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How Does a Spectrometer Work? Principles & Optics


Spectrometer component diagram
A spectrometer consists of (1) an entrance slit, (2) a diffraction grating or prism, (3) a detector, (4) routing optics, and (5) higher order filters

Optical spectrometers take light and separate it by wavelength to create a spectra which shows the relative intensity of each. This basic principle has a wide range of applications and uses; optical spectrometers are the most common type of spectrometer.

Broadly speaking, all optical spectrometers consist of an entrance slit, a diffraction grating or prism, a detector, and routing optics. The entrance slit allows light into the spectrometer, where a system of mirrors or lenses routes it first onto a diffraction grating or prism, and then onto the detector. The grating or prism splits the light into its constituent wavelength components, and the detector records the light intensity as a function of wavelength. If the spectrometer has a large spectral range, it may also have filters to stop higher order light from reaching the sensor. Most optical spectrometers operate over the UV, visible, and infrared (or near-infrared) regions of the electromagnetic spectrum.

Spectrometers can be designed and built using a number of different optical configurations. These include the Littrow configuration, the Ebert-Fastie configuration, the Czerny-Turner configuration, and the concave aberration-corrected holographic grating configuration. Careful choice of components and configuration can avoid aberrations, which result in distorted or blurred spectra.

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Spectrometer Components


Spectrometer components
Optical spectrometer components: entrance slit (1), diffraction grating or prism (2), a detector (3), routing optics (4), higher order filters (5)

Entrance slit

Light enters the optical spectrometer via the entrance slit. Similarly to how the aperture size of a camera affects the brightness and resolution of the photos it takes, the width of the spectrometer entrance slit determines both its ability to measure in low-light conditions and the maximum spectral resolution that can be achieved. These two characteristics have to be balanced against each other as one always comes at the expense of the other.

A wide entrance slit allows a lot of light to enter the spectrometer, which allows fainter sources to be measured but reduces the spectral resolution of the system. Conversely, a narrow entrance slit can increase the spectral resolution, but at the cost of signal intensity.

Larger optical spectrometers may have a controllable slit width, while more compact devices like the Ossila Optical Spectrometer (which has an entrance slit width of 25 μm) usually have a fixed width.

Diffraction grating or prism

The optical diffraction grating is the component that splits the light into its constituent wavelength components. There are a number of different types of gratings including transmissive, reflective, ruled, and holographic. Each has their own advantages and disadvantages when compared to one another, and there is no one superior design.

The design of the grating determines to what degree the light is spread out. Much like the slit, there is a trade-off between resolution, range, and signal strength.

Diffraction gratings can be described by the equation:

Where d is the grating spacing, θm is the diffraction angle of the mth diffraction order, θi is the angle of incidence, and λ is the wavelength of the light. It can be seen from this that decreasing the grating spacing increases the angular range of diffraction. Therefore, a smaller range of wavelengths will reach the detector, with reduced signal strength, but with higher resolution. Conversely, increasing the grating spacing gives a bigger range of wavelengths but with lower resolution.

The grating spacing is usually quoted in terms of groove density, which is equal to 1/d and is given in units of grooves mm-1.

In some spectrometers, the diffraction grating can be rotated to allow different wavelengths to hit the detector and the acquisition window to be selected according to need. Similarly, some spectrometers have multiple gratings with different groove densities, which can be selected between.

Some designs of optical spectrometer use a prism as the dispersive element in place of a diffraction grating, but due to the higher cost of prisms and the lower resolution images that they give, this is not common.

Detector

The optical detector records the intensity of the light that reaches it as a function of its wavelength. Spectrometer detectors consist of a row of light sensitive pixels, each of which corresponds to a particular wavelength. Each pixel generates an electrical signal of intensity proportional to how much light is falling on it.

Charged-coupled devices (CCDs) are the detector of choice for spectrometers due to their high dynamic range and uniform pixel response. To reduce unwanted noise in the spectra, CCDs are usually cooled to combat dark current signals.

Routing optics

Internal routing optics direct the light from the entrance slit onto the diffraction grating or prism, and then onto the detector.

Curved mirrors are generally preferred over lenses as they introduce fewer image aberrations. There are many possible configurations for the optics (e.g. Fastie-Ebert, Czerny-Turner) which each have relative advantages and disadvantages regarding optical aberrations, stray light, and size.

Higher order filters

If the wavelength detection range of an optical spectrometer spans more than one diffraction order, a filter may be necessary to partially cover the detector and block higher order light from reaching the sensor.

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Spectrometer Optics


Littrow configuration

The Littrow configuration is the simplest design utilising a plane reflection grating. Although it is not commonly found in spectrometers today, it is still used to characterise diffraction gratings (see 'Grating blaze wavelength').

This configuration consists simply of a spherical mirror and a plane grating. The light enters the spectrometer through an entrance slit and is collimated by the mirror. The reflected light is then incident on the diffraction grating, as is shown below. The diffraction order of interest is directed back towards the mirror, where it is reflected towards the exit slit, which is spatially very close to the entrance slit.

Schematic of the Littrow configuration

Although this configuration has a very high wavelength resolution, the risk of stray light, internal reflections and multiple dispersions is significant.

Ebert-Fastie configuration

The Ebert spectrograph was first described by Hermann Ebert in 1889. After many decades of relative obscurity, the design was resurrected by William G. Fastie in 1952, who included curved slits to remove astigmatism (see 'Aberrations present in spectrometers') and reduce wavelength errors at the exit slit [1].

The Ebert-Fastie (sometimes referred to as Fastie-Ebert) configuration is composed of a large spherical mirror and a single plane diffraction grating. The light enters the spectrometer through the circularly curved entrance slit and is incident on one portion of the mirror, as illustrated below. The mirror directs the now-collimated light onto the plane grating and the diffracted light is then reflected from a second, separate portion of the mirror. The light reflected from the mirror is then focused through the circularly curved exit slit, after which point it is collected by the detector. Here, the angle between the incident and reflected rays, a, is the same for both reflections from the mirror [2].

Limitations of the Ebert-Fastie configuration include the risk of light being reflected directly from the mirror towards the exit slit without being diffracted and of multiple diffractions.

Schematic of the Ebert-Fastie configuration

Czerny-Turner configuration

Quite similar in design to the Ebert-Fastie configuration, the most common design used in spectrometers today is the Czerny-Turner configuration. First described in 1930 by M. Czerny and A.F. Turner, the design has since been altered to remove and reduce certain aberrations and has several advantages over the Ebert-Fastie configuration [2].

Instead of a single large spherical mirror, the Czerny-Turner configuration uses two smaller spherical mirrors, as depicted below. Here, the light enters the spectrometer through the entrance slit and is reflected from the first spherical mirror onto a plane diffraction grating. The dispersed light is then reflected by the second mirror and is collected by the detector on the other side of the exit slit.

In Czerny-Turner configurations, the mirrors don't have to be the same size, or placed the same distance from the slits or the diffraction grating. They can even have different radii of curvature. In addition, the reflection angles for the two mirrors, a and b, do not have to be equal and the grating can even be "off-axis", i.e. the distances xa and xb can be different [3].

Schematic of the Czerny-Turner configuration

This configuration does not allow light to be directly reflected from the entrance to the exit slits, which reduces unwanted reflections and multiple dispersions compared to the Ebert-Fastie configuration. The asymmetrical design allows for better coma correction and a flattened spectral field compared to the symmetrical version (see aberrations).

It is possible to fabricate holographic gratings to include physical aberrations that cancel out all optical aberrations at a particular wavelength and drastically reduce them for a large range of wavelengths [4].

Concave aberration-corrected holographic grating configuration

Instead of a plane grating, it is also possible to fabricate concave holographic gratings that correct for optical aberrations. In this case, the diffraction grating is the only optic needed: the light enters the spectrometer through the entrance slit and is diffracted by the grating, which focuses the light onto the exit slit.

Schematic of a concave aberration-corrected holographic grating configuration

As only a grating is needed for this configuration, errors due to multiple reflections, imperfect mirrors, and thermal effects are reduced. A higher signal-to-noise ratio is also possible due to decreased reflection losses. This design is simple to align, inexpensive and compact.

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Spectrometer Aberrations

There are several different types of aberration present in spectrometers that can cause images and spectra to be distorted or blurred. It is possible to significantly reduce the effect of these aberrations using specific components and configurations. In general, mirrors (and gratings) are used for collimation instead of lenses as they result in a much lower degree of aberration. However, certain aberrations can still arise.

Spherical aberration

Spherical aberration arises when rays are reflected from a spherical surface; for example, a spherical mirror. When collimated light rays are incident far from the optical axis (the centre) of the mirror, the reflected rays are focused closer to the mirror surface than those that were incident on or near the optical axis. This is illustrated in the figure below (where it should be noted that the different colours are simply for ease of viewing and do not correspond to different wavelengths/colours of light).

Spherical aberration can be avoided by using parabolic mirrors; however, these are more difficult to make and therefore more expensive.

Illustration of parallel rays affected by spherical aberration from a spherical mirror

Coma

A point source - for example, a star - as viewed through a telescope with comatic aberration will appear to have a comet-like tail; hence, the term "coma". This is due to the fact that when parallel rays are incident at an angle to the optical axis of a spherical mirror, the reflected rays do not have a common focus. This is illustrated in the left-hand figure below (where it should be noted that the different colours are for ease of viewing and do not correspond to different wavelengths/colours of the rays) and results in a blurred image. In a spectrum, coma appears as an increased signal on one side of a spectral feature, i.e. an asymmetrical broadening, as illustrated in the right-hand side of the figure below.

Illustration of parallel rays (left-hand figure) and an example spectrum (right-hand figure) affected by comatic aberration (coma) from a spherical mirror

In Czerny-Turner spectrometers, it is possible to completely eliminate coma at one wavelength, and using a concave aberration-corrected holographic grating configuration, it can be eliminated at a wide range of wavelengths.

Astigmatism

Astigmatism also occurs during the off-axis illumination of a spherical mirror. Here, the rays in the horizontal (transverse) and vertical (sagittal) planes are focused at different points. This is illustrated in the figure below, where it can be seen that the rays in the horizontal plane are focused closer to the mirror than in the vertical plane. This effect results in an elongation of the image and can lead to a loss in spatial resolution and signal-to-noise ratio in a spectrometer.

Effect of astigmatism: (a) Shows an off-axis parallel beam being reflected by a spherical mirror, parts (b) and (c) show the focus in the horizontal plane and the vertical plane respectively, and in (d), it can be seen that these foci occur at different distances from the mirror

Astigmatism can be avoided by using curved slits, as in the Ebert-Fastie configuration, or an aberration-corrected grating [1]. It can also be removed by replacing spherical mirrors with toroidal ones; however, these are still affected by coma and spherical aberration.

Spectrometer Specifications Explained


Wavelength range

The wavelength range is the spectral range over which the spectrometer works, and is dependent on both the grating or prism used and the arrangement of the components (grating or prism, mirrors or lenses, and detector) within the spectrometer. For optical spectrometers, the wavelength range includes the visible region of the spectrum and parts of the UV and NIR region.

Grating blaze wavelength

The grating blaze wavelength is a specification that applies to blazed diffraction gratings, which are commonly used in spectrometers and have a 'sawtooth' profile. In this case, the grating spacing, d, is defined by the width of each triangular 'tooth' (step) as shown below. The tilt angle of each step relative to the grating surface is known as the blaze angle, θ.

In spectrometers, blazed reflection gratings are often characterised using the "Littrow configuration". In this case, the angle of the incident light and the mth order of diffracted light are the same and are equal to θ. The wavelength of this light is known as the blaze wavelength, λ, and is the wavelength at which the grating has maximum efficiency.

Spectrometer blazed (sawtooth) diffraction grating
Blazed (sawtooth) diffraction grating, with grating spacing d, blaze angle θ, and blaze wavelength λ.

Resolution

The resolution of a spectrometer is the minimum wavelength difference that can be resolved. In other words, if two spectral lines exist very close together, as shown below, the resolution would be the minimum separation between them that allows the system to distinguish them as two separate lines. In (a), it can be seen there is a distinct separation between the lines, which is greater than the resolution of the system. In (b), the separation is equal to the resolution, and in (c), the lines are closer together than the resolution and therefore cannot be separately distinguished.

Definition of spectral resolution
Definition of spectral resolution. In (a), the two spectral lines are easily resolvable, in (b) they are at the resolution limit, and in (c) they are unresolvable.

Often spectral resolution is quoted in terms of the full-width at half maximum (FWHM) the spectrometer would measure for a truly monochromatic source. For example, this could be an atomic spectral line, such as from a mercury or argon lamp, or a narrow-linewidth laser.

Dark noise

In a spectrometer, when photons land on a pixel of the detector, electron-hole pairs are created, with their number proportional to the number of incident photons. This charge is converted into a voltage and then a digital signal, which is displayed as a spectrum. However, electron-hole pairs can also be generated by thermal effects. These "dark" electron-hole pairs are indistinguishable from those generated by photons and so will affect the resultant spectrum. These unwanted signals are therefore known as "dark noise".

Dark noise is dependent on the integration time used and can be reduced by cooling the detector.

Signal-to-noise ratio

In order for a signal to be useful, it has to be significantly higher than the noise level. Therefore, an important property of spectrometers is the signal-to-noise ratio (SNR or S/N). This is a measure of the sensitivity of the spectrometer and compares the intensity of the signal, i.e. the spectral feature(s) you are looking at, to the intensity of the background noise.

SNR is often defined as the maximum signal height divided by the root mean square (RMS) of the noise in the background signal. It can be expressed as a ratio (e.g. 500:1) or in decibels (dB). If the ratio is greater than 1:1 (0 dB), the signal is greater than the noise.

Stray light

Stray light is a measure of the light collected by the detector that is of a different wavelength to the expected value for that pixel. This occurs because pixels can only measure the intensity of the incident light and cannot distinguish wavelength. Sources of stray light include (but are not limited to) unwanted reflections or scattering from lenses, imperfect mirrors or optical components; leakage into the spectrometer from its surroundings; and re-entrant spectra.

Re-entrant spectra arise from light that is diffracted by the grating more than once. For example, light that has already been diffracted can be reflected by optical components, such as the detector or the entrance slit, back onto the diffraction grating, where it is diffracted a second time. If this light reaches the detector, it will produce an unwanted signal.

Stray light can also arise from imperfections in the diffraction grating. This can be minimised by using holographic gratings, which are fabricated using optical techniques and have a sinusoidal profile, rather than blazed gratings, which are fabricated using mechanical techniques.

  

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References


  1. W.G. Fastie, "Ebert Spectrometer Reflections", Physics Today 44(1), 37 (1991)
  2. W. Neumann, "Fundamentals of Dispersive Optical Spectroscopy Systems", SPIE (2014)
  3. G. Wünsch, A. Wennemer, J.W. McLaren, "On the design and performance of the Czerny-Turner monochromator in ICP-AES", Spectrochimica Acta Part B: Atomic Spectroscopy, 46(11), 1517-1531 (1991)
  4. A. Thevenon, et al., "Aberration-Corrected Plane Gratings", Proceedings of SPIE, 0815, 136-145 (1987)

Contributing Authors


  • David Coles
  • Kirsty McGhee
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