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Designed to Disperse Easy modelling of prism and grating spectrometers and more Geoff Adams, Thomas Thöniß, and Christoph Gerhard
Optical emission spectroscopy is a widely recognised and well-established tool in a number of different branches of science. In this contribution, simple modelling of imaging prism and grating spectrometers using optical design software as well as a comparison of both principles are presented. Further, basic considerations on the design of such spectrometers and a transfer lens for imaging a given light source onto the spectrometer are presented. Optical emission spectroscopy (OES) is one of the most important and reliable methods for quantitative analysis of elemental and material compositions. For instance, it has become a powerful tool in the evaluation of starlight in astronomy [1] or specific characteristics in biophysics [2]. In order to undertake material analysis of non light-emitting objects, optical emission can be achieved by laser-induced breakdown spectroscopy (LIBS) [3]. For example, this technique allows the detection of heavy metals in environmental samples [4] or minor element concentrations in food [5] by analysing the resulting laser-induced plasma and debris plume. Another novel method is the use of atmospheric pressure plasmas for radiation excitation [6]. When characterising plasmas, where a non-invasive measurement process is required, OES is the evaluation and diagnostic method of choice [7], since other techniques typically cannot be applied due to a limited access to the plasma volume. Given this background, we look at some basic principles of spectroscopic systems, and highlight some simple software tools for modelling the system.
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Fig. 1 Calculation of key geometric parameters.
Basic considerations The first task is to collect as much light as possible from the plasma and supply it to the spectroscope slit. Typically a transfer lens or mirror system is used according to the waveband. The basic geometric design for this sub-system must take into account (where the values in brackets are those for an exemplar OES spectrometer): n Object size: given by the size of the plasma volume (1 mm). n Image size: given by the height of the entrance slit of the spectrometer (0.5 mm). n Image side numerical aperture (NA) of the transfer lens: should match the entrance NA of the spectrometer (0.15). This last point is vital in order to achieve high light efficiency and to minimise stray light which could cause a spurious signal.
Two field parameters and one aperture parameter are known. In order to fix the basic properties of the transfer lens design, one last parameter, to specify the conjugates, is required. This could be one of the following: n the lens focal length (if using a specific lens), n the total track (fixed distance from investigated volume element to spectrometer), n the object distance or n the image distance and will be chosen according to specifics of the task and equipment. Using basic geometric optics equations, these will determine the size, power and location of the lens needed. Such calculations could be done by hand, but we have used an elegant Android lens calculator app, PreDesigner, shown in Figure 1 – the parameter val-
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Optical Design
dence αd is given by
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αd = 0.5 . (Dmin – A).
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Dmin, αd, αTIR in deg.
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1.65 1.7 1.75 Index of refraction
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Fig. 2 Angle of minimum deviation Dmin, angle of incidence αd and angle of total internal reflexion αTIR vs. index of refraction n.
ues were exaggerated to give a nice diagram. PreDesigner offers a wide range of key parameters and has a touch editable ray diagram; useful for understanding and evaluating ‘what if ’s’ involved.
Modelling of prism spectrometers A prism spectrometer typically consists of an entrance slit, a collimator, a prism and a lens for focussing the image on the detector. The wavelength-dependent variation in refractive index within the prism, i.e. the material-specific dispersion, gives rise to the typical spectrum when white light is passed through the spectrometer. Typically, the prism is ori-
entated to the minimum deviation position for the central wavelength, where the angle of minimum deviation Dmin is given by Dmin = sin–1(n . sin(A/2))–A.
(1)
Here, A is the apex angle of the prism and n its index of refraction. At the minimum deviation, it can be shown that the difference in possible optical path is maximised, determining the fundamental resolution of a spectrometer. Using the prism at minimum deviation, resulting in a symmetric beam path, thus optimises the possible performance. At this prism orientation, the angle of inci-
Company
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Qioptiq Photonics GmbH
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Qioptiq designs and manufactures photonic products and solutions that serve a wide range of markets and applications in the areas of medical and life sciences, industrial manufacturing, defence and aerospace, and research and development. Qioptiq benefits from having integrated the knowledge and experience of Avimo, Gsänger, LINOS, Optem, Pilkington, Point Source, Rodenstock, Spindler & Hoyer and others. Qioptiq’s people work in Europe, Asia and the USA.
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(2)
Figure 2 visualises the interrelationship of both Dmin and αd and the index of refraction. It further turns out that for minimum deviation, total internal reflexion TIR does not affect the operating range of the prism spectrometer. Due to the dispersive behaviour of optical media, the prism is normally orientated for minimum deviation at the centre of the waveband of interest. The spectral resolving power RP, i.e. the capability of resolving two close wavelengths λ1 and λ2, can be expressed by RP = λ = B dn , Δλ dλ
(3)
where B is the effective prism base width β' + sinby β) the compariin microns. (sin As shown RP =W . . λ glasses at two difson for two different ferent centre wavelengths in Figure 3, RP can thus be increased by increasing the prism size and/or using a higher dispersion glass. The actual resolution of a real spectrometer will be much less due to aberrations introduced by the system, and will require proper raytracing in a full lens design program, such as WinLensTM3D [8, 9]. To setup the prism spectrometer shown was straightforward, using various tools: n Prism wizard: Easy to create and edit any of a range of prisms
SF1 (400 nm)
Göttingen, Germany
www.qioptiq.com
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N-LAK33B (400 nm)
15000 10000
SF1 (600 nm)
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0 0
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Fig. 3 Resolving power RP for different glasses and centre wavelengths vs. prism size.
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Fig. 4 Model and spot diagram at 420, 410, 400, 390 and 380 nm of a classical dispersive prism spectrometer.
100 μm
n Tilt and decentre: Can be applied to surfaces or whole components, including the image. This was used to tilt the prism by αd – A/2 to get the required αd. n Global coordinate break: Tilt the reference axis to Dmin and also applied decentre for cosmetic purposes. n Drag and drop of standard Qioptiq doublets from the database as collimator and focuser n One click reverse to orientate the collimator properly Figure 4 shows a setup made of two Qioptiq catalogue doublets and a custom SF1 prism. A good resolution of approx. 100 microns can be achieved for the investigated wavelengths (380–420 nm) with a simple model of a prism spectrometer.
Snell’s law equivalent is given by sin β' = –sin β + K . λ . s
(4)
where β is the angle of incidence, β’ is the angle of the diffracted beam, K is the diffraction order (0, 1, 2 etc) and s is the number of lines per mm. Often the resolving power RP is expressed by the product of both K and N, which is the total number of grooves illuminated. RP = λ = B dn , However,ΔλRP candλbetter be re-written as: RP =W .
(sin β' + sin β) . λ
(5)
Here, W is the grating width. Eq. 5 thus implies that RP is independent of the line width. We can thus see that,
fundamentally, a grating offers an RP much higher than that of an equivalent prism. But as noted for the prism spectrograph, the actual resolution is much lower than the theoretical RP. One new problem of gratings can be the efficiency, since the incoming light is spread over several orders, but this can be overcome by the use of blazed gratings. In general, reflective systems have many advantages. For example, the optics introduces no extra chromatic aberration. However, a complex path is required in order to avoid obscuring the light beam partially or entirely. Figure 5 shows the WinLensTM3D-model of a simple example, the Ebert-Fastie spectrometer setup. The grating (s = 300 lines/mm) was easily ‘applied’ to a mirror surface and then rotated with the standard tiltfunction mentioned above. In this setup, one portion of a single large spherical mirror collimates the beam onto the grating and another portion collects the beam and focuses it onto the detector. In comparison to the prism spectrometer above, the scale of the resulting spot diagram is worse because of various aberrations. The mere use of a spherical mirror introduces spherical aberration, whilst the ‘large’ field angles introduce field curvature, coma and astigmatism in considerable amounts. In order to overcome these disadvantages, more complex mounting schemes can be used, such as the Czerny-Turner setup. It is also possible to combine the
Modelling of grating spectrometers Though the prism spectrometer was invented much earlier than the grating spectrometer, the latter has replaced the former in many applications. Transmissive gratings can be used in spectrometers, in which case the system design is similar to that used by the prism. However, it is more normal to use a reflective grating as there are no transmission problems. Although the dispersion mechanism of optical gratings is completely different compared to prisms, many of the same system considerations apply. For example, the design of the transfer optics must again neither underfill nor overfill the grating. For a reflection grating, the
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Fig. 5 Model and spot diagram at 420, 410, 400, 390 and 380 nm of an Ebert-Fastie grating spectrometer. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Optical Design
focusing action of the spectrometer and the dispersive power into one element as first developed by Rowland. By using a standard linear ruled grating on a concave surface, coma can be controlled, whereas astigmatism remains as disturbing effect. With the advent of holography, gratings with more complex forms can be generated and by careful design aberrations can be significantly reduced. These are known, logically, as aberration corrected holographic gratings, and are an excellent way to achieve higher resolutions.
[3] E. Tognoni, V. Palleschi, M. Corsi, G. Cristoforetti: Spectrochimica Acta B 57 (2002) 1115–1130 [4] R. Wisbrun, I. Schechter, R. Niessner, H. Schröder, K. L. Kompa: Analyt. Chem. 66 (1994) 2964–2975 [5] S. Beldjilali, D. Borivent, L. Mercadier, E. Mothe, G. Clair, J. Hermann: Spectrochimica Acta B 65 (2010) 727–733 [6] S. Brückner, S. Rösner, C. Gerhard, S. Wieneke, W. Viöl: Mat. Test. 53 (2011) 639–642
[7] S. Wieneke, S. Brückner, W. Viöl: IEEE Trans. Plasma Sci. 35 (2007) 601–605 [8] WinLensTM3D optical design software package from Qioptiq, www.winlens.de [9] T. Thöniss, G. Adams, C. Gerhard: Opt. Photonik 4 (2009) 30–33
Authors Dr. Geoff Adams studied phys-
Summary and conclusions Prism and grating spectrometers feature specific advantages and disadvantages. By the use of optical evaluation and design software, the choice and characterisation of appropriate spectrometers for given applications and determining factors are facilitated. For fast modelling of prism spectrometers with catalogue lenses or components, or complex mirror-grating systems, appropriate optical design software is required. In particular, tools to create custom prisms, easytilt components and coordinate breaks are key resources. DOI:10.1002/opph.201300005 [1] J. B. Hearnshaw: Vistas in Astronomy 30 (1987) 319–375 [2] E. J. Milton: Int. J. for Remote Sensing 8 (1987) 1807–1827
ics at the Imperial College of Science & Technology, London, followed by a period at the research department of British Aerospace. He returned to Imperial College to undertake a PhD in optics on “Tolerancing of Optical Systems”. Working with Kidger Optics, he developed their tolerancing program and a lens library. Since 1992, he, at the Optical Software Company, has designed and developed the WinLens suite for the Qioptiq (former Spindler & Hoyer) R&D department.
Thomas Thöniß is R&D man-
ager at Qioptiq in Göttingen. His department mainly develops optical systems and components for semiconductor and vision technologies. After completing his high-school
education, he worked at Zeiss, then studied optical engineering in Jena and took his degree at the Fraunhofer Institute for Applied Optics and Mechanics. After working as a scientific associate in the field of spectroscopy in Berlin, he moved to Spindler and Hoyer (now Qioptiq) as optical designer in 1997.
Christoph Gerhard studied
precision production engineering in Göttingen and Paris and subsequently worked as product manager for optics and university lecturer in Göttingen. During his following occupation as research associate in Bremen, he extra-occupationally studied Optical Engineering/Photonics. He now works as research associate at the University of Applied Sciences and Arts and the Fraunhofer Application Center for Plasma and Photonic in Göttingen.
Thomas Thöniß, Qioptiq Photonics GmbH & Co. KG, Königsallee 23, 37081 Göttingen, Germany, Tel.: 0551/6935-198, Fax: 0551/6935-181, E-Mail:
[email protected]
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