Since the late 1960s, a method distinct from mechanical ruling has also been used to manufacture diffraction gratings. This method involves the photographic recording of a stationary interference fringe field. Such interference gratings, more commonly (though inaccurately) known as holographic gratings, have several characteristics that distinguish them from ruled gratings.

In Aimé Cotton produced experimental holographic gratings,¹³ fifty years before the concepts of holography were developed by Gabor. A few decades later, Michelson considered the interferometric generation of diffraction gratings obvious, but recognized that an intense monochromatic light source and a photosensitive material of sufficiently fine granularity did not then exist.¹⁴ In the mid 1960s, ion lasers and photoresists (grainless photosensitive materials) became available; the former provided a strong monochromatic line, and the latter was photoactive at the molecular level, rather than at the crystalline level (unlike, for example, photographic film).

In the late 1960s, researchers independently produced the first holographic diffraction gratings of spectroscopic quality.¹⁵

When two sets of coherent equally polarized monochromatic optical plane waves of equal intensity intersect each other, a standing wave pattern will be formed in the region of intersection if both sets of waves are of the same wavelength l (see Figure 4-1).¹⁶ The combined intensity distribution forms a set of straight equally-spaced fringes (bright and dark lines). Thus a photographic plate would record a fringe pattern, since the regions of zero field intensity would leave the film unexposed while the regions of maximum intensity would leave the film maximally exposed. Regions between these extremes, for which the combined intensity is neither maximal nor zero, would leave the film partially exposed. The combined intensity varies sinusoidally with position as the interference pattern is scanned along a line. If the beams are not of equal intensity, the minimum intensity will no longer be zero, thereby decreasing the contrast between the fringes. As a consequence, all portions of the photographic plate will be exposed to some degree.

The centers of adjacent fringes (that is, adjacent lines of maximum intensity) are separated by a distance d, where

d =

(4-1)

and q is the half the angle between the beams. A small angle between the beams will produce a widely spaced fringe pattern (large d), whereas a larger angle will produce a fine fringe pattern. The lower limit for d is l/2, so for visible recording light, thousands of fringes per millimeter may be formed.

Master holographic diffraction gratings are recorded in photoresist, a material whose intermolecular bonds are either strengthened or weakened by exposure to light. Commercially available photoresists are more sensitive to some wavelengths than others; the recording laser line must be matched to the type of photoresist used. The proper combination of an intense laser line and a photoresist that is highly sensitive to this wavelength will reduce exposure time.

Photoresist gratings are chemically developed after exposure to reveal the fringe pattern. A photoresist may be positive or negative, though the latter is rarely used. During chemical development, the portions of a substrate covered in positive photoresist that have been exposed to light are dissolved, while for negative photoresist the unexposed portions are dissolved. Upon immersion in the chemical developer, a surface relief pattern is formed: for positive photoresist, valleys are formed where the bright fringes were, and ridges where the dark fringes were. At this stage a master holographic grating has been produced;

Figure 4-1.   Formation of interference fringes. Two collimated beams of wavelength l form an interference pattern composed of straight equally spaced planes of intensity maxima (shown as the horizontal lines). A sinusoidally varying interference pattern is found at the surface of a substrate placed perpendicular to these planes.

its grooves are sinusoidal ridges. This grating may be coated and replicated like master ruled gratings.

Lindau has developed simple theoretical models for the groove profile generated by making master gratings holographically, and shown that even the application of a thin metallic coating to the holographically-produced groove profile can alter that profile.¹⁷

An interference pattern can be generated from a single collimated monochromatic coherent light beam if it is made to reflect back upon itself. A standing wave pattern will be formed, with intensity maxima forming planes parallel to the wavefronts. The intersection of this interference pattern with a photoresist-covered substrate will yield on its surface a pattern of grooves, whose spacing d depends on the angle q between the substrate surface and the planes of maximum intensity (see Figure 4-2)¹⁸; the relation between d and q is identical to Eq. (4-1), though it must be emphasized that the recording geometry behind the single-beam holographic grating (or Sheridon grating) is different from that of the double-beam geometry for which Eq. (4-1) was derived.

The groove depth h for a Sheridon grating is dictated by the separation between successive planes of maximum intensity (nodal planes); explicitly,

h = ,

(4-2)

where l₀ is the wavelength of the recording light and n the refractive index of the photoresist. This severely limits the range of available blaze wavelengths, typically to those between 200 and 250 nm.

Figure 4-2.   Sheridon recording method. A collimated beam of light, incident from the right, is retroreflected by a plane mirror, which forms a standing wave pattern whose intensity maxima are shown. A transparent substrate, inclined at an angle q  to the fringes, will have its surfaces exposed to a sinusoidally varying intensity pattern.

The double-beam interference pattern shown in Figure 4-1 is a series of straight parallel fringe planes, whose intensity maxima (or minima) are equally spaced throughout the region of interference. Placing a substrate covered in photoresist in this region will form a groove pattern defined by the intersection of the surface of the substrate with the fringe planes. If the substrate is planar, the grooves will be straight, parallel and equally spaced, though their spacing will depend on the angle between the substrate surface and the fringe planes. If the substrate is concave, the grooves will be curved and unequally spaced, forming a series of circles of different radii and spacings. Regardless of the shape of the substrate, the intensity maxima are equally spaced planes, so the grating recorded will be a classical equivalent holographic grating (more often called simply a classical grating). This name recognizes that the groove pattern (on a planar surface) is identical to that of a planar classical ruled grating. Thus all holographic gratings formed by the intersection of two sets of plane waves are called classical equivalents, even if their substrates are not planar (and therefore groove patterns are not straight equally spaced parallel lines).

If two sets of spherical wavefronts are used instead, as in Figure 4-3, a first generation holographic grating is recorded. The surfaces of maximum intensity are now confocal hyperboloids (if both sets of wavefronts are converging, or if both are diverging) or ellipsoids (if one set is converging and the other diverging). This interference pattern can be obtained by focusing the recording laser light through pinholes (to simulate point sources). Even on a planar substrate, the fringe pattern will be a collection of unequally spaced curves. Such a groove pattern will alter the curvature of the diffracted wavefronts, regardless of the substrate shape, thereby providing focusing. Modification of the curvature and spacing of the grooves can be used to reduce aberrations in the spectral images; as there are three degrees of freedom in such a recording geometry, three aberrations can be reduced (see Chapter 6).

Figure 4-3.   First-generation recording method.. Laser light focused through pinholes at A and B forms two sets of spherical wavefronts, which diverge toward the grating substrate. The standing wave region is shaded; the intensity maxima are confocal hyperboloids.

The addition of auxiliary concave mirrors or lenses into the recording beams can render the recording wavefronts toroidal (that is, their curvature in two perpendicular directions will generally differ). The grating thus recorded is a second generation holographic grating.¹⁹ The additional degrees of freedom in the recording geometry (e.g., the location, orientation and radii of the auxiliary mirrors) provide for the reduction of additional aberrations above the three provided by first generation holographic gratings.²⁰

The use of aspheric recording wavefronts can be further accomplished by using aberration-reduced gratings in the recording system; the first set of gratings is designed and recorded to produce the appropriate recording wavefronts to make the second grating.²¹ Another technique is to illuminate the substrate with light from one real source, and reflect the light that passes through the substrate by a mirror behind it, so that it interferes with itself to create a stationary fringe pattern.²² Depending on the angles involved, the curvature of the mirror and the curvature of the front and back faces of the substrate, a number of additional degrees of freedom may be used to reduce high-order aberrations. [Even more degrees of freedom are available if a lens is placed in the recording system thus described.²³]

Holographic gratings are recorded by placing a light-sensitive surface in an interferometer. The generation of a holographic grating of spectroscopic quality requires a stable optical bench and laser as well as high-quality optical components (mirrors, collimating optics, etc.). Ambient light must be eliminated so that fringe contrast is maximal. Thermal gradients and air currents, which change the local index of refraction in the beams of the interferometer, must be avoided. Newport records master holographic gratings in a clean room specially-designed to meet these requirements.

During the recording process, the components of the optical system must be of nearly diffraction-limited quality, and mirrors, pinholes and spatial filters must be adjusted as carefully as possible. Any object in the optical system receiving laser illumination may scatter this light toward the grating, which will contribute to stray light. Proper masking and baffling during recording are essential to the successful generation of a holographic grating, as is single-mode operation of the laser throughout the duration of the exposure.

The substrate on which the master holographic grating is to be produced must be coated with a highly uniform, virtually defect-free coating of photoresist. Compared with photographic film, photoresists are somewhat insensitive to light during exposure, due to the molecular nature of their interaction with light. As a result, typical exposures may take from minutes to hours, during which time an extremely stable fringe pattern (and, therefore, optical system) is required. After exposure, the substrate is immersed in a developing agent, which forms a surface relief fringe pattern; coating the substrate with metal then produces a master holographic diffraction grating.

Due to the distinctions between the fabrication processes for ruled and holographic gratings, each type of grating has advantages and disadvantages relative to the other, some of which are described below.

The efficiency curves of ruled and holographic gratings generally differ considerably, though this is a direct result of the differences in groove profiles and not strictly due to method of making the master grating. For example, holographic gratings made using the Sheridon method described in Section 4.2.1 above have nearly triangular groove profiles, and therefore have efficiency curves that look more like those of ruled gratings than those of sinusoidal-groove holographic gratings.

There exist no clear rules of thumb for describing the differences in efficiency curves between ruled and holographic gratings; the best way to gain insight into these differences is to look at representative curves of each grating type. Chapter 9 in this Handbook contains a number of curves; the paper²⁴ on which this chapter is based contains even more curves, and the book Diffraction Gratings and Applications²⁵ by Loewen and Popov has an extensive collection of efficiency curves and commentary regarding the efficiency behavior of plane reflection gratings, transmission gratings, echelle gratings and concave gratings.

Since holographic gratings do not involve burnishing grooves into a thin layer of metal, the surface irregularities on its grooves differ from those of mechanically ruled gratings. Moreover, errors of ruling, which are a manifestation of the fact that ruled gratings have one groove formed after another, are nonexistent in interferometric gratings, for which all grooves are formed simultaneously. Holographic gratings, if properly made, can be entirely free of both small periodic and random groove placement errors found on even the best mechanically ruled gratings. Holographic gratings may offer advantages to spectroscopic systems in which light scattered from the grating surface is performance-limiting, such as in the study of the Raman spectra of solid samples, though proper instrumental design is essential to ensure that the performance of the optical system is not limited by other sources of stray light.

The groove profile has a significant effect on the light intensity diffracted from the grating (see Chapter 9). While ruled gratings may have triangular or trapezoidal groove profiles, holographic gratings usually have sinusoidal (or nearly sinusoidal) groove profiles (see Figure 4-4). A ruled grating and a holographic grating, identical in every way except in groove profile, will have demonstrably different efficiencies (diffraction intensities) for a given wavelength and spectral order. Moreover, ruled gratings are more easily blazed (by choosing the proper shape of the burnishing diamond) than are holographic gratings, which are usually blazed by ion bombardment (ion etching). Differences in the intensity diffracted into the order in which the grating is to be used implies differences in the intensities in all other orders as well; excessive energy in other orders usually makes the suppression of stray light more difficult.

Figure 4-4.   Ideal groove profiles for ruled and holographic gratings.. (a) Triangular grooves, representing the profile of a mechanically ruled grating. (b) Sinusoidal grooves, representing the profile of a holographic grating.

The distribution of groove profile characteristics across the surface of a grating may also differ between ruled and holographic gratings. For a ruled concave grating, the facet angles are not aligned identically and the effective blaze wavelength varies from one side of the grating to the other. A holographic grating, on the other hand, usually demonstrates much less variation in efficiency characteristics across its surface. Gratings have been ruled by changing the facet angle at different places on the substrate during ruling. These so-called "multipartite" gratings, in which the ruling is interrupted and the diamond reoriented at different places across the width of the grating, demonstrate enhanced efficiency but do not provide the resolving power expected from an uninterrupted ruling (since each section of grooves may be out of phase with the others).²⁶

Limits on the number of grooves per millimeter differ between ruled and holographic gratings: ruled gratings offer a much wider range of groove spacings. Below a few hundred grooves per millimeter, the recording optical system necessary to generate holographic gratings becomes cumbersome, while ruled gratings can have as few as thirty grooves per millimeter. As an upper limit, holographic gratings can be recorded with several thousand grooves per millimeter, producing a groove density almost as high as those ruled gratings with over 10,000 grooves per millimeter.

Classical ruled plane gratings, which constitute the vast majority of ruled gratings, have straight equally-spaced grooves. Classical ruled concave gratings have unequally spaced grooves that form circular arcs on the grating surface, but this groove pattern, when projected onto the plane tangent to the grating at its center, is still a set of straight equally spaced lines. [It is the projected groove pattern that governs imaging.²⁷] Even ruled varied line-space (VLS) gratings (see Chapter 3) do not contain curved grooves, except on curved substrates. The aberration reduction possible with ruled gratings is therefore limited to that possible with straight grooves, though this limitation is due to the mechanical motions possible with present-day ruling engines rather than with the burnishing process itself.

Holographic gratings, on the other hand, need not have straight grooves. Groove curvature can be modified to reduce aberrations in the spectrum, thereby improving the throughput and spectral resolution of imaging spectrometers. A common spectrometer mount is the flat-field spectrograph, in which the spectrum is imaged onto a flat detector array and several wavelengths are monitored simultaneously. Holographic gratings can significantly improve the imaging of such a grating system, whereas classical ruled gratings are not suitable for forming well-focused planar spectra without auxiliary optics.

The interference pattern used to record holographic gratings is not dependent on the substrate shape or dimension, so gratings can be recorded interferometrically on substrates of low ƒ/number more easily than they can be mechanically ruled on these substrates. Consequently, holographic concave gratings lend themselves more naturally to systems with short focal lengths. Holographic gratings of unusual curvature can be recorded easily; of course, there may still remain technical problems associated with the replication of such gratings.

The substrate shape affects both the grating efficiency characteristics its imaging performance.

• Grating efficiency depends on the groove profile as well as the angle at which the light is incident and diffracted; for a concave grating, both the groove profile and the local angles vary with position on the grating surface. This leads to the efficiency curve being the sum of the various efficiency curves for small regions of the grating, each with its own groove profile and incidence and diffraction angles.
• Grating imaging depends on the directions of the diffracted rays over the surface of the grating, which in turn are governed by the local groove spacing and curvature (i.e., the groove pattern) as well as the local incidence angle. For a conventional plane grating used in collimated light, the groove pattern is the same everywhere on the grating surface, as is the incidence angle, so all diffracted ray are parallel. For a grating on a concave substrate, though, the groove pattern is generally position-dependent, as is the local incidence angle, so the diffracted rays are not parallel - thus the grating has focal (imaging) properties as well as dispersive properties.

While ruled master gratings can generally be as large as 320 x 420 mm, holographic master gratings are rarely this large, due to the requirement that the recording apparatus contain very large, high-quality lenses or mirrors, and well as due to the decrease in optical power farther from the center of the master grating substrate.

A ruled master grating is formed by burnishing each groove individually; to do so, the ruling diamond may travel a very large distance to rule one grating. For example, a square grating of dimensions 100 x 100 mm with 1000 grooves per millimeter will require the diamond to move 10 km (over six miles), which may take several weeks to rule.

In the fabrication of a master holographic grating, on the other hand, the grooves are created simultaneously. Exposure times vary from a few minutes to tens of minutes, depending on the intensity of the laser light used and the spectral response (sensitivity) of the photoresist at this wavelength. Even counting preparation and development time, holographic master gratings are produced much more quickly than ruled master gratings. Of course, an extremely stable and clean optical recording environment is necessary to record precision holographic gratings. For plane gratings, high-grade collimating optics are required, which can be a limitation for larger gratings.