Triple Range Imager and POLarimeter (TRIPOL) --- A Compact and Economical Optical Imaging Polarimeter for Small Telescopes

TL;DR

TRIPOL is a compact, economical optical imaging polarimeter designed for small telescopes, capable of simultaneous imaging and polarimetry across three wavelength bands, enabling studies of time-variable and wavelength-dependent phenomena.

Contribution

This paper introduces TRIPOL, a novel, lightweight polarimeter that combines simultaneous imaging and polarimetry in three bands for small telescopes, with demonstrated performance and applications.

Findings

Achieved limiting magnitudes of g' ~ 19.0, r' ~ 18.5, i' ~ 18.0 mag with S/N=10.

Instrumental polarization measured at ~0.3% across bands.

Successful application to star-forming cloud IC 5146 and variable star GM Cep.

Abstract

We report the design concept and performance of a compact, light-weight, and economic imaging polarimeter, TRIPOL (the Triple Range Imager and POLarimeter), capable of simultaneous optical imagery and polarimetry. TRIPOL splits the beam from wavelength 400 to 830 nm into g'-, r'-, and i'-bands with two dichroic mirrors, and measures polarization with an achromatic half-waveplate and a wire-grid. The simultaneity makes TRIPOL a useful tool for small telescopes for photometry and polarimetry of time variable and wavelength dependent phenomena. TRIPOL is devised for a Cassegrain telescope of an aperture of ~1 m. This paper presents the engineering considerations of TRIPOL and compares the expected with the observed performance. Using the Lulin 1-m telescope and 100 seconds integration, the limiting magnitudes are g' ~ 19.0 mag, r' ~ 18.5 mag and i' ~ 18.0 mag with a signal-to-noise of 10, in agreement with design expectation. The instrumental polarization is measured to be ~ 0.3% at three bands. Two applications, one to the star-forming cloud IC 5146, and the other to the young variable GM Cep, are presented as demonstration.

Tables

Table 1. Table 1 : TRIPOL Measurements of Unpolarized Standard Stars

Star,mag/$P_{\lambda }$ (Schmidt et al. 1992)	Date	$P_{g^{\prime }}(\%)$	$P_{r^{\prime }}(\%)$	$P_{i^{\prime }}(\%)$
BD+$32\text{degr}3739$, $V=9.31$	2011 Aug 14	$0.12\pm 0.11$	$0.12\pm 0.10$	$0.17\pm 0.15$
$P_B=0.039\pm 0.021$	2011 Aug 15	$0.14\pm 0.16$	$0.32\pm 0.14$	$0.19\pm 0.23$
$P_V=0.025\pm 0.017$	2018 Oct 25	$0.27\pm 0.27$	$0.26\pm 0.19$	$0.32\pm 0.18$
	2018 Oct 28	$0.20\pm 0.20$	$0.16\pm 0.16$	$0.17\pm 0.12$
BD+$28\text{degr}4211$, $V=10.53$	2011 Aug 15	$0.20\pm 0.19$	$0.34\pm 0.21$	$0.25\pm 0.10$
$P_B=0.063\pm 0.023$	2011 Aug 17	$0.08\pm 0.13$	$0.29\pm 0.14$	$0.32\pm 0.28$
$P_V=0.054\pm 0.027$	2018 Oct 26	$0.25\pm 0.12$	$0.20\pm 0.20$	$0.20\pm 0.20$
$P_V=0.054\pm 0.027$	2018 Oct 27	$0.28\pm 0.13$	$0.17\pm 0.17$	$0.21\pm 0.19$
HD 212311, $V=8.10$	2018 Oct 23	$0.15\pm 0.05$	$0.15\pm 0.06$	$0.20\pm 0.05$
$P_B=0.028\pm 0.025$	2018 Oct 24	$0.20\pm 0.09$	$0.24\pm 0.06$	$0.13\pm 0.07$
$P_V=0.034\pm 0.021$	2018 Oct 25	$0.26\pm 0.12$	$0.23\pm 0.12$	$0.28\pm 0.14$
	2018 Oct 26	$0.11\pm 0.11$	$0.10\pm 0.15$	$0.32\pm 0.21$
	2018 Oct 27	$0.12\pm 0.12$	$0.23\pm 0.15$	$0.16\pm 0.16$
	2018 Oct 28	$0.07\pm 0.11$	$0.21\pm 0.10$	$0.12\pm 0.12$

Table 2. Table 2 : TRIPOL Measurements of Polarized Standard Stars

Star/mag/$P_{\lambda }$, ${\theta }_{\lambda }$ (Schmidt et al. 1992)	Date	$P_{g^{\prime }}(\%)$, ${\theta }_{g^{\prime }}\left(deg\right)$	$P_{r^{\prime }}(\%)$, ${\theta }_{r^{\prime }}\left(deg\right)$	$P_{i^{\prime }}(\%)$, ${\theta }_{i^{\prime }}\left(deg\right)$
HD 154445, $V=5.61$	2015 Feb 17	$3.8\pm 0.1,87\pm 3$	$3.4\pm 0.2,82\pm 2$	$3.7\pm 0.1,67\pm 3$
$P_V=3.780\pm 0.062$, ${\theta }_V=88.79\pm 0.47$	2015 Feb 26	$3.8\pm 0.1,92\pm 3$	$3.7\pm 0.2,90\pm 2$	$3.7\pm 0.1,92\pm 3$
$P_{Rc}=3.683\pm 0.072$, ${\theta }_R=88.91\pm 0.56$	2015 Feb 27	$3.8\pm 0.1,88\pm 3$	$4.0\pm 0.2,86\pm 2$	$3.5\pm 0.1,87\pm 3$
$P_{Ic}=3.246\pm 0.078$, ${\theta }_I=89.91\pm 0.69$
HD 161056, $V=6.32$	2015 Feb 27	$3.9\pm 0.1,67\pm 3$	$4.1\pm 0.2,66\pm 2$	$3.7\pm 0.1,67\pm 3$
$P_V=4.030\pm 0.025$, ${\theta }_V=66.93\pm 0.18$
$P_{Rc}=4.012\pm 0.032$, ${\theta }_R=67.33\pm 0.23$
$P_{Ic}=3.575\pm 0.030$, ${\theta }_I=67.78\pm 0.24$
HD 204827, $V=7.93$	2011 Aug 11	$5.5\pm 0.2,60\pm 1$	$5.3\pm 0.2,61\pm 1$	$4.7\pm 0.2,63\pm 2$
$P_V=5.322\pm 0.014$, ${\theta }_V=58.73\pm 0.08$	2018 Oct 23	$5.5\pm 0.3,59\pm 3$	$5.0\pm 0.2,58\pm 2$	$4.5\pm 0.3,58\pm 2$
$P_{Rc}=4.893\pm 0.029$, ${\theta }_R=59.10\pm 0.17$	2018 Oct 24	$5.8\pm 0.2,61\pm 1$	$5.3\pm 0.2,60\pm 1$	$4.5\pm 0.2,62\pm 1$
$P_{Ic}=4.189\pm 0.030$, ${\theta }_I=59.94\pm 0.20$	2018 Oct 25	$5.9\pm 0.1,59\pm 1$	$5.3\pm 0.1,60\pm 1$	$4.5\pm 0.1,60\pm 1$
	2018 Oct 26	$5.9\pm 0.1,57\pm 1$	$5.2\pm 0.0,59\pm 1$	$4.2\pm 0.1,60\pm 1$
	2018 Oct 27	$5.6\pm 0.2,57\pm 1$	$5.3\pm 0.2,58\pm 1$	$4.4\pm 0.2,58\pm 1$
	2018 Oct 28	$5.6\pm 0.1,59\pm 1$	$5.1\pm 0.1,59\pm 1$	$4.3\pm 0.1,60\pm 1$
HD 19820, $V=7.11$	2018 Oct 23	$4.5\pm 0.1,115\pm 1$	$4.4\pm 0.1,115\pm 1$	$4.2\pm 0.1,114\pm 1$
$P_V=5.322\pm 0.014$, ${\theta }_V=114.93\pm 0.08$	2018 Oct 24	$4.6\pm 0.2,114\pm 2$	$4.7\pm 0.1,111\pm 1$	$4.0\pm 0.1,115\pm 2$
$P_{Rc}=4.893\pm 0.029$, ${\theta }_R=114.46\pm 0.17$	2018 Oct 25	$4.9\pm 0.2,110\pm 2$	$4.0\pm 0.2,115\pm 2$	$4.5\pm 0.1,117\pm 2$
$P_{Ic}=4.189\pm 0.030$, ${\theta }_I=114.48\pm 0.20$	2018 Oct 26	$4.2\pm 0.1,111\pm 2$	$3.8\pm 0.1,113\pm 1$	$3.5\pm 0.1,115\pm 2$
(Variable, this work)	2018 Oct 27	$4.4\pm 0.1,111\pm 1$	$4.3\pm 0.1,113\pm 1$	$3.6\pm 0.1,115\pm 1$
	2018 Oct 28	$4.6\pm 0.2,114\pm 1$	$4.6\pm 0.2,113\pm 1$	$4.0\pm 0.1,113\pm 1$

Equations

$$I$$

$$Q$$

$$U$$

$$P$$

$$\theta$$

Full text

1 Introduction

Polarization provides information about a celestial object additional to that by photometry and spectroscopy (Tinbergen 1996; Clarke 2010). Yet a polarimeter has been considered as a special instrument for an optical telescope with a small aperture size. Nowadays, with commercial CCD cameras and other optical and electronic components readily available with good performance, it becomes feasible to design and fabricate a compact, and economical polarimetric imager to be used for scientific programs with small telescopes. We report on an imaging system, TRIPOL (Triple Range Imaging POLarimeter), capable of simultaneous imaging photometry and polarimetry at three optical ($g^{\prime},r^{\prime},i^{\prime}$) bands. TRIPOL was designed for a telescope with the primary mirror around one meter and located at a moderate observing site, under typical seeing 1 to 2 arcseconds. The telescope is assumed to have a Cassegrain f-ratio from F/6 to F/15, and the CCD pixel scale is from 10 to 20 $\mu$m to sample properly the point spread function. The optics uses no lenses to magnify or reduce the image, and the elements, such as the dichroic mirrors, spectral filters, a half wave-plate, and wire-grid, are all flat and thin for easy optical alignment. TRIPOL is compact, measuring $300\times 350\times 250$ mm in width, length, and height, weighing only 15 kg including the data acquisition system, and is easy to operate. It was devised to an accuracy $\sim 3\arcsec$ for alignment, and $\sim 0.05$ mm for machining and positioning.

This paper describes the performance of the first (TRIPOL1) and second (TRIPOL2) units of TRIPOL adapted to the Lulin One-meter Telescope (LOT) in Taiwan. In the F/8 beam of the LOT, hence a $\sim 3\degr$ cone-angle, effects such as spherical aberration, chromatic aberration, and astigmatism are small compared to the 20 $\mu$m pixel size. We compare the design parameters with observational results on the polarization measurements of polarization standard stars, and demonstrate the use of TRIPOL in the star-forming cloud IC 5146 and the young star GM Cep.

2 Design of TRIPOL

TRIPOL is composed of three parts, the polarization unit, the color-decomposition unit, and the data-acquisition unit, plus three CCD cameras and a desktop computer. The overview and layout of the optical components are shown in Figure 1. Light from the telescope passes through a half-wave plate (HWP) and a wire-grid polarizer(WG), and then is decomposed by two dichroic mirrors (DM1 and DM2) and band-pass filters (BPFs) into three ($g^{\prime}$, $r^{\prime}$, $i^{\prime}$) channels. The incident photons are detected and converted to electrons in the CCD camera with the built-in readout electronics.

The polarization unit, consisting of a rotatable HWP and a fixed WG, working as a phase-retarder and polarization analyzer, respectively, is located in front of the color-decomposition unit. The HWP, with a size 33 mm square and thickness 3 mm, made of $SiO_{2}MgF_{2}$, is procured from the optical shop, Kogaku-Giken Co. We employ a commercial (from Edmund Optics Co.) WG plate of Al-wire grid, with a size 50 mm square and thickness 1.5 mm, sandwiched by thin glass plates, affording a field-of-view as wide as the detector size. While using birefringent materials such as a Wollaston prism would allow for, alternatively, a dual beam design, thus minimizing instrumental and sky effects on polarization measurements, our design is much more compact and economical. The WG is slightly tilted to avoid ghost images due to reflection glaring.

For the color-decomposition unit, the central wavelengths ($\lambda_{0}$) and bandwidths ($\Delta\lambda$) are defined by multiplying the transmission or reflection curves of the DMs and BPFs for each of the $g^{\prime}$-, $r^{\prime}$-, and $i^{\prime}$-bands. The spectral response functions of the DMs and BPFs are shown in Figure 2.

Even though the TRIPOL optics makes no use of mirrors or lenses with power, astigmatism from tilted DMs and spherical aberration from flat-parallel BPFs may still exist. The $g^{\prime}$-band optical train contains the BPF-$g^{\prime}$ and a CCD camera, the $r^{\prime}$-band optical train contains DM1 tilted at an angle of $30\degr$, and the $r^{\prime}$-$i^{\prime}$ optical train contains DM1 and DM2 at angles of $\pm 30\degr$.

Ray-tracing was executed using the software ZEMAX for classical Cassegrain-type telescopes with apertures $D$=0.7, 1.0, and 1.5 m, and $f$-ratios F/6, F/8, F/10, F/12.5, and F/15. We evaluated the tolerance of aberrations by comparing the root-mean-square (RMS) radius in the spot diagram with the detector pixel size and the seeing size. It was confirmed that the RMS radius of the spot, due mostly to astigmatism, was smaller than 50 $\mu$m, or $\sim$2.5 times of the pixel size, even near the corners of the detector, and much smaller than the seeing size, $1\farcs 5$. With various parameters for apertures and focal-ratios, the optics is found tolerable for an F/7 or a slower beam. Astigmatism can be remedied by wedging DM1 and DM2 by $0\fdg 18$ and $0\fdg 24$ , respectively, even for a system as fast as F/7.

TRIPOL was designed to use commercially available CCD cameras, with the specific model in accordance with scientific and budgetary requirements. TRIPOL1 and TRIPOL2 employed SBIG ST-9 XEi cameras using KAF-0261E plus TC-237, having $512\times 512$ pixels, each with 20 $\mu$m on a side. The detector response shows linearity up to $\sim$50,000 counts, or about 1/3 of the full well. The dark current is 10 [e/s] at temperature $\sim 0\degr$C, and the readout noise is 15 [e] per sampling.

The CCD cameras are located on the bottom plate so as to align each of the array centers to the focal point of the telescope within an accuracy of less than 0.1 mm ($\sim$5 pixels) relative to each other. The SBIG ST-9 camera model satisfied our initial need for point-source targets, but the model is no longer available. Subsequent TRIPOL units were upgraded to the camera model STT-8300. A computer (Intel DN2800MT) controls simultaneous readout of the three CCD cameras and the polarization units according to position angles of HWP via three USB2.0 cables. The overall cost of TRIPOL, excluding the cameras and the computer, was about US$17,000 in 2010.

3 Evaluation of performance

In this section we evaluate the performance of TRIPOL in photometric and in polarimetric measurements. In each case, the engineering design parameters are compared with those measured in actual observations.

3.1 Limiting magnitudes for photometry

The limiting magnitudes of TRIPOL2 were measured in December 2012 using the LOT, for which each SBIG ST9-XEi 20 $\mu$m pixel corresponds to $0\farcs 5$, giving a field of view of about $4\farcm 7$ across.

We observed the Landolt Field 101-404 (Landolt 1992) for 100 s, and analyzed the images of the 12 stars with a photometric aperture of $4\farcs 0$, or 8 pixel in diameter, and derived the limiting magnitudes of 19, 18.5 and 18, for S/N$\sim 10$, respectively, at the $g^{\prime}$-, $r^{\prime}$-, and $i^{\prime}$-bands. In every band, the measured and expected values are in agreement with each other within the uncertainties of $\sim 0.5$ mag. For a photometry-only observing run, the WG could be removed to gain an increase of about 60% incident flux.

3.2 Efficiency and reliability of polarization measurements

The combination of a rotatable HWP and a fixed WG, as described in section 2, follows the same design as the near-infrared(J,H,Ks) polarimeter, SIRPOL, on the IRSF (Kandori et al. 2006, InfraRed Survey Facility,). We describe below the performance papameters measured in laboratory, in comparison with observations of standard stars.

3.2.1 Efficiency of the polarization devices

The phase retardant of the HWP was designed and measured by Kogaku Giken Co. to be $180\pm 2\degr$ over the wavelength range 400 to 950 nm (see Figure 3(a)). The transmittance of the WG was measured in this wavelength range in steps of $\Delta\lambda=50$ nm. Two identical WG polarizers were arranged such that one was fixed while the other was rotatable. When rotating relative to each other, a silicone photodiode was illuminated with a white light through the intermediate bandpass filters of $\Delta\lambda=50$ nm. A single rotation gives a double sinusoidal curve. Fitting by a sinusoidal curve, we obtain $I(\theta)=A\sin~{}2(\theta-\phi)+B$, where $A$ is the amplitude, $B$ the residual, and $\phi$ the phase-difference. For this we parameterized the transmittances, $T_{\rm max}$ and $T_{\rm min}$ in parallel and perpendicular with each other, respectively, shown as 3(b) and 3(c). The contrast parameter, defined as the extinction ratio, $T_{\rm max}/T_{\rm min}$, should be as high as possible (infinite for a perfect polarizer), but in practice is considered satisfactory for a value above $\sim 100$ to suppress substantially the perpendicular component of polarization, i.e., the crosstalk. The contrast parameter measured for TRIPOL, presented as Figure 3(d), increases toward long wavelengths, and remains sufficiently high above 500 nm.

3.2.2 Observations of Polarization Standard Stars

The TRIPOL images were reduced by standard procedures for bias and dark subtraction, and correction with flatfielding. For each polarization measurement, target frames acquired with each filter at four HWP positions are aligned using DAOPHOT (find, daomaster, and daogrow) and IRAF (geomap and geotran) packages. Then multiple frames for each HWP are average-combined using IRAF/imcombine. These four images, taken at each of the four HWP positions, become the science images used for photometry and polarimetry.

Aperture photometry is performed using DAOFIND (for source detection with a threshold of $5\sigma$ of the sky variation) and PHOT (for aperture photometry) tasks of DAOPHOT for point sources. Typical image FWHMs for these runs varied between 2 and 4 pixels ($1\arcsec$–$2\arcsec$). Fluxes of each star at four positions of HWP were estimated using IRAF/DAOPHOT with an aperture size of 2.5 times of FWHM, as flux (and thus polarization measurements) versus aperture size reveals constant measurements after 2.5 times FWHM pixels. The inner and outer sky annuli are chosen to be 5 and 10 pixels more than the star aperture. Fluxes at four angles are used to compute the Stokes parameters as follows,

[TABLE]

where $I_{0}$, $I_{22.5}$, $I_{45}$, $I_{67.5}$ are intensities at the four HWP angles in degree, with the corresponding error as the square-root of the sum of the square of each intensity error, i.e., $\delta I=\sqrt{(\delta I_{0})^{2}+(\delta I_{22.5})^{2}+(\delta I_{45})^{2}+(\delta I_{67.5})^{2}}$. The errors $\delta Q$, and $\delta U$ are computed similarly.

The level of polarization $P$ (in percentage) and the polarization position angle $\theta$ (in degree) are then derived accordingly,

[TABLE]

for which $\delta P$, and $\delta\theta$ are estimated from the respective $\delta Q$ and $\delta U$.

Because $P$ is positively defined, the derived polarization is over-estimated, especially for low S/N sources. To correct for this bias, the debiased value $P_{\rm db}=\sqrt{P^{2}-(\delta P)^{2}}$ (Wardle & Kronberg 1974) is computed.

A polarization measurement relies on photometry at different polarization angles, therefore all conditions pertaining to reliable photometric measurements apply. Even under a perfect photometric sky, though, our observations, via a fixed sequence of images taken at 0-45-22.5-67.5 degrees, is subject to a small but noticeable flux drift due to airmass changes, leading to spurious polarization signals. Figure 4 illustrates the results observed by LOT/TRIPOL on 14 August 2011 for BD$+$32\degr 3739, a standard star known to have null polarization (Schmidt et al. 1992). The total $g^{\prime}$ count, that is, the sum $g^{\prime}_{0}+g^{\prime}_{22.5}+g^{\prime}_{45}+g^{\prime}_{67.5}$ indicates varying sky conditions during the first session (a total of 10 sets of data, each set consisting of images at four polarization angles per filter), starting at UT 12:53 (local time 20:53), but relatively stable skies during the second session (also with 10 sets), starting local time 02:12. The ratio of the standard deviation of the total counts to the average counts, used as a measure of the sky stability, changed from about 13% in each of the $g^{\prime}$-, $r^{\prime}$-, and $i^{\prime}$-bands in the first session, to about 1% in the second session. The data taken in the first session hence would be discarded.

A further correction is the polarization introduced by the instrument, which is estimated by observing unpolarized standard stars. The mean and standard deviation of the measured polarization of unpolarized standards were found to be $P_{g^{\prime}}=0.27\pm 0.12$%, $P_{r^{\prime}}=0.32\pm 0.23$%, and $P_{i^{\prime}}=0.25\pm 0.13$%. These values, summarized in Table 1 are considered as the instrumental polarization. For the unpolarized standard stars, with brightness up to ${\rm V}\sim 12$ mag, the overall accuracy of polarization measurements with TRIPOL, is estimated to be $\sim 0.3$% with an uncertainty of $3\degr$ for the polarization angle.

In every TRIPOL run, polarized standard stars are to be observed to calibrate the measured polarization angle to the equatorial coordinate system. The TRIPOL measurements of known unpolarized standard stars and polarized stars are listed in Table 1 and in Table 2, demonstrating a general agreement with the published values, given the observing wavelengths are slightly different. An observing run was carried out exclusively for standard star calibration in 2018 October to assess the intranight and internight consistency of the TRIPOL measurements. For unpolarized standard stars, accuracy is kept to two decimal digits, and no polarization angle is listed. For polarized standard stars, the fractional polarization is kept to one decimal digit, with the polarization angle in inger to reflect the uncertainties. In the 2018 October run, each target was measured a few times, and the entries in Table 1 and Table 2 for each date are the average values of individual measurements and the associated errors. Because we relied on the standard stars to correct for the polarization angles (one offset per night for each angle at each band), so the values of angles scatter around the offset. From the observations of polarization standards, we conclude that the WG polarizer has a high efficiency to measure polarized light, and there is no need to correct for instrumental polarization except an angular offset.

Note that only standard stars from Schmidt et al. (1992) known not to vary were selected. In the passing of our experiment, we found that one target, HD 19820, however, exhibits noticeable variability in the polarization level, but with a relatively steady polarization angle in our measurements. The mechanism of the variability is unclear, but this O-type star is reported to be a binary system with a period of 3.366324 days (Hilditch & Hill 1975; Hill et al. 1994). Its polarization variability requires further study, but in any case, using it as a standard is not advised.

4 Scientific Demonstration

Data acquired by TRIPOL provide simultaneous information such as flux, linear polarization and the source coordinates in three bands, enabling the study of the spectral energy distribution (SED), the color-magnitude and color-color diagrams, and polarization. The combination of wavelength-dependence of polarization with the SED could distinguish various emission and propagation processes, such synchrotron emission, scattering or extinction.

For imaging photometry, the time resolution of TRIPOL is as fast as about 1 s, whereas for polarimetry it is $\sim 15$ s. As a single-beam instrument, TRIPOL is susceptible to polarization caused by the instrument itself, and to sky variations. The effects of internal polarization are assessed by observing standard stars. To mitigate the sky effects, multiple sets of observations are taken, and those with comparable total counts in four polarization angles are used in polarization analysis. This compromises the time resolution to a few minutes, but because of the simultaneity in three bands, TRIPOL still proves efficient. TRIPOL should be especially useful to investigate variability phenomena on timescales from a few seconds to years or longer. These include, but not limited to, gravitational-wave counterparts (Morokuma et al. 2016), gamma-ray bursts, cataclysmic variables, eclipsing binaries, Cepheids, novae, supernovae, blazars, Miras, and T Tauri stars (Chen et al. 2015; Huang et al. 2019).

We are pursuing several programs for polarimetric monitoring of Galactic star-forming regions. An organized polarization pattern of background stars, as the result of dichroic extinction by magnetically aligned dust grains, provides the magnetic field structure in a dark cloud (Davis & Greenstein 1951), whereas scattered light reveals the radiation fields and spatial distribution of circumstellar matter of young stellar objects. Polarimetric observations with TRIPOL2 on the Lulin 1-m telescope were carried out for IC 5146 on 27 and 28 July 2012. Seven fields were observed toward the north-west part of this filamentary cloud, with a total exposure time of 1.5 hour (22.5 min for each HWP angle). Polarization measurements simultaneously acquired in $g^{\prime}$-, $r^{\prime}$-, and $i^{\prime}$-bands were corrected for both instrumental polarization as well as offset polarization angles by observing polarized and unpolarized standard stars. Figure 5 shows the $i^{\prime}$-band polarization of the north-west part of IC 5146 (Wang et al. 2017).

Also plotted in Figure 5 are the AIMPOL (ARIES Imaging Polarimeter) $R$-band and Mimir $H$-band polarization data. AIMPOL (Reutela et al. 2004), an optical polarimeter adapted to the 1.04 m Sampurnanand Telescope of the ARIES in Nainital, India, has been well calibrated over the years by observing unpolarized and polarized standard stars (Medhi et al. 2007, Eswaraiah et al. 2013). Mimir is a near-infrared imager for polarization measurements (Clemens et al. 2007) mounted on the 1.8 m Perkins Telescope in Arizona, operated by Lowell Observatory.

While TRIPOL2 and Mimir observations each covered a larger part of the filament than the AIMPOL data did, the measured polarization results by the three instruments, two working in optical and one in near-infrared, are consistent with each other, suggesting a global magnetic field roughly parallel to the long axis of the filament. On average TRIPOL2 detected more prominent polarization than Mimir, a manifestation of a higher fractional polarization in visible wavelengths because the extinction difference is amplified. Infrared polarimetry, on the other hand, probes denser parts of a molecular cloud. A combination of optical and infrared polarimetry, together with millimeter and submillimeter interferometric observations of polarization, hence offers the opportunity to scrutinize the magnetic field structure from scales from a cloud core to the central protostar. The detailed results of IC 5146 can be found in Wang et al. (2017).

Another application of TRIPOL is on the point source GM Cep, a 4-Myr T Tauri star undergoing abrupt photometric variations caused by obscuration of protoplanetary dust clumps (Chen et al. 2012; Chen & Hu 2014; Huang et al. 2019). The long-term photometric and polarimetric monitoring data, shown in Figure 6 show a noticeable polarization up to 8% with temporal variability on a time scale of years, while the comparison star exhibits a steady level of polarization, with a standard deviation less than 1%. Such polarization observations provide valuable information of the distribution and properties of the circumstellar dust clumps from grain growth from micron-size dust in transition to km-size planetesimals (Huang et al. 2019).

5 Summary

The simultaneous three-color ($g^{\prime}$, $r^{\prime}$, $i^{\prime}$) polarimeter, TRIPOL, is simple, compact and economical, suitable for a small telescope in a moderate astronomical site. This paper presents the design concept, and compares the performance to data taken on the 1-m telescope located in Taiwan. The limiting magnitudes for photometry are found to be $g^{\prime}\sim 19$ mag, $r^{\prime}\sim 18.5$ mag, and $i^{\prime}\sim 18$ mag, with a signal-to-noise of 10 and an integration time of 100 s. The internal instrumental polarization is at the level of 0.3% for a 100-s integration at all three bands. The simultaneous photometric and polarimetric capability should open up new research opportunities for time-domain astronomy on small or amateur telescopes.

Acknowledgements.

We are thankful to N. Takeuchi and A. Yamanaka for their laboratory experiments, and to Drs. M. Kino, M. Kurita, T. Nagayama, K. Kawabata, M. Ishiguro, and H. Takami for valuable comments throughout the development of this project. We appreciate Dr. Y. Nakajima for his kind assistance for the data reduction and Drs. M. Ishiguro and K  Murata for preparation of the figures. This work is supported by Grant-in-Aid for Science Research from the MInistry of Education, Culture, Sports, and Technology of Japan. SS owes his scientific activity to Dr. H. Fujiwara for his generous support of astronomy.