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Selecting Diffraction Gratings Diffraction gratings are used in a wide variety of applications where light needs to be spectrally separated. Understanding the varying types of surface relief gratings will aid in the selection of the best options for your application. Optometrics Corporation operates several modern master diffraction grating production laboratories, producing both interferometrically controlled classically ruled and holographically recorded replication masters to optimize its OEM customers’ instrument performance. Hundreds of standard replication masters are inventoried for fast delivery of many common designs. Optometrics also supports new OEM customers in need of regenerating less efficient grating replication masters, resulting in improved quality, manufacturing efficiencies, and lower costs. With production exceeding 1,000 replicated optics and diffraction gratings daily, and capacity for over 500,000 ft2/year of high quality Dielectric and Dichroic Beamsplitter, Bandpass, Longpass, Shortpass, Neutral Density, Hot/Cold Mirrors, Reflective, Anti‐reflective, Enhanced, Protected, and Color Corrected filters, Optometrics is your preferred ISO certified and ITAR registered supplier! An introduction to surface relief diffraction gratings Diffraction gratings are passive optical components that produce an angular separation of an incident light source as a function of wavelength. Each wavelength exits the device at a different angle, allowing precise spectral selection for a wide range of applications. A diffraction grating consists of a series of equally spaced parallel grooves formed in a reflective coating deposited on a suitable substrate. The distance between adjacent grooves and the angle the grooves form with respect to the substrate influence both the dispersion and efficiency of a grating. If the wavelength of the incident radiation is much larger than the groove spacing, diffraction will not occur. If the wavelength is much smaller than the groove spacing, the facets of the groove will act as mirrors and, again, no diffraction will take place. SelectingDiffractionGratings(1/2015)
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Grating Equation The general grating equation is usually written as: nλ = d(sin i + sin i’) where n is the order of diffraction, λ is the diffracted wavelength, d is the grating constant (the distance between successive grooves), i is the angle of incidence measured from the normal and i' is the angle of diffraction measured from the normal. For a specific diffracted order (n) and angle of incidence (i), different wavelengths (λ) will have different diffraction angles (i'), separating polychromatic radiation incident on the grating into its constituent wavelengths. Ruled and Holographic There are two main classes of surface relief diffraction gratings, each defined by the way the grooves on the grating surface are formed. Ruled and holographic gratings differ in their optical characteristics and each type has advantages for specific applications. Optometrics is one of the few companies that produces both ruled and holographically recorded master gratings in‐house, and has full replication facilities and expertise for high volume low cost production. Ruled diffraction gratings Ruling a master grating begins with the selection of an appropriate substrate, typically glass or copper, and optically polishing the substrate to a high degree of flatness. The substrate then receives a high purity thin layer vacuum deposition coating of aluminum, gold or other application appropriate reflective metal. A “Ruling Engine” equipped with specialized diamond tooling is used to form the grooves on the surface of the thin metal coating. This process of ruling tens of thousands of parallel, equally spaced grooves is time consuming, and can require several days of set‐up and testing prior to the actual ruling itself. The ruling engine is able to retrace the exact path of the diamond forming tool on each stroke, and aided by interferometric controls, is capable of advancing the substrate a predetermined nano‐scale distance after each cut. Both groove parallelism and displacement are controlled with great precision. SelectingDiffractionGratings(1/2015)
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A series of "test" rulings are made and evaluated, allowing critical adjustments in the formed groove profile, thereby optimizing the grating for design efficiency. After exhaustive testing and optimization, a master grating is ruled on the prepared large substrate, which is subsequently used for cost effective optical replication of precision gratings in a wide variety of standard and custom sizes. Holographic diffraction gratings Initial preparation of the substrate for holographic grating production is similar to that for ruled gratings, although rather than a thin coating of metal, a photosensitive (photoresist) material is applied to the top surface of the substrate. The substrate is then positioned within intersecting monochromatic coherent laser beams which produce parallel, equally spaced interference fringes whose intensities vary in a sinusoidal pattern, exposing the resist differentially. Since the solubility of the resist is dependent on its exposure to light, the development process transfers the varying intensities of the interference fringes to the surface of the resist, forming a surface relief groove pattern with extraordinary precision. Because the grooves are generated optically, holographic diffraction gratings are often considered when very low stray light from surface scattering is desired. Once the grooves have been generated, the substrate is coated with a reflective material and can be used as is, or replicated by the same process used for ruled diffraction gratings. Cost Control: Replicated diffraction gratings The costly and time consuming task of producing a “Master” diffraction grating is often amortized and made affordable by an optical replication process. Precision optical replication is a procedure that results in the transfer of the three dimensional topography of a master grating to another substrate, allowing reproduction of a master in full relief to extremely close tolerances. Replicated gratings are produced with a high degree of accuracy and repeatability, leading to affordable high volume availability on a commercial basis. This process is not limited to glass substrates, and is therefore often used to transfer the precision diffraction grating surface onto integral metal components within an optical design with pinned pre‐
alignment features, scanning posts, or other features which aid instrument assembly. SelectingDiffractionGratings(1/2015)
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Which diffraction grating is best for your application? It is important to take the time to select the right diffraction grating for your requirements. This means assessing what you need the grating to achieve, the environment you will be working in, and the equipment you will be using. There are many variables to review, though the following highlighted grating performance characteristics generally take precedence, and should be considered before making your selection: There are several factors that affect the efficiency of a diffraction grating. These include the shape of the grooves, the incidence angle of the groove relative to the input light path, and the reflectance of the coating. The absolute efficiency of a grating is the percentage of incident monochromatic radiation that is diffracted into the desired order. In contrast, relative efficiency compares the energy diffracted into the desired order with that of a plane mirror coated with the same material as the grating. When comparing grating performance curves, it is important to keep this in mind. A relative efficiency curve will always show higher values than an absolute efficiency curve for the same grating. Angle of incidence plays an important role in diffraction grating efficiency performance. Because of the infinite number of optical configurations that a grating can be used in, the Littrow (autocollimation) mounting configuration has become the industry standard. In this mounting configuration, the diffracted order and wavelength of interest is directed back along the path of the incident light (i=i), and hence the blaze angle of a ruled grating is calculated based on this configuration. This practical configuration is also necessary for laser tuning applications, and most applications will require some deviation between the incident and diffracted beams. Small deviations from the Littrow configuration seldom have an appreciable effect on grating performance other than limiting the maximum wavelength achievable. The angle that is created by the longer side of the groove and the plane of the substrate on a ruled grating is referred to as the “blaze angle”. The blaze angle occurs on ruled gratings because the diamond shaping process produces a saw tooth profile with one side longer than the other. Changing this blaze angle allows the designer to concentrate diffracted radiation into either narrow or broad spectral regions, as well as optimize for the peak wavelength efficiency. The spectral location where maximum efficiency occurs is known as the blaze wavelength. This is a common characteristic of ruled gratings, whereas typical holographic gratings have sinusoidal shaped grooves with equal sides. However, the groove profile of holographic gratings can be modified or altered in some cases and, where the spacing‐
to‐wavelength ratio is near 1, a holographic grating and a ruled grating are virtually equally efficient. In addition, a special process enables Optometrics holographic gratings to achieve a saw tooth profile peaked for 250 nm, an ideal configuration for UV applications requiring good efficiency with low stray light. The spectral range that a diffraction grating can efficiently disperse light is dependent on the groove spacing, or groove frequency. This applies equally to both ruled and holographic grating designs with the same grating constant. Therefore, the spectral range required by your application will lead to the SelectingDiffractionGratings(1/2015)
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desired groove spacing on whichever type of grating is best for your needs. The maximum wavelength that a grating can diffract is equal to two times the grating period, and this would be achieved when the incident and diffracted light were at ninety degrees to the grating normal. Various reflective metals and other materials may be deposited on the diffraction grating. These optical coatings are used to optimize, and sometimes avoid, reflectance within portions of the spectrum of interest. Gratings used in the ultraviolet, visible and infrared are normally replicated with an aluminum coating. Aluminum is used rather than silver because it is more resistant to oxidation and has superior reflectance in the ultraviolet. Aluminum averages over 90% reflectance from 200 nm to the far infrared, except in the 750 to 900 nm region where it drops to approximately 85%. When maximum reflectance is required in the near infrared, as is the case with some fiber optic applications, the aluminum coating may be over coated with gold. Though gold is soft, it is resistant to oxidation and has a reflectance of over 96% in the near infrared and over 98% above 2.0 μm. The reflectance of gold drops substantially below 600 nm and is not recommended for use in the visible or ultraviolet regions. Dielectric over coatings, such as magnesium fluoride (MgF2), protects aluminum from oxidation, maintaining the original high reflectance of bare aluminum in the visible and ultraviolet. While gold over coating can increase reflectivity beyond 600 nm, over coating may also reduce the damage threshold of a diffraction grating. The resolution of an optical system, usually determined by the ability (limit) to distinguish closely spaced absorption or emission lines in accordance to the Raleigh criteria (R = λ/Δλ), depends not only on the grating dispersion but on focal length, slit size, f number, the optical quality of all components and system alignment. The resolution of an optical system is usually less than the dispersion of the grating. Angular dispersion of a grating is a product of the angle of incidence and groove spacing. Angular dispersion can be increased by increasing the angle of incidence or by decreasing the distance between successive grooves. A grating with a large angular dispersion can produce good resolution in a compact optical system. Angular dispersion is the slope of the curve given by λ = f(i). In Littrow, the equation for dispersion is given by: SelectingDiffractionGratings(1/2015)
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This formula may be used to determine the angular separation of two spectral lines or the bandwidth that will be passed by a slit subtending a given angle at the grating. For a given set of angles (i,i´) and groove spacing, the grating equation is valid at more than one wavelength, giving rise to several diffracted orders of the dispersed radiation. The reinforcement (constructive interference) of diffracted radiation from adjacent grooves occurs when a ray is in phase but retarded by a whole integer. The number of orders produced is limited by the groove spacing and the angle of incidence, which obviously cannot exceed 90 degrees. At higher orders, efficiency and free spectral range decrease while angular dispersion increases. Order overlap can be compensated for by the judicious use of light sources, detectors, and optical filters, and is often not an issue when gratings are used in low orders. Typical efficiency curves illustrate that, in all cases, orienting the polarization of the E vector (P‐Plane) perpendicular to the grooves (E) increases the efficiency over a specific wavelength region. This should be considered when optimizing the figure of merit (Q) of a cavity, particularly when it is polarized by auxiliary components such as Brewster angle windows. SelectingDiffractionGratings(1/2015)
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Additional factors to consider Ghosts are defined as spurious spectral lines arising from periodic errors in the groove spacing of ruled gratings, or unintended artifacts which are exposed within the photoresist while producing an original holographic diffraction grating. Our Interferometrically controlled ruling engines minimize ghosts, while careful setup during the holographic process minimizes this risk. On ruled gratings, stray light may originate from random errors or irregularities on the reflecting surface occurring during the groove forming process. Holographic gratings are considered to generate less stray light because the optical process which transfers the interference pattern to the photoresist is not subject to these mechanical irregularities or inconsistencies. We design and rule custom Gratings directly in gold for IR (4 to 12 microns) laser applications. Gold gratings are particularly important to IR lasers since their increased efficiency allows more of the generated light to be used. Their resistance to degradation allows them to be used in high power applications that might damage gratings having a thin gold coating over aluminum, for example. These gratings are available on both INVAR and ceramic substrates ‐ if you are interested in working with other materials please contact us for more information. Transmission gratings offer a basic simplicity for optical designs that can be beneficial in fixed grating applications such as diode array spectrographs. The incident light is dispersed on the opposite side of the grating at a fixed angle, and can be very forgiving for some types of grating alignment errors. Transmission grating dispersion characteristics also lend themselves to compact systems utilizing small detector arrays, and are also relatively polarization insensitive. Broadband anti‐reflection (AR) coatings are offered on the back surface of transmission gratings which increase the throughput and minimizes any secondary spectra concerns caused by the back surface reflection. UV transmission gratings are manufactured with select UV materials allowing for optimal performance down to 235 nm. Diffraction gratings are available in several standard square and rectangular sizes ranging from 12.5 mm square up to 50 mm square. Larger and smaller non‐standard sizes are available upon request to help optimize an instrument design. And, unless otherwise specified, rectangular gratings are cut with grooves parallel to the short dimension. Typical substrate materials used for replicated gratings include float glass, Pyrex® or Zerodur®. Optometrics carries all three types of substrates in stock, in 3mm, 4mm, 5mm, 6mm, 9.5mm, and 12mm thicknesses. Other materials and thicknesses are available upon request. Common Questions and Answers Q. What are OEM custom size capabilities? A. Thicknesses of 2mm, 3mm, 4mm, 5mm, 6mm, 9.5mm, 12mm and 16mm are routinely available for faster delivery. Sizes in round, rectangular or square shapes as small as 6 mm up to 90 mm are possible. SelectingDiffractionGratings(1/2015)
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Q. What substrate materials are available? A. Pyrex, float glass and Zerodur are routinely available as standard materials. However, gratings can generally be replicated on any hard surface such as Fused Silica, Metals and hard plastics. Q. Should I choose float glass, Pyrex or Zerodur? A. Your application will generally dictate. The primary advantage of Pyrex is that it has a lower coefficient of thermal expansion and has better thermal stability than float glass. Zerodur has, as its name implies, a zero coefficient of thermal expansion. Q. Which way are grooves oriented on a rectangular grating? A. Unless otherwise specified, rectangular gratings are cut with grooves parallel to the short dimension. Q. What types of surface over‐coatings are available? A. Bare aluminum offers good visible and infrared performance. MgF2 (magnesium fluoride) is used as an overcoat for enhanced UV performance. Gold is used as an overcoat to increase reflectivity in the near infrared. Other materials such as silver and others are also available. Q. Can I clean the grating surface? A. The surface of a diffraction grating can be easily damaged by fingerprints, aerosols, moisture or the slightest contact with any abrasive material. Gratings should only be handled when necessary and always held by the sides. Latex gloves or a similar protection should be worn to prevent oil from fingers from contaminating the grating surface. Any attempt to clean a grating with a solvent voids the warranty. No attempt should be made to clean a grating other than blowing off dust with clean, dry air or nitrogen. Q. Are published efficiency curves based upon actual or theoretical data? A. Typical grating efficiency curves are based upon actual measurements of the gratings Optometrics sells. Q. What is the difference between absolute and relative efficiency? A. Grating efficiency is typically expressed as either "absolute" efficiency or "relative" efficiency. Optometrics’ efficiency curves are expressed as absolute efficiency. The absolute efficiency of a grating is the percentage of incident monochromatic radiation on a grating that is diffracted into the desired order. This efficiency is determined by both the groove profile (blaze) and the reflectivity of the grating¹s coating. In contrast, relative (or groove) efficiency compares the energy diffracted into the desired order with the energy reflected by a plane mirror coated with the same material as the grating. A relative efficiency curve will always show higher efficiency values than an absolute efficiency curve for the same grating. SelectingDiffractionGratings(1/2015)
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