The Optical Characteristics and Production of Diffraction Gratings A Quantitative Explanation of Their Experimental Qualities with a Description of Their Manufacture and Relative Merits William E. L. Grossman Hunter College of CUNY, 695 Park Avenue, New York, NY 10021
Diffraction gratings are still critical components of most soectrosco~icsvstems. Although there have been meat imthey are still p k e m e n i s to ~nterferometric~spectrometers, relatively costly and are not reasonable choices for m a w regions of the Spectrum. In contrast, gratings can be usefully employed in any spectral region; and, because they perform what is effectively a "mechanical" Fourier transformation on the output of the light source to produce a spectru, gratings not only obviate the need for ancillary computing equipment, but also give the spectrum in real real time. It is important for students to know about diffraction gratings, and their study is appropriate in any instrumental analysis course. Gratings, along with some detectors, are the "high-tech" components in the system. The production of a diffraction grating, whether by optical or mechanical means, requires state-of-the-art instrumentation. Because the quality of the grating depends on how it is produced, it is important also to have some knowledge of the production process. Their Experimental Qualities and Manufacture
My purpose in this paper is to concentrate two areas of information about diffraction gratings for students and instructors of instrumental analysis. First, I cover the mathematical analysis typically found in books on optics. My emphasis will be on how the experimental qualities ofgratings, such as resolution and dispersion, can be explained quantitatively. Next, I include information that adds interest and a fresh perspective to the study and selection of diffraction gratings: I describe how the gratings are made. This material is largely anecdotal. I found it scattered through the literaturebr-picked it up informally a t meetings and company visits. It provides an important background to one's knowledee of ~nectrosconicinstrumentation. It is often ----~ more u s e k ~ t h a nthe thebretical material when attempting to evaluate the relative merits of different gratings.
infrared. Often, however, there is no overcoating on the re. flecting metal. Theoretical Principles Fraunhofer Diffraction
The behavior of a diffraction grating is explained by Fraunhofer diffraction of the light incident on it. Fraunhofer diffraction assumes that the light source and the observer are far from the diffracting object. Thus, any curvature in the wavefronts can be ignored, whether they are incident upon the grating surface or emanating from it. This is the usual situation in experimental spectroscopy. Relating Diffraction Pattern and Interference The intensity pattern produced when light is diffracted by a grating can be shown to be a combination of patterns observed for diffraction by a single slit interference among the diffractionpatterns produced by a number of closely spaced slits Each groove of the grating acts as a slit in this model. The explanation of the diffraction pattern observed is based on the classical wave model of Huygens, which treats every point on the grating as a new source of light. Young and Fresnel independently extended Huygens' model to include interference between the secondary waves ( I ) . These waves are in phase with the wavefront that is illuminating the grating surface. The word diffraction is used to describe the effect observed when the phase or amplitude'of a wavefront of light is changed (2,3),for example, by a partial obstruction such as a slit. When this haooens. the lieht amears not to travel co&onli expi&ned as due to the in a straight line. ~his'i$ interference of lieht waves generated bv secondarv sources a t the region of ibstructioi. Thus, thediffraction pattern is caused by interference. The Geometry
Gratings for Research Applications
Because this material will be used mainly in advanced undergraduate and graduate courses, I will confine the discussion to gratings used in research, that is, front surface reflection eratines. Phvsicallv. thev consist of a support called thelblank,whi& is normall; glass or ceramic. One side is carefully polished, typically to be flat to within one-tenth of a wavelength. (The sodium D lines are often used.) Then grooves are formed on the polished side in a thin layer of vacuum-deposited metal, usually either gold or aluminum. Reolica matings. discussed below, will also have a layer of epoxy bitween the blank and the'metal. An aluminum grating may be overcoated with a material such as magnesium fluoride, adiclectric that prevents 0x1dation. An overcoating of gold improves reflectivity in the
The standard treatment of Fraunhofer diffraction bv a grating begins with the geometry of the situation, as shown in Figure 1.The important ohservahles are t h e angle of incidence i, which is the angle at which the light is incident onta the grating 'the angle of diffraction8, which is the angle at which the diffractedlight is observed Two other angles are helpful in describing the intensity variation in the diffracted light - as the point of observation is moved: a,one-half the phase differencebetween waves originating at equivalent points in adjacent grooves
p, one-half the phase difference between waves originating at apposite edges of the same groove.
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Figure 2. Variation in diffracted intensity with angle of diffraction
Figure 1. Fraunhofer diffraction by a grating These are defined from trigonometric considerations (4).
where d is the groove spacing; and As is the width of a groove. As shown in the texts referenced and in many others, the change in intensity in a plane that is far (compared to the dimensions of the slit) from a single slit is proportional to
The pattern due to interference of light from N slits is proportional to
a sin2a
Thus, for a grating with N grooves, the diffracted intensity as a function of the angle of diffraction (5)is
The intensities of both sets of maxima will decrease as (sin2P)I(P2)decreases, falling off on both sides of the central maximum (0 = 0). (A portion shown in Figure 2.) Principal Maxima Principal maxima are the major features of a spectrum created by a diffraction grating. If a grating is illuminated by monochromatic light, the angles at which the different orders of diffraction of the incident light appear will be those of the principal maxima.Those angles are for a = 0,hr,a n ,etc. At these angles (sin2Na)l(sin2 a) will have its greatest value (P). Although the fraction is apparently indeterminate, it can be evaluated because (6) sin Na Na - Ncos lim 7 --W sm a cos a Interestingly enough, the positions of the principal maxima are exactly the same for any number of slits (or grooves) equal to or greater than 2,,as long as the groove spacing d doesn't change. However, as seen above, the intensity of the maximum does vary with the number of grooves. Also, at these values of a ,
where I, is the intensity in the direction 0 = 0. Features of the Spectra
The standard grating equation can be derived from eq 3, as shown below. Information about the dispersion and resolving power of a grating can also be derived. Looking a t eq 3, we can see that the term in N a will vary much more rapidly than sin2 a or the term in P, especially when the number of grooves N is large. The term (sin2Na)l(sin2a ) will vary somewhat more slowly, and (sin2P)/(P2)will vary still more slowly. Consequently, we will observe three kinds of features: principal maxima, secondary maxima, and minima. Principal maxima occur when (sin2Na)l(sin2a ) is a maximum. Secondary maxima occur when sin2Na only is s maximum. Minima occur when sin2Na = 0.
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so that nh=dsin8
(6)
where n is the order of diffraction. This is the standard form of the eratine criven in everv instrumental - eauation. . analysis textbook, for the sit&ion i n whiih the incident light is arrivineon the normal LO the mating. When this is not the case, tKe equation can be gen&alizeA to nh = d(sin i + sin 8) (71
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where i is the angle of incidence. This behavior is the source of one of the important weaknesses of diffraction gratings as compared to prisms: AU the light of one wavelength is not diffracted at the same angle by a grating as it is by a prism. Further, the central maximum (where n = 0, the zeroth order) is the brightest and the one at which there is no dispersion. All wave-
lengths will show their central maximum in that direction, and the grating will look like a mirror. I show how this problem can be minimized below in the discussion on efficiency. Minima Minima between principal maxima will be found when the numerator in the interference term becomes equal to zero, which occurs when For the special cases in which m is a multiple of N, that is, when m = O,N, 2N, ...
we get The denominator will also equal zero, and a principal maximum will occur. Therefore, the minima will come when
except when where n is the order of diffraction. Thus there will be N - 1 minima between neighboring principal maxima (7). The distance across a principal maximum, from the minimum on one side to the minimum on the other, will be double the separation of the other minima. This helps explains the criterion for resolution (see below). Secondary Maxima Secondary maxima will lie between the minima. There will be N - 2 secondary maxima between the minima, and they will have much lower intensity than the principal maxima. AsN increases, the pattern of secondary maxima around a principal maximum increasingly resembles the intensity pattern due to single-slit diffraction. Essentially, it can be shown that (8) The dlmensams of the pattern correspond to thgw of a smgle "slit" of width rqunl to that o f t h r e m r e g m u n g .
The wider a slit, the narrower its diffraction pattern. Thus, the wider the grating for a given groove spacing, the narrower the intensity pattern associated with a principal maximum. This directly influences the resolving power of the grating. Figures of Merit of Diffraction Gratings Resolving Power
The resolvine nower of a eratine is a measure of its ability to separate'iko adjacenLaveTengths. Resolving power d e ~ e n d son the width of the intensitv function for each wavelength and is measured by deter&ning the angular difference between two wavelengths a t a given wavelength. The basis for deciding whether two lines are resolved is the Rayleigh Criterion:
. .
Two lines are resolved when the center of a nrincioal maximum of one line comes at the same angle as the minimum adjacent tc a principal maximum of the other.
The following treatment is due to Andrews (9). Sawyer takes a somewhat different approach (10)in reaching the same conclusion. Differentiating eq 1, we get the variation of a as a function of changes in the angle of diffraction 8.
$-
COS
0
For large values ofN, the approximation that differentials can be replaced by f d t e differences is a good one. Thns, we
Similarly, by differentiating eq 6, we can determine the change in wavelength as a function of the angle of diffrac-
Again, we expect that when two lines are just resolved, the difference between their wavelengths will be small compared to those wavelengths. Thus, the replacement used to get eq 9 will again give a good approximation.
We now solve eq 9 for h and eq 11 for Ah, and divide the former by the latter. This gives an expression that is a measure of the ability of the grating to separate two lines of average wavelength h that are so closely spaced as to meet the Rayleigh criterion.
In the discussion of minima, we saw that the angular distance between minima is ordinarily
except that the minima on either side of a principal maximum are separated by twice that difference. In the latter case, eq 13 also gives the separation between a principal maximum and the minimum to one side of it, which is exactly the separation between two wavelengths that meets the Rayleigh criterion. This value of Aa can he substituted into eq 12 to derive the well-known result for the resolving power of a diffractiongrating. -
AL -nN
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(14)
The grooves on the grating surface, as shown inFigure 3, have a wide side and a narrow side. Most gratings use the wide side to diffract the light, as shown inthe figure. These are called echellettes. Gratings designed to use the narrow side are called echelles. The intergroove spacing d is substantially larger for echelles. Thns, the number of grooves N on a given size blank is less. Nevertheless, echelles are used where the highest resolution is required; they provide it by working a t very high orders of diffraction n. Dispersion
The dis~ersionof a eratine is the change in the anele of diffraction for a given change in w a v e l k h (de/dhj. As shown bv Sawver (11).it is Dossible to determine this bv differentiatinithe grating equation (eq 7). Assuming that the angle of incidence is a constant, we get n&=dcoseae
(15)
Rearranging, we get
One of the advantages that gratings sometimes have over prisms can be seen from this equation. If the grating is mounted so that the angle of diffraction 8 is small (less Volume 70 Number 9 September 1993
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than about 20') (12), then the value of the cosine term remains within 5%of 1,and the dispersionvaries only slowly with wavelength. Effectively, it is constant over a useful working range, and this makes the design of gratingmonochromators simpler. Two other features can he explained using this equation. Over a given small wavelength interval, the separation of two wavelengths is directly proportional to the order of diffraction n. In other words, the second-order spectrum is twice as wide as the first-order spectrum, the third-order spectrum is three times as wide, and so on. The width of the dispersed spectrum is inversely proportional to the groove spacing d; the closer together the grooves, the further apart the given pair of wavelengths will be (13). Efficiency
As shown above, one of the advantages that prisms have over grating? 's the potential presence of many principal maxima in e grating spectrum. Because each wavelength will l: diffracted at more than one angle by a grating, the amollnt of light diffracted into any order will he a small fraction of the total. Thus, unless something is changed, the observed spectrum in any one order will be of low intensity compared with the incident light or with the amount of light specularly reflected from the grating surface (the zeroth order). What is changed for many gratings, of course, is the angle that the surface of the groove makes with the surface of the grating, as shown in Figure 3. This angle is called the blaze angle because a blaze of light can be seen a t that angle (14). Shaping the grooves in this way has the effect of substantially increasing the intensity of light diffracted in the order whose angle of diffraction corresponds to the angle of specular reflection from the groove face. Ghost Spectra Two other major causes of light loss, which lead to lowered efficiency, are stray light and ghosts. The term ghost is used to describe stray light that has the appearance of spectral lines. These ghost lines are due to periodic variations in the spacing ofthe grooves. They are,as we will see, very difficult to avoid when the grating is ruled mechani~ali~. When the groove spacing is not constant, hut varies regularly from a maximum distance to a minimum one, the effect is that of two gratings superimposed upon each other. The groove spacing of one "grating" is the average spacing. The other "grating" is much coarser, and it has the spacing of the repeating spacing variation. The latter "grating" also gives rise to a diffraction pattern in which the principal maxima are much more closely spaced because the effective groove spacing is much greater. A second set of lines is formed symmetrically around each of the principal maxima of the main spectrum. This principal maximum is the parent or center of the ghost spectrum. These ghosts, known as Rowland ghosts, are due to periodic errors in the pitch of the lead screw or to faults in its end bearing (15). &other source of ghost spectra is periodic vibrations arising from outside the ruling engine. Such a disturbance can eive rise to ghost intensity far from the parent line; the resultant gh&ts are callid Lyman ghosts (16,171.
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Stray Light Other important sources of stray light are scattering of the incident light caused by roughness of the grating surface or random errors in groove spacing. These are usually by-products of the ruling process, particularly for mechanically ruled gratings. For example, the furrow thrown up 744
Journal of Chemical Education
GRATING NORnRL GROOVE BLAZE R N G L E 7
NETRL LAYER BLANK
Figure 3. Grating cross-section, showing the blaze angle. by the ruling diamond as it forms the groove obviously roughens the surface, although this effect is lessened in manv replica matinm. as discussed below. ~ i o t h k rso&e of scattering is a slight variation in groove position caused by "jitter" in the relative positions of the diamond and the blank carriage in interferometricallv controlled ruling e n ~ n e (explained s later) or by other apeLodic motion in thesystem. andom om errors such as these tend to ~ v rise e to "mass", or low-level intensity that appears to be spread over a relatively large spectfal region. Reporting the Efficiency Efficiencycan be reported in two ways. The absolute effkiencv is the ratio of the enerw at a oarticular wavelengrh dXfrnrrrd in the urder of lnterest to the total energy or that uavrlrngth m c d e n t on rhe gratlng T h e relative efficiency is the ratio of the energy at a particular wavelength diffracted in the order of interest to the energy at that wavelength reflected by a mirror with the same coating as the grating under similar worldng conditions (18, 19).
Care must be used in comparing specifications of gratings from different manufacturers because the word efficiency is sometimes used without qualification. Absolute efficiency is a more stringent measure. The efficiency to be expected of a grating will vary widely, depending on many factors, such as the way it has been made or the wavelength region concerned. Relative efficiencies will generally range from about 45% to 80%. Plane gratings for use in the visible and infrared are a t the higher end of this range, and devices used at shorter wavelengths and grazing incidence are a t the lower end. Production of Diffraction Gratings Mechanically Ruled Gratings
The only way to make gratings until recently-and it is still the ureferred method for manv to " a~~lications--was .. use a diammd cutting tool to make grooves on the surface ofa metal reflector. With his method. rrratinrrs withmoove densities up to 30,000lin. (1,200Icmj'~anhe produced routinelv-if the word can ever be applied to the manufacture of any research-grade grating. his density is an appropriate one for use in the visible and near ultraviolet. Obtaining a Master Gmting In the eeneral procedure used. the metal-coated mating blank is kounted on a carriage. The carriage is supportea on wavs: two parallel metal bars on which the carriage - can only move freely along one axis. The carriage is moved
Figure 4. Schematic diagram of a grating ruling engine. along the ways by a lead screw that is threaded through a nut attached to the carriage. Acutting tool is mounted above the carriage. It can move at right angles to the direction of motion of the carriage and blank. The grating is formed by repeatedly moving the cutter across the top so that it cuts groove after groove in the blank coating as the carriage advances. A schematic drawing of such a ruling engine is shown in Figure 4. A grating thus made is called a master grating. However, it is not commonly used in spectroscopy. It is usually kept at stud: Replicas are made from it in a process that is both quicker and less expensive than creating the master. The replicas are sold for use in monochromators, spectrographs, etc. The metal normally used for the surface of the master grating is gold, which is soR enough to minimize wear on the diamond cutter over the long distance required. (For example, for a 2-in. x %in. grating, which is one of the smallest made, a groove density of 30,000lin. means that the ruling diamond has cut nearly two miles of groove.) Under the force applied by the diamond, the metal flows rather than chips, so a smooth surface is formed. The quality of the metal coating is important: Slight variations mav cause the diamond to behave erraticallv. ". resulting in areas of irregular rulings. Shaping and mountine the diamond to get the desired blaze anele is still sometGug of an art; an< as it wears, the blaze angle changes. 'IblemncesRequired The difficulties inherent in this approach to grating manufacture can be best seen byconsidering the tolerances that must be achieved to make a device of high quality (20).Grooves should be straight and parallel to within A. 20 sin (blaze angle)
where his the lower wavelength limit in the observed spectrum. This leaves very little margin for error, especially when ruling gratings with high blaze angles, such as echelles. Stray light, including ghosts and scattered light, should be less than about 10" of the intensity ofthe strong lines in the parent spectrum. The extent of camage rotation or yaw must also be carefully controlled. Yaw is caused largely by curvature of the ' ways on which the blank camage moves. It is due to small temperature differences between the two sides of the ruling engine (20). Control of the Environment a n d the Process Control of environmental variables is essential to meet these performance levels. The rwms in which ruling eugines are housed are temperature-controlled to about
0.001'. The humidity and even the barometric pressure are also controlled. Every attempt is made to minimize external vibrations. The ruling engines I have seen were kept in the basement. They were actually set on their own foundations and completely isolated from the foundation of the surrounding structure. In terms of dimensional stability, the above tolerances require that the diamond carriage hold the diamond in the ruling plane to within approximately 1x lo4 in.; the position of the carriage carrying the blank must also be controlled to about 1 x lo4 in. The total allowable ueriodic error should be held to 1%of the groove spacing, or about 3 x lo-' in., to achieve the desired low-ghost intensity. These performance limits must be maintained over the time needed to rule the grating. Preparation and warm-up time for a ruling engine is around one week; at a cutting speed of 9 in. s-' the ruling time can be as long as two weeks for very large gratings (211. (The speed of 9 in. s-' is about the highest practicable. Higher speeds greatly increase the likelihood that the metal will grow hot enough to weld to the diamond.) To put the above numbers into clearer perspective, it is interesting to link them to the physical properties of common materials. Imagine a 4-ft-long girder of solid aluminum, l-R thick and supported at its ends. If a penny is placed on top of it in the middle, the center of the girder will sag about lo4 in.' From this it can be seen that there is no possibility of building a rigid ruling engine. At the level of mechanical precision that must be attained, any machine will appear to be made of rubber. Even a small grating blank will weigh enough to seriously distort the ways on which the carriage is supported, and movement of the diamond and the camage will further stress the system. Ruling Engine Design and Precision
This--the fundamental problem of mechanical grating production-has been solved in two ways. The Brute Force Method The first approach uses what might be called a "brute force" method (although it clearly requires clever and sophisticated mechanical design). It requires the creation of a ruling engine that can directly perform to the tolerances required. This approach has been successfully used to rule gratings as large as 5-in. x 5-in. in size with 100,000 grooveslin. (for use in the vacuum ultraviolet), and a t lesser groove densities has gone 'as high as a 10-in. ruled width (22). Horace Babcock (16)has described some of the steps necessary to build an engine capable of such precision. These include building a special device to keep the carriage from creeping forward when the lead screw stops turning by demupling the camage from the screw aRer each advance 'taking extraordinary care to make the lead screw as errorfree as possible using unusual hinges to lift the diamond cutting tool above the blank on the return stroke 'Unfortunately,this splendid image did not originate with me, and I cannot now remember where I first saw or heard it. I can only apologize to its creator, and thank him. Volume 70 Number 9 September 1993
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The attention to detail extends even to the base of the engine: cast iron, made in a single casting and undergoing thermal cycling for two years to ensure dimensional stability. The result is a machine that is mechanically at the state of the tool-makers art but that still cannot rule the largest gratings that could be used in some areas of spectroscopy Interferornetric Control The sewnd approach to ruling engine design can be considered a refinement of the first. It consists of building an engine that is as capable, or nearly as capable, as the ones described above. Then its operation is wntrolled with a closed-loop feedback system that uses interferometers to monitor the position of the grating and diamond carriages (20). One or more interferometers are mounted so that the moving mirror of the interferometer is on the part of the engine whose position is to be controlled. As that part moves. the frinees eenerated bv the interferometer are counted so that &e p k i s e extent of the motion can be controlled to within a fraction of a fringe. Thus, for example, the lead screw would normally be turned through a certain angle to move the grating carriage a certain distance. The distance moved would depend on the pitch of the screw. This is a major source of Rowland ghosts because periodic errors in cutting a screw are extremely difficult to prevent. Under interferometric control, the screw would instead be turned until the camage had moved a certain number of fringes and was centered on a fringe. Thus, the distance moved could be made consistently the same, without having to rely on a completely error-free screw. In a similar way, an interferometer can be used to control unwanted motions, such as yaw of the grating carriage, which gives rise to "fanning" of the grooves. Such an engine can, in fad, be made to operate so that the blank is moved continuously, thus avoiding the positioning errors associated with the "start-stop" operation altoeether. This is ~ossiblebecause the controller now kno& the position i f both the blank and the diamond at all times. It can drive them with the DmDer relative velocities needed to cut parallel, evenly sp&ed grooves. This has the great advantage of reducing spacing errors due to "creep" of the blank carriage after i t has supposedly s t o -~ ~ e d . There is a disadvantage: Because the corrections in blank and diamond motion are made continuously, there is some jitter in the system. This shows up as sideways vibrations in the sides of the sooves. These inhomo~eneities are small compared to ti;e groove spacing, but-they do cause some increase in the level of stray l i ~ h tAeood . sense of the actual groove shape is given b i t h e ele&on microe r a ~ of h a eratine surface in Harrison's article (23). Mechanical &ng of gratings has been enormously successful in producing relatively inexpensive gratings of every size and configuration. Near-theoretical resolution and fairly high efficiencies have been achieved, especially for plane gratings. What more can we ask? There is always more. With the increasing importance of Raman spectroscopy and a general desire for higher sensitivity and lower instrument costs, by astronomers as well as chmical spectroscopists, improvements have been sought in areas where mechanical ruling methods have not been completely successful.
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Problem with Mechanical Ruling: Stmy Light The reduction of stray light would clearly lead to better spectrometerperformance. Stray light is partly due to both periodic and random ruling errors. Both are present to 746
Journal of Chemical Education
some extent in mechanically ruled gratings, as we have seen above. Controlling Reflection A second cause of light losses in spectrometers is reflection, or the lack of it, from the focussing elements necessary in instruments that use plane gratings. Reflection lossesfrom lenses are about 5-10% per surface, andmirror reflectivities are around 90-95%. (Both ranges pertain to coatings with reasonably broad spectral coverage). These losses add up quite quickly. The traditional way to minimize them is to minimize the number of optical surfaces in the spectrometer by using a diffracting element that also has focussing properties. In grating spectrometers, that means a concave grating. Problem: Ruling Concaue Gratings There is no lack of eood designs or mounts for concave grating spectrometers: This inciudes everything from the Wadsworth mount or the older Rowland circle mounts (e.g., the Eagle), which are most suitable for spectrographs, to newer ones, which are probably more useful as monochromators. The problem in the past has been to mechanically rule a concave grating of sufficiently high quality to compare with a plane grating mount in both resolution and throughput. The main difficulty is that, for a grating of moderate acceptance angle, the angle of incidence of the light varies across the face of the grating. The blaze angle, therefore, also must vary so that it is the same across the grating surface (24).Otherwise,the efficiency will be much lower than that of a plane grating of equivalent size. Unfortunately, it has not been possible to make a ruling enfie that can effect this. Therefore a concave blank is noAal~ remounted ~ twice, so the grating is ruled in three sections. This has the desired efTect of increasing the eficiency. However, there is still room for improvement because the blaze angle will be exactly correct only for a very small number of grwves jn each section. Moreover, the resultant grating behaves as if it were a composite of three smaller gratings because the rulings of the different sections are usually out of phase with each other. One then observes that the resolution of the grating is no greater than that of any of the three sections. Holographically Ruled Gratings A marked improvement in both the above-mentioned areas has been made by developing a method whereby the grooves can be laid down by a nonmechanical process. The method is called holoma~hicruline. and it was first successfully demonstraGd by ~ a b e ~ iand i e co-workers in France (25). In this procedure a blank is prepared in the same way as for a mechanicah ruled eratine. exce~tthat it is coated with a insteaz of a metal. ?A photoresist is a photosensitive polymer whose solubility is altered by exposure to light.) The coated blank is then exposed to an interference pattern generated by a laser beam that has been divided into two halves, which are then allowed to recombine at the photosensitive surface. The pattern consists of a set of interference fringes, alternate lines of light and dark. The photoresist is thus exposed to different intensities of light at different points on its surface. When it is subsequently developed, it is etched or washed away by the developer in proportion to the extent of this exposure, forming grooves. The grooves thus formed are more or less sinusoidal in cross-section. Thus, it is oRen useful to alter the groove shape in order to improve the scattering efficiency of the resulting grating, as is done in blazing a mechanically
more evenly over all dispersion angles, thus lowering the background level at any one angle. Other advantages of the holographic production process are the absence of ruling spacing errors due to inhomogeneities in the quality of the metal coating, as mentioned above. Variations in scattering efficiency across the grating surface should also be largely absent. These are found in mechanically ruled gratings when wear of the cutting diamond causes changes in the blaze angle.
Figure 5. (a) Hologram formation from perfect and imperfect wavefronts.(b) Regeneration of an imperfectwavefrontby a perfect wavefmnt. ruled eratine. This is done bv process known as ion etch" a * ing (26,27).In the procedure eenerallv followed. the ohotoresist is exposed A d developed, as described above. '?he result is a series of grooves etched into it. The device is then exposed in a vacuum chamber to an unfocussed beam of argon ions. The ions sputter awav surface atoms. at the rate of a few atoms pe;ion. Grooves are etched into the underlying blank, with the photoresist acting as a mask. The shape of those grooves is determined by the angle at which the ion beam impinees on the device. and bv the etch rate of the photoresist. 1 t is possible to make triangular grooves or grooves with square wave or other configurations, as desired. The efficiencies ofboth plane and concave gratings can be increased to those expected of similar meihanieally ruled gratings, with esse&ally no increase in stray light - production. . &r processing, the shaped surface is vacuum-coated with a reflective layer of aluminum and can then be used. As can be seen, the use of the word "holographic" in this c o ~ e c t i o nis something of a misnomer because the device is actually produced by an interference pattern. Nevertheless, the surface of the grating can be considered a hologram that contains inforhation about the wavefronts used to form it. The power of this point of view will be seen below in the discussion on the formation of aberration-corrected gratings. Decreasing tthe Stmy Light The stray light intensity from holographically ruled gratings is lower for several reasons. The first is that the surface is smoother, in general, than that of a similar mechanically ruled device. so less strav lieht is eenerated. A second is-that random aperiodic vahatiins i n b v e spacing are less likely to occur as a result of the holoera~hic d i n g process; therefore, the general level of stray fight from this cause should also be lower. Stray light due to certain groove spacing errors, especially periodic ones, will tend to behave like diffracted light. It will also be focussed in the same way as the desired spectrum. Thus. one observes exoerimentallv (16.28) that the stray light in a mechanically k l e d grating L d& concentrated in a fairlv small anrmlar spread in the direction in which dispersibn is mostefficiek. If the observed spectrum falls within this region, the stray light background willbe relatively high. By contrast, the stray light from holographically mled gratings tends to be distributed
Aberration Correction The production of aberration-correctedgratings is an excellent example of the advantages of optical grating formation. The use of spherical mirrors in plane-grating monochromators necessarily gives rise to certain aberrations, especially because the mirrors must be used off-axis. Although these aberrations can be minimized by good desim and by the use of aspherical mirrors ran expe&ive alternative~,they cannot be eliminated in these ways. In principle, however, complete aberration elimination at one angle of diffraction can be achieved by constructing a grating whose surface will introduce aberrations into the diffracted wave that will exactly cancel the system aberrations. The principle can be illustrated as follows. Instead of forming grooves in the photoresist by allowing two perfect wavefronts to interfere, suppose that the grating surface were formed from the interference pattern generated bv a perfect wavefront and an imperfect one, a s in Figure ka. The imperfections in the latter would be due to the optical aberrations in the system to be corrected. The deveioped and aluminized surface would now be a hologram from which the imperfect wavefront courd be regenerated by illuminatmg the surface with a perfect one. The direction of propagation of the regenerated wavefront would be opposite to that of the generating one, as shown by. F i-w e 5b. To he useful in practice, things must he more complicated. The generating wavefront must not be perfect. but rather must contain-the aberrations introdiced b i the spectrometer optics that precede the grating (the collimating optics); and, the regenerated wavefront must contain aberrations that will be exactly cancelled by theo~ticalimperfections of the spectrometer between the and the eldt plane (the focussing optics). It is possible to produce a grating surface that will do this, as described by Lerner and co-workers (29). The essential extra step is to produce a second hologram that, when illuminated by a perfect wavefront, will produce a wavefront that contains the aberration information fmm the focussing optics. The grating surface is then formed by interfering the wavefront from this holoeram with the wavefrontformed by the collimating opticsWhen the grating thus formed is illuminated by a signal that has been distorted by the collimating optics, it will produce a wavefront whose imperfections will be cancelled by the aberrations introduced by the focussing optics. The result is a wavefront in the exit plane that is fully aberration-corrected at one wavelength. It will also show lowered aberrations over a significant wavelength range. Replication
Both holographically and mechanically ruled gratings can be replicated, whi+ brings the cost per grating within ordinary budgets. The process is essentially the same for both kinds of device. A parting layer is applied to the master grating. This layer is a very thin coating of nonadherent material. Vacuum pump oil has been used for mechanically ruled grating replication. The ruled surface is then covered with a thin film of epoxy. The epoxy layer may be a few microns to Volume 70 Number 9 September 1993
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