws. 5" from the center of the Center of the

:ays a mortise is cut so that a brass bar 3/8" thick will set

17ertically on this carriage. This bar carries the slit and its

(15)

 

 

 

 

 

 

 

 

 

Details at M Fun at N

“4'
Mil

 

 

I"

 

 

 

 

 

 

 

 

JIM

 

 

 

 

 

 

 

 

 

 

 

 

. ' u’, ’1 .
I p I ’ I
A ” a "
i.) . a
1' . y.. ' I ' I

..... “a.
I 5' o 5
.u L t o , u
. 11'” J-
. . o 0'
. u
. u; .
xv "'
:7 ‘3'"

JectLon at C

 

 

The S]. 1 t Carriage

 

 

~ mount :5 and shield. The mounting is made by taking a heavy l"
brass tube and fitting a brass collar to a press fit and then
sweating the two together leaving L" of the tube extending on one
end to fit in the square block which backs up the slit. This block
fits over this tube against the collar and is held in place by a
ring nut conntersurflc flush. with the square block. The block is
held to the slit by means of four studs, two of which have "roles
drilled and tapped at right angles in their heads to carry ad-
Justing screws. These adjusting screws face each other and en-
gage pins set in the collar, thus controlling the rotation of
the slit in its mount. This collar is turned to fit the hole
in the vertical brass bar and to carry on its other end a 5/4"
brass tube which acts as a shield to the pencil of rays from the
slit to the prism.

At the center of the ways on the slit mounting carriage is
a 5/16" hole with a permanent key mounted in one side of the hole
and a set screw with.knurled nut on the ogposite side. A brass
shaft with a keyway fits in this hole and carries at its upper
extremity a double brass plate. The lower plate is fixed rigidly
to the vertical support, the upper one is left free to turn as tw
screws arranged Opposite in a slot in the upper diSk engage a pin
in the lower disk which extends into the slot of the upper disk.
This unner disk carries the totally reflecting quartz prism. Thus
‘we have two adjustments on this prism; one a rotational movement in
the horizontal plane and the other'a movement of translation along

the axis of rotation.

(17)

A hood covers the lower end up to the slit. This hood has
a hand door in the top for convenience and is connected to the camera
by means of a lit-fiat tight cloth hood. The bottom of the lathe bed
is covered with a piece of sheet iron. This allows the apparatus
to be Operated in a light room thus adding greatly to its adapt-
ability and efficiency.

Plate V shows photographs of the various Darts of the

equipment and plate VI the finished spectrograph.

(18)

l

mmfigqmmd mmm. ho m.....mH>

 

 

 

 

 

 

 

 

PLATE V

(19)

 

 

 

 

 

 

 

 

 

""3 1". ‘9' " 'I ." fi'r‘n)1\.") '
LLLJ {\A-g‘ “can “Jr U‘A—aJ‘L‘V a-“ LA

 

 

 

 

ADJUSTIEZFJIT AID ORQJsTICN

To arrange the snectrograph to photOgraph any narticalar
spectral region two major and one minor adjustments are necessary.
The major adjustments consist of a lateral movement of grating with
respect to plate and a rotational adjustment of grating and plate.
The minor adjustment consists of a small additional rotation of the
plate.

In this discussion the rotational motion "R" controlled by the
left hand dial will be considered the indenendent variable and the
other adjustments will be considered in respect to it. The rotation-
al dial controls both the camera and the grating, giving to one a
left hand and to the other a right hand motion simultaneously. This
is accomplished by a left hand screw on the camera and a right hand
screw on the grating. 1fibch revolution of the screw inmarts a ro-
tation of 7([100 radians, which is equivalent to one division of the
graduated dial. There is approximately 1/1; turn of backlash in this
train. Any difference in backlash between the two gears is eliminated
by setting as the dial reading increases. The bearings on the screws
are cones and can be adjusted if necessary.

The lateral adjustment is obtained by the central dial. There
is about 1/6 turn of backlash in this adjustment hit all settings are
taken as the scale readings increase. Any lateral play in the screw
may be eliminated by tightening the centering pin at the rear of the
instrument.

A small knob at the right of the camera rotates the plate holder
independently and can be used to amply the necessary correction to
keep the plate on the Rowland circle. This correction is also read on

the graduated d is]. .

(21)

When setting up the instrument thesiit is set to give vertical
lines on the elate. Then the grating is rotated by means of screws
at the top of its mounting until the ends of the lines seem to be
symmetrical. If the rulings of the grating and the slit are not
Optically oarallel the lines will have a carellelogrsm shape caused
by the successive images not exactly coinciding a ”I” .
The spectrum is brought into the slot in the camera by means of the
three leveling screws on the grating carriage.

Themes}: may be set to give different widths of snectra across
the plate.

The prism should be set so that the entering beam of light is
normal to the longitudinal axis of the instrument. When the slit is
Opened and no condensing lens is used the pencil of rays form an
outline of the slit which should center on the grating.

The curvature of the plate holder must be relatively high in
order that the emulsion coincide with the Rowland circle. Extra thin
glass plates have been tried with poor success. The necessary curve;—
ture breaks them. Films were used for the exoosures for this naner. '

Trial emosures have been taken of different snectral regions
and the results correlated in Plate VII from which dial settings for
any particular range may be obtained. At the top of the figure three
shaded areas give the part of the spectrum. covered by the plate at any
setting of "R". The center line of each shaded part gives the a‘onrox-

Lmté wavelength in Angstrom units at the center of the plate. The .:
main curve gives the corresponding lateral setting for each rotation-
al setting. A very interesting correlation should be pointed out, the

circles, from which the curVe is plotted, are from experimental results
.rhile thetx's are the theoretically computed results from table 1.

(22)

Reset trials using this curve as a standard have given very

favorable evidence of its reliability.

(23)

 

1.’1), .‘.Ir, 4 .4 u "l‘.’ I‘Q. '.
IIIIL. ’r'\ .3“.,‘ .v r u

 

1:33 ‘hmvftorwssw . .ISU‘QU v< Oslufi $135.9 ‘0 303301
On. . . L Q

'

 

“\ x \g .m . 14w WK

 

 

 

 

 

 

 

 

 

 

 

 

5"“. .... .«.. H.»W H..H .. A v... . 4 .r. . . . M. o
.a. .... o¢o. co. .o.. . .. *— . n o ...C ....A~\ ... ..... . .r . . . _
1-.. 1...:U .bl . . b . .@..aq..;fi.. “H. H. m .. H . H
. . . J .. .. .. . “h 4 . . .
k . .. . . . . _ . . . . ... ..J?:.‘.... v
H ... b. » . r . .. ‘.
L313; 1 H w 4 r
o - .w .0 p o N- ‘

 

 

 

 

 

 

 

 

 

flout, CU'AJ

 

 

u\

 

 

 

 

 

‘wnhc, {a

 

 

“3'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q
\

 

 

 

. a n .
. - .
n n . . ‘ ..
*O—HH
. . . . .
~ . .

 

 

 

 

 

 

 

toyauI

 

 

 

 

 

 

 

£330 in

Luwpa wrfi

 

 

--.¢*4

:2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1—.

LIKITATIOKS, AEEEEATICIS, and RESQLVIYG PfiwlR

'v II

of this GRATIEG

Limitations
This instrument has very definite limitations, and some very
definite advantages. The collodion of which the grating is made gives
a share limit in thC'ultra violet at about 3100 A. It annears that
below this limit a raoidly increasing amount of absorjtion take
place. The newer limit, as far as observable, is denendent only
on the photograuhic emulsion available. However, suitable filters

must be used to eliminate the overlapping hiaher order as illus-

V

‘

trated by the cverlapning of tne shaded areas in Plate VII, and
explained on page seven of this paper.
The rotation of the plate is limited to about 25 7t /loo

radians or “5° by the reflecting prism and its mounting. From
Table 1 it is seen that the green line of iron ,1: 1.659.757 A. in
the thi d 615E? will be near the center of the plate at this limit.

tier rotational adjustment is of no advantage with this instrument,
however, as the imperfections of the grating are such.as to give
poor definition in the third order and, therefore, no advantage over

lower orders. The reflecting prism and mounting could easily be

moved if any advantage were to accrue.

(21+)

[m

z“.

 

Several aberrations should be mentioned. The central in we

Cun sic (rat le diffused

5,-
H.
a o.
}.'J
' J

slit r

9‘
)
3

(Y)

I'.

}

’1

if)

{1

U)

9

(.0

:3

{x

H

X

t‘
'5

f

I

(I)

O

‘ 5

c+

light on each side and with several fslse instrs e"::€tric; 11y

‘

ed. On nlate VII a gict re of this centrel imuge is snown.
As a narrow musk was moved over the grating the mttnsity of these
fal se “Lit: :s varied continously. The 1:10 st nrobeble err-flautxtion

seems to be the Skll narts of +;is 5rtting are acting ‘nderend—
ently as 7911 as collectively to form various irar s. This may
be due to untVJn Tlu<r«C of various “arts of the collcdion
t‘ans fer. The diff1s ed light, no doubt, comes from the dust on
the em} rfc f the collodion.

These false images carry over into the suectra and aonear
as li ht lines on one side of the werent line giving to the

V

spectrogram the a e;arance of oeing out of focus.

In the rulin~ of a grating any periodic error in the ruling
engine eroduces in tne snectra fiom that grating false images of
a line which are called e:hosts. These by their nature are
symmetrica with the parent line. They have been st udi(.=d by

Rowland, Anderson, Quincke, Pierce, and others and many of their

causes have been analyzed.‘

( 2

kn

)

*—Chas. F. refer--The Diff action of Light,—b. 173

Plate VIII gives a oicture of the ghosts present near the
mercury line Shoo A and the weir 5679 A and 5790 A. In order to
photograph these the plate was exposed about_l5_minutes under
conditions, such that an exposure of_;_minute nroduced an over-'
exposed line. This slate shows that the ratio of intensity of
parent line to ghost is high. So high, in fact, that only when
dealing vith faint lines near a very intense line is there any
danger of mistaki;g the”.

The only ghosts found are those which are coaronly known as
Rowland ghosts. They are caused by a oeriodic error in the screw
of the ruling engine. They are symmetrical obout the parent line
and relatively close to it. Their relative intensity increasesin
the higher orders. However, this 5h60 A line showed no 5h0sts in
the second order after an exposure of 80 minutes. However, the

second order shows Slight ghuss after an exoosure of 8 hours.

sagas Else.

The images formed by a grating are, in general, astigmatic.‘
That is, a concave grating produces a line inege of a point source.
Since a slit source is a succession of point sources the spectral
lines will be a composite of sunerimposed lines. These lines when
combined will form a line which decreases in intensity toward its
ends.

This astigmatism has two serious disadvanteges; 1) it decreases
the intensity of any given line thus requiring longer exoosures,

2) it prohibits the use of a mask in front of the slit to facilitate

(26)

*Chrzs- F- Beyer—3314:: Piff‘rnntinn of T.1' fink-..“ "Er!

comparison soectra. The characteristics of the E 51s mounting
are such that this astigmatism is considerably less than in the
common mountings. It is about one half, in the first order, of
that orcduced by the Rowland mounting. This mounting is sufficiently
stigmatic that a wedge may be used in front of the slit (See Elate
VIID from the ultra violet through the green of the first order.
For above the red of the first order and for other orders a mask,
which may be adjusted easily without disturbing the camera, has
been placed in front of the camera carriage. This facilitates

the use of the instrument in comoerison soectra work.
Resolving Power

The resolving power of the Optical instrument is its ability
to seourate the images of two objects which are close together.
In snectroscooy the resolving power is determined by the ability
of a spectrograph to separate wavelengths that are nearly the
same. It may be defined by the ratio ééi where 2, is the wave—
length of either of a oeir of lines which can just be resolved

and A.A is the difference of their vavelengths.

A
N

-\.

V

(7)

 

Ff

Figure

I
wavelength A = A1541} will give rise to e. diffraction estte

 

By mensn of Figure 5 the re-

5 lotion of the resolving power to t’i
constants of a :.__:leme grating may be
develOped. This result may then be
enolied to any grating. If A; is
the grating surface having m lines
and if n is the order of the
snectra. Then BF must be equal to
’fiwn X . This wave front will

give rise to the diffraction pattern

3;, and the first minimum of the

diffraction pattern will be. given by

1

the wavefront 53 when E”

Therefore, 43

The wave front necessary to produce this gettern will be

increment of FE will be
equnl to (”M A + WM».

develOps that, *

Which gives the theoretical resolving power of a

(31131 to ”WAR Therefore,

By equating these two values of

‘Y‘
A

a
.—

=(mn2+2 ).

A

n p'.

“IT?
J

‘8‘

E7".

0’1

.4

L:

E

an

dt

‘1
is

will be

i

t

M941 +MWAR :mMA—r") 1 M

h

grating snectro—

graph as dependent only on the trial total number of lines of the

grating and the order.

For a prism instrument the resolving power

*-Chs.s. F. I.:eyer--The Diffraction of Light—~page 198.

8

(8')

is given by the formula,*

is - .- t M
A A A 3
21ers t is the thickness of the prism at its bose, end /A’ is the
index of refraction of the material of the orism for the particular
A,”’ . . , .

region of 2‘ . :Eii” ,wnich is the disper51ve power of the
prism, varies for different wavelengths and various su sta nces.

By equation 7 the theoretical resolving power of this grating
is 50000 n, or anoreximntely 50000 in the first order. From

I I I ‘l
exoerimentel results the two iron lines at }1:’M934A.are well de-
fined at about 1/10 mm. separation on the plate. The resolving
. 3" 07 '1 n s o ’ ~ V r.
power is then h/JH- 27320 WHICH is about 1/o of tne theoretic .
.o(5

At 123mm two lines are well defined giving a resolving power
of 3h02.:5330. In the second order the iron lines atJK=M957 are

é~o

OVJJ
barely resolved which is equal to a resolving power of MG? ._
.301
16%00. In comnarison with these results, the Littrow, L-253, in
this labretory, gives the following resolving powers in the some
regions. The Littrow barely resolves two lines at )1h919A and
has a resolving power in this region of “312 :3260, while at
1.51

1A::3MOBA it easily resolves .320A which is a.resolving power of
3uog_-1o,6oo approximately. These two lines give, in brief,
.320
the comoarison of the resolving power of the two instruments.
Below MEOOA the Littrow hes a greater resolving power than the

grating in the first order. At 3700 A the dispersion of the

Littrow end the grating in the first order are almost idontice .

(29)

*Ches. F. Meyer-The Diffraction of Lightun. 20h.

Above H200A the disoersion of the quartz trein rnoidly decreases
while that of the grating remains almost COnStGLt. The disoersion
of this instrument in the visable region in the first order is such
that this region covers more than a ten inch photographic plate.
Therefore, for wavelengths in the visnhle end above,‘this grating
has a definite sueeriority then compared with the Littrow. In

the second order this resolution is anoreximutely doubled.

Illustrative Soectrn

 

Plate VIII is composed of photographic prints of various
plates and illustrates some of the possibilities and limitations
of the apparatus. Though the detail of the original is lost in a
print much can be shown in this way.

"A" is a picture of the central image. The extraneous lines
are verv definite on the plate although they blend in the print.

"B" is the green line of Hg‘125h60A :ith its ghosts
in the first order, and "C" the same line in the second order.

"D" is a photOgreeh of the iron are from 3200A to MQOOA

in the first order. #1 corresponds to,k33993 , #2 to,R=MOh5A

D
and #3 to )2H283A .

"E" is a photdgranh of the iron are from MSOCA to 7100A in
the first order. As an illustration of the cloee proximity to
linear dispersion even in this region the separation of the lines
2—;H859A ('1) and )53281; (#2) is 511.111. giving; 9.18 13/111111.

(3o)

and the sep:.retion of the lines 2: 5523 and A: -c 1"».7 (7,3)
is 8’9 mm. which gives 0 Ode/11111.. 121:; the se1"ra.ion of the lines

- |:“| g 'J‘! O ‘. -« ...— o n I” u .A ('1 _ '1.
)5 6137 and A —'-" 31311-41 (3,“) is “U 312.. '-..:.ch‘1 $th.18 0.3:}:I/II-1.
carbon arc and an iron coxr'31a1‘ison was placed by {'1'208 11s 0. the

o H, A {'A _ - .‘ ' ‘ ‘. ‘. \
lines, 325330. and 5390.11. 1-} is the lithium line}: c1033.

. o J- ! ' I _ f N o u
in is the lithium line 2:070:5211 doublet t, Yinlch is resolved

sh! 3

with this spectrograoh.

In "G” the mercury arc was used and its spectra is she 1m
in the region fi=3100A to A: l#30011. The c marison is iron
placed by means of the sedge in front of the list. The dis-
persion is almost linear, for frcm the triplet lines 27565011.,
36,551 "1nd 36531-1 to the pair *313111 and/7512511 the dist “rice
is 57:11:11 which gives a disners cio n of SSA/mm. (See "1").

11 A'éfi‘jSIA. tM-«houox. =15} $35011. to =h331' .

"H" is a photosreph of the cyanoe‘en bonds in the region
A: 330 0A to )é‘u 500A This was ob ained by photographing a
naked carbon arc.

7f 1, 2 and 3 are band heads at A 2: 3590A, 3233833111, and

A : 1421611 respectively. The com... arisen is iron.

(31)

”QBoWnHm mbofimfiw

 

 

 

    

e s a. 1,

1_.-_.__-;.=___=__=__ _,___:__=______.-.,| Q

m <

.U

 

 

 

 

VIII

PLATE

(32)

CONCLUSIUH

This instrument proves novel in several weys. The direct
mechanical link between the grating end camera rotation has proved
successful nnd is of great convenience in re id resetting to
previous values. The dispersion and resolving power in the visable
and infra red is definitely much better then .nn be found in any

glass or quartz instrument of an equnl cost. It is easily port—
able. It can be used in a light room the some as a prion spectro—
graph. It is sufficiently stigmatic tint weak sources may be used
with good success. The ghosts are extremely weak compared to

any parent line and should never offer any serious problem. The
spectra in the first order is Very near to a normal spectra, that
is, the dispersion along the plate is almost a linear dispersion.

The diffused light from the grating is a problem and if an
original could be obtained much better results would be expected.
The threads of the worms and norm wheels would be better if made

nstead of the ‘45 type. The grating

flu

after the Acme typ
mounting could be improved by a provision for a rotational notion

about the normal to the center of the grating.

(33)

BIBLIOGRthY

Chas. F. heyer - The Diffraction of Light, X-rays, and
material nrrticles.

E. C. Baly -- Snectroscooy Vol. 1

Kayser -— Han buch der Snectrosconie Vol. 1

John Browning - Spectroscone

Schuster and Hicholscn -— The Theory'of Optics pas. Ill—130

Preston -~ The Theory of Light pgs. 261-278

a a 0‘ V H‘I ‘
-- Hancbuch oer Phys1fi - Band XVlII pgs 3eO-345
" " " " XIX mg. 821
" " " " XX page 57-65. 298-305

H. T. Smyth -- Some Stignmtic Grating Mountings

Journal'of the Cntical Society of America
Vol. 25, to. 9, pg. 312

G. W. Koffitt - Auto Collhnating SnoctrOSrnph

Journal of the Optical Society of America
Vol. 25, E0. 5, pg. 1k2

D. L. KacAdam -— Focus of a Concave Gratine Snectro rash
o i s M

Journal of the Optical Society of America
Vol. 23. E0. 5. pg. 175

T. H. Osgood - Portable Vacuum Spectrog anh

Review of Scientific Instruments
V01. 5, 1‘30. 10’ pg. 368

(31%)

'w‘H-‘D '-"r.'-".
.‘I'. :17 .‘0‘ '
. v 'I ‘ "I'.

to .-)-. .' . . .1 .‘ .
v.3 _'.. .‘5 ...(....f.' ‘. \"'\.
_ . “Ringgit; 19“.!“ :3 3'“ , H _
\ J’:«. 0’. ' "LtI;-e\.1f;l:;.v . I 17.. . ." I'. .l - l. g . “1-5 A ‘ : ".t 4.1: ' " ‘ (0‘3...
'_ . ...‘ ..~ 0 ‘7 I. - , _ ' . tr .‘n. _ ,' ., " ‘ "‘. ‘.'.In-' - ‘ It
, .3. .fYM-Whfik”; 1-13. 1,, , $ ; 7. _. ‘ ‘, . “Law a...“ L“. .4. ,1... . .- “
*‘Jrfl'; ,“nf' ~ '1" 5 x' " . I -' .' .- ..’.‘- "13"- ‘ TJL «,r.~£;‘,.l',.y;£lfvil‘. ,AH" it,"
' h. "‘u‘: L4}.- v'.’ . k. -. -. -- .. {31:0 sum-g” -..~ 1:53". . ' '
. ‘0" ’* '. ,‘V‘.)'-\ . J‘I ‘.‘ . . " . ' ' _ ‘0' , '1 ' ‘ ,\’..o"lv'. {AM "i"\ -- 3' ~".'
. . ' O,” . J". “...' In“ " ma. '1‘“. q' ..nob~ ‘ A" ”1 ""-
.l".:‘-‘-' " .v - .‘ .‘_J’..’ '9 .
.w 2‘ r. m. '.~ " .~ «, . ~ .4 -
‘ . o .‘ i Q: ‘v‘fi “ '0." a. 5 ‘ ' I. -.' ‘ .:' " ' . .‘J .l a.
f‘H ' '{v' 3141" ‘ r"'n""'~' ‘ ' ' -"«' ~'.‘"—\“o
.. 6' J. ‘ VIN V 'I.'r- . 'd‘. a H ' fg " . '.'
v ‘Q ' tantrufimur: ‘1" 0w" ~. -' f‘ '* -.
t -v';.*_*'1‘\“.§. ‘ ' ’9 '

. is 1

v

a }_ .1 ‘ f »
‘nfiyvo‘v"; ‘ 7',
‘4 * ‘-“.

. ..«..

U"
I) 2“.
p

.
fl
1 . _

‘,"l‘ . “
. 0.: ‘3‘... '.. ‘
, ~qu'ti-W I . "I I
, , W '4. ' 'v ‘9’"- '.'.‘ e'
I~. ' O ', "v Q ' . i
. . a w “in; "of. Moi/.-
‘ ,I'l.) “’4‘1,“ Y's-yak. d." _\ ', I'l':‘:!-‘ ‘.
, M j, ._ j" J,‘ . bl: ~ ““t 4“" ’ L”... . h
. H - ‘ o."'r' v'.
'I . a" y“.’l-‘I ' ‘
‘ ‘.. - ‘ .. .1. ‘-‘I -
\ . -. I'.A_.' v. I w
‘-' I, ‘. I. "
4s I 4'...

.y"._ '.u fill. ‘1‘.
~. rub- M .,_‘.-4§;}..v .

‘5

.‘A

q

,. ;‘_.y ..|’ J.
. fl 3635f}... # >'.~"'.{i-‘

r ' “ \l‘vé‘.‘ v: V
u ‘ _ _ " ¥ ~‘ _' I" ," .. .0 ‘ I. .‘ ,’1“__,
I . o 'Ii‘j‘gf') 5. } ‘ ”“le I“ ‘qj'EW-K'f-.. 3')“. .
.35 I .V " E‘ II: 0‘}. ' .' ' "I; .. J‘ ' .C i; "All” ‘.' "l' " .‘I
I t . ’ _ ' . ‘ a . .. . .
m1 . "n "(d d " . . )- ‘| .- ~ I“ ~ ' .- ,I‘ h, ' ‘ I} .I. - _ " ... '. .

’ o .. . , g9».-\_.--:.:;.;¢i:--;~
~'."'$" "w" ‘ ~ ' w.” 2.
Md‘.\ ,(3 IL); ‘- ' {t ‘ol‘gfik ‘6} I"? ‘ )t ‘
, I. I w! a D . ,('| '1} ‘ .‘ -’ Hr '[‘lt"b «.1 ' ..
[U ‘7 : ‘. {4‘1 )0 _"v _~Y‘

V
’I- .-

«S
v. I

J n.- “ asp-Tu. “3*".~,;,'.,I. u ,7
\ . I . .v . . .

» ~ .. .. was ~.- M
,. New».-. 5: s 5v;— E". .
-- ‘ .»..;. - W w .. .

I. °-'."|‘\:"'{‘ '0.'.I‘J.'$‘gr. "1.5-2. . -. 1" t
. 4 ~' 1"“??j- -;".|--3' -(IIS-‘~ '05 . w .
‘ ."J.','~" 1". L1".) kr"ll :“r' -" -{‘t ‘ . o
w.‘. 1", [I l,".\fi-I,‘ ht. ' o
f-‘W’fl'dl' ‘5' ..' A
..,.l 1 “9“.“ .‘fn' .fifz'.“ " -_
. cl J--vl~."4“ #fA‘ J 2" ‘3 -
' WAV- m“; mg: ,

A
., ‘.
7'

1:‘~"

‘..;'.~‘5 "IA: ~ fol, F." . 3", .‘1 V '
.. .2 ‘ ' v-4’-t:*(-}.IA LA “w; . :v '4
. IA '» . s a in ~ ~- ' "
‘. \?‘..“,: ,~ I ‘p. ,(I.*J_-n.’ '15,; P“, .' ‘
* ‘ - 3. ' ',»"?‘-'«'!'f-:

d
. .
ul' 0*
,n... .

.‘I h -. ' v a
_ ‘-b ' . .1.
, ...,,
I‘l’c'~ 3., 0‘. . 4 ‘ I.. )r ‘- '
'_ ..'~ "1-"3' ' v f; ~19 5 f," 3.3,
' " ‘4“ LVJ'K‘B. ( 3" .

1' ‘\, i. — -J.
I 3' " '0. ‘ I .I\}-."".‘a.‘ ’ ..

‘ J
4'.
‘9

V

 

lllll”WIIllllll”MillilllllllllllllfllUllllllllllllillllll

17010947