The Thirty Millimeter Telescope

In this paper, we use the term “camera” as the vacuum vessel (dewar), a cryocooler, a detector and a filter wheel. An objective lens is placed on the lens mount attached in front of the camera to construct a “telescope”. Figure 3 shows our observing system, which consists of the telescope, an equatorial mount, and a dome. A close-up of the telescope is also shown in the figure.

Based on the motivations mentioned in the previous section, we have developed a NIR telescope based on an engineering grade Raytheon VIRGO 2048 $\times$ 2048 pixels HgCdTe array (Love et al. (2004)). The telescope has an effective aperture size of 30 mm and is named the Thirty MilliMeter Telescope²²2The telescope is formerly called as IR-TMT but renamed to TMMT. (TMMT).

The camera is cooled with a cryocooler. The array temperature is monitored with platinum (Pt) temperature sensors and maintained at 76.3 K using a temperature controller and a resistive heater. The camera has a long cylindrical “nose” that houses a cold baffle. The diameter of the upper part of the cold baffle is 30 mm and defines the effective aperture of TMMT. At the top of the nose, an objective lens (CaF₂ Plano-Convex lens) mount is attached via a linear stage for focusing. TMMT and auxiliary equipment, e.g., an array controller (TUFPAC; Ichikawa et al. (2003)) and a DC power supply are assembled in a bracket of aluminum frames. The total weigh of TMMT including the mounting bracket is $\sim$50 kg.

TMMT is installed on a commercial fork equatorial mount in the 4 meter dome at Subaru Telescope Okayama Branch Office (OBO; formerly known as Okayama Astrophysical Observatory), National Astronomical Observatory of Japan (NAOJ) at Okayama prefecture, Japan. The dome is located at 34.56^∘ North and 134.58^∘ East with an altitude of 372 m. The typical seeing in the optical at OBO is $\sim$1.5${}^{{}^{\prime\prime}}$ full width at half maximum. The assemblage of TMMT, the dome, and the equatorial mount is called as the TMMT observing system hereafter.

The TMMT observing system consists of seven main subsystems: observation console, mount and dome control system, filter exchanger, array controller, camera, temperature monitor and controller, and focus adjustor. Figure 4 is the hardware block diagram of TMMT, which lists the components of each subsystem. All the subsystems are connected to the LAN via a PC or a terminal server, so that the observation console, PC #1, can collect all statuses, and then issue commands as requested by observers or controllers. All of the collected statuses are stored in a database on the PC #1. The observing system is designed so as to be friendly for semi-automated remote observations (see section 2.4).

The main specifications of the TMMT observing system are listed in Table 2.1.

The equatorial fork mount (R.A. and DEC. axes), dome rotation, dome slit, and power supplies have in-house Local Control Unit (LCU³³3LCU is a microcomputer based parallel I/O board with a serial interface, that is used to control subordinate devices and to make the subsystem a discrete controller.) boards, and are controlled from a PC (PC #2 in Figure 4) using the RS232C protocol through a terminal server⁴⁴4Terminal server is a Linux based appliance used to convert messages from serial to TCP/IP or vice versa.. In case of emergency, such as a power or network failure, the power supplies can be automatically shut off. It also monitors the rain sensor and automatically closes the dome slit when rain is detected. Thanks to this system, semi-automatic remote observations can be done safely. The specifications of the mount and dome, as well as the details of the control system, are found in Tsutsui et al. (2016).

We have developed a software that links the subsystems together to enable semi-automatic remote observations. The software simply receives the list of target coordinates. Then the software sequentially repeats target pointing, exposure, dithering, filter exchange, etc. until the twilight time. Targets closer to the western horizon will be given priority to maximize the cadence of the observations. Since we can leave the observation to the software, survey-type observation can be easily done. It also requires less manpower, so that nightly observations can be continued over a long period of time.

Here we define an inoperable pixel as the one that produces no useful signal, namely, bad, dead, and hot pixel, that has poor sensitivity, poor linearity, and/or that is located in seriously vignetted region. The number of inoperable pixels was counted as follows.

First, an image was made by dividing the dome ceiling image of 60 s exposure with that of 20 s exposure. No correction was made for the temporal variation due to the change of thermal radiation from the dome ceiling. The charges accumulated in the 60 and 20 s exposures are $\sim$60 and $\sim$20% of the full-well of the detector, respectively. Ideally, the signal counts of every pixel in this image should be equal to the ratio of the exposure times, which is 3 in this case. Figure 7 is a histogram of the signal counts of every pixel in the image. The distribution has a peak at 2.91 with the standard deviation $\sigma$ of the distribution of 0.04. Then we refer to pixels whose values deviate from the peak value by more than 5 $\sigma$ as group A of inoperable pixels. Obviously, the histogram is affected by the nonlinearity of the detector and/or the temporal variation of the thermal radiation from the dome ceiling. In addition, the dark current is ignored for this study. However, these factors are not important for our purpose to identify inoperable pixels.

Next, ten dark images with an exposure time of 20 s are combined to obtain the median image. The median and standard deviation of the pixel values of the median combined image are calculated. Then we choose pixels whose values deviate from the median by more than 5 $\sigma$ as group B of inoperable pixels.

Finally, a disjunction operation (i.e. logical OR) between candidate of groups A and B is performed to identify final inoperable pixels. The number of inoperable pixels is 396,835. As a result, the pixel operability of the detector is approximately 90.5%. This is consistent with a report by Raytheon Corporation, in which 92 $\sim$ 94% of the pixels passed their quantum efficiency test. Figure 8 shows the map of inoperable pixels identified by our study. The identified inoperable pixels will be masked and not be used for further analyses.

The conversion gain (e^- ADU^-1) relates the raw detector unit of analog-to-digital unit (ADU) to the electron unit (e^-). Because we employ the 4-channel readout of the VIRGO detector with a vertical strip of 512 $\times$ 2048 pixels for each channel, the gain and the readout noise are derived for each channel. For convenience, we define the N-th channel as an image section of 512 $\times$ (N-1) to 512 $\times$ N-1 pixels in the column direction and 0 to 2047 pixels in the row direction.

We use a photon transfer curve method to obtain the conversion gain $g$ and the readout noise $R$ in e^- of the detector. The method assumes that number of photons detected by the detector follows the Poisson statistics, and that all the pixels used for the measurement have same properties and same illumination. Then, $g$ and $R$ are related by

where $C$ is the count of pixel value in ADU and $\Sigma$ the standard deviation.

The $g$ and $R$ are calculated using the data described in section 3.1.2 after calibrating the temporal variation of the thermal radiation from the dome ceiling. A pair of the dome ceiling images with the same exposure time is subtracted from each other, and the median and variance are calculated with an iterative 3-sigma clipping for every 8 $\times$ 8 pixels bin using the ceiling images and the subtracted images, respectively. The size of the bin of 8 $\times$ 8 pixels is chosen to ensure both statistical sufficiency and uniform illumination. Then half of the variance corresponds to the $\Sigma^{2}$ and the median to $C$, whose plots are shown in Figure 9. The running median of the variance with a step of 100 ADU in signal is calculated and a linear relation is fitted using data with signal values larger than 1500 ADU and smaller than 15000 ADU, where the linearity of the detector is relatively good (see section 3.5). The results of the fits and the calculated gain and readout noise for each channel are summarized in Table 3.3.

The dark current generation rate is estimated using the data described in section 3.1.1. For each median-combined dark image, mode and sigma of the count distribution (see Figure 10 for example) are estimated by fitting a normal distribution function to the distribution to obtain representative values of dark current and its scatter. The dark current generation rate is estimated from the relationship between the exposure time and the number of electrons generated. Figure 11 shows the result, where a linear relation with a fixed intercept of zero is fitted. Its slope corresponds to the dark current generation rates, which are 0.3-0.5  e^- s^-1 as summarized in Table 3.3. The detector data report provided by Raytheon Corporation gives a dark generation rate of 1.51 $\pm$ 1.54 e^- s^-1 at an operating temperature of 78 K. The possible cause of the difference is the difference in the temperature, where we operate the detector at 76.3 K (see section 2.2.1).

The linearity of the detector is evaluated using the data described in section 3.1.2. First, we fit a linear relation to the signal counts in the range of 2000 to 8000 ADU. The top panel of Figure 12 shows the result of the regression for a pixel ($x=$548, $y=$1002) as an example. Dots in the bottom panel of Figure 12 indicate deviation from the linear regression as ratio. Finally, a sixth-order polynomial curve is fitted to the signal count vs. ratio data. The correction for linearity can be made by dividing the signal count by the best fit prediction ratio. The results of the polynomial regression and the linearity correction are shown as thick solid line and crosses in the bottom panel of Figure 12. We define the applicable range of the linearity correction such that the ratio between the predicted and corrected signal counts fall within $\pm$1% from unity. The series of analysis is performed for all operable pixels to obtain the linearity correction of sixth-order polynomial equation and its range of application. Signal counts outside the range are masked in practical data analysis. With a few exceptions, the properties of linearity are more or less the same for operable pixels. The median and standard deviation for all operative pixels of the full well and the $<$1% linearity range without and with the non-linearity correction are summarized in Table 3.5 and their histograms are shown in Figure 13.

More than a hundred twilight sky images (corrected for linearity and dark) are median-combined and are normalized with respect to the median value of the whole pixels. So-called flat-fielding image is made in this way.

Figure 14 shows the $K_{{\rm s}}$-band flat-fielding image and its histogram. There is a non-uniform illumination pattern in the flat-fielding image due to vignetting of the incoming light caused by the cold baffle. Note that the physical array size is 40.96 mm by 40.96 mm and the diameter of the cold baffle is 30 mm. This is the cause of the double-peaked distribution of pixel values seen in the bottom panel of Figure 14.

The primary purpose of the TMMT development is to observe northern bright stars in the $J$, $H$, and $K_{\rm s}$ bands, and to provide their accurate photometric data. To achieve this goal, we have carried out a survey of the belt-like area along the northern Galactic plane. Specifically, the survey area ranges within declination of $\delta\geq-30^{\circ}$ and galactic latitude of $|b|\leq 5^{\circ}$ as illustrated in Figure 15. We use a hexagonal mosaicking pattern with a spacing of $\frac{\sqrt{3}}{2}\times 5^{\circ}$ between the adjacent pointings. Thanks to the wide FOV ($\sim$ 25 square degrees) of TMMT, the whole survey area can be covered by 173 pointings. We have carried out 20-dithering observation at each pointing for the photometric survey, where dithering positions are located on a circumference with a radius of 40${}^{{}^{\prime}}$ with an equal spacing. A 7 s exposure image is taken at each dithering position, and the total exposure time is 140 s.

As an example of the image taken with TMMT, we show a $K_{\rm s}$-band image toward the Galactic center in Figure 16. Note that size of the image is slightly larger than the FOV of TMMT (5^∘ $\times$ 5^∘), as it is the result of a median combination of 20 dithered images. The prominent black area in the lower left is caused by inoperable pixels (see Figure 8). We perform the photometry on the combined image referring to its exposure map. To achieve high photometric accuracy, we have chosen the stars in the area with 10 or more exposures in their exposure map.

The photometric survey has been completed. More than 13$\times 10^{5}$, 29$\times 10^{5}$, and 19$\times 10^{5}$ stars have been detected in the $J,H$, and $K_{\rm s}$ bands, respectively (Ita et al., in preparation). We plan to gradually expand the survey area in the future.

The secondary purpose of the TMMT observation is to characterize infrared variability of bright stars in the Galactic plane. It is known that some types of variable stars, such as Cepheids and Miras, have a statistical relationship between their brightness and light variation periods. The relation is called the period-luminosity relation (Leavitt & Pickering (1912)) and is widely used as a good distance scale (e.g., Freedman (2013)). The infrared period-luminosity relation is preferable, due to smaller effects of interstellar extinction. Also, the scatter of the relation becomes smaller at longer wavelength (e.g., Madore & Freedman (2012)). In addition, there are currently no or insufficient infrared time-series data of bright (bright in the infrared) variable stars. We have been monitoring the same area as that of the photometric survey since October 2016 with a typical cadence of twice a month. We use 15 dithering mode for the variable star survey with the effective exposure time of 105 s. This monitoring survey will provide systematic time series data of the bright stars for the first time. We plan to continue this survey as long as possible.

To demonstrate our multi-epoch survey data, we show in Figure 17 two examples of the light curves, Lomb-Scargle periodograms (Lomb (1976), Scargle (1982)), and phased (phased with the primary period) light curves for a Mira-like variable (KK Sge) and a classical Cepheid variable ($\delta$ Cep).

In both photometric and variable star surveys, we intentionally take slightly defocused images so that the full width at half maximum (FWHM) becomes 3 to 4 pixels in order to avoid under-sampling.