The development of coherence imaging

In recent years, solid-state interferometric systems based on birefringent crystals have been developed at the Australian National University for use in the imaging of simple spectral scenes. These systems replicate the functionality of a mechanically scanned interferometer by exploiting the birefringent and electro-optic properties of optical crystals.

Birefringence is a difference in refractive indices along optical axes of a crystal plate which results in a delay between the orthogonally polarised components of the transmitted light (this will be discussed in more detail in section 3.1). The optical delay between the polarisation components is determined by the material of the crystal and the thickness of the crystal. Some birefringent crystals also exhibit electro-optic properties.

Snapshot coherence imaging systems are based on the standard polarising interferome- ter, shown in figure 2.6. The interferometer operates by collecting quasi-monochromatic emission light and selecting linear polarisation through an initial polarising optic. The emission passes through a waveplate (see details in section 3.2) where a net phase delay is introduced between the components polarised parallel and perpendicular to the principal axis (opical axis) of the crystal. The components are then recombined through a final polariser and the spectral line of interest is isolated using a narrow bandwidth filter. The lens focuses the interference fringes onto a screen (such as a photodetector or CCD) for viewing. The optical configuration of the polarisation interferometer, is shown in figure 2.6. The fringe pattern can be decoded to obtain useful information about sufficiently simple spectral scenes.

In order to obtain Doppler information the contrast, phase and intensity must be measured (see equation 2.26). As the polarisation interferometer only makes a single measurement of the coherence (fixed delay) it cannot deliver enough information to retrieve these three unknown features. Therefore, in order to measure spectral information the signal must be modulated or scanned across the interferometric delay. One way to achieve this is by modulating the interferometric delay with time. For mechanical interferometers this may be achieved by making measurements while extending the length of one of the interferome- ter arms. For polarisation-based systems, electro-optic crystals can be used. Pockels cells are voltage controlled waveplates where the birefringence of the crystal varies with the applied electric field. Devices such as MOSS (Modulated Optical Solid-State) or ToMOSS (Tomographic Modulated Optical Solid-State) interferometers employ such strategies [40]. These devices were the forerunner to snapshot coherence imaging systems.

The MOSS system (shown in figure 2.7 a) operates similar to the standard polarisation interferometer. The horizontal polarisation component is selected by the first beam splitter polarising cube. The birefringent optic is orientated with the optical axis at 45◦ to the horizintal axis. The polarised component is then split into two polarisation components parallel and perpendicular to the optical axis of the electro-optic (E-O) birefringent crystal. The birefringent property causes a delay between these components which is varied by

§2.1 Spectroscopic diagnostics in plasmas 19

a)

b)

φ

polariser waveplate polariser filter+lens CCD

Light source

Figure 2.6: (a) Optical setup for a fixed delay polarisation interferometer. (b) Ray diagram showing the functionality of the interferometer, depicting the polarisation state and waveplate delay at different angles of incidence.

applying a voltage across the crystal. The components are then recombined through the second polarsing cube and focused onto a detector array. The output from the detector is a sample of the coherence, selected over the delay range provided by the applied voltage (see figure 2.7 b). The coherence envelope (amplitude) is determined by the temperature of the plasma and therefore higher temperatures cause a more rapid decay of the envelope with delay. The phase will vary depending on the flow of the plasma.

By sweeping the delay the coherence is sampled for each pixel. These systems can either be single-channel where the emission light is collected through the system by a single photomultiplier tube, or they can be multi-channel where a series of fiber optics can be coupled into the MOSS system using angular multiplexing allowing features from a range of views to be measured [40].

The multi-channel ability, along with high light throughput and stability of the MOSS sys- tems offered significant advantages over standard spectrometers and interferometers and as such are able to achieve the resolution required for plasma spectral studies. The voltage modulation operates at frequencies between 0 and 50 MHz [40], giving these instruments the added advantage of high temporal resolution.

A phase-stepped coherence imaging spectrometer, adapted from the MOSS system by coupling to a CCD and using an additional birefringent plates, was used to study the Doppler features of the HeII 468 nm transition line on the WEGA stellarator [50]. In

20 Spectroscopic and probe diagnostics on MAGPIE

(a)

(b)

Figure 2.7: (a) Instrumental components of the Modulated Optical Solid State (MOSS) system. (b) sample of the signal obtained from MOSS at two different temperatures. This figure was supplied courtesy of Professor John Howard. Additional details can be found at [40].

this system the voltage of the electro-optic crystal was varied in synchronisation with the camera exposure so that a sequence of 2D images of the plasma, over-laid with a fringe pattern, were obtained. The stepped voltage resulted in the phase of the fringe pattern shifting by π/2 radians between each image.

Snapshot coherence imaging is a technique which evolved from the MOSS and phase- stepped systems and allows for 2D time-resolved plasma imaging without the need to apply the voltage modulation. Like the polarisation interferometer and MOSS systems, the snapshot systems exploit the birefringent property of uniaxial crystals to cause a phase delay between the orthogonal polarisation components. The voltage modulation is however replaced by another ‘static’ birefringent optic crystal called a shearing plate. This plate adds an additional phase shear, replacing the need to manually sample delay and encoding the coherence directly into the measured interferometric fringe pattern. The functionality

§2.1 Spectroscopic diagnostics in plasmas 21

of the shearing plate is described in more detail in chapter 3.3.

Figure 2.8: Instrumental components of the snapshot coherence imaging system. The use of the static optic allows a 2D spatial snapshot of the coherence to be obtained in a single image, without the complexity of encoding the coherence in a time modulation. The acquisition speed for snapshot systems is only limited by the brightness of the plasma and the frame-rate of the camera. For a good signal-to-noise ratio (SNR) the exposure time is typically on the order of milliseconds and therefore suitable for dynamical plasma studies. Intensified cameras, which employ an inbuilt gain and phase-locking, can be used in conjunction with the coherence imaging systems to study coherent plasma wave phenomena up to the MHz range.

Coherence imaging has been successfully deployed to measure Doppler spectral features on fusion focused experiments [43–45, 47, 51, 52]. Work to investigate internal magnetic and electric fields through the Zeeman and Motional Stark spectral effects using coherence imaging has also been undertaken on the K-STAR, DIII-D, ASDEX-U and TEXTOR fusion experiments [53–56].