An annoying characteristic of all optical surfaces is their ability to scatter light. This undesirable light is often referred to as stray radiant energy (SRE). When this light reaches the detector of an instrument designed to measure an optical signal, the SRE contributes to the noise of the system and thereby reduces the signal-to-noise ratio (SNR).

The terminology of SRE in grating systems is not standard, so for clarity we refer to unwanted light arising from imperfections in the grating itself as scattered light or grating scatter, and unwanted light reaching the detector of a grating-based instrument as instrumental stray light or simply stray light. [We choose this definition of scattered light so that it will vanish for a perfect grating; we will see below that this does not generally cause the instrumental stray light to vanish as well.] With these definitions, some scattered light will also be stray light (if it reaches the detector); moreover, some stray light will not be scattered light (since it will not have arisen from imperfections in the grating).¹¹³

Of the radiation incident on the surface of a reflection grating, some will be diffracted according to Eq. (2-1) and some will be absorbed by the grating itself. The remainder is scattered light, which may arise from several factors, including imperfections in the shape and spacing of the grooves and roughness on the surface of the grating. An excellent analysis of grating scatter can be found in Sharpe & Irish,¹¹⁴ and measured grating scatter was compared to predictions of Beckmann's scalar theory and Rayleigh's vector theory by Marx et al.¹¹⁵

Two types of scattered light are often distinguished. Diffuse scattered light is scattered into the hemisphere in front of the grating surface. It is due mainly to grating surface microroughness. It is the primary cause of scattered light in holographic gratings. For monochromatic light of wavelength l incident on a grating, the intensity of diffuse scattered light is higher near the diffraction orders of l than between these orders.^† In-plane scatter is unwanted energy in the dispersion plane. Due primarily to random variations in groove spacing or groove depth, its intensity is generally higher than the background diffuse scattered light.

Consider a diffraction grating consisting of a pattern of grooves whose nominal spacing is d. We have defined scattered light as all light leaving the grating due to its imperfections; this is equivalent to the operational definition that scattered light is all light energy leaving the surface of a diffraction grating that does not follow the grating equation for the nominal groove spacing d,

This is analogous to the concept of scattered light for a mirror, which may be defined the light leaving its surface that does not follow the law of reflection for the nominal mirror surface.

This definition of grating scatter – as being caused by imperfections in the grating – does not consider light diffracted into different orders {m} as scattered light. That is, diffraction into multiple orders is not an artifact of grating imperfections, but a direct consequence of the phenomenon of constructive interference on which the grating operates (see Section 2.1). However, light diffracted into other orders can contribute to instrumental stray light (see Section 10.2 below).

A grating surface that is rough on the scale of the incident wavelength (or somewhat smaller) will cause a small portion of the incident light to be scattered diffusely (i.e., into all directions) with intensity that varies approximately with the inverse fourth power of the wavelength.¹¹⁶ Surface roughness is due in part to the surface quality of the master grating, either ruled or holographic, since the metal coating of a ruled master, and the photoresist coating of a holographic master, are not perfectly smooth. Moreover, the addition of a reflective coating may contribute to the surface roughness due to the coating's granular structure.

Each speck of dust, tiny scratch, and pinhole void in the surface of a reflection grating will serve as a "scatter center" and cause diffuse scatter. This is evident upon inspecting a grating under a bright light: dust, scratches, pinholes etc. are easily visible and bright when looked at from many different angles (hence the diffuse nature of their scattered light).

The presence of spatial frequencies in the groove pattern other than that of the groove spacing d will give rise to constructive interference of the diffracted light at angles that do not follow the grating equation for the nominal groove spacing d, but for different spacings
d' ¹ d.

Until the recent advent of interferometric control of ruling engines, mechanically ruled gratings exhibited secondary spectra, called ghosts, due to slight deviations in the placement of its grooves compared with their ideal locations. Ghosts that are close to and symmetric about the parent diffracted line are called Rowland ghosts, and are due to longer-term periodicities (on the order of millimeters), whereas Lyman ghosts are farther from the parent line and are caused by short-term periodicities (on the order of the groove spacing). Both Rowland and Lyman ghosts appear at angular positions given by the grating equation, but for spatial frequencies other than 1/d (see Section 11.1).

The presence of random (rather than periodic) irregularities in groove placement leads to a faint background between orders, rather than sharp ghosts, whose intensity varies roughly with the inverse square of the wavelength.¹¹⁷ This background is called grass because it resembles blades of grass when observed using green Hg light.

Ghosts and grass are in-plane effects (that is, they are seen in and near the dispersion plane) and lead to interorder scatter. Holographic gratings, whose grooves are formed simultaneously, do not exhibit measurable groove placement irregularities if made properly and therefore generally exhibit lower levels of interorder scatter. With the use of sophisticated interferometric control systems on modern ruling engines, though, this advantage has been reduced when holographic gratings are compared with recently-ruled gratings.

A distribution of groove depths about the nominal groove depth is a natural consequence of the burnishing process and the elasticity of metal coatings (in the case of ruled master gratings) or to local variations in exposure intensities and developing conditions (in the case of holographic master gratings). These variations have been shown to generate a continuous distribution of scattered light that varies with the inverse cube of the wavelength.¹¹⁸

For holographic gratings, care must be taken to suppress all unwanted reflections and scattered light when producing the master grating. Light from optical mounts, for example, may reach the master grating substrate during exposure and leave a weak fringe pattern that causes scattered light when the grating is coated with a metal and illuminated.¹¹⁹ A scratch on a lens in a recording beam can create a "bulls-eye" pattern on the master grating that serves as a scatter center for every replica made from that master. Recording the holographic master in incoherent light can reduce the stray light attributable to recording artifacts.¹²⁰

From the perspective of scattered light, a perfect grating would have a pattern of perfectly placed grooves (no variation in spacing from any groove to the next, and no additional pattern to the grooves leading to spacings d' ¹ d), each of the proper depth (no variation), and the surface irregularities on the grooves would be so much smaller than the wavelength of incident light that these irregularities would have no effect on the diffracted light. Moreover, this perfect grating would have no scratches, digs, blemishes or other visible surface features, and (if holographic) would contain no holographic artifacts of the recording optical system. In this ideal case, we might be forgiven in thinking that all light incident on the grating would leave according to the grating equation (2-1) for the nominal groove spacing d.

A general expression for the light intensity from a perfect grating is given by Sharpe and Irish¹²¹ as

(10-1)

where l is the illumination wavelength, is the monochromator setting (which determines the orientation of the grating: it is not a wavelength), l_B is the blaze wavelength, B is the spectral bandpass of the instrument, and N is the number of grooves under illumination. We see that this equation is generally non-zero, so we must abandon any hope that a perfect grating will have provide no radiant flux anywhere except in its diffraction orders.

Consider a spectrometer aligned so that the detector records the analytical wavelength l in spectral order m. Our definition of instrumental stray light leads to its operational definition as light of either the wrong wavelength l' ¹ l or the wrong spectral order m' ¹ m that reaches the detector; this is generally a problem because most detectors are not wavelength-selective and cannot distinguish between light of wavelength l and light of wavelength l' ¹ l. Also included in our definition of stray light is any light that reaches the detector that does not follow the optical path for which the system was designed, even if this light is of wavelength l and diffraction order m.

Instrumental stray light can be attributed to a number of factors.

Light scattered by the grating, as discussed in Section 10.1 above, may reach the detector and contribute to instrumental stray light. This type of stray light is absent for a "perfect" grating.

Light of the analytical wavelength l is not only diffracted into order m, but into any other orders that propagate. The zero order, which always propagates but is almost always of no value in the instrument, is particularly troublesome. The other diffracted beams are not oriented toward the detector by the grating, but if these beams are reflected by a wall, a mount or another optical component, or if these beams scatter off any interior surfaces in the instrument, some fraction of their intensity may reach the detector and contribute to instrumental stray light. This type of stray light is not absent even for a perfect grating, and requires proper instrumental design (e.g., baffles, light traps, order-sorting filters etc.) to reduce.

Fraunhofer diffraction from the illuminated edges of optical surfaces can be a significant cause of instrumental stray light. All optics in the path should be underfilled (that is, the illuminated area on the surface of each optic should fall within the edges of the optic), with masks or other apertures if necessary. Verrill has suggested that the intensity in the incident beam fall off (from the center) according to a Gaussian function, to avoid an abrupt cut-off of intensity at the edge of the beam.¹²²

Another important contributor to the instrumental stray light in some optical systems is the illumination of optical components downstream from the grating by light of wavelengths in the same diffraction order near the analytical wavelength l (i.e., the wavelength for which the monochromator is tuned). For example, in a Czerny-Turner monochromator (see Figure 6-1), the instrument may be designed so that light of wavelength l underfills the concave mirror after the grating, but light of wavelength l±Dl will diffract at slightly different angles and may impinge upon the edges of the grating: these rays will scatter from these edges and may reach the detector.¹²³

The dispersive quality of diffraction gratings causes each wavelength incident on it to be diffracted into a different set of directions (according to the grating equation), which in turn will illuminate the interior of the optical system.¹²⁴ Light in another order m' ¹ m or at another wavelength l' ¹ l for which m'l' ¹ ml will not be diffracted toward the exit slit, but as in Section 10.2.2, this light may be reflected or scattered by other optical components, mounts or interior walls and directed toward the exit slit.

For certain wavelengths, light may reflect from another surface toward the grating and be rediffracted to the detector (called multiply diffracted light).¹²⁵ For example, in a Czerny-Turner monochromator (see Section 6.2.1), light can be diffracted by the grating back toward the first concave mirror and reflected toward the grating; this light will be diffracted again, and may reach the second mirror and then the exit slit. [Of course, the analogous situation may arise involving the second mirror instead of the first.] These possibilities can be eliminated by proper system design,¹²⁶ filtering,¹²⁷ or the use of masks.¹²⁸

Proper instrument design and the use of baffles and light traps can reduce the effects of these unwanted reflections on instrumental stray light. Care in the analysis of the causes of stray light is especially important for monochromators, since all wavelengths in all diffraction orders (including the zero order) move as the analytical wavelength is scanned, so a wall or mount that does not cause stray light when the grating is in one orientation may be a major cause of stray light when the grating is rotated to another orientation.

Reflection (and diffuse scatter) from interior instrument walls can be reduced by using highly-absorbing paint or coatings on these surfaces, and moving these surfaces as far from the optical train as possible (for this reason, it is generally more difficult to reduce stray light in smaller instruments).

Light can also scatter (or be reflected) by the exit slit.¹²⁹

Tilting the detector element or array slightly, so that any reflections from its surface propagate out of the dispersion plane, can reduce the effects of this cause of stray light.

In analytical instruments, care must be taken to choose sample cells that are properly designed (given the characteristics of the optical path) and made of materials that do not fluoresce; otherwise the cell will be a source of stray light. Moreover, some samples will themselves fluoresce.

For work in the far infrared, the blackbody radiation of all components in the instrument (as well as the instrument walls) will generate a background in the same spectral range as that of the analytical wavelength (e.g., at room temperature (293 K = 20 °C = 68 °F), objects radiate with a spectrum that peaks at c. l = 10 µm).¹³⁰

It is clear that a spectrometer containing a perfect grating (one that exhibits no detectable scattered light) will still have nonzero instrumental stray light. The often-made statement "the grating is the greatest cause of stray light in the system" may well be true, but even a perfect grating must obey the grating equation.

Although a thorough raytrace analysis of an optical system is generally required to model the effects of scattered light, we may approach the case of a simple grating-based instrument conceptually. We consider the case in which the grating is illuminated with monochromatic light; the more general case in which many wavelengths are present can be considered by extension.

A simple case is shown in Figure 10-1. Light of wavelength l enters the instrument through the entrance slit and diverges toward the grating, which diffracts the incident light into a number of orders {m} given by the grating equation (for all orders m for which b given by Eq. (2-1) is real). One of these orders (say m = 1) is the analytical order, that which is designed to pass through the exit slit. All other propagating orders, including the ever-present m = 0 order, are diffracted away from the exit slit and generally strike an interior wall of the instrument, which absorbs some of the energy, reflects some, and scatters some.

Figure 10-1.   A simple grating system. Monochromatic light enters the system through the entrance slit ES and is diffracted by grating G into several orders by the grating; one of these orders (the analytical order) passes through the exit slit XS. Also shown are various rays other than that of the analytical order that may reflect or scatter off interior walls or other optics and reach the exit slit. [For simplicity, focusing elements are not shown.]

Some of the light reaching the interior walls may reflect or scatter directly toward the exit slit, but most of it does not; that which is reflected or scattered in any other direction will eventually reach another interior wall or it will return to the grating (and thereby be diffracted again).

This simple illustration allows us to draw a number of conclusions regarding the relative intensities of the various rays reaching the exit slit. We call E(l,m) the diffraction efficiency of the grating (in this use geometry) at wavelength l in order m; therefore we choose a grating for which E(l,1) is maximal in this use geometry (which will minimize the efficiencies of the other propagating orders: E(l,0), E(l,-1), etc.; see Section 9.12). We further call e the fraction of light incident on an interior wall that is reflected and f the fraction that is scattered in any given direction, and stipulate that both e and f are much less of unity (i.e., we have chosen the interior walls to be highly absorbing). [Generally e and f depend on wavelength and incidence angle, and f on the direction of scatter as well, but for this analysis we ignore these dependencies.]

With these definitions, we can approximate total intensity I (l,1) of the light incident on the grating that reaches the exit slit when the system is tuned to transmits wavelength l in order m = 1 as

I(l,1) =

I0(l) E(l,1) + I0(l) + I0(l) + I0(l) + I0(l) + I0(l) + O(3)

(10-2)

where I₀(l) is the intensity incident on the grating and O(3) represents terms of order three or higher in e and f.

The first term in Eq. (10-2) is the intensity in the analytical wavelength and diffraction order; in an ideal situation, this would be the only light passing through the exit slit, so we may call this quantity the "desired signal". Subtracting this quantity from both sides of Eq. (10-2), dividing by it and collecting terms yields the fractional stray light S(l,1):

S(l,1)

= =

(10-3)

The first term in Eq. (10-3) is the sum, over all other propagating orders, of the fraction of light in those diffracted orders that is reflected by an interior wall to the exit slit, divided by the desired signal; each element in this sum is generally zero unless that order strikes the wall at the correct angle. The second term is the sum, over all other orders, of the fraction of light in those orders that is scattered directly into the exit slit; the elements in this sum are generally nonzero, again divided by the desired signal. Both of these sums are linear in e or f (both << 1) and in E(l,m¹1) (each of which is considerably smaller than E(l,1) since we have chosen the grating to be blazed in the analytical order). The third through fifth sums represent light that is reflected off two walls into the exit slit, or scattered off two walls into the exit slit, or reflected off one wall and scattered off another wall to reach the exit slit – in all three cases, the terms are quadratic in either e or f and can therefore be neglected (under our assumptions).

If we generalize this analysis for a broad-spectrum source, so that wavelengths other than l are diffracted by the grating, then we obtain

S(l,1) =

(10-4)

Note that, in each term, the integral over wavelength is inside the sum, since the upper limit of integration is limited by the grating equation (2-1) for each diffraction order m. Of course, the integration limits may be further restricted if the detector employed is insensitive in certain parts of the spectrum.

From Section 10.3, we can identify some suggestions for designing a grating-based system for which instrumental stray light is reduced.

First, start with a grating as close to the definition of "perfect" in Section 10.1.6 as possible (easier said than done), and blaze it so that E(l,m=1) is as high as possible and
E(l,m¹1) are as low as possible for all other m. Provided other design considerations (e.g., dispersion) are met, it may be advantageous to choose a groove spacing d such that only the first and zero orders propagate; by the analysis in Section 10.3, this will reduce each sum in Eq. (10-2) and Eq. (10-4) to one element each (for m = 0).

Use an entrance slit that is as small as possible, and an exit slit that is as narrow as possible (without being narrower than the image of the entrance slit) and as short as possible (without reducing the signal to an unacceptably low level).

Underfill the grating and all other optical components, preferably by using a beam with a Gaussian intensity distribution. This will ensure that essentially all of the light incident on the grating will be diffracted according to the grating equation (2-1).

Next, design the system to contain as few optical components between the entrance slit and the exit slit (or detector element(s)), for two reasons: each optic is a source of scatter, and each optic will pass less than 100% of the light incident on it – both of these effects will reduce the signal-to-noise (SNR) ratio. Specify optical components with very smooth surfaces (a specification which is more important when a short wavelength is used, since scatter generally varies inversely with wavelength to some power greater than unity¹³¹).

Design the optical system so that the resolution is slit-limited, rather than imaging-limited (see Section 8.3); this will reduce the spectral bandwidth passing through the exit slit (whose width, multiplied by the reciprocal linear dispersion, will equal the entire spectral range passing through the slit; otherwise, the imaging imperfections will allow some neighboring wavelengths outside this range to pass through as well).

The choice of mounting (see chapters 6 and 7) can also affect instrumental stray light. For example, a Czerny-Turner monochromator (with two concave mirrors; see Section 6.2.1) will generally have lower stray light than a comparable Littrow monochromator (with a single concave mirror; see Section 6.2.4) since the former will allow the entrance and exit slits to be located father apart.¹³²

Make the distances between the surfaces as large as possible to take advantage of the inverse square law that governs intensity per unit area as light propagates; an underused idea is to design the optical system in three dimension rather than in a plane – this reduces the volume taken by the optical system and also removes some optics from the dispersion plane (which will reduce stray light due to reflections and multiply diffracted light).

Use order-sorting filters where necessary (or, for echelle systems, cross-dispersers¹³³). Also, the use of high-pass or low-pass filters to eliminate wavelengths emitted by the source but outside the wavelength range of the instrument, and to which the detector is sensitive, will help reduce stray light by preventing the detector from seeing these wavelengths.

It may be advantageous to make the interior walls not only highly absorbing but reflecting rather than scattering (i.e., use a glossy black paint rather than a flat black paint). The rationale for this counterintuitive suggestion is that if all unwanted light cannot be absorbed, it is better to control the direction of the remainder by reflection rather than to allow it to scatter diffusely; controlled reflections from highly-absorbing surfaces (with only a few percent of the light reflected at each surface) will quickly extinguish the unwanted light without adding to diffuse scatter. Of course, care must be taken during design to ensure that there are no direct paths (for one or two reflections) directly to the exit slit; baffles can be helpful when such direct paths are not otherwise avoidable.

Avoid grazing reflections from interior walls, since at grazing angle even materials that absorb at near-normal incidence are generally highly reflecting.

Ensure that the system between the entrance slit and the detector is completely light-tight, meaning that room light cannot reach the detector, and that only light passing through the entrance slit can reach the exit slit.

Finally, hide all mounting brackets, screws, motors, etc. – anything that might scatter or reflect light. Any edges (including the slits) should be painted with a highly absorbing material; this includes the edges of baffles.

While it is always best to reduce instrumental stray light as much as possible, a lock-in detection scheme can be employed to significantly reduce the effects of instrumental stray light. The technique involves chopping (alternately blocking and unblocking) the principal diffraction order and using phase-sensitive detection to retrieve the desired signal.¹³⁴

A useful technique at the breadboard stage (or, if necessary, the product stage) is to operate the instrument in a dark room, replace the exit slit or detector with the eye, and look back into the instrument (taking adequate precautions if intense light is used). What other than the last optical component can be seen? Are there any obvious sources of scatter, or obvious undesirable reflections? What changes as the wavelength is scanned? Before the availability of commercial stray light analysis software, this technique was often used to determine what surfaces needed to be moved, or painted black, or hidden from "the view of the exit slit" by baffles and apertures; even today, optical systems designed with such software should be checked in this manner.