Voltage-to-temperature calibration of the High Altitude THz Solar telescope acquisition system

Imagine trying to listen to a whisper in the middle of a roaring hurricane. That is essentially what astronomers face when they try to study the Sun using a specific type of invisible light called Terahertz radiation. This light sits between microwaves and infrared on the spectrum, and while it holds the secrets to how the Sun's atmosphere reacts to massive magnetic explosions, it is incredibly hard to catch. Our planet's atmosphere is full of water vapor that acts like a thick fog, soaking up this radiation before it ever reaches the ground. To get a clear signal, scientists have to build telescopes high up in the mountains, use super-sensitive detectors, and then figure out exactly how to translate the tiny electrical "pings" their machines receive into real, physical temperatures. It's a bit like trying to guess the temperature of a campfire just by listening to the crackle of the wood, but the crackle is being drowned out by a jet engine.

This paper is the story of how a team of scientists tuned the "ears" of a special telescope called HATS (High Altitude THz Solar) to make sure they aren't just hearing noise. They didn't look at the Sun directly; instead, they set up a controlled experiment in a lab. They used a device that acts like a perfect, glowing heater (a blackbody calibrator) to send known amounts of heat to the telescope's detector. The goal was simple: create a perfect dictionary that translates the voltage (electrical signal) the machine produces into the exact temperature of the heat source. They tested two different ways to read the signal—one like fitting a smooth curve to a wiggly line, and another like using a digital filter to isolate a specific musical note. They found that while both methods worked well, one specific digital filter (called the Hamming window) was the most precise, giving them a clear, linear map to turn raw data into scientific truth.

The Sun's Secret Language and the Telescope's Ear

To understand this research, we first need to meet the star of the show: the Sun. The Sun isn't just a steady ball of fire; it's a chaotic, magnetic beast. Sometimes, it releases massive bursts of energy called solar flares. These flares shoot out light across the entire electromagnetic spectrum, from radio waves to X-rays. While we are very good at watching the Sun in radio and X-ray light, there is a "blind spot" in the middle: the Terahertz (THz) range.

Think of the THz range as a hidden language the Sun speaks during these flares. Scientists believe this light comes from the dense, hot layers of the Sun's atmosphere (the chromosphere) and could tell us exactly how the magnetic energy is being released. However, Earth's atmosphere is like a heavy blanket made of water vapor that blocks this specific language. To hear it, we need to go high up, above most of the blanket. That's where the HATS telescope comes in. It sits high in the Andes mountains, designed to catch these THz signals.

But catching the signal is only half the battle. The telescope uses a special detector called a Golay cell. You can think of this cell as a tiny, super-sensitive balloon that expands when it gets warm. When THz radiation hits it, the balloon expands just a tiny bit, creating a small electrical voltage. The problem is, this voltage is tiny and gets mixed up with background noise. To make the signal stand out, the scientists use a mechanical "chopper" (a spinning wheel with holes) to cut the light beam on and off very quickly, 20 times a second. This turns the steady heat into a rhythmic pulse, like a flashing light, which is much easier for the electronics to spot.

Now, here is the tricky part: The telescope sees a voltage (like 5 millivolts). But scientists need to know the temperature (like 500 degrees Celsius). They need a calibration curve—a mathematical recipe that says, "If the machine reads X volts, the source is actually Y degrees." If this recipe is wrong, all their data about solar flares will be wrong, too. This paper is all about baking that perfect recipe.

The Experiment: Cooking with a Perfect Heater

The researchers didn't just guess the recipe; they cooked it up in a lab. They set up a "kitchen" with four main ingredients:

1. The Heater: A high-precision blackbody calibrator. Imagine a metal box that can be heated to exact temperatures, acting as a perfect source of heat radiation.
2. The Chopper: A spinning fork that cuts the heat beam 20 times a second, turning the steady heat into a 20 Hz pulse.
3. The Detector: The Golay cell, which turns that pulsed heat into an electrical signal.
4. The Recorder: A digital oscilloscope that captures the electrical signal as a squiggly line on a screen.

They heated the blackbody box to different temperatures, starting at 100°C and going all the way up to 375°C (which is 373.15 K to 648.15 K). They did this in steps of 50°C. At each temperature, they recorded the signal. They did this twice: once while heating the box up, and once while cooling it down, to make sure the results were consistent.

The Detective Work: Two Ways to Read the Signal

Once they had the squiggly lines of voltage data, they had to figure out how to measure the "loudness" (amplitude) of the 20 Hz pulse. They tried two different detective methods:

Method 1: The Sine Fit
Imagine the signal is a wiggly line that looks like a wave. The first method simply tried to fit a perfect sine wave (a smooth, rolling hill shape) over the data. It asked, "What is the height of this wave?" This is a straightforward way to measure the signal.

Method 2: The Windowed FFT
The second method was a bit more high-tech. They used a mathematical tool called the Fast Fourier Transform (FFT). You can think of the FFT as a magical prism. If you shine a white light (a complex signal) through a prism, it splits into individual colors (frequencies). The FFT takes the electrical signal and splits it into its frequency components. Since they knew the signal was exactly 20 Hz, they just looked at the "color" at 20 Hz to see how strong it was.

However, there was a catch. When you use a prism on a short piece of data, the colors can get blurry and spill over into each other (a problem called "spectral leakage"). To fix this, the scientists used "windowing functions." Imagine the signal is a song playing on a radio. If you suddenly turn the radio off, you hear a click or a pop. A window function is like a smooth fade-out; it gently turns the volume down at the start and end of the signal so there are no clicks. The team tested six different "fade-out" styles: Rectangular, Hamming, Hann, Bartlett, Blackman, and Flat-top.

The Results: Finding the Perfect Filter

After running all the numbers, the team compared the results. They wanted to see which method gave them the most accurate "dictionary" to translate voltage to temperature.

They found that both methods worked very well. The relationship between the temperature of the heater and the voltage from the detector was incredibly straight and predictable (highly linear). This means the telescope is behaving exactly as it should.

However, when they looked at the precision, one method stood out slightly. The Hamming window (one of the fade-out styles) produced the cleanest results with the lowest error. The error was measured as a Root Mean Square Error (RMSE) of 15.48. In comparison, the Bartlett window had the highest error at 16.02.

The "Sine Method" (fitting the wave directly) gave slightly different numbers than the windowed methods, but the difference was small enough that both are considered reliable. The most important number they found is the calibration factor: 10.32 ± 0.13 mV/K. This means for every 1 Kelvin (degree) increase in temperature, the detector's voltage goes up by about 10.32 millivolts.

Interestingly, the choice of window function didn't change the final calibration factor much. Whether they used Hamming, Blackman, or Flat-top, the factor stayed between 10.32 and 10.43 mV/K. This tells the scientists that they have a lot of flexibility; they can choose the window that is easiest to use, and the results will still be accurate.

Why This Matters

This paper doesn't just give us a number; it gives the HATS telescope a reliable voice. Now that the scientists have this precise calibration, they can point the telescope at the Sun and know exactly what temperature they are seeing. When a solar flare happens, they won't just see a "blip" on a graph; they will know, "That blip means the temperature jumped by 50 degrees."

This work also shows that the techniques used here—modulating the signal and using windowing functions to clean up the data—can be used in other fields too. Whether it's checking the temperature of metal in a factory, monitoring water vapor in the atmosphere, or even developing new medical imaging tools that use Terahertz radiation to look at tissues without hurting them, the lessons from this "Sun-telescope tuning" are widely applicable.

In short, the team successfully built a bridge between the raw electrical signals of their telescope and the physical reality of solar heat. They proved that with the right tools and a little bit of digital magic, we can finally start listening clearly to the Sun's hidden language.