Toward Next Generation Solar Coronagraph: Diagnostic Coronagraph Experiment

In order to provide successful observation of the TSE, the optical system has several requirements. The major requirements are system resolution and accuracy of the measured intensity. To achieve the system resolution, the RMS spot diameter of the optical system should be less than two pixels of the CCD whose pixel size is 7.4 $\mu$m, thus the RMS spot diameter should be less than 14.8 $\mu$m. For the measured intensity accuracy, the intensity variation due to stray light or polarization angle offset should be less than $\pm$ 1$\%$. Table 1 summarizes the requirements of the overall optical system.

The optical design works are carried out based on the requirements. Beside those specifications, the design works should consider two plane windows for bandpass and polarization filters. Figure 2 shows the final optical design which consists of 4 lenses and 2 filters. Each surface of the lens is a spherical surface except the back surface of the lens 2. Using the aspherical surface on the lens 2 provides an advantage for simplifying the overall system. In the past time for the optical designing works, the aspheric surface is rarely used due to fabricating and testing difficulties. However, recently those works are not challenging in these days. The stop is located at the center of the lens group to reduce odd aberrations. As shown in Figure 2, the distance between the last surface of the lens 4 and CCD is about 30 mm, which allows a space for CCD camera moving to find the best focusing position.

Figure 3 is a spot diagram to show the expected performance of the system. The RMS diameter is about 5.6 $\mu$m which is much less than 14.8 $\mu$m of two-pixel sizes. The different value between nominal design and the requirement would be a margin for other parameters such as fabricating, manufacturing, and aligning errors which are usually difficult to achieve the nominal requirements.

The tolerance processing is done by Zemax, ray-tracing software package for the optical design works. In that process, all parameters are perturbed and analyzed for the performance. The tolerance for each optical element is simulated with random perturbation to see if the performance still meets the requirements. Most of the tolerance values are reasonable if the lens maker fabricates in the specified precision level. One of the difficulties to fabricate the lenses is the aspheric surface in the back surface of the lens 2. The tolerance of the conic constant is $\pm$0.0125, and the performance still meets the requirements with that error. The lens 2 was fabricated by a local lens manufacturer in Korea who uses Magnetorheological Finishing (MRF) for the finishing process and Aspheric Stitching Interferometer (ASI) for testing surface error.

To reduce the first-order scatter light, we take a ghost focus analysis that is related to the lens group and baffles. We perform the analysis to understand how much unwanted photon energy from Fresnel refraction and reflection of the lens interface reaches on the CCD surface. The DICE is optimized at the 405nm of the central wavelength, and all lenses are anti-reflection (AR) coated in wavelength from 385nm to 410nm for 10^∘ of incident angle such that the reflection against the lens surface is less than 0.7% of the incident light. We take the analysis in Zemax to find any critical optical elements causing any unexpected beam on the CCD. As a result, we find that the filters consisting of the flat surfaces causes double bouncing, and ghost focus is imaged on the CCD. It is also confirmed that the polarization filters, if not AR coated, produce some amount of ghost effects on the CCD (Figure 4). After applying AR coating on the polarizer, we can achieve less than 1% of the photon energy loss due to ghost image, which indicates that the ghost effect for the bandpass filter is minor. In fact, the bandpass filters could not be AR coated since AR-coating on the surface reduces bandpass performance.

The bandpass filters are purchased from Andover custom bandpass filters for each center wavelength with 10 nm of bandwidth, and blocking in other wavelengths up to far infrared. We use the Thorlabs’ WP50L-UB which is ultra broadband wire grid polarizer with AR coating. Originally it comes with no coating on both surfaces, and its transmission and extinction ratio are $\sim$ 70$\%$ and $\sim$ 5000 respectively. We apply AR coating on the polarizer to reduce ghost effects as shown in Figure 4. The total powers are 3.4755 and 3.6174 out of 5 watts of total incoming power before and after the AR coating on the polarizer, respectively. The difference is about 0.14 watt or about 4% of noise reduction. Figure 5 shows the filter and polarizer units.

Another factor that reduces the system performance is the light coming from outside of the field of view of the system. In the simulation, those unwanted light produces a little noise on the CCD. Limiting the bundle of the light with 64.5mm of a baffle in front of the first lens can remove those noise. The baffles are also the mount of the lens and filter. We used Lambertian scatter model, which is an ideal diffuser surface, for the scattering model of the baffle surface. We compared the CCD view with and without front baffles, and found that the difference between with and without the baffle is about 0.02% of noise introduced.

The requirement for the resolution of the DICE is to make the RMS spot diameter smaller than two CCD pixels. During the DICE system assembly and test process, a CCD camera was not ready yet. Thus Thorlabs’ DCU22M CCD camera with 4.65 $\mu$m of the pixel size was used for the test. For the test setup, we placed a white light point source at the long-distance and imaged it on the CCD through the DICE optics. As a result, we found that the image of the point source in the maximum intensity occupies two pixels or 9.3 $\mu$m, which is less than the requirement of 14.8 $\mu$m. Although the spot is too small to identify, the spot shape looks elliptical, which means the system has a little aberration. It is also found that the image also does not show any noticeable noise. The maximum peak value of the point source image is 255 with noise level 18.1$\pm$ 6.12.

The other requirement is to make the polarization angle accurate so that the intensity variation is less than 1% in the same orientation in every rotation. During the TSE observation, the orientation of the polarizer rotates every 60^∘, and the image in each angle is used to obtain polarization information such as polarization brightness and degree of linear polarization. For the test of the polarization angle accuracy, a linearly polarized 405nm laser source is used with the polarizer in the DICE. The intensity measurements are carried out with 10 revolutions of the polarizer. As shown in Figure 6, the standard deviation is 0.68% which is less than 1%.

A computer used in the DICE control system is ASUS UN65U model, which has 2.5GHz of clock speed, 4GB of program memory for the operating system and control software, and 256GB of mass storage for observation data. We installed Ubuntu 16.04 LTS 32bit on this computer to build an operating environment for the DICE control software. The computer supports USB3 and Ethernet ports as an interface for communication with peripherals. The filter wheel connects two motors with an RS-232 interface in series using USB-RS232 converters, and the camera connects to a USB2.0 compliant interface. The two operation systems use a separate Ethernet port to connect to the wireless Ethernet switch and establish a network environment that allows them to connect the user’s computer via a wireless connection.

We use the core Flight System (cFS) of NASA to develop DICE control software as shown in Figure 7. The cFS is a reusable software framework for real-time systems especially in space missions (McComas et al., 2016). The DICE control software is aimed at the successful observation of the TSE. The control software is configured in a layered architecture as shown in the upper panel of Figure 7. We developed four mission applications consisting of the camera control (CAM), two filter wheel control (WHL), science data processing and storing (DAP), and observation automation (OBS). With the mission applications, the DICE control software was built integrating three open-source applications of command ingestion (CI), telemetry output (TO), and scheduler (SCH) for periodic command generation. The Lower panel of Figure 7 shows the graphical user interface of the DICE remote control software. The remote control software sends and receives command and telemetry packets through UDP communication with the control software running on the DICE control computer. The remote control software was developed to control the filter wheel and camera using various parameters and to display observation progress and down-sampled images. It was utilized from the DICE assembly and alignment to the TSE observation.

Figure 8 shows the transmissions of the optical elements with the quantum efficiency of the CCD ($QE_{ccd}$) and the calculated coronal irradiance at 1.2R_⊙. $QE_{ccd}$ is measured using a spectrograph with integration sphere with 2% of measuring tolerance. The bandpass filter transmission ($Tr_{fil}$), the polarizer transmission ($Tr_{pol}$), and the extinction ratio of the polarization $ext_{pol}$ is provided by manufacturer, Andover and Thorlabs, with a tolerance of 2.5%, 1%, and 1% of transmission and extinction variation. We assumed the tolerance of the bandpass filter central wavelength as 2.5 Å by considering the transmission tolerance of 2.5% of the filter with 100 Å bandwidth. The lens transmission ($Tr_{lens}$) is simulated using Zemax software. We assumed the tolerance of $Tr_{lens}$ as 1%.

The signal recorded in a specific pixel of the CCD is given as,

, where $E_{ph}$ is photon energy, $A_{ap}$ is the aperture size of the optics, $\Omega_{pixel}$ is the solid angular size per a pixel, $t_{exp}$ is the exposure time, $g$ is the gain of the camera, $\theta$ is the polarization filter angle with respect to the tangential direction, and $ext_{pol}$ is the extinction ratio of the polarization filter. $I_{t}$, $I_{r}$, and $I_{unpol}$ denote the tangentially and radially polarized brightness and the unpolarized brightness coming through the aperture, respectively. $I_{t}$ and $I_{r}$ contains K-coronal brightness, while $I_{unpol}$ contains the unpolarized light coming from sky and F-corona. $I_{t}$ and $I_{r}$ are described as the sum and subtraction of polarized brightness ($pB_{kcor}$) and the total brightness ($tB_{kcor}$) of the K-corona.

For the calculation, $tB_{kcor}$ and $pB_{kcor}$ are imported from the Thomson scattering calculations by assuming the isothermal corona and the coronal electron density model of Baumbach (1937), in the condition of the electron temperature of 1 MK and the solar wind speed of 400 km $s^{-1}$. The detailed calculation scheme is done following Cho et al. (2016). The second term of the equation 1 represents the light polarized orthogonal to the polarizer which is not perfectly extinct, while the first term of the equation 1 represents the polarized light passing through the polarizer.

Figure 9 presents the estimated filter ratio of the 4025 Å and 3934 Å  filters for temperature calculation. The ratio is calculated using the Monte-Carlo method, which is often used to model how the different errors propagate over a system. We generate the gaussian distributed random errors of optical and mechanical tolerance, photon noise, dark, and readout. We apply the exposure times given in Table 3, which were taken during the TSE observation. The random sampling is repeated for $10^{6}$ samples. The 3-$\sigma$ deviation from 1.29 to 1.59 centering at 1.44 of the value represents the systematic tolerance propagates on the observed result. For example, if we made a DICE with no error on the instrument and there was no noise during the observation, the filter ratio shall be 1.44. Otherwise, the ratio shall be shifted to obtain the deviating temperature.

Electron temperature can be calculated following the anti-correlated relation between the filter ratio and the temperature as shown in Figure 10.

The deviation of calculated temperature due random noise during the observation is decreased by stacking the images as shown in Figure 11. Temperature derived from single image with $3\times 3$ binning scatters from 0.55 MK to 1.70 MK (3-$\sigma$ of temperature). The deviation is decreased by stacking the images. This deviation is mainly caused by the photon noise. Uncertainty of the sky brightness, F-coronal brightness, dark, and readout noise also contribute to it. We expect temperature ranged from 0.77 MK to 1.26 MK (about $1\pm 0.25$ MK) if we stack 5 images. Note that, even though the filter ratio follows gaussian distribution, the temperature deviation is asymmetric in y-axis because the function transforming the ratio to temperature is not linear.

On August 21, 2017, the total solar eclipse was visible across the entire United States continuously. We observed the eclipse at a site near Jackson hole, Wyoming, where it was anticipated to have good weather. The eclipse began to darken the observation site as the partial eclipse progressed from 16:16:57 UT. The total eclipse began from 17:35:08 UT with 140 seconds duration time. Maximum eclipse occurred at 17:36:18 UT and the solar position was 50.5^∘ of altitude and 135.1^∘ of azimuth. The eclipse ended at 19:00:42 UT. Table 2 shows the eclipse times and positions of the Sun at the observation site during the eclipse.

The observation started about two hours before the total eclipse after aligning the optical system and commissioning the electronics and mechanics of the observation system. Observation modes consist of dark imaging, partial eclipse pinhole imaging, and total eclipse imaging. The dark images were acquired for image preprocessing by shielding the front open aperture of the DICE from light using pinhole cover and dark pouch over the front baffle. One set of dark imaging takes 10 images for 13 levels of exposure time from 0 to 5 seconds, so the total count was 130 images. The pinhole observation was done by a 200$\mu$m pinhole in front of the aperture. The pinhole image is necessary to obtain the brightness of the Sun and the atmospheric transmission of each filter, so a total of 120 images in a set were acquired in 10 repeats of 12 images for four bandwidth filters and three polarization angles. They were taken every 10 minutes during the partial eclipse phases.

Table 3 denotes the total eclipse observation sequence including filter wavelength, exposure time, polarization angle, duration time, and number of images. The exposure times of each sequence for different filters were determined by using the pinhole observation taken one day before the eclipse. Firstly we determined exposure times for pinhole observation of the solar disk. We then estimate the exposure times of the TSE by using assumed disk to corona brightness ratio of 10⁶ and pinhole to full aperture ratio. Finally we confirmed the exposure times during the partial eclipse observations.

In the filter wheels, there are four filters: 393.4 nm and 402.5 nm for coronal electron temperature sensitive lines, and 399.0 nm and 424.9 nm for speed sensitive lines to determine coronal electron temperature and speed respectively. For the polarizer wheels, there are three polarization angles: 0, 60, and 120 (actually 180, 240, and 300 for 402.5 nm and 424.9 nm filters) degrees to take polarized brightness of the solar corona. Exposure times for each filter (393.4, 402.5, 399.0, and 424.9 nm) are 192, 236, 288, 69 milliseconds, respectively. The spatial pixel size is about 13 arcsec. A total of 162 images were acquired for 136 seconds during TSE from one DICE system. Unfortunately we failed to obtain data from the other CCD camera of the other unit due to a frame transfer error of the camera.

We took flat field images before and after the TSE covering the aperture with white cloth as diffuser, but the obtained images were not consistent. After the observation, we also tried to obtain a flat field image using the dispersed light of the pinhole observation. But we failed to get the flat field because the light passing through the pinhole was not dispersed enough to cover the whole image plane of the CCD. However, the pixel to pixel sensitivity variations and the effect of dust or scratches on the optics and CCD window is expected to be negligible across a few pixels of tracking drift during the TSE. Therefore, the flat field will be cancelled out when we calculate the filter ratio and our result will not be affected. After aligning each filter images, the images were stacked to each polarization to improve the signal to noise ratio.

Figure 12 shows a white light (WL) image and filtered images during the TSE. The WL image was taken by using the Canon 400 mm lens, 2X extender, and camera with the exposure time of 16 msec. The filter images were taken using 402.5 nm filter for three different polarization angles (0^∘, upper right; 60 ^∘, lower left; 120 ^∘, lower right). By combining the three polarization angle images in a specific wavelength, we calculate the polarized brightness ($pB_{obs}$), total brightness ($tB_{obs}$), linear polarization degree ($pD_{obs}$), and linear polarization angle ($pA_{obs}$) (Billings, 1966; Lu et al., 2017):

where $I_{0^{\circ}}$, $I_{60^{\circ}}$, and $I_{120^{\circ}}$ are brightness at polarization angles of 0^∘, 60^∘, and 120^∘, respectively.

We adopted pinhole observation with a diameter of 0.2 mm to correct the difference of the intensity attenuation of the Earth’s atmosphere at different wavelengths. The correction factors of the filter ratio are obtained by comparison between the theoretical model intensity and the observed intensity. The theoretical model intensity is calculated by using the instrumental transmissions and the quantum efficiency shown in Figure 8. We used the 2000 ASTM standard extra-terrestrial spectrum reference E-490-00 for the calculation (ASTM E490-00a, 2000). The intensity of the pinhole observation of each filter is obtained by integrating the counts in the CCD after dark subtraction. As a result, the atmosphere correction values of about 1.02 and 1.01 for temperature and the speed ratios respectively were obtained.