The Calibration of the 35–40 GHz Solar Radio Spectrometer with the New Moon and a Noise Source

Calibrating solar radio flux has always been a concern in the solar community. Previously, fluxes were calibrated by matching load or the new Moon for relative calibration, and at times with the assistance of other stations’ data. Moreover, the frequency coverage seldom exceeded 26 GHz. This paper reports the upgraded and calibrated Chashan Broadband Solar millimeter spectrometer (CBS) working from 35 to 40 GHz at the Chashan Solar Observatory (CSO). Initially, the calibration of the solar radiation brightness temperature is accomplished using the new Moon as the definitive source. Subsequently, the 35–40 GHz standard flux is achieved by establishing the correlation between the solar radio flux, brightness temperature, and frequency. Finally, the calibration of the solar radio flux is implemented by utilizing a constant temperature-controlled noise source as a reference. The calibration in 2023 February and March reveals that the solar brightness temperature is 11,636 K at 37.25 GHz with a standard deviation (STD) of 652 K. The solar radio flux’s intensity is ∼3000–4000 solar flux units (SFU) in the range of 35–40 GHz with a consistency bias of ±5.3%. The system sensitivity is about ∼5–8 SFU by a rough evaluation, a noise factor of about 200 K, and the coefficient of variation of the system transmission slope of 6.5% @ 12 hr at 37.25 GHz. It is expected that the upgraded CBS will capture more activity during the upcoming solar cycle.


Introduction
Solar activity has a significant influence on the solarterrestrial space environment.The solar radio flux, particularly F107 (Tapping 2013), which serves as an indicator of solar activity, can provide weather forecasts for the space environment and mitigate the detrimental impact of solar activity on human activity in space.Currently, most solar observing systems in the community operate below 26 GHz.Accurate monitoring of solar flux in the millimeter band is critical to understanding the properties of nonthermal electrons in solar bursts in the optically thin regime.Therefore, we upgraded the Chashan Broadband Solar millimeter spectrometer (CBS) and calibrated the solar flux to ensure the generation of reliable, trustworthy, and high-quality data (Shang et al. 2022;Yan et al. 2022).
Numerous studies have investigated the calibration of solar radio flux, either through relative calibration based on matched load or Moon temperature, or absolute calibration using blackbodies to determine fluctuations in solar brightness temperature (in kelvin) or solar radio flux (in solar flux units, SFU).Table 1 displays the forms of calibration and the frequency calibrated for solar radio flux (Tsuchiya & Nagame 1965;Reber 1970;Tanaka et al. 1973;Kuseski & Swanson 1976;Fu et al. 1982;Nakajima et al. 1985;Zhou et al. 1992;Hafez et al. 2014;Kallunki et al. 2015;Tan et al. 2015;Jing et al. 2016;Geng et al. 2018;Kallunki & Tornikoski 2018).Solar radio flux in the field is usually based on data from the Nobeyama Radio Polarimeters (NoRP; Nakajima et al. 1985) and the Siberian Solar Radio Telescope (SSRT; Lesovoi et al. 2017;Altyntsev et al. 2020) stations, which cover a range of frequencies from 1 GHz to 3.75/9.4/17/35GHz, and 2-24 GHz.However, only the NoRP 35 GHz (single point) operates in the millimeter band.Therefore, an updated and calibrated CBS for the solar radio flux at 35-40 GHz is presented in this paper.The calibration of the instrument is based on the new Moon, a noise source, and the relationship between solar brightness temperature and flux.It has no dependence on data from other stations.The calibrated solar radio flux intensity is estimated to be ∼3000-4000 SFU at 35-40 GHz.By rough estimation, the system's sensitivity is ∼5-8 SFU.The system noise factor is about 200 K.The system transmission slope has a coefficient of variation of 6.5% @ 12 hr at 37.25 GHz (the slope is defined as R = ax + b, where R is the system output value, a is the system transmission slope, b is the intercept, and x is the input (access to the antenna output or noise source)).Section 2 illustrates calibration theory.Section 3 deals with the upgrading and calibration of instruments.Section 4 gives the calibration results, Section 5 presents future work, and a conclusion and summary are presented in Section 6.

The Principle of Radiometers
The two most commonly used radiometer structures are the total-power radiometer and the Dicke radiometer; the latter improves sensitivity by reducing the impact of gain stability and is more sensitive than the former.Both structures use the square-law detector (SLD) to convert the power signal directly Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.into voltage by applying a low-pass filter to eliminate highfrequency components; the voltage is then quantized using an analog-to-digital converter (ADC) for acquisition.This structure is simple and easy to maintain.The SLD assumes a linear relationship between its input and output when the input signal is within a small range.However, when the input signal spans a large range, nonlinearity can be introduced in the SLD.As depicted in Figure 1, the nonlinearity of the SLD introduces an obvious error when the noise temperature at the antenna output is T1 during a quiet Sun and T2 during a burst.Moreover, using the matched load (noise source) directly to calibrate the noise temperature at the antenna output is not possible during the calibration process because of the varying transmission losses of the path channel.

The Methods of Calibration
The radiometer calibration includes both absolute and relative methods.Tanaka et al. (1973) described the theoretical process of absolute calibration: where T represents the temperature of the horn antenna with subscripts a_Sun, a_sun_bg, 0, and z indicating the Sun, background, matched load, and cosmic radiation.R is the system output value.ΔT a_sun is the increment in the antenna temperature toward the Sun.The temperature increment is converted into the solar radio flux according to where κ is the Boltzmann constant, A e is the antennaʼs effective area, and F sun (ν) is the solar radio flux.Accurate measurement of matched load temperatures T 0 is crucial.Obtaining the sky temperature T z is challenging due to the impact of oxygen and water vapor, particularly at higher frequencies where this impact is more substantial.Fu et al. (1982) refined the absolute calibration and introduced the following formula for solar flux density: where F sun (ν) is the solar radio flux in SFU at frequency ν, κ is the Boltzmann constant, D 0 is the direction factor of the antenna, η is the antenna efficiency, the antenna gain factor G = ηD 0 , K is the correction factor of the antenna directional pattern, λ is the wavelength corresponding to the frequency ν, the temperature increment is ΔT a_sun , Γ 0 is the atmospheric absorption factor, Z is the zenith distance, and e Z sec 0 G is the atmospheric correction factor(generally taken as 1).This model accounts for the width of the main flap of the antenna and for the atmosphere while using the hot and cold blackbodies as calibration sources, alternately covering the antenna to obtain the temperature increment ΔT a_sun .Since the gain G of the horn antenna is known, the absolute solar radio flux F sun (ν) can be determined using this method.The method's downside is the costly fabrication of a blackbody and difficulty in covering the antenna, particularly if it has a large diameter.
Relative calibrations often rely on external sources, internal sources (e.g., the Moon as an external source and a noise source as an internal source)or known data (e.g., solar flux calibrated by other stations) to obtain F sun (ν).Kallunki & Tornikoski (2018) utilized the Metsähovi Radio Observatory (MRO) RT-14 telescope with the new Moon as a calibration source, according to T sun (ν) is the brightness temperature of the Sun, T a_sun , T a_sun_bg , T a_moon , and T a_moon_bg are the output temperatures of the antenna when it is pointed at the Sun, the background of the Sun, the Moon, and the background of the Moon respectively.The brightness temperature of the Moon is dependent solely on the Moon's phase, according to where T moon (ν) represents the Moon's temperature, and T 0 , T 1 , ω, and ξ represent the first and second constant components of the Moon's temperature (214 K @ 37.5 GHz and 38 K @ 37.5 GHz, .The structure of a typical total-power radiometer with a matched load and the input-output relationship of the SLD.The nonlinearity of the SLD causes errors since the antenna output is T1 when the Sun is quiet and T2 when it is in burst. respectively), the Moon cycle (12.26deg/day), and the optical phase relative to the moment of the new Moon (32°@ 37.5 GHz).The system's small beam bandwidth (0°.04) limits observations to a single point of the solar disk at any given time.When using smaller-diameter antennas, the signal-to-noise ratio (S/N) may be poor and may make observations of the Moon difficult.
where F sun (ν) represents the measured solar radio flux, and R refers to the system output accessing the Sun, sky, internal noise sources, and ambient loads.Moreover, F sun_cal (ν) denotes the international standard flux, and C(ν) represents the coefficient of calibration derived from the international flux.

Upgrade of the Analog Front End
Radio-frequency signals are acquired directly using an ADC or a frequency converter, which not only provides the spectrum but also allows for the averaging of a bandwidth spectrum to obtain the solar radio flux intensity.After calibration, the solar radio flux can be determined.This approach mitigates the nonlinearity issue of the SLD as long as enough dynamic range is reserved, particularly because the intensity of a millimeter-wave solar burst is relatively weak and does not require a high dynamic range.
Figure 2 shows an updated CBS that features a calibration reference (noise source), a first stage amplifier (LNF-LNR23_42WB_SV)3 connected by waveguide to the antenna, and a thermostatically controlled calibration unit.The upgraded analog front end (AFE) uses a waveguide connector to minimize system noise and boost the S/N.Additionally, two amplifiers are linked in series to lessen the noise added at the back-end.Figure 3 shows that the noise factor of the temperature-controlled calibration unit is estimated to be around 200 K, which is approximately equal to the system noise.As shown in Figure 4, the slope of the system transmission was tested using the periodic opening and closing of the noise source.After opening the temperature control for an hour, the calibration unit is temperature-stabilized at 20°C.The slope coefficient of variation is 6.5% @ 12 hr at 37.25 GHz after 12 hr of tests.

The Process of Calibration
According to previous studies and results from the CBS observations, a constant-coefficient method of calibration using the new Moon and the noise source as reference is proposed.With the 80 cm aperture antenna, the whole Sun can be covered and the new Moon can be observed.The new Moon serves as a relative calibration source for obtaining the solar brightness temperature.The standard radio flux at each frequency point is derived by using the relationship between solar radio flux and brightness temperature, followed by coefficient adjustment for calibration.The sky background and noise sources are observed at fixed intervals during daily observation, and the solar radio flux is eventually obtained.
(a) Obtain T sun (ν) from T moon (ν).According to Equations (4) and (5), the ratio between the brightness temperature of the new Moon and that of the Sun can be calculated.The lunar brightness temperature is 241.2K, 246.2 K, and 249.8K @ 37.25 GHz on the day before new Moon, the day of new Moon, and the day after it, respectively.The solar brightness temperature (T sun (ν)) remains relatively constant within the range 35-40 GHz, so the average temperature of 11,636 K at 37.25 GHz is used.
(b) Obtain F sun_model from T sun (ν).Following Equation (7) for the relationship between solar radio flux and brightness where ΔT a_sun is the increment in output noise temperature when the antenna is pointed at the Sun and background, T h and T c are temperatures with the noise source on (hot) and off (cold), C tran is the coefficient of transfer from the noise source channel to the antenna channel, R is the output of the system (a) Slope tests for system transmission based on the noise source were performed every 6 minutes during regular observations.Values below 2500 (the system output power, without calibration) are the output of the Sun, the solar background, and the cold of the noise source feeding into the system.(b) After opening the temperature control for an hour, the calibration unit was stabilized at 20°C.The gain changes quickly before the temperature of the calibration unit stabilizes (at 22:00:00).The figure suggests that the room-temperature component of the AFE is affected by the external ambient temperature, causing the slope of the system to fluctuate slowly depending on the AFE's room temperature, and it can be seen that the slope is lowest at around 06:00, due to the high external temperature at midday, while the slope rises in the morning and evening when the temperature is low.This variation in slope introduces a consistency bias that might be improved on summer days and days with low temperature differences, while daily observations reduce the effect of slope variation through periodic calibrations.
access to the Sun, sky, internal noise sources (T h /T c ), F sun (ν) is the solar radio flux caused by ΔT a_sun , A e is the effective area of the antenna, and C(ν) is the correction factor for the system (difficult to measure accurately and directly).
(d) Obtain the calibration coefficient C(ν) from F sun_model and the system output (R).To get C(ν), the solar radio flux (F sun_model , Equation (7)) is used (this is similar to Geng et al. 2018): ) Calibration: obtain the solar radio flux ( * F sun ( ) n ) from the system output (R) and the calibration coefficient (C(ν)).For normal observations, a constant factor C(ν) is applied and substituted into the calibration equation: is the solar radio flux at the moment of observation.* R sun is the output of the receiver for the Sun at the moment of observation, and R • is the output of the receiver at the moment of calibration for solar background and noise sources (on and off).The solar background and the noise source are accessed at fixed intervals to correct for the effects of variations in the sky background and fluctuations in the system gain respectively.

The Results of the Calibration
In 2023 February and March, the solar brightness temperature was calibrated using the new Moon.At each frequency point, the ratio of solar to lunar brightness temperature was measured.Based on the lunar brightness temperature being 241.2 K, 246.2 K, and 249.8K at 37.25 GHz, the average solar brightness temperature for 37.25 GHz was obtained as 11,636 K with a standard deviation (STD) of 652 K and a coefficient of variation (CV) of 5.6%, as shown in Figure 5(a).
When comparing the solar brightness temperatures obtained by CBS (11,636 K) and MRO RT-14 (8100 K, Kallunki et al. 2015;Kallunki & Tornikoski 2018), the difference between them could be attributed to differences in the observing system, environmental factors, and solar variations.CBS observes the entire solar disk, whereas MRO RT-14, with its 13.7 m antenna, only observes a single point on the Sun.There may exist a deviation between the brightness temperature of a point on the Sun's quiet surface and the equivalent brightness temperature of the entire solar disk.MRO RT-14 benefits from its large-aperture antenna and is less susceptible to environmental influences.CBS is susceptible to environmental influences that can lead to errors during the new-Moon calibration process due to its small-aperture antenna.During the approach to the peak of the solar cycle, differences in solar surface activity affect the calibration of the new Moon.
Based on the solar brightness temperature of 11,636 K, the fluxes for each frequency point were derived according to Equation (7) and are shown in Table 2.According to Equation (9), the correction coefficient C(ν) with a maximum CV of 5.3% was derived by processing the data of February and March (as shown in Figure 5(b) and Table 2).In daily observations, the error in obtaining * F sun ( ) n mainly comes from the correction factor C(ν), which produces a consistency bias of 5.3%, and the bias is fixed for a given correction factor C(ν).
The daily observations shown in Figure 6 were calibrated using the correction coefficients provided in Table 2 according to Equation (10).Comparing the multiday data under various weather conditions from March to July (Figure 6), we can deduce that: (1) Both CBS and NoRP experience adverse weather conditions.For example, the data from May 29 to June 2 in NoRP are expected to show significant fluctuations due to weather.Similarly, on May 28, CBS experiences a transition from cloudy to rainy conditions.(2) In the case of routine observations, the NoRP data appears as a relatively steady line, seemingly unaffected by the Sun's elevation angle.This could be attributed to the calibration method of NoRP, which employs a fixed value of solar radio flux, or it could be a result of the favorable environmental conditions and high altitude of the NoRP station site.Conversely, the solar radio flux of CBS demonstrates a pattern of increase followed by decrease, possibly attributed to varying atmospheric absorption at different solar positions.Additionally, the change in the system transmission slope may also exert some influence, although it is not the primary factor.(3) On 2023 July 7, the data from CBS exhibit significant fluctuations (as indicated by the thicker orange line in the graph), despite it being a sunny day.This could be attributed to atmospheric turbulence or the presence of humid air, which potentially diminishes observational sensitivity.
Figure 7 compares the CBS and NoRP observations over a period of almost five months, from late February to early July.Based on these long-term data, NoRP demonstrates greater stability than CBS.This can be attributed to NoRP's calibration  methodology utilizing a fixed solar radio flux, favorable observation conditions, and stable equipment.In contrast, fluctuations in CBS primarily stem from environmental factors and the stability of its equipment (the impact of the system transmission slope).CBS is situated in a coastal city characterized by frequent adverse weather conditions and higher levels of water vapor.The M5.6 outburst at UT 01:50 on 2023 January 11, the M5.8 outburst at UT 02:30 on 2023 March 6, and the X1.2 outburst at UT 02:30 on 2023 March 29 were calibrated, as depicted in Figure 8. Comparing CBS and NORP, it can be concluded that the CBS measured burst increment is essentially the same as the NoRP one when the background flux before the burst is accounted for.

The Evaluation of System Sensitivity
With the cold and hot calibration sources in front of the system, system sensitivity was obtained using the sensitivity calculation as where T c and T h represent the temperatures of the cold and hot blackbody calibration sources, respectively, and R c and R h are the corresponding system output values.The maximum standard mean square error of the receiver value is max s , and κ represents the Boltzmann constant.The system sensitivity in kelvin and SFU was calculated as T min D and F _ sun min ( ) n , respectively, taking into account the effective area of the antenna (A e ).Due to the difficulty in implementing a physical blackbody calibration source with a large aperture (antenna diameter of 80 cm) and high temperature, we use the noise source for sensitivity evaluation (as shown in Figure 9(a)).
The sensitivity of the system while observing the Sun is shown in Table 3 and Figure 9(b).The system sensitivity was Figure 6.The calibrated solar radio flux at 37.25 GHz in various weather conditions (fog on March 8, sunny to cloudy on March 12, cloudy to rain on May 28, cloudy on May 29, cloudy on May 30, cloudy to sunny on June 2, and sunny on July 7).The system was calibrated five times by observing the solar background, and the cold and hot noise sources, using the first calibration parameters before 2:00:00, the second calibration parameters between 2:00:00 and 4:00:00, and so on.However, there is a gap (as shown by the pink circles) at each calibration caused by freshly selecting the sky background, changes in solar pitch angle, and the slow change in the system transmission slope.Until 02:00:00, the data were calibrated using the first set of calibration parameters, resulting in no gap at 0:00:00.Based on a measured solar brightness temperature of 11,636 K, a flux of approximately ∼3000-4000 SFU was derived.This differs significantly from the NoRP measurement.NoRP sets the flux at 2400 SFU for the quiet Sun, relying only on observations of the solar background at regular intervals without any additional calibration.evaluated roughly as ∼5-8 SFU.The true sensitivity of the system is better than 40 SFU, as can be demonstrated by the X1.2 level outbreak of ∼40 SFU on 2023 March 29.

Future Work
In order to enhance system stability and performance, three main aspects will be considered for system upgrades.First, relocation to high-altitude sites such as the Lenghu Observatory in Qinghai Province or the Daocheng Observatory in Sichuan Province, China, may be beneficial.These sites offer thin air, clear weather throughout the year, and excellent options for high-altitude stations that can mitigate the impact of weather.Second, it is important to control the antenna feed and the AFE temperature.Accurate measurement of the increment in output noise temperature (ΔT a_sun ) caused by the antenna pointing toward the Sun and the solar background is necessary.However, variations in the antenna feed due to external   Note.The sensitivity is calculated using a rough estimate of system sensitivity based on the noise source.The table gives the dates corresponding to the maximum of σ max .A e is taken with an experience value of A e = (0.5-0.6)πr 2 .
temperature changes should not be allowed, necessitating the maintenance of a constant temperature for the feed to eliminate the effect of ambient temperature changes.Similarly, the AFE should be kept at a constant temperature to avoid changes in transmission slope with variations in gain.Lastly, after completing the two steps above to ensure stability, reliability, and an optimal environment, absolute calibration can be considered.Absolute calibration requires a blackbody source that covers the entire antenna aperture to calibrate ΔT a_sun , as well as calibration of the antenna gain (G).In daily observations, a blackbody-calibrated noise source (as shown in Figure 9(a), where the blackbody can be used to calibrate the noise source to the front of the antenna) can serve as the standard source for daily calibration.
The three aforementioned future projects are all complex, especially in regard to the system's absolute calibration (additional studies on blackbody calibration are also underway, Zou et al. 2023).The completion of these projects is expected to improve the system's performance and make the generated data more reliable.

Conclusion and Summary
This paper presents a comprehensive overview of current equipment for millimeter-wave observation of the solar radio flux, including the principles and methods of radiometer calibration.We propose a novel constant-coefficient calibration solution based on the new Moon, a noise source, and the solar radio flux model, which can provide independent and reliable solar flux measurements in the 35-40 GHz range without relying on data from other stations.The calibrated solar flux values obtained with the constant-coefficient method were ∼3000-4000 SFU at 35-40 GHz with a consistency bias of ±5.3% (the deviation is fixed after a given correction factor C(ν), and the deviation is simultaneously larger or smaller within the bandwidth), a system sensitivity of ∼5-8 SFU measured by the noise source, a noise factor of about 200 K, and the coefficient of variation of the transmission slope was 6.5% @ 12 hr at 37.25 GHz, which is eliminated by periodic calibration.We verified the reliability of this calibration method through routine observations and comparison with NoRP station data.
Nonetheless, there are possibilities for improvement in several aspects.These include relocating to higher-altitude sites to mitigate the impact of atmospheric absorption, implementing temperature control for the frequency converters in the AFE system, enhancing tracking accuracy, and conducting absolute calibrations in order to obtain more reliable data.Although there are shortcomings and limitations, the system captured several solar outbursts, including the smallest currently captured (M5.15 outburst at 00:15 on 2023 January 10), and we believe it is capable of capturing more events during the upcoming solar activity cycle.
Geng et al. (2018) derived the solar radio flux based on the calibrated flux measured by other stations.To obtain the coefficient of correction for daily observations, they employed a noise source as an internal reference.Then

Figure 2 .
Figure 2. (a) Block diagram of the AFE with a noise source and temperature controller, utilizing the waveguide form to decrease noise.(b) A real item of the upgraded calibration unit with the thermoelectric cooler for thermostatic control, which is currently maintained at a constant temperature of 20°C due to limited cooling power.

Figure 3 .
Figure 3.The noise factor of the upgraded calibration unit.It is reduced by 70 K compared to the pre-upgrade stage.

Figure 4 .
Figure4.(a) Slope tests for system transmission based on the noise source were performed every 6 minutes during regular observations.Values below 2500 (the system output power, without calibration) are the output of the Sun, the solar background, and the cold of the noise source feeding into the system.(b) After opening the temperature control for an hour, the calibration unit was stabilized at 20°C.The gain changes quickly before the temperature of the calibration unit stabilizes (at 22:00:00).The figure suggests that the room-temperature component of the AFE is affected by the external ambient temperature, causing the slope of the system to fluctuate slowly depending on the AFE's room temperature, and it can be seen that the slope is lowest at around 06:00, due to the high external temperature at midday, while the slope rises in the morning and evening when the temperature is low.This variation in slope introduces a consistency bias that might be improved on summer days and days with low temperature differences, while daily observations reduce the effect of slope variation through periodic calibrations.

Figure 5 .
Figure 5. (a) Solar brightness temperature at 37.25 GHz is obtained using the new-Moon calibration in 2023 February and March.(b) The correction factor C(ν) was measured multiple times in February and March, with a CV of 5.3%.The deviation of the correction factor C(ν) can lead to an overall high or overall low for F sun (ν) in the range 35-40 GHz.

Figure 7 .
Figure 7.Comparison of CBS and NoRP data over a long period of time (almost five months).Both select data at midday (CBS data at 4:00 UT, NoRP data at 3:00 UT).

Table 1
The Various Forms and Frequencies of Calibration that are Currently Adopted for the Calibration of Solar Radio Flux

Table 2
Solar Radio Flux at 11,636 K @ 37.25 GHz and Calibration Correction Factors

Table 3
The Sensitivity of the System when Observing the Sun