When light encounters an obstacle, such as an opaque screen with small openings (or holes), the intensity distribution behind the screen looks completely different from the shape of the aperture through which the light passes. Since light is an electromagnetic wave, the wavefront changes, just like a water wave encounters an obstacle. Interference occurs between different parts of the wavefront, resulting in the diffraction of light, resulting in an intensity distribution called a diffraction pattern. Similarly, when light passes through an opaque screen with multiple narrow apertures (or slits) with fixed spacing, the resulting wavefront interacts concurrently, resulting in diffraction patterns with intensity maxima in certain directions as shown in Figure 1. These directions are strongly dependent on the slit spacing and the wavelength of the incident light. As a result, a surface determined by the position of the slit can be used to direct a specific wavelength of light in a specific direction.
Figure 1.Wavelength of monochromatic light is diffracted through a series of small holes spaced with dg. Angled lines represent the constant phase region, and arrows indicate the direction of the intensity peak in the diffraction pattern.
A diffraction grating is essentially a multi-slit surface that causes angular dispersion of light, i.e., the ability to separate wavelengths based on the angle at which light is emitting from the grating. The grating can be transmissive, like multi-slit aperture, or reflective, where the groove surface is coated with a reflective material such as aluminum. A typical grating consists of a large number of parallel grooves (representing slits) with groove spacing (denoted as dg) about the wavelength of light. The density of the glines (g) is the reciprocal of dg, e.g. the g-value of a typical grating is 30-5000 lines per millimeter. The notch spacing determines the angle at which a single wavelength will undergo constructive interference to form a diffraction order, which is equivalent to the intensity peak. In addition to the notch spacing, the notch profile (see Figure 2) also plays a key role in the encoder performance. When monochromatic light hits a grating, a portion is diffracted to each order (known as diffraction efficiency). It is often desirable to maximize the efficiency over a single stage (usually the first stage) to ensure increased light collection. In order to optimize the efficiency of individual wavelengths, a sparkle operation is performed, which involves modifying the notch profile, including the facet angle, shape, and depth. The flare wavelength is the wavelength with the highest diffraction efficiency of grating.
Figure 2.Top view of the diffraction grating groove pattern (top left) and side view of different groove profiles (bottom left). SEM image of a diffraction grating (right).
The basic grating equation determines the discrete direction in which monochromatic light with wavelength is diffracted by . The raster equation is as follows:
Figure 3 illustrates the diffraction process. Light of wavelength is incident at an angle and is diffracted by the grating (notch spacing d g) along the angle m. The angle is measured from the raster normal, which appears in the diagram as a dashed line perpendicular to the center of the grating surface. If m and are on either side of the raster normal, they have opposite signs. In the formula, m is the diffraction order and m is an integer. For 0 order diffraction (m = 0), and 0 are equal in magnitude but opposite in direction, the beam is only reflected, not diffraction. The sign convention for m: m is positive if the diffracted ray is to the left of the zero order (counterclockwise side), and negative if the diffracted ray is on the right side of the zero scale (clockwise side). When a beam of monochromatic light is incident on the grating, the light is diffracted from the grating to the corresponding direction of m = -2, -1, 0,1,2,3, etc. When a beam of multichromatic light is incident on the grating, the light is dispersed so that the wavelengths satisfy the grating equation, as shown in Figure 3. Usually only the first order of diffraction (+1 or -1 order) is desired, so it may be necessary to block higher wavelengths. In many monochromators and spectrometers, a constant-biased base is used to change the wavelength by rotating the grating around the axis while the angle (or deflection angle) between the incident and diffracted light remains constant.
Figure 3Polychromatic light diffracted by grating.
Fixed the angle of incidence in the grating equation, differentiating for , and determining the difference in the diffraction (d) or the diffraction angle per unit wavelength as.
For a given diffraction order m, d represents the ability to distinguish between signals of different wavelengths and increases as the density of the line (g) increases. When a grating is combined into a spectrometer with an effective focal length (f), the linear dispersion of the system is the product of d and f. In fact, the reciprocal of dispersion (sometimes referred to as the plate factor p) is usually considered
is a measure of the change in wavelength (in nm) for a given lateral distance (in mm) and can be used to determine the bandpass and resolution of a spectrometer. Bandpass refers to the width of the spectrum that passes through a spectrometer when illuminated by light with a continuous spectrum. In a monochromatic, the bandpass is the product of p and the width of the slit. Reducing the slit width until the limit bandpass is reached yields the resolution of the instrument. In spectroscopic analysis, resolution is a measure of an instrument's ability to resolve two spectral lines that are fairly close together. Figure 4 shows the effect of reducing the slit width on the ability to resolve sharp spectral lines in the light source. The resolution of the monochromator is also affected by the aberration of the optical system and the illumination of the grating, and these influencing factors should be eliminated as much as possible in practice to ensure that the resolution is mainly determined by p and slit width. The bandpass and resolution of a spectrometer depends primarily on the detector parameters (see below).
Figure 4By p=13Incoherent lamp source spectra of a 2 nm mm monochromator. Reducing the slit width from 760 m (left) to 120 m (right) makes the spectral resolution from 101 nm to 16 nm。
Rasters are made in two ways, engraving and holography. The high-precision wire engraving machine uses a diamond cutter to polish and groove the evaporated metal film applied to the surface to form the main grating. The reproduction of the main grating makes it possible to produce scribed gratings, and most of the diffractive light used in dispersive spectrometers is the inscribed grating. Scribed gratings can shine for specific wavelengths, are often highly efficient, and are often used in systems that require high resolution. A stepped grating is a rough grating (low density) with a high flare angle and uses a high diffraction order. The advantage of stepped encoders is their ability to provide high dispersion and high resolution in a compact system design. The overlapping of diffraction orders is an important limitation of stepped gratings, which require a prism or other grating to achieve a certain type of order separation. The use of sinusoidal interference patterns etched into the glass results in holographic gratings that scatter less than graduations and are designed to minimize aberrations and can be very efficient for a single polarization plane. The grating can be reflective or transmissive, and the surface of the grating can be flat or concave. Planar gratings generally have high efficiency over a wide wavelength range, while concave gratings can be used as both dispersive and focusing elements in spectrometers.