Introduction

Nd:YAG Thomson scattering diagnostics with interference filters in polychromators [1] has been used as a reliable method to measure electron density and temperature of plasma. Light from the Nd:YAG laser (1064 nm) passes through plasma, and its scattered light is collected and guided to polychromators. Since each interference filter transmits light in a specific wavelength range, one polychromator generally has as many interference filters as spectral channels, specifically 3–7 channels [2,3,4,5,6,7,8,9,10,11,12], and the interference filters account for a large part of the cost of the polychromator. The total number of interference filters in the system amounts to the number of spectral channels times the number of measuring points in plasma unless scattered light from several points is guided to the same polychromator.

One method to reduce polychromators is 2D measurement with multiple reflection and time of flight of laser light [13]. It realized the 2D (m×n points) measurement with only a single laser and few polychromators equivalent in a 1D (m points) measurement system. However, it still needs the number of spectral channels (3–7) times m interference filters, leading us to develop a new polychromator with a single filter.

Fig. 1
figure 1

Measured intensity dependent on angles of incidence on an interference filter

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We focused on a well-known effect that interference filters change the wavelength range of transmitted light depending on the angle of incidence (AOI) of the light [14]. This effect is used to tune the wavelength in various devices, such as a telescope [15], a surface plasmon resonance microscope [16], and an external cavity diode laser [17]. We also used this effect to develop a cost-effective polychromator, where light was repeatedly made incident on one interference filter at varied AOIs.

Note that a similar visible-light spectral analyzer with a single interference filter was proposed by A. DeSilva for a ruby Thomson scattering system in 1979 [18], but the Nd:YAG Thomson scattering system in ASDEX [1] did not adopt the single-filter spectral analyzer, nor did the following systems [2,3,4,5,6,7,8,9,10,11,12]. However, the single-filter polychromator is also suitable for Nd:YAG systems, where the scattered light is generally not dispersed by a diffraction grating but separated into spectral channels by interference filters.

Dependence of Transmitted Wavelengths on AOIs

First, investigated was the property of one interference filter custom-ordered for transmission of 1059 nm light at \(3^\circ\) AOI. A specific wavelength of light was selected by a monochromator with 0.3 nm resolution and was injected into the interference filter. Light it transmitted was detected at an avalanche photodiode (APD). For various AOIs, the wavelength of the monochromator was scanned. Figure 1 shows the measured intensity as a function of the wavelength. Here, the measured intensity is averaged at each wavelength. Predictably, as the AOI increases, the wavelength of the transmitted light decreases. Meanwhile, the bandwidth increases with the AOI. However, it is not necessarily undesirable from the viewpoint of spectra of Thomson scattered light. Although intensity of the scattered light at the wavelength far from Nd:YAG 1064 nm is relatively low, the wide bandwidth of the spectral channel makes its total intensity high. In fact, general polychromators often have wider bandwidths for channels farther from the laser wavelength [1,2,3,4,5,6,7,8,9], [19,20,21,22,23,24,25]. Also, the ratio of transmitted light intensity to that measured when the interference filter was removed, or transmittance, is lower at the shorter wavelength, but this disadvantage is somewhat compensated by the wide bandwidth.

From Fig. 1 and intensity of other AOIs, Fig. 2 was calculated. For each AOI, the center wavelength \({\lambda }_{\text{c}}\) was numerically calculated from the interpolated transmittance \(T\) as follows:

$${\lambda }_{\text{c}}=\frac{\sum _{i}{\lambda }_{i}T\left({\lambda }_{i}\right)}{\sum _{i}T\left({\lambda }_{i}\right)} ,$$
(1)

where \({\lambda }_{i}\) is the wavelength arranged at regular intervals. \({\lambda }_{\text{c}}\) as a function of the AOI \(\theta\) was curve-fitted by

$${\lambda }_{\text{c}}={\lambda }_{0}\sqrt{1-{\left(\frac{\text{sin}\theta }{n}\right)}^{2}} ,$$
(2)

where \({\lambda }_{0}\) is \({\lambda }_{\text{c}}\) for normal incidence (\(\theta =0\)), and \(n\) is the effective refractive index of the interference filter [14]. The obtained values were \({\lambda }_{0}=1059.6\) nm and \(n=1.804\), which enabled us to design and evaluate the single-filter polychromator. In addition, transmittance in Fig. 2 was calculated as \(T\left({\lambda }_{\text{c}}\right)\). Since \(T\left({\lambda }_{\text{c}}\right)\) is lower at the larger AOI, the channel of the largest AOI at the single-filter polychromator should be CH1, the first channel (CH) to detect transmitted light, to avoid the extra loss of light by lenses and mirrors, if possible.

Fig. 2
figure 2

Wavelengths and transmittance of transmitted light dependent on angles of incidence on an interference filter

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The Cost-Effective Polychromator with a Single Interference Filter

In Fig. 3, the experimental setup of the single-filter polychromator with the interference filter used in the previous section is depicted. Light from the monochromator was guided to this polychromator by an optical fiber with the core diameter of approximately 2 mm and the numerical aperture of approximately 0.25. This fiber is almost identical to those used in LHD [26]. The light diverged, but a lens formed an image around the interference filter. The transmitted light in the specific wavelength range was converged by a lens and collected at the CH1 APD, while light out of this range was reflected. Subsequently, the reflected light was reflected by a mirror and reentered the interference filter at the smaller AOI. A lens was placed on the mirror, and it formed an image around the interference filter again. Light of the longer specific wavelength than that of CH1 passed the interference filter and reached the CH2 APD similarly to CH1. The AOI of CH3 was even smaller. The transmitted light of CH3 was detected as well, but an additional mirror was placed for spatial constraints. This additional mirror and two mirrors which reflect the light reflected by the interference filter are not necessary for general polychromators. However, the costs of the single-filter polychromators will be lower, because an interference filter costs one order of magnitude higher than a mirror.

Fig. 3
figure 3

The experimental setup of the single-filter polychromator

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Fig. 4
figure 4

Performance of the single-filter polychromator and the CH1 intensity without the interference filter

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Figure 4 shows performance of the single-filter polychromator as a function of the wavelength. As in Fig. 1, the resolution of the monochromator was 0.3 nm, and the measured intensity was averaged at each wavelength. Wavelength scanning ranged from about 1065 nm to about 1025 nm. Since no signal was detected at Nd:YAG 1064 nm, a 1064 nm continuous-wave laser was used to confirm that laser-blocking ability satisfies transmittance of less than 0.001. Intensity of CH2 and CH3 was corrected on the basis of their sensitivity. Three spectral channels were successfully separated. From Eq. (1), center wavelengths were calculated to be approximately 1043.2, 1051.9, and 1058.4 nm. Here, \(T\) was replaced by the corrected intensity of each spectral channel normalized by CH1 intensity measured when the interference filter was removed. The normalized values of intensity at the center wavelengths were approximately 58, 49, and 64% in order of the channels. The normalized intensity of CH2, 49%, was relatively low, suggesting light loss somewhere other than the interference filter. The ratio of CH3 higher than that of CH2 can be explained by the higher transmittance at the smaller AOI in Fig. 2. It is noted that electron temperatures which can be measured by these three spectral channels of the single-filter polychromator will range from a few ten to a few hundred eV for 90° scattering measurement.

Summary

We developed the cost-effective polychromator with a single interference filter using the measured dependence of transmitted wavelengths on AOIs and examined its performance. Three spectral channels were successfully separated, and achieved values of intensity normalized by that of CH1 without the interference filter were 58, 49, and 64% at 1043.2, 1051.9, and 1058.4 nm, respectively. We can probably improve the CH2 ratio to over 50% by replacing the present aluminum mirrors with dielectric mirrors. This single-filter polychromator is a prototype but has potential to be upgraded to realize a more cost-effective 2D measurement system and tune the wavelength range in keeping with electron temperature in plasma.