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Spectrometers

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Optical Radiometry for Ocean Climate Measurements

Charles R. McClain, . Bryan Monosmith, in Experimental Methods in the Physical Sciences , 2020

7.4 MERIS

MERIS was an earth-observing spectrometer onboard ESA’s ENVISAT satellite (altitude = 800 km, 10:00 am, descending). Remarkably, MERIS did not show significant performance degradation during its 10 years on-orbit.

The primary objective of MERIS was ocean color applications, but land and atmosphere products are an important part of the MERIS product suite as well. MERIS measured (12-bit digitization) the TOA radiances in 15 discrete bands with center wavelengths from 412 to 900 nm, with bandwidths from 3.75 to 20 nm. MERIS operated as a pushbroom scanner with five distinct cameras, pointing at five different angles in the cross-track direction, resulting in a swath width of 1150 km (FOV = 68°). This resulted in global coverage every 3 days. Each camera had its own CCD, with an imaging area of 520 lines for the spectral dimension and 740 columns in the spatial (cross-track) dimension for each CCD. Gratings are used for spectral dispersion. All MERIS bands can measure at a spatial resolution of 300 m (selected acquisitions only), but in the standard mode, 4 × 4 pixels are averaged to obtain an image with 1.2 km pixel size (global data set).

The calibration of MERIS was based on three solar diffusers: a white diffuser viewed frequently (diffuser-1, every 15 days), another white diffuser viewed rarely (diffuser-2, every 3 months), and a diffuser doped with Erbium. The doped diffuser was used for the spectral calibration (every 3 months), the other two to monitor (and correct) the radiometric sensitivity degradation of the instrument. The degradation of diffuser-2 was kept to a minimum by minimizing its exposure to solar radiation. The unavoidable small degradation due to the solar exposure during the rare diffuser-2 calibration events was modeled based on the degradation measured for diffuser-1 and the different solar exposure times for the two solar diffusers.

The MERIS instrument did not have a tilt capability, which leads to a relatively large loss of coverage due to glint contamination (MERIS equator crossing time was 10:00 am, so glint occurs in the eastern part of the scan) because the MERIS swath is narrow compared to MODIS for instance. The swath of the MERIS follow-on sensor, OLCI, will be shifted to the west to reduce glint contamination (this is accomplished by skewing the camera fields of view to the west side of nadir). This will increase the maximum scan angle for the western part of the scan of OLCI. Due to the pushbroom design, pixel growth for high scan angles is minimal relative to MODIS and SeaWiFS.

Each camera is an independent optical system, each with its own polarization scrambler, grating, filters (inverse filter to improve NIR performance and avoid saturation in the visible and a second-order filter to remove the second-order grating reflection), and CCD (thinned/backside illuminated for greater quantum efficiency). The transition region in the image from one camera to the next has been a challenge regarding calibration consistency, in many cases vertical lines appear in the ocean color products at the camera boundaries. The SNRs achieved vary by spectral band from 575 to 1060 for typical ocean radiances (300 m resolution [5] ). The MERIS dynamic range includes typical cloud radiances without having to use different gain states.

Spectrometry: Definitions and Basic Principles

12.1.b SPECTROMETER MODES; PLATE FACTOR

Spectrometer configurations to which Eq. (12.1.1) applies include both the slit spectrometer and a slitless mode where a prism or grating is placed in front of a telescope. In the case of a slit spectrometer a separate collimator provides a collimated beam to the dispersing element and f is the focal length of the camera optics. Fabry–Perot spectrometers also have separate collimator and camera optics. The type of slitless mode noted here is often called the objective mode; in this case f is the focal length of the telescope.

Configurations to which Eq. (12.1.2) applies include the slitless mode where a disperser, usually a grating or grism, is placed in a converging telescope beam ahead of the focal surface, either prime or Cassegrain. The grism is a combination of a grating and prism, with the grating as the main dispersing element. This type of slitless mode has been called the nonobjective mode by Hoag (see Hoag and Schroeder (1970) ). Equation (12.1.2) also applies to the so-called Monk-Gillieson spectrometer, in which a mirror preceding the grating is both collimator and camera.

For any of the spectrometer modes noted here it is convenient to define P, the reciprocal linear dispersion or plate factor, where

for the modes in Figs. 12.2 and 12.3 , respectively. The units of P are usually given as Angstroms per millimeter or nanometer per millimeter.

THE USE OF THE LIQUID SCINTILLATION SPECTROMETER FOR MEASURING NADH AND FMN BY THE PHOTOBACTERIUM LUCIFERASE AND ATP BY THE FIREFLY LUCIFERASE

Use of cooled spectrometers for the assays

Cooled spectrometers may be used in this assay provided the vial and contents are fully equilibrated at a desired temperature. The following procedure is useful to ensure adequate temperature control. A scintillation vial is filled with distilled water, and the assay buffers are dispensed into a 5 ml glass or plastic tube which is placed in the vial. The vial and contents are equilibrated in a constant temperature bath and then the bioluminescent reaction is initiated. This micro-environment for the reaction provides a constant temperature for at least three minutes, even in spectrometers operating at −5°.

CRYSTAL DIFFRACTION SPECTROSCOPY OF NUCLEAR γ-RAYS

3.2.2 The line focus transmission spectrometer

This type of spectrometer makes use of an extended source and focuses the diffracted radiation, transmitted through the bent crystal, to a point on the focusing circle.

The spectrometer was first used by Cauchois 4 and since that time the original design has been improved considerably 5 . A Cauchois spectrometer with a two-metre focal length has been constructed by Beckman 28 and another by a group at Livermore. Recently a 7.0-metre Cauchois spectrometer has been constructed at M.I.T. 9a .

The focusing geometry of the Cauchois spectrometer is identical to that of the line source transmission spectrometer except that the source and detector are interchanged. Gamma-rays of different energy are focused to different points on the focal circle, the source and crystal remaining stationary. The energy spectrum is detected with a photographic plate positioned on the focal circle so that large portions of the spectrum are recorded simultaneously. Because of its geometric simplicity and freedom from mechanical motion, this type of spectrometer has great practical usefulness and potentially has the mechanical stability necessary for very precise γ-ray measurement.

As may be inferred from § 2 , the transmission efficiency of the Cauchois spectrometer is less than that of the line source spectrometer by the ratio of the crystal diffraction angular line width ωM’ to the angle subtended at the source by the bent crystal. This ratio is about 1 : 200 for the two-metre curved crystal spectrometers described. However, the low efficiency of the Cauchois spectrometer is offset by its ability to record extended regions of the γ-ray energy spectrum simultaneously. The spectrometer is particularly suited to the measurement of γ-rays below 1 MeV. The energy range of the Cauchois spectrometer has recently been extended to energies above 2 MeV by groups working at Livermore 8 and at M.I.T. 9b . At high energies poor transmission efficiency of the bent crystal and poor γ-ray detection efficiency of photographic emulsions make such measurements difficult.

X-ray Fluorescence Applications for the Study and Conservation of Cultural Heritage

2.2 Portable spectrometers

These spectrometers are designed for in situ non-destructive investigations; the simplification of the system, aimed at reducing weight and dimensions, results in relatively poor precision and detection limits. Usually the primary radiation source is an X-ray tube; if portability is the main requirement, radioisotopic sources can also be used, though with further deterioration of sensitivity. Also among X-ray tubes, one may have different options, obviously affecting the detection limits: low-weight, low-power tubes usually work at relatively low voltages and are therefore unable to excite the K-lines of elements like Ag, Sn, Sb; high-power tubes are heavier and more complex due to the shielding and the cooling system but offer a wider detection range. Table 1 shows typical detection limits for portable spectrometers equipped with X-ray tubes; the one of ref. 19 also has a radioisotopic source, the concerned detection limit for Sn is that of the K line.

Table 1 . Detection limits of portable XRF spectrometers [weight %].

Matrix: Cu alloys

Sample: presumably calibration std.

X-ray tube operated at 30 kV + Am-241 source

Matrix: Cu alloys

Sample: drill shavings

X-ray tube operated at 35 and 50 kV

Matrix: Cu alloys

Sample: surface of the object, with no abrasion

X-ray tube operated at 60 kV

As regards detection, Si(Li) and intrinsic planar Ge detectors, cooled by liquid nitrogen, are well established; Figures 4 and 5 show the layout of two portable spectrometers using an X-ray tube and a radioisotopic source, respectively. Peltier-cooled semiconductor detectors have recently achieved comparable energy resolution and will soon be improved in dimensions and intrinsic efficiency. A particular use of portable spectrometers is compositional mapping of the object’s surface [ 31 ], which clearly relies on large numbers of measurements. For these applications the support system, which has to be easily transportable and provided with the requisite flexibility, becomes a further important component of the XRF spectrometer; Figure 6 shows the layout of the support used by the ENEA research group in Rome, Italy.

Figure 4 . Layout of a portable XRF spectrometer using an X-ray tube as excitation source.

Figure 5 . Layout of a portable XRF spectrometer using a radioisotopic souce for excitation.

Figure 6 . Support system for in situ investigations with the portable spectrometer.

Radiation spectroscopy

B.3 Disk chopper spectrometer

A DCS is an instrument that uses time-of-flight information of neutrons to determine the inelastic scattering spectrum of the sample. Its working principle is fairly simple: Mono-energetic neutrons are allowed to pass through the sample and the scattered neutrons are detected through a large array of detectors. The time of arrival of the neutrons is used to determine the type of scatterings they have gone through. The basic idea is that the neutrons that gain energy during the scattering process arrive earliest. They are followed by the elastically scattered neutrons. The neutrons that lose energy during collisions arrive latest. This implies that the timing information can give insight into the dynamics of scattering.

The design principle of a DCS is shown in Figure 12.3.5 . Such an instrument is generally designed to work on a nuclear reactor where high-intensity beams of neutrons are available. The experiment is performed in neutron bursts. The reason is that the precise time or arrival of neutrons at the sample is required for proper time-of-flight measurements. Since neutron sources produce neutrons continuously, a DCS uses a chopper assembly to produce burst of neutrons, hence the name disk chopper spectrometer. A typical DCS has about 1000 neutron detectors for time-of-flight measurements. Since the detectors are used for timing measurements, their timing resolution is of high importance.

Figure 12.3.5 . Design principle of a DCS.

An important practical consideration for disk choppers and similar instruments is that they should have proper beam-stop assemblies. The reason is that a typical neutron source used in such an experiment produces an intense beam of neutrons. Not all of these neutrons get reflected from the sample. In fact, a good fraction of these neutrons simply pass through the sample without undergoing any interaction. These neutrons must be stopped for safety reasons. In Figure 12.3.5 such a beam-stopping assembly is symbolically represented by a black circle.

Atomic, Molecular, and Optical Physics: Atoms and Molecules

18.2.5 Optics Design

All spectrometers make use of the constructive interference of light by dividing the wavefront (e.g., gratings), by dividing the amplitude of the wavefront (e.g., Fabry–Perots), or by decomposing the wavefront into orthogonal polarization components (e.g. Lyots). The design of a spectrometer is in essence a competition between a dispersing element that deviates light into different angles according to wavelength, and optics that focus the light at the detector with minimum aberration. Two lenses in the optical path are normally sufficient to counteract the dominant aberrations [ 12 ]. In most cases, the dispersing element must be illuminated with parallel (collimated) light. Hence, the acceptance angle (i.e., f/ratio) of the collimating optic must be the same as that of the primary concentrating optics to transfer all the light. If the collimated beam is too small, the Jacquinot advantage of the spectrometer is reduced [ 27, 28 ]. If the collimated beam is too large, light is lost from the optical system.

It is important to realize that all optical systems lose light at surfaces along the optical path. On occasion, the scattered light will simply leave the system. More often, the stray light finds its way back into the optical path to be imaged at the detector as a spurious “ghost” signal that can be difficult to distinguish from real signals. Scattered light can also dramatically increase the background signal at the detector, thereby reducing contrast and setting a limit on the sensitivity that can be reached within a given exposure time. The manner in which this happens is specific to the instrument. In later sections, we describe a few of the ghost families that occur within gratings and Fabry–Perot spectrometers. Antireflective coatings (including newly developed coatings whose index of refraction increases smoothly through their thickness), aperture stops, baffles, and ingenious optical designs are part of the arsenal to combat these anomalies.

In later sections, we describe diffraction gratings (18.4) , interference filters ( 18.5.1 ), Fabry–Perot (18.5.2) and Fourier Transform spectrometers (18.6) . We also discuss recent technological developments for selecting a bandpass whose central wavelength can be tuned over a wide spectral range. The most promising of these developments are those which utilise anisotropic media, particularly the Lyot filter ( 18.5.3 ) and the acoustooptic filter ( 18.5.4 ).

Plane Grating Spectrometers

15.5.d ECHELLE SPECTROMETER CONFIGURATIONS

Echelle spectrometers have been built in many different configurations, but each is a variant of one of two choices of angles of the chief ray relative to the echelle. One choice is the so-called in-plane design in which γ = 0. In this design the collimator and camera beams are separated by choosing α > β. The other choice is the off-plane design with γ ≠ 0. Choosing α = β gives a quasi-Littrow design, hence no anamorphic magnification in the direction of echelle dispersion. Figures 15.11 and 15.12 show off-plane and in-plane schematic layouts, respectively. A summary of the characteristics and modes for selected echelle spectrometers is given in Table 15.5 .

Table 15.5 . Characteristics and Modes of Selected Echelle Spectrometers

Reference Fe Ni Zn Pb Ag, Sn, Sb Notes
Hall et al. [ 19 ] 0.005 0.03 0.1 0.03 (AgK), 0.01 (AgL), 0.1 (SnK), 1.5 (SnL)
Lutz et al. [ 23 ] 0.05 0.01 0.5 0.006÷0.01
Ferretti et al. [ 31 ] 0.5 0.7÷1.0 0.03÷0.07
R-value W (mm) Mode Cross-Disperser
In-Plane Designs
HIRES a 2.8 1260 1 Gratings
Hectochelle b 2.1 840 filter
HROS c immersed echelle 2.0 410 2 Prisms
CARCES d 2.0 410 1 Prisms
Off-Plane Designs
HDS e 2.8 840 1 Gratings
HRS f white-pupil 3.8 840 1 Gratings

A consequence of nonzero γ in the off-plane design is that the entrance slit is reimaged by the spectrometer optics with a tilt, as discussed in Section 14.1 , with the tilt proportional to γ and the slope given by Eq. (14.1.9) . Substituting A from Table 15.4 into Eq. (14.1.9) , the slope or tilt of the reimaged slit is, to a good approximation, dβ/dγ = 2 tan γ tan δ. This tilt is of little consequence for a single point source at the entrance slit, but must be taken into account in data reduction for a long slit.

The choices for collimator and camera optics are about as varied as the number of operating echelle spectrometers; examples of some of these choices are listed in Table 15.6 . Details on the designs of these spectrometers, and versions based on a modified Czerny-Turner arrangement, are found in the references at the end of the chapter.

Table 15.6 . Optics of Selected Echelle Spectrometers a

Focus Collimator Camera
HIRES Nasmyth f/14 Tilted Sphere Catadioptric
Hectochelle Bench b Off-axis Paraboloid Catadioptric
HROS Cassegrain f/16 Paraboloid Catadioptric
CARCES Nasmyth f/10 Paraboloid Schmidt
HDS Nasmyth f/13 Paraboloid Catadioptric
HRS Bench b Off-axis Paraboloid All-Refractive

One optical layout of echelle spectrometers not yet discussed is the so-called white-pupil design. In this design additional optics between the echelle and the cross-disperser in mode (1) reimage the echelle onto the cross-disperser with unit magnification. Thus the beam size at the prism or grating is the same as that of a monochromatic beam emerging from the echelle and the extra cross-disperser size needed to capture the dispersed light in each echelle order in an in-plane design is not required. Examples of designs that incorporate the white-pupil concept are the UV-Visual Echelle Spectrograph (UVES) for the ESO Very Large Telescope (VLT) and the fiber-fed High Resolution Spectrograph (HRS) for the Hobby-Eberly Telescope designed by Tull (1994) . Both of these instruments use an R-4 echelle to get the largest possible R ϕ ϕ product from existing echelles. A schematic layout of a white-pupil design is shown in Fig. 15.14 .

Fig. 15.14 . Schematic layout of intermediate optics for white-pupil spectrometer design. Dispersed light from the echelle (E) is recollimated by the M1, M2 mirror pair and the pupil at the echelle is reimaged at the white pupil (WP).

A final approach to increasing the R ϕ product is to use an immersed echelle, as discussed in Section 13.3 . This is the choice for the high-resolution optical spectrograph (HROS) for a Gemini 8-m Telescope.

Spectrophotometry

4.2.4.1 Spectral Multiplexing

Consider an FTS instrument using a source with spectral radiance Lσ (W/cm 2 /sr/cm − 1 ) and optical throughput πa 2 Ω, where a is the beam radius and Ω is the solid angle of accepted rays in the interferometer, and interferometer modulation efficiency η. Typically, in the mid-infrared spectral region, the SNR of an FTS instrument using a moderate temperature (approximately 1200 K) thermal source is limited by noise in the detector rather than in the source. In this case, the SNR for a given spectral interval δσ and averaging time Δt is given by

where NEP is the noise equivalent power of the detector (W/Hz 1/2 ). The key feature of this otherwise generic expression is that for an FTS, all of the spectral bins are averaged for time Δt simultaneously, as opposed to a dispersive instrument where the averaging is done sequentially, and each interval is only observed for time Δt/N, where N is the number of spectral bins. Thus, the FTS in principle has a SNR advantage compared to a dispersive instrument given by the square root of the number of spectral bins in the measurement. This is sometimes called the multiplexing advantage or Fellgett’s advantage [9] .

Equation (4.17) assumes that the beam solid angle is small enough that self-apodization effects can be ignored and the spectral resolution is only limited by the OPD in the FTS. This is often true in practice as the limiting aperture for the source is typically set to smaller than required for a given resolution because of the need to limit the flux on the detector or because of sample or detector size limitations. If the FTS is operated at the limit of its spectral resolving power, then we can use Eq. (4.11) to substitute for Ω in Eq. (4.17) and arrive at

where the SNR is now seen to be proportional to resolution squared, as in the case of a dispersive instrument where both the entrance and exit slits are reduced in width to achieve finer spectral resolution. This expression also indicates the importance of using largest possible value for δσ, which does not cause significant spectral errors due to convolution of the sample or reference spectra with the ILS. A typical rule of thumb is that δσ should be equal to 1/5 of the smallest line width of interest in the spectrum [3] .

The multiplexing advantage of an FTS relative to a dispersive spectrometer of similar wavenumber coverage and resolution assumes that both instruments are using single-element detectors. Some dispersive spectrometers make use of one-dimensional array detectors configured to average over multiple spectral bins at the same time, thus achieving the same advantage as a single-detector FTS. Of course, FTS instruments can also use multiple detectors, in particular two-dimensional arrays to achieve imaging capability, or enhanced spectral resolution. Many different designs have been realized for both types of instruments that trade-off spectral and spatial degrees of freedom for various applications.

In general, there are other significant sources of noise in addition to thermally induced electrical fluctuations in the detector. In particular, in the near-infrared, visible, and near-ultraviolet spectral region, where low-noise Si or InGaAs photoconductive detectors are available, photon shot noise in the source may be the dominant contributor. The denominator of Eq. (4.17) would then be proportional to (Lσ) 1/2 for an FTS instrument but only (Lσ/N) 1/2 for a dispersive instrument. The factors of 1/N 1/2 in the numerator and denominator would cancel for the dispersive case, and there would be no difference in SNR between the FTS and dispersive spectrometers. In this case, a dispersive instrument with an array detector used for spectral averaging would have a SNR advantage of N 1/2 compared to the single-element FTS.

Another limiting case occurs when the noise in the system is dominated by fluctuations in overall source output. This can be caused for instance by instability in the source power supply or mechanical vibrations. In this case, the noise per spectral bin is proportional to Lσ for an FTS but only Lσ/N for a dispersive spectrometer, and the dispersive design SNR wins by a factor of N 1/2 even for a single-detector element. These SNR considerations, in addition to the difficulty and expense of making an interferometer work well at very short wavelengths, explain the predominance of dispersive spectrometers over FTS instruments in use for the 250–2500 nm spectral region. However, at longer infrared wavelengths for spectrophotometry over a wide spectral range, the FTS advantage from Eq. (4.17) does apply and is realized in superior performance in practice as long as other sources of error ( Section 4.3 ) are kept under control.

Measurement of the longitudinal phase space at the Photo Injector Test Facility at DESY Zeuthen

J. Bähr, . F. Stephan, in Free Electron Lasers 2003 , 2004

2 Momentum distribution

A spectrometer dipole and a YAG screen are used for the measurement of the momentum distribution of the electron bunch. The electrons gain different energies depending on the time when the laser hits the cathode. The latter can be expressed in terms of a phase between laser pulse and accelerating field (SP phase). The maximum mean momentum of an electron bunch is (4.72 ± 0.03) MeV/c, the corresponding SP phase is choosen to be 0°. According to simulation this corresponds to a gun gradient of (41.8 ± 0.3) MV/m and a RF power of (3.15 ± 0.05) MW.

The smallest momentum spread of (33 ± 7) keV/c is observed at a SP phase of 10° and an electron bunch charge of 1 nC (see Fig. 1 ).

Fig. 1 . RMS momentum spread of the electron bunch as a function of SP phase for a gradient of 41.8 MV/m compared to simulation results (dashed line) [ 2 ].

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