Vistas in Astronomy. Vol. 29. pp.137-141. IYX6 Printed in Great Britain. All rights reserved.

0083-6656186 so.00 + .50 Copyright 0 1986 Pergamon Journals Ltd.

ROWLAND’S DIFFRACTION-GRATING ART

Strong

136 GrayStreet,Amherst,MA01002,U.S.A

It is a pleasure for me to participate in your celebration since I have been

interested in the diffraction-grating art for over half a century -- an interest

aroused by Dr. John Anderson, who put the gratings back in production after

Rowland's death -- and with whom I was associated at Cal. Tech. for a decade. It

is an interest fueled by Prof. R. W. Wood, who was in charge of the engines until

I became involved directly.

Dr. Anderson made such a success of his involvement that Dr. Hale invited

him to come to Mt. Wilson Observatory and set up facilities to rule gratings for

astronomy. That project finally came to abundant fruition under the hands of the

Babcocks, father and son.

I shall introduce my remarks today by relaying two Rowland anecdotes: one

from Dr. Anderson; the other from Dr. Wood.

The first is concerned with the Rowland dictum, "No mechanism operates

perfectly -- its design must make up for imperfections."

When Dr. Joseph Ames assigned the Rowland engines to Anderson he suggested

an alteration in them. Anderson never followed it up because he saw in Rowland's

arrangement an embodiment of his dictum.

The grating grooves are ruled on the grating blank by repeated, straightline

strokes of a diamond point -- a point guided by a carriage that spanned the

blank. It is carried on a divided cross-ways; guided by one sliding shoe on the

right side of a rectangular-bar way at one end of the carriage, together with a

second shoe on the other end of the carriage, bearing on the left side of another

rectangular-bar, aligned and parallel. Professor Ames had suggested the shoes

might better slide on the same side -- right or left.

In Rowland's arrangement, using opposite sides, the motion of the diamond

midway between the two shoes becomes immune to lateral shifts due to the

lubricating oil thickness, as long as the variations of the oil film during the

ruling stroke are equal. And the arrangement also makes the motion immune to

wear.

Rowland reported that the diamond repeated a straight-line stroke to within

half a wavelength of light -- a precision owed directly to design.

Dr. Wood related an addition to the story that appears in John A. Brashear's

autobiography -- an addition he got from Rowland directly. Prof. Rowland had

inaugurated a program of ruling gratings on flat, speculum-metal blanks --

gratings produced in response to the urgent demands from spectroscopists the

world over. The optically flat blanks for these gratings were supplied by

Brashear's optical shop at Pittsburgh.

137

138 J. Strong

Rowland, having acquired a glass test-plate from Steinheil in Germany, had

found that it showed deviations from flatness compared to the speculum flats from

Brashear. Notified of this by telegram Brashear came promptly to Baltimore to

resolve the matter. According to Wood, he brought three of his own glass test-

plates, and demonstrated that any one of the three matched the surfaces of the

other two as revealed by straight interference fringes, and further, that all

three showed the same deviations for the Steinheil plate. His grating blanks all

proved to be flat indeed.

The ruling engine involved here was Rowland's own response to the wide

interest that the success of Rutherfurd's gratings had aroused: his gratings

with only one-inch span of rulings had yielded spectra with greater resolution

than any prisms. Several efforts were made to produce larger gratings for even

greater resolution. All these efforts had failed -- even Rutherfurd's own

efforts to rule 1.5 and Z-inch gratings. But, in good time, after Rowland had

brought the facilities of the Johns Hopkins physical laboratory to bear on the

problem, including the skill of his instrument maker, Mr. Schneider, a precision

screw was produced which, in a ruling engine, yielded gratings with a 5-inch span

of rulings that gave orders of magnitude gain in spectral resolution.

In Rowland's day, a problem arose with the emergence of such large and

excellent gratings through their requirement of auxiliary equipment: the problem

of providing two large, expensive, and clumsy telescopes. When I considered the

question of what to add to my anecdotes, having just reread Rowland's papers on

the grating art, I decided to apply my experience and perspective and present a

commentary on Rowland's remark, "I got to thinking about what would happen if a

grating were ruled on a surface not flat; I thought of a new method of attacking

the problem, and soon found that if the lines were ruled on a spherical surface

the spectrum would be brought to a focus without any telescope."

While this remark and other clues imply that the concept of the concave

grating, with its Rowland circle, came as a result of thinking, his writings do

not rule out the alternative that he simply ruled a spherical surface for

orientation and the Rowland circle emerged from a plot of test results, since

such results made on an optical bench with adjacent source and eyepiece would

reveal it. While I believe this was his probable path, the commentary below

traces an analytical path based on a hypothetical pre-emergence of the Rowland

circle -- a commentary introduced by Rowland's responses to some of the

practitioners of the prior grating art.

Mr. C. S. Peirce found an error of run in the groove spacings of a

Rutherfurd grating which caused the spectrum to focus slightly closer, or farther

out, than the horizontal dust lines in the spectrum that mark the focus for a

flat reflector -- closer for one angle of incidence, and farther out for opposite

incidence. In short, the error of run on a flat grating introduced a slight

positive lens power for one angle of incidence, and negative lens power for the

opposite incidence.

In Rowland's consideration of such effects of the variations in grating-

groove spacing he found that the results of straightforward calculation, by

integration, yielded results not commensurate with the labor involved. He sought

and soon found an indirect method of treating the problem.

According to his indirect method, he discarded the auxiliary telescopes that

Peirce employed and considered a distant point source of illumination as nearly

parallel as possible. Then he investigated to find "the proper ruling of the

Rowland's Diffraction-Grating Art 139

grating to bring the rays back to the point from which they started." This

investigation led him to a general theorem. Considering monochromatic wave

fronts from a point source, at some instant in time, as concentric and equally

spaced spherical shells, the theorem states that if grooves are cut in any

surface along the lines where such shells intersect it, then a portion of the

diffracted monochromatic light will not only be returned to the source: but also,

the grooves will produce a spectrum of the other wavelengths on both sides.

A calculation of such intersections gave concentric circular grooves. And

further, considering concentric cylindrical shells, representing the wave fronts

from a distant slit, instead of a point, the intersections gave straight grating-

groove locations that were tangents to the circular grooves.

Such spacings explained the focusing power of the Rutherfurd flat grating.

The formula that Rowland developed for this case allows an estimate of the

difference in groove spacings at the edge of the grating, referred to the

spacings at its center; and the formula gives the difference as a fraction of one

hundredth of a millionth of an inch. This seemingly insignificant cause that

produced a significant result becomes important in light of the fact that the

grooves of a grating ruled on a spherical surface are comparably broader, at the

limits of its span of ruling, that at the center.

For some reason Rowland did not identify his circular grooves as the even

zone plate -- known to have focusing power. Indeed, R. W. Wood used a phase-

reversal zone plate as a camera lens to photograph a Dutch windmill.

From these clues, it is supposed that Rowland considered how the groove

spacing variations his engine produced on a spherical surface might compare to

the "proper ruling -- to bring the rays back to the point from which they

started."

Rowland, in his thinking of rulings on a surface not flat, probably first

considered a grating ruled on a sphere, of radius R, and tipped to make the angle

of incidence a at its center for rays from a point P. It may be further supposed

that he chose the distance for P such that the grating focused its central order

at an equal distance, R cos a -- that being twice the astigmatic focal length of

a sphere for rays at angle a. If so, it was a portent of the Rowland circle.

Figure 1 The geometry of the concave grating.

140 J. Strong

Figure 1 represents the geometry involved if Rowland compared the variation

of spacings his engine produced -- ruling uniformly spaced grooves along the

chord of the sphere -- with the spacings that the application of his theorem

specified.

In Figure 1 the grating spacings, a at the center and b at the limit of the

span of rulings, are greatly exaggerated to show that the engine produced the

variation given by b = a/cos0. And the half width of the span of grooves, AB, is

exaggerated with respect to the sphere's radius==== R. Actually, for

inferences here accredited to Rowland, the spacing a is taken as that of 14,400

grooves per inch; the span of rulings as 5 inches; and R is taken as 250 inches

(about 21 ft). Thus the exaggerated angle 0 in the figure is only 6 = l/100, or

00.57. And the grating is taken as tipped to make the angle of incidence at the

center, A, such as will return light rays from P in the third grating order.

The angles a at A and B at B being bounded on one side by grating normals,

AR and BR, the spacings b satisfy Rowland's theorem if b and @ at B, as well as

at all points on the grating between A and B, satisfy the relationship:

b sin B = a sin a = 3U2.

In a consideration of such a conformity of the engine rulings to the theorem

requirement, if Rowland considered such a drawing as Figure 1, he could hardly

miss noticing a compensation: while b is very slightly larger than a, f3 is very

slightly less than a at C -- which must be equal to u at A -- by geometry: both

angles have vertices on a common circle.

Several approximations are involved in evaluating the degree of this

compensation for the special case of rays diffracted by grooves where they cut

the plane of the Rowland circle. These approximations are:

% = R(1 - cos 9) 2 Re2/2

E = r = R cos (a-e)

(a-@) = Aa = EE sin a cos a

r

sin @ = sin (u-Aa) 4 sin Q - cos aha

=sina(l-e2cos2a ) 2 cos(a+3)

And, doubling the discrepancy to account for return paths:

b sin B =” a sin a(1 + a(1 - COS2a/COS(~-e))

This for a = 25" yields

(kA) returned = (1 + l/102,000) (kQncident)

If Rowland got such an encouraging but incomplete result as this before

ruling a sphere it would certainly have led him to test it out to see the full

aptness of the only spacing variations his engine could produce without major

changes. But his papers do not define just where in his path to put the

Rowland's Diffraction-Grating Art 141

emergence of his elaborate theory -- a theory carried through first and second

approximations, which predicted, as he wrote: "practically no aberration and in

this respect there is nothing further desired."

I have not summarized the many practical instrumental ingenuities with which

the concave grating was involved, nor Rowland's important applications of them --

as, for spectroscopy, his establishment of the first reliable scale for atomic

wavelengths, from the ratio of overlapping wavelengths as the ratio of integers -

- their order numbers; and, for astronomy, his tables of wavelengths in the solar

spectrum (not to mention the many important uses in astronomy of his flat

gratings).

DISCUSSION

Osterbrock: I've often wondered, are there mechanical difficulties in ruling on

the concave grating compared to the plane, at the beginning?

Strong: There was, and remain, difficulties arising from the required vertical

motion of the ruling diamond as it follows the curved surface in its ruling

strobe. These difficulties are minimized by a judicious tipping of the spherical

blank on its carriage -- a tipping that results in a more nearly invariant angle

between the diamond and the ruled surface. Thus tipped, a 21 foot curve is ruled

much as a flat.

Fastie: Rowland had to rule on the chord, so the only way to do it was the exact

way to do it. It's one of the most remarkable coincidences I know, that the only

way you could rule a concave grating is exactly the way you want to do it.

Strong: Yes, if you'd been writing my speech for the last two weeks, you'd have

been struck, as Fastie just indicated, by the mystery of this whole business. It

must have overwhelmed Rowland. He was certainly a favorite of the Muses to be

granted such a remarkable coincidence.