Guidelines for Specifying Diffraction Gratings

Specifications should meet the following criteria.

• They should refer to measurable properties of the grating.
• They should be as objective as possible (avoiding judgment or interpretation).
• They should be quantitative where possible.
• They should employ common units where applicable (metric is preferred).
• They should contain tolerances.

A properly written engineering print for a diffraction grating will be clear and understandable to both the customer and the manufacturer. All grating prints should contain, at a minimum, the following specifications.

The free aperture, also called the clear aperture, of a grating is the maximum area of the surface that will be illuminated. The free aperture is assumed to be centered within the ruled area (see below) unless otherwise indicated. For configurations in which the grating will rotate, such as in a monochromator, it is important to specify the free aperture as the maximum dimensions of the beam on the grating surface (i.e., when the grating is rotated most obliquely to the incident beam). Also, it is important to ensure that the free aperture specifies an area that is completely circumscribed by the ruled area, so that the illuminated area never includes part of the grating surface that does not have grooves.

The free aperture of the grating is that portion of the grating surface for which the optical specifications apply (e.g., Diffraction Efficiency, Wavefront Flatness or Curvature, Scattered Light – see below).

The ruled area of a grating is the maximum area of the surface that will be covered by the groove pattern. The ruled area is assumed to be centered on the substrate face unless otherwise indicated. By convention, the ruled area of a rectangular grating is specified as "groove length by ruled width" – that is, the grooves are parallel to the first dimension; for example, a ruled area of 30 mm x 50 mm indicates that the grooves are 30 mm long.

Most rectangular gratings have their grooves parallel to the shorter blank dimension. For gratings whose grooves are parallel to the longer dimension, it is helpful to specify "long lines" to ensure that the grooves are made parallel to the longer dimension.

The blank dimensions (width, length, and thickness) should be called out, as should their tolerances. If the grating is designed to be front-mounted, the blank specifications can be somewhat looser than if the grating surface will be positioned or oriented by the precise placement of the substrate. Front-mounting a grating generally reduces its cost and production time (see Alignment below).

A grating blanks should have bevels on its active face, so that it is easier to produce and to reduce chipping the edges while in use. Bevel dimensions should be specified explicitly and should be considered in matching the Ruled Area (above) with the substrate dimensions. For custom (special-size) blanks, certain minimum bevel dimensions may be required to ensure that the grating is manufacturable – please contact us for advice.

Grating size is usually dictated by the desired throughput, which is a function of the source and detector characteristics, the resolution of the optical system, and the required data-acquisition rate. The *Product tables* list the ruled area of each plane grating as the groove length followed by the ruled width (for example, 65 x 75 mm indicates a groove length of 65 mm and a ruled width of 75 mm). The dimensions of the ruled area and the substrate may be altered from the regular catalog sizes at an additional cost. Substrates of special configuration can also be supplied.

The standard substrate material for small and medium-sized gratings is specially annealed borosilicate crown glass (BK-7). Float glass (plate glass) may be used for small cut-up gratings. However, low expansion material, such as Zerodur® or fused silica, can be supplied on request. For certain applications, it is possible to furnish replicas on metal substrates (such as copper or aluminum) that act as good heat sinks.

The particular substrate material should be specified. If the material choice is of little consequence, this can be left to the manufacturer, but especially for applications requiring substrates with low thermal expansion coefficients, or requiring gratings that can withstand high heat loads, the substrate material and its grade should be identified. For transmission gratings, the proper specification of the substrate material should include reference to the fact that the substrate will be used in transmission, and may additionally refer to specifications for inclusions, bubbles, striae, &c.

Plane (flat) gratings should be specified as being planar; concave gratings should have a radius specified, and the tolerance in the radius should be indicated in either millimeters or fringes of red HeNe light (l = 632.8 nm) (a "wave" being a single wavelength, equaling 632.8 nm, and a "fringe" being a single half-wavelength, equaling 316.4 nm). Deviations from the nominal surface figure are specified separately as "wavefront flatness" or "wavefront curvature" (see below).

This specification refers to the allowable deviation of the optical surface from its Nominal Surface Figure (see above). Plane gratings should ideally diffract plane wavefronts when illuminated by collimated incident light. Concave gratings should ideally diffract spherical wavefronts that converge toward wavelength-specific foci. In both cases, the ideal radius of the diffracted wavefront should be specified (it is infinite for a plane grating) and maximum deviations from the ideal radius should also be called out (e.g., the tolerance in the radius, higher-power irregularity in the wavefront). It is important to specify that grating wavefront testing be done in the diffraction order of use if possible, not in zero order, since the latter technique does not measure the effect of the groove pattern on the diffracted wavefronts. Deviations from a perfect wavefront are most often specified in terms of waves or fringes of red HeNe light (λ = 632.8 nm). Generally, wavefront is specified as an allowable deviation from focus ("power") and allowable higher-order curvature ("irregularity").

The angular dispersion of a grating for a given wavelength is a function of the angles of incidence and diffraction. Once these angles have been determined, the corresponding groove spacing becomes a function of the order in which the grating will operate. Most gratings are used in the first order, thereby minimizing the effects of overlapping wavelengths, and resulting in high efficiency over a wide range. Many systems, however, operate successfully in the second or even higher orders, although this usually requires order-sorting of some kind.

The number of grooves per millimeter, or the spacing between adjacent grooves, should be specified, but not both (unless one is subjugated to the other by labeling it as "reference"). For a grating whose groove spacing varies across the surface (e.g., an aberration-corrected concave holographic grating), the groove spacing (or frequency) is specified at the center of the grating surface.

Alignment refers to the angle between the groove direction and an edge of the grating substrate. Sometimes this angular tolerance is specified as a linear tolerance by stating the maximum displacement of one end of a groove (to an edge) relative to the other end of the groove. Generally a tight alignment specification increases manufacturing cost; it is often recommended that alignment be allowed to be somewhat loose and that the grating substrate dimensions not be considered for precise alignment but that the grating surface be oriented and positioned optically instead of mechanically (see comments in Substrate Dimensions above).

The efficiency behavior of diffraction gratings is one of the most important properties a user needs to know. Efficiency curves for most of our master gratings can be viewed by clicking on the Master Grating Code shown on the leftmost column of our grating product tables.

Grating efficiency is generally specified as a minimum at a particular wavelength; often this is the peak wavelength (i.e., the wavelength of maximum efficiency). Occasionally efficiency specifications at more than one wavelength are called out.

Either relative or absolute diffraction efficiency should be specified.

• Relative efficiency is specified as the percentage of the power (or, more loosely, energy) at a given wavelength that would be reflected by a mirror (of the same coating as the grating) that is diffracted into a particular order by the grating (that is, efficiency relative to a mirror).
• Absolute efficiency is specified as the percentage of the power incident on the grating that is diffracted into a particular order by the grating.

In addition to the wavelength and the diffraction order, grating efficiency depends on the incidence and diffraction angles a and b (the "conditions of use"); if these angles are not explicitly stated, the standard configuration (namely the Littrow configuration, in which the incident and diffracted beams are coincident) will be assumed. Unless otherwise noted on the curves themselves, all standard Richardson Grating Laboratory efficiency curves are generated for the standard (Littrow) conditions of use: a = b.

Generally diffraction gratings are polarizing elements, so that the efficiency in both polarizations should be considered:

• P-plane TE light polarized parallel to grooves
• S-plane TM light polarized perpendicular to grooves

For each wavelength that has an efficiency specification, the following should be indicated: the wavelength, the efficiency (in percent), whether the efficiency specification is relative or absolute, the diffraction order, the polarization of the light, and the conditions of use. In some cases, the bandwidth of the exit slit in the spectrometer used to measure the grating efficiency may need to be called out as well.

Additional specifications are sometimes required based on the particular application in which the grating is to be used.

• Blaze Angle. Although it is better to specify diffraction efficiency, which is a performance characteristic of the grating, sometimes the blaze angle is specified instead (or additionally). A blaze angle should be specified only if it is to be measured and verified (often done by measuring efficiency anyway), and a tolerance should be noted. In cases where both the diffraction efficiency and the blaze angle are specified, the efficiency specification shall be controlling and the blaze angle specification shall be for reference only. Gratings are listed with their blaze angles and corresponding first-order Littrow blaze wavelengths, even though a few high-blaze angle gratings are not intended for first-order use. For practical reasons, blaze angles are usually chosen to favor the short end of the spectral region to be covered.
• Coating Material. Aluminum (Al) is the standard reflection coating. Fast-fired aluminum with an over-coating of magnesium fluoride (MgF2) can be used to enhance reflectivity in the region of 120-160 nm. For the extreme ultraviolet region below 50 nm, gold (Au) replicas are recommended. Gold replicas also have higher reflectivity in the infrared spectrum. Generally the Diffraction Efficiency specifications will dictate the coating material, but sometimes a choice exists and a particular coating should be specified. Additionally, dielectric overcoatings may be called out that are not implied by the efficiency specifications.
• Scattered Light. Grating scattered light is usually specified by requiring that the fraction of monochromatic light power incident on the grating and measured a particular angle away from the diffracted order falls below a certain upper limit. Increasingly, this specification is provided in decibels. The proper specification of scattered light would call out the test configuration, the polarization and wavelength of the incident light, the incidence angle, the solid angle subtended by the detector aperture, and the dimensions of the exit slit. Grating scatter is measured at the Richardson Grating Laboratory using red HeNe light.
• Cosmetics. The cosmetic appearance of a diffraction grating does not correlate strongly with the performance of the grating, and for this reason specifications limiting the type, number and size of cosmetic defects are not recommended. Nevertheless, all Richardson Grating Laboratory gratings undergo a rigorous cosmetic inspection before shipment.
• Imaging Characteristics. Concave holographic gratings may be aberration-corrected, in which case they can provide focusing without the use of auxiliary optics. In these cases, imaging characteristics should be specified, generally by calling out the full width at half maximum intensity (FWHM) of the images.
• Damage Threshold. In some instances, such as pulsed laser applications, diffracted gratings are subjected to beams of high power density that may cause damage to the delicate grating surface, in which case the maximum power per unit area that the grating surface must withstand should be specified.
• Other specifications. Other specifications that relate to the functional performance of the grating should be called out in the print. For example, if the grating must perform in extreme environments (e.g., a satellite or space-borne rocket, high heat and/or humidity environments), this should be noted in the specifications.