Diffraction grating

“ B0 we see that no lateral spectrum can surpass the central image in brightness; but this result depends upon the hypothesis that the ruling acts by opacity, which is generally very far from being the case in practice. In an engraved glass grating there is no opaque material present by which light could be absorbed, and the effect depends upon a difference of retardation in passing the alternate parts. It is possible to prepare gratings which give a lateral spectrum brighter than the central image, and the explanation is easy. ”

“ Newton’s experiment thus shews that a prism sorts out light of a composite nature according to the wave-length of the different kinds of light present. The same thing can be done by substituting for the prism a so-called diffraction-grating, and this is for many purposes superseding the prism. In general it is necessary, to ensure purity in the spectrum and to make it large enough, to admit light through a narrow slit, and to use certain lenses in combination with one or more prisms or a grating ”

“ The latter found that certain gratings exercised a converging power upon the spectra formed upon one side, and a corresponding diverging power upon the spectra on the other side. Let us suppose that the light is incident perpendicularly, and that the grating interval increases from the centre towards that edge which lies nearest to the spectrum under observation, and decreases towards the hinder edge. ”

“ The electric ray at first falls on the grating at a large angle of incidence. A series of flashes of electric radiation are now produced by manipulating the key, and the angle of incidence gradually decreased till the receiver suddenly responds. The angle of incidence corresponding to the zero angle of diffraction is thus determined. The receiver is then placed at a new position on the focal curve, and the corresponding angle of incidence determined as before. In this way a series of angles of incidence, with their corresponding angles of diffraction, are found for each grating. ”

“ Irrationality of Dispersion.—If we compare the spectrum produced by refraction in a glass prism with that of a diffraction grating, we find not only that the order of colours is reversed, but also that the same colours do not occupy corresponding lengths on the two spectra, the blue and violet being much more extended in the refraction spectrum. The refraction spectra for different media also differ amongst themselves. This shows that the connexion between the refrangibility of light and its wave-length does not obey any simple law, but depends on the nature of the refracting medium. ”

“ If the incident rays make an angle θ with the normal (fig. 6) , and the diffracted rays make an angle φ (upon the same side) , the relative retardation from each element of width (a + d) to the next is (a + d) (sinθ + sinφ) ; and this is the quantity which is to be equated to mλ. Thus
The “deviation” is (θ + φ) , and is therefore a minimum when θ = φ, i.e. when the grating is so situated that the angles of incidence and diffraction are equal. ”

“ Another variety of the same experiment is to place a ruled diffraction-grating of 100 lines to the inch (ruled in a silvered surface on glass) close to a bright light, and with a short-focus lens project the lines upon a screen. Then interpose the magic mirror to throw the luminous lines upon another screen, when they will be seen with the usual magic image; the bright lines concentrating into the bright parts and avoiding the darker parts of the luminous pattern. ”

“ The sine of an angle can never be greater than unity; and consequently under the most favourable circumstances only 1/m2π2 of the original light can be obtained in the mth spectrum. We conclude that, with a grating composed of transparent and opaque parts, the utmost light obtainable in any one spectrum is in the first, and there amounts to 1/π2, or about 1/10, and that for this purpose a and d must be equal. ”

“ The effect just described may be much intensified by constructing an acoustic diffraction grating and using it in place of the simple disk. The explanation of the principle on which such a grating is made is beyond the scope of the present paper. [1] Assuming its use, the sensitive flame enables us to detect a focal area of noise, at which the flame is violently agitated, and around this are alternate rings of silence and fainter noise diminishing in strength with increase of distance from the central focus. ”

“ So exact are they that a star can be brought from the edge of the field and stopped instantaneously behind the micrometer wire."
Dividing engines are used for ruling parallel lines on glass and metal, to aid in the measurements of microscopical objects or the wave-lengths of light. A diffraction grating, used for measuring the latter, has the lines so close together that they would be visible only under a powerful microscope. Glass being too brittle, a special alloy of so-called speculum metal is fashioned into a highly polished plate, and this is placed in the machine. ”

“ With a diffraction grating of copper strips 2 in. broad and 2 in. apart, I have not yet succeeded in getting good results. It is difficult to get sharp [Pg 40] nodes and interference effects with these sensitive detectors in a room. I expect to do better when I can try out of doors, away from so many reflecting surfaces; indoors it is like trying delicate optical experiments in a small whitewashed chamber well supplied with looking-glasses; nor have I ever succeeded in getting clear concentration with this zone-plate having Newton’s rings fixed to it in tinfoil. ”

“ Great improvements have been effected in the stereoscope. Binocular instruments with enhanced stereoscopic vision, an effect achieved by increasing the distance between the object glasses, have been introduced. In the study of diffraction phenomena, which led to the technical preparation of gratings, the early attempts of Fraunhofer, Nobert and Lewis Morris Rutherfurd, were followed by H. A. Rowland’s ruling of plane and concave gratings which revolutionized spectroscopic research, and, in 1898, by Michelson’s invention of the echelon grating. ”

“ Here is the center of the grating, and there is the first spectrum. You will note that the violet light is least diffracted and the red light is most 7450 diffracted. This diffraction of light first proved to us definitely the reality of the undulatory theory of light.
You ask, Why does not light go round the corner as sound does? Light goes round a corner in these diffraction spectrums; it is shown going round a corner, it passes through these bars and is turned round an angle of thirty degrees. ”

“ It is evident that the waves from both halves of the grating are accelerated in an increasing degree, as we pass from the centre outwards, as compared with the phase they would possess were the central value of the grating interval maintained throughout. The irregularity of spacing has thus the effect of a convex lens, which accelerates the marginal relatively to the central rays. ”

“ This is the ordinary formula for a reflecting plane grating, and it shows that the spectra are formed in the usual directions. They are here focused (so far as the rays in the primary plane are concerned) upon the circle OQ′A, and the outstanding aberration is of the fourth order.
In order that a large part of the field of view may be in focus at once, it is desirable that the locus of the focused spectrum should be nearly perpendicular to the line of vision. ”

“ If x and y be co-ordinates in the plane of the wave-surface, the axis of y being parallel to the lines of the grating, and the origin corresponding to the centre of the beam, we may take as an approximate equation to the wave-surface
and, as we have just seen, the term in x2 corresponds to a linear error in the spacing. In like manner, the term in y2 corresponds to a general curvature of the lines (fig. 10) , and does not influence the definition at the (primary) focus, although it may introduce astigmatism. ”

“ The diffraction-phenomenon of two slits proved to be considerably different from what Fraunhofer had anticipated, and in following up this circumstance he was led to the important discovery of grating-spectra. Faraday's induction-phenomenon departed widely from the initial conception which occasioned his experiments, and it is precisely this deviation that constitutes his real discovery.
Every man has pondered on some subject. Every one of us can multiply the examples cited, by less illustrious ones from his own experience. ”

“ By introducing the concave grating which (see Diffraction of Light, § 8) allows us to dispense with all lenses, Rowland produced a revolution in spectroscopic measurement. At present we have still to content ourselves with a much diminished intensity of light when working with gratings, but there is some hope that the efforts to concentrate the light into one spectrum will soon be successful. ”

“ From (5) we see that, when the light falls perpendicularly upon a grating (θ = 0) , there is no spectrum formed (the image corresponding to m = 0 not being counted as a spectrum) , if the grating interval σ or (a + d) is less than λ. Under these circumstances, if the material of the grating be completely transparent, the whole of the light must appear in the direct image, and the ruling is not perceptible. From the absence of spectra Fraunhofer argued that there must be a microscopic limit represented by λ ”

“ The most interesting phenomena of diffraction are those presented by gratings, as are technically denominated the systems of linear and very narrow openings situated parallel to one another and at very small intervals. ”

“ The resolving power in the case of gratings is simply mn, where m is the order of spectrum used, and n the total number of lines ruled on the grating. In the case of prisms the resolving power is − t (dμ/dλ) , where t is the effective thickness of the medium traversed by the ray. If h and U are thicknesses traversed by the extreme rays, t = t2t−1, and if, as is usually the case, the prism is filled right up to its refraction cap, t−1 = 0, and t becomes equal to the greatest thickness of the medium which is made use of. ”

“ The larger the aperture the smaller are the angles through which it is necessary to deviate from the principal direction in order to bring in specified discrepancies of phase—the more concentrated is the image.
In many cases the subject of examination is a luminous line of uniform intensity, the various points of which are to be treated as independent sources of light. If the image of the line be ξ = 0, the intensity at any point ξ, η of the diffraction pattern may be represented by
the same law as obtains for a luminous point when horizontal directions are alone considered. ”

“ If, however, as in practice, the light be heterogeneous, the source of finite area, the obstacles in motion, and the discrimination of different directions imperfect, we are concerned merely with the mean brightness found by varying the arbitrary phase-relations, and this is obtained by simply multiplying the brightness due to a single aperture by the number of apertures (n) (see Interference of Light, § 4) . The diffraction pattern is therefore that due to a single aperture, merely brightened n times. ”

“ It will be observed that, while the total intensity is proportional to ab, the intensity at the focal point is proportional to a2b2. If the aperture be increased, not only is the total brightness over the focal plane increased with it, but there is also a concentration of the diffraction pattern. ”

“ One-twentieth to one-fiftieth of an inch is suitable. The aperture and the number of bands being both fixed, the condition of blackness determines the angular magnitude of a band and of the spectrum. The use of a grating is very convenient, for not only are there several spectra in view at the same time, but the dispersion can be varied continuously by sloping the grating. ”

“ If, however, we are looking at a star which is almost a point, it is simpler to invert the idea; the object, not being an ideal point, will slightly blur the detail of the diffraction pattern. We shall only perceive the blurring if the diffraction pattern contains detail fine enough to suffer from it. Betelgeuse on account of its finite size must theoretically blur a diffraction pattern; but the ordinary diffraction disk and rings produced with the largest telescope are too coarse to show this. We create a diffraction image with finer detail by using two apertures. ”

“ Again, if the rays be transmitted in two directions, as with certain crystals, “double refraction” (see Refraction, Double) takes place, and the emergent rays have undergone Polarization. A Shadow is cast by light falling on an opaque object, the complete theory of which involves the phenomenon of Diffraction. ”

“ Dark Field Illumination.—As was seen when discussing the physical theory, the minute details of the object cause diffractions, and can only be examined if the objective can take up at least two consecutive diffraction spectra. These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up ”

“ However, there is a relation which can be traced out between the clearness of the diffraction fringes and the size and shape of the object viewed. This relation is very complex.
The result of such calculation is that the intensity is greatest at the center, whence it rapidly falls off to zero at the first dark band. It then increases to a second maximum, where it is not more than one-ninth as great as in the center. ”