Extending geodetic and astrometric Very Long Baseline Interferometry VLBI observations from traditional centimeter wavebands to millimeter wavebands offers numerous scientific potentials and benefits. However it was considered quite challenging due to various factors including the increased effects of atmospheric opacity and turbulence at millimeter wavelengths. Here we present the results of the first geodeticmode VLBI experiment simultaneously observing 82 sources at 224388132 GHz KQWD bands using the Korean VLBI Network KVN. We introduced the frequency phase transfer FPT method to geodetic VLBI analysis an approach for calibrating atmospheric phase fluctuations at higher frequencies by transferring phase solutions from lower frequencies. With a 2 minute scan FPT improved the signaltonoise ratio of most fringes some by over 100 thereby enhancing the detection rate of weak sources at millimeter wavebands. Additionally FPT reduced systematic errors in group delay and delay rate with the weighted root mean squares WRMS of the postfitting residuals decreasing from 25.0 to 20.5 ps at the W band and from 39.3 to 27.6 ps at the D band. There were no notable differences observed in calibrating atmospheric phase fluctuations at the K band WRMS  12.4 ps and Q band WRMS  11.8 ps. This experiment demonstrated that the millimeter waveband can be used for geodetic and astrometric applications with high precision.
['Quasars', 'Very long baseline interferometry', 'Radio source catalogs', 'Radio astrometry', '1319', '1769', '1356', '1337', 'Astrophysics - Instrumentation and Methods for Astrophysics', 'Astrophysics - Earth and Planetary Astrophysics', 'Astrophysics - Astrophysics of Galaxies']
A Geodetic and Astrometric VLBI Experiment at 224388132 GHz
{'A Geodetic and Astrometric VLBI Experiment at 22/43/88/132 GHz': "Shuangjing Xu , 1 Taehyun Jung , 1 Bo Zhang , 2 Ming Hui Xu , 3, 4 Do-Young Byun , 1 Xuan He , 2, 5 Nobuyuki Sakai , 6 Oleg Titov , 7 Fengchun Shu , 2 Hyo-Ryoung Kim, 1 Jungho Cho, 1 Sung-Moon Yoo, 1 Byung-Kyu Choi, 1 Woo Kyoung Lee , 1 Yan Sun , 2 Xiaofeng Mai , 2, 5 and Guangli Wang 2  \n1 Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of Korea  \n2 Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, People's Republic of China 3 GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany  \n4 Aalto University Metshovi Radio Observatory, Metshovintie 114, 02540 Kylml, Finland  \n5 University of Chinese Academy of Sciences, No.19 (A) Yuquan Rd, Shijingshan, Beijing 100049, People's Republic of China 6 National Astronomical Research Institute of Thailand (Public Organization), 260 Moo 4, T. Donkaew, A. Maerim, Chiang Mai, 50180,  \nThailand  \n7 Geoscience Australia, PO Box 378, Canberra 2601, Australia", 'ABSTRACT': 'Extending geodetic and astrometric Very Long Baseline Interferometry (VLBI) observations from traditional centimeter wavebands to millimeter wavebands offers numerous scientific potentials and benefits. However, it was considered quite challenging due to various factors, including the increased effects of atmospheric opacity and turbulence at millimeter wavelengths. Here, we present the results of the first geodetic-mode VLBI experiment, simultaneously observing 82 sources at 22/43/88/132 GHz (K/Q/W/D bands) using the Korean VLBI Network (KVN). We introduced the frequency phase transfer (FPT) method to geodetic VLBI analysis, an approach for calibrating atmospheric phase fluctuations at higher frequencies by transferring phase solutions from lower frequencies. With a 2-minute scan, FPT improved the signal-to-noise ratio (SNR) of most fringes, some by over 100% , thereby enhancing the detection rate of weak sources at millimeter wavebands. Additionally, FPT reduced systematic errors in group delay and delay rate, with the weighted root-mean-squares (WRMS) of the post-fitting residuals decreasing from 25.0 ps to 20.5 ps at the W band and from 39.3 ps to 27.6 ps at the D band. There were no notable differences observed in calibrating atmospheric phase fluctuations at the K band (WRMS = 12.4 ps) and Q band (WRMS = 11.8 ps) with the KVN baselines. This experiment demonstrated that the millimeter waveband can be used for geodetic and astrometric applications with high precision.  \nKeywords: reference systems / astrometry / techniques: interferometric / quasars: general / galaxies: nuclei/radio continuum: general', '1. INTRODUCTION': "Geodetic and astrometric Very Long Baseline Interferometry (VLBI) observations have made significant contributions to astronomy and geodesy over the past 40 years, particularly in the areas of the terrestrial reference frame (TRF), the celestial reference frame (CRF), and the earth orientation parameters (EOPs) (Sovers et al. 1998). The basic concept of geodetic and astrometric VLBI involves using pairs of radio telescopes to observe the signals of compact extra-galactic objects that emit radiation in the radio frequency regime. By analyzing the differences in the arrival times of the same wavefront between two telescopes, geodetic parameters such as telescope coordinates, positions of celestial objects, and EOPs can be inferred for various scientific and practical applications (Nothnagel 2019). In  \naddition to the traditional S/X band (2.3/8.4 GHz), multiple frequency bands have recently been employed to enhance the potential of geodetic VLBI observations.  \nThe accuracy of geodetic and astrometric measurements relies on the precision of derived group delays, baseline length, and systematic delay errors. The broadband geodetic VLBI system at 2-14 GHz, known as VLBI Global Observing System (VGOS), has improved the precision of group delays to a few picoseconds (ps; 1 ps = 10 -12 s) (Niell et al. 2018), however, uncompensated systematic errors at the level of 20 ps still dominate the error budget (Xu et al. 2021a). Further efforts are required to calibrate systematic errors originating from tropospheric delay (Petrov 2024) and source structure (Xu et al. 2022) to achieve the VGOS's goal of 1 mm position accuracy.  \nHigher frequency bands offer advantages such as achieving higher-resolution imaging of radio sources, mitigating source structure effects (de Witt et al. 2023), measuring frequency-dependent position shifts in Active Galactic Nuclei (AGN) jets (i.e., core-shift) (Blandford & Konigl 1979; Hada et al. 2011), and reducing interference from scattering (Koryukova et al. 2022) and ionospheric plasma effects (Fomalont et al. 2009). The K band (24 GHz) ， X/Ka band (8.4/32 GHz), and Q band (43 GHz) (Lanyi et al. 2010; Charlot et al. 2020) have been used for establishing a multifrequency International Celestial Reference Frame (ICRF). In the meantime, the Gaia satellite mission realized the first extra-galactic frame at optical wavelengths (Gaia Collaboration et al. 2022). How to realize a fully consistent and integrated multi-waveband celestial reference frame becomes an important issue (Charlot 2022). In addition, the use of millimeter wavebands for geodesy is valuable for determining the station coordinates of antennas without receivers operating at lower frequencies.  \nThe independent geodetic VLBI programs operating at different frequencies may have astrometric limitations in detecting the core-shift in most ICRF sources (Petrov 2024). As frequency increases, the signal-to-noise ratio (SNR) of VLBI fringes is affected by decreased flux densities of sources, shorter coherence times, increased atmospheric absorption, and higher receiver temperatures, limiting the precision of group delays at millimeter wavelengths. The single K band observation also has difficulty in calibrating the ionospheric delay (Lanyi et al. 2010).  \nThe Korean VLBI Network (KVN) has the capability of simultaneously observing at multiple frequencies (Han et al. 2013), including K band at 18-26 GHz, Q band at 35-50 GHz, W band at 85-116 GHz, and D band 1 at 125-142 GHz. A similar K/Q/W band system is being developed globally (Dodson et al. 2023). This kind of system is particularly useful for extending the coherence time at millimeter wavelengths using the frequency phase transfer (FPT) technology (Rioja & Dodson 2020). Specifically, it achieves this by calibrating the tropospheric phase at higher frequencies through transferring phase solutions from lower frequencies. This enables the observation of more sources and facilitates the measurement of core shift effects using source-frequency phase-referencing (SFPR) astrometry (Rioja et al. 2015; Jung et al. 2015). The global K/Q/W band system may also benefit the ICRF by employing geodetic and astrometric VLBI across a broad frequency range from 20 to over 100 GHz. This approach offers several advantages: 1) simultaneous multi-frequency investigation of core shift effects and source structures; 2) monitoring numerous ICRF source images with resolutions of a few tens of microarcseconds; 3) overcoming limitations in group delay precision at millimeter wavelengths through very broad bandwidth synthesis.  \nIn this paper, we present the first geodetic VLBI observation at 22/43/88/132 GHz simultaneously using the KVN as a pilot experiment for future broad bandwidth synthesis from 20 to over 100 GHz.", '2. OBSERVATIONS AND GENERAL DATA ANALYSIS': 'We conducted the first geodetic and astrometric VLBI experiment observed at K/Q/W/D bands (22/43/88/132 GHz) simultaneously using the KVN under the East Asian VLBI Network (EAVN) (Akiyama et al. 2022) program a2129a . The KVN consists of three 21-m antennas: KVN-Yonsei (KYS), KVN-Ulsan (KUS), and KVN-Tamna (KTN), with baseline lengths ranging from 305 to 476 km. We used a 24-hour track for the session from 2021-Dec-07/15:25:00 to 2021-Dec-08/15:25:00. The received signals were recorded with four 512 MHz base-band channels (BBCs) and recorded right (for K band) or left (for Q/W/D bands) circularly polarized signals with Nyquist sampling and 2 bits per sample for a total sampling rate of 8 Gbps. A summary of the observation is listed in Table 1.', 'GeoVLBI at 22/43/88/132 GHz': 'Table 5 (continued)  \nNote -The flux density values are obtained from KVN baseline ( < 500 km) amplitude using AIPS , while the SNR with 2-min scans is produced by fourfit . These values (weighted averages and standard deviations) are provided as a reference for conducting observations and may not be accurate for AGN astrophysics studies. The different standard deviations observed in the baseline amplitudes and SNRs may be attributed to variations in weather conditions, elevation angles, and pointing accuracy.  \nThis work utilized the KVN under the EAVN program. We are grateful to all staff members in KVN and EAVN who helped to operate the array. The KVN and a high-performance computing cluster are facilities operated by the KASI (Korea Astronomy and Space Science Institute). The KVN observations and correlations are supported through the high-speed network connections among the KVN sites provided by the KREONET (Korea Research Environment Open NETwork), which is managed and operated by the KISTI (Korea Institute of Science and Technology Information). The presented figures were generated using Matplotlib (Hunter 2007) and Astropy (Astropy Collaboration et al. 2013). This research was supported by the National ResearchCouncil of Science & Technology(NST) grant by the Korea government (MSIT) (No. CAP22061-000). BZ was supported by the National Natural Science Foundation of China (Grant No. U2031212 and U1831136), and Shanghai Astronomical Observatory, Chinese Academy of Sciences (Grant No. N2020-06-19-005). SX thanks Dr. John Barrett and Dr. Daniel Hoak for solving the technical problems with HOPS , and thanks to Dr. Sergei Bolotin for the guide on nuSolve .  \nFacilities: KVN, EAVN  \nSoftware: HOPS (Hoak et al. 2022), nuSolve (Bolotin et al. 2014), SKED (Gipson 2018), SCHED (Walker 2022), DiFX (Deller et al. 2011), AIPS (Greisen 2003), ParselTongue (Kettenis et al. 2006).', '2.2. Correlation and Fringe fitting': "The observations were correlated using the DiFX software correlator (Deller et al. 2011) in Daejeon, South Korea. The output of the correlator was converted to Mark 4 format in order to be compatible with the Haystack Observatory Processing System ( HOPS ) suite of programs (Whitney et al. 2022) and converted to FITS format for imaging with NRAO Astronomical Image Processing System ( AIPS ) (Greisen 2003).  \nThe HOPS main tool, fourfit , was used to estimate group and phase delays, phase, delay rate, and cross-correlation amplitude for each observation using the Mark 4 data. As the hardware phase calibration system to cover the entire frequency range of KVN (18 - 142 GHz) is under development, we implemented manual phase calibration through a single scan of the bright source OJ287, to align the delays and phases among different frequency bands. Contrary to the standard practices in geodetic VLBI, we introduced the utilization of FPT to address the effects of atmospheric turbulence in millimeter wavebands. This method is elucidated in Section 3. A database in vgosDb format (Bolotin et al. 2016) was finally produced in three steps: ' vgosDbMake ' produced the skeleton database for all observables (version 1); ' vgosDbCalc ' added the apriori values and partial derivatives (version 2), and ' vgosDbProcLogs ' added meteorological information (version 3; no cable cal in KVN log file)(Bolotin et al. 2014).", '2.3. Geodetic data analysis': "The geodetic analysis was conducted using the nuSolve program (Bolotin et al. 2014). This program operates on the vgosDb database to perform least-squares estimation of various geodetic, geophysical, astronomical, and instrumental  \nparameters. We disassembled the database into individual bands (e.g., K, Q, W, D) and dual-bands (e.g., Q/K, W/K, D/K) by manually editing the 'wrapper' file in the vgosDb database.  \nObtaining the final geodetic estimate utilized multiple steps proceeding from least precise to most precise. The detailed steps can be found in the User Guide of nuSolve and Niell et al. (2021). External files containing a priori information are used in the analysis, such as updated station coordinates from the multi-epoch EAVN geodetic observations (Xu et al. 2021b), source positions from the ICRF3 K band catalog (Charlot et al. 2020), and earth rotation parameters from the VLBI solution provided by NASA Goddard Space Flight Center (GSFC). The group delays with the single 512 MHz channel in our data are unambiguous. We start with simple parameterization, only clock shifts and rates, and perform an analysis of the group delays. At this stage, we use the KYS station as the clock reference and have not identified any clock breaks at any of the stations. Then we add zenith delays and station positions to the list of estimated parameters.  \nAlso, we test ionospheric corrections for dual-frequency (Q/K, W/K, D/K) band data. Usually, geodetic VLBI uses multi-frequency channels for each frequency band, i.e., the bandwidth synthesis technique, to improve the group-delay measurement precision. In this case, an 'effective frequency' is calculated and assigned to ionosphere group delays as the approximate reference frequency (Bohm & Schuh 2013). We calculated the central frequencies of each band (22240 MHz for K band, 42876 MHz for Q band, 88192 MHz for W band, 132160 MHz for D band) as the effective frequency and used them latter in ionospheric calibration.  \nTime-varying models of clock and tropospheric parameters are introduced in the latter stage. They are modeled as continuous piece-wise linear (PWL) functions with incremental rates. For such a PWL model, the estimated values are, for each parameter, an initial value and rate for the first interval and a new rate for each of the successive equalduration intervals. The results reported in the remainder of this paper are based on a PWL interval of 30 min for the troposphere and 60 min for the clock. The daily averaged atmospheric gradients (MacMillan 1995) are estimated with constraints in this independent solution. In the last stage of data processing, additional parameters such as the rate of Earth rotation and angles of nutation are included. We also re-weight the observations by examining the additive noise required to achieve a chi-squared per degree of freedom (chi2pdof) of approximately 1. Any post-fit delay residuals greater than 3.5 times their re-weighted uncertainty are marked for exclusion. We iterate through the estimation, re-weighting, and outlier-check sequence until no outliers are detected, resulting in the final solution. To efficiently compare results from different frequency bands and/or parameters, we use the script mode with nuSolve (Bolotin et al. 2023).", '3. APPLICATION OF FPT IN GEODETIC VLBI': "The inherent challenges of geodetic VLBI in millimeter wavebands, such as sensitivity, can be effectively addressed due to the impressive performance of the KVN telescopes (Lee et al. 2014), characterized by their high aperture efficiency, precise pointing accuracy, receivers with low noise temperature, wide-band digital backend, and rapid slewing speed. Of particular significance is the telescopes' ability to operate at multiple frequencies, which enables us to mitigate atmospheric phase fluctuations using the FPT method. In the FPT method, high-frequency (target frequency) observations are calibrated using scaled solutions obtained from a lower, more easily manageable frequency (Jung et al. 2011; Rioja & Dodson 2020).  \nThe majority of mm-VLBI observations serve imaging purposes, wherein the rapid nonlinear phase (atmospheric phase fluctuations) is usually estimated per scan using self (on-source) detections from a single reference station to other stations (Blackburn et al. 2019). The correlated signal must have a high SNR so that the atmospheric phase can be estimated on a short timescale (a few seconds). Therefore, this method is limited to using bright sources or using a high-sensitivity station as the phase reference. In addition, it is difficult to distinguish nonlinear atmospheric phase from the linear phase drift due to delay rate, and can lead to the loss of frequency-dependent information in the phases. The FPT method can be effectively employed to overcome these limitations, either simultaneously or through fast frequency switching.  \nWe effectively employed the FPT method using the packets HOPS for geodetic data, drawing from the guidance provided in the fourfit user's manual and a tutorial (Fish 2015). This implementation involved the following steps:  \n- · Initiating fringe fitting using the fourfit program and employing the alist program to track the fringe phase, SNR, and other information for each observation, leading to the creation of a corresponding text file.\n- · Employing the fringex program to segment data from a single scan time ( ∼ 2 min) into a few seconds. This step utilized the aforementioned text file ( alist ) as input and provided atmospheric phase fluctuations using  \nFigure 1. Comparison atmospheric phase fluctuations with self detection ( ϕ Self ) and FPT ( ϕ FPT ) method using a strong source 3C279 on KTN-KYS baseline. The four panels represent distinct frequency bands. The 2 π ambiguity of phase is ignored for clarity.  \n<!-- image -->  \nself detection at each bands (e.g., ϕ Self K , ϕ Self Q , ϕ Self W , and ϕ Self D ). Choosing a reference station and an appropriate cadence for segmented phases is crucial; it should be short enough to capture the atmospheric phase fluctuations while maintaining enough SNR. In this experiment, we used KYS as the reference station and examined cadences of 1 second, 3 seconds, 5 seconds, and 10 seconds. Subsequently, we selected the smallest cadence with an SNR exceeding 10. Given the high SNRs in the K band, ∼ 90% of the scans adopted a 1-second cadence. However, for a small number of weaker scans with an SNR below 10 at the 10-second cadence, we refrained from applying FPT to prevent the potential deterioration of results.  \n- · Calculating atmospheric phase fluctuations at higher frequencies by transferring phase solutions from a lower frequency (i.e., K band), based on frequency ratios. As illustrated in Table 1, the frequency ratios are 1.93 (approximately equal to 2) for Q/K bands, 4 for W/K bands, and 6 for D/K bands, resulting in ϕ FPT Q = ϕ Self K × 2, ϕ FPT W = ϕ Self K × 4, and ϕ FPT D = ϕ Self K × 6. We have applied phases from one polarization (LCP of K band) to the other (RCP of Q/W/D band), as atmospheric phases remain unaffected by polarization.\n- · Within the HOPS framework, the solutions were based on baselines. We designated KYS as the reference station and 'viewed' the atmospheric phases ( ϕ Self K , ϕ FPT Q , ϕ FPT W , ϕ FPT D ) originating from KUS and KTN stations. Finally, we integrated this ' ad hoc ' phase information into fourfit and re-performed the process of fringe fitting.  \nFigure 2. Same as Figure 1, but for a weaker source 0642+449.  \n<!-- image -->  \nAs shown in Figure 1 and 2, the FPTed phases exhibit close agreement with the trends observed in self detected phases at each K/Q/W/D bands. The clear linear phase differences ( Diff : ϕ Self -ϕ FPT in Figure 1) between self detection and FPT method indicate the different delay rates. In Table 2, it is noteworthy that the fringe quality ('Qcodes') of FPT-derived detection is comparable to those of self-detection. The term 'Qcodes' represents the fringe quality code as defined by HOPS-fourfit , where higher Qcodes indicate better quality. Subsequent to the application of FPT, the proportion of all usable observables with Qcodes of 9 has improved from 79% to 99%, characterized by heightened SNR and improved delay/rate precision. The improvements in group delay and rate accuracy are presented in Section 4. After applying FPT, the presence of phase differences among different bands in Table 2 necessitates further investigation through precise instrumental phase calibration. However, their influence on group delay and delay rate measurements is negligible in the following analysis.", '4. RESULTS': "The weather conditions were clear during the observation period, with median system temperature (Tsys) ranges as follows: 87-131 K for the K band, 96-103 K for the Q band, 189-193 K for the W band, and 186-270 K for the D band at the three KVN stations. These favorable conditions have led to excellent detection (SNR > = 7), with the detection rate of 99.8% at K band, 99.8% at Q band, 95.5% at W band (or 96.3% with FPT), and 68.2% (or 70.9% with FPT) at D band for 485 scans on KYS-KTN baseline. However, the Q band data from the KUS station exhibited a rare  \nTable 2. The fringe information with observables in Figure 1 and 2  \nlower SNR compared to other stations, for unknown instrumental reasons at this time. Therefore, we didn't use the Q band data of KUS station in the final results.", '4.1. The group delay and delay rate measurements at 22/43/88/132 GHz': 'As shown in Figure 3, FPT improved the SNR of most fringes, some by more than 100% with a 2-minute scan length, resulting in a higher detection rate (over 100 observables) for weak sources at millimeter wavebands. Note that most sources in this experiment are bright. Detection can be further improved in experiments with weaker sources and longer scan lengths. √  \nThe theoretical uncertainties of group delays produced by fourfit are calculated using 12 / (2 π *SNR*512 MHz) for the single 512 MHz channel data. Figure 4 shows the measurement noise of group delays on KYS-KTN baseline for each band. The median formal errors of group delays are 3.5 ps at K band, 5.0/4.7 ps at Q band, 22.5/19.5 ps at W band, and 49.7/43.0 ps at D band without/with FPT. Similarly, the median formal errors of delay rates are 6.6E-4 ps/s at K band, 5.0E-4/4.8E-4 ps/s at Q band, 1.1E-3/9.8E-4 ps/s at W band, and 1.7E-3/1.5E-3 ps/s at D band without/with FPT.  \nThe closure group delay for a triangle of three stations simultaneously observing the same source is given by the sum of the three baseline group delays going around a closed loop of the triangle (Xu et al. 2016). In this summation, the effects of station-based delays (tropospheric delays, ionospheric delays, station position errors, station thermal deformation errors, clock offset errors, cable delay errors, EOP errors, errors from pointing offsets, and so on) cancel exactly. The major error terms at centimeter wavebands that remained in the closure quantities, the so-called nonclosing errors, are source structure and measurement noise (Anderson & Xu 2018). However, in millimeter wavebands, atmospheric phase fluctuations become significant within seconds and differ at each triangle baseline, leading to errors in baselinedependent fringe fitting when employing a 2D linear model (phase vs. time, phase vs. frequency) over a 2-minute  \nFigure 3. Comparison of the SNR with and without FPT within a 2-minute scan length. The left figure shows the percentage increase in SNR after using FPT, and the right figure compares the SNR of weak sources (SNR < 15). The dashed lines indicate the fourfit detection limit (SNR = 7). For clarity, the results with an SNR below 6 using FPT are not shown.  \n<!-- image -->  \nFigure 5 and Table 3 show the closure observables in the KVN triangle baseline (KTN-KUS-KYS, with SNR > = 7 on each single baseline). With the exception of notable errors in the Q band attributed to the KUS station issue, the weighted standard deviations of closure group delays are 3.7 ps at K band, 19.9/15.7 ps at W band, and 47.2/36.7 ps at  \n<!-- image -->  \nDelay Rate Precision  \nWithout FPT  \n10  \n4  \nDelay Rate Precision  \nWith FPT  \n10  \n4  \n10  \n10  \n3  \n3  \nThe formal error of the delay rate  (ps/s)  \nFigure 4. The histogram of measurement noise for group delay and delay rate produced by fourfit on the KYS-KTN baseline. Different bands are represented by different colors.  \nscanning duration. As a result, uncalibrated atmospheric phase fluctuations will contribute to non-closure errors in millimeter wavebands when using HOPS-fourfit .  \n40  \n35  \n30  \n25  \n20  \n15  \n10  \n5  \n0  \n40  \n35  \n30  \n25  \n20  \n15  \n10  \n5  \n0  \nCount  \nCount  \n22 GHz  \n43 GHz  \n88 GHz  \n132 GHz  \n10  \n2  \n22 GHz  \n43 GHz  \n88 GHz  \n132 GHz  \n10  \n2  \nD band without/with FPT. These values commendably align with their corresponding formal errors, as illustrated in Figure 4. Moreover, the application of FPT noticeably enhances the accuracy of the closure group delays at the W and D bands. Similarly, the weighted standard deviations of closure delay rates are 1.7E-3 ps/s at K band, 3.5E-2/1.3E-3 ps/s at W band, and 6.1E-2/1.3E-3 ps/s at D band without/with FPT. And the weighted standard deviations of closure phases are 2.1 · at K band, 24.4 · /3.1 · at W band, and 55.9 · /4.4 · at D band without/with FPT. The FPT method significantly enhances the closure delay rate and closure phase by over an order of magnitude at the W and D bands.  \nTable 3. Statistics of the closure observables in KVN triangle baselines', '4.2. The tropospheric and ionospheric effects with KVN': "The path delay of radio waves caused by the troposphere is one of the major error sources. Modeling the tropospheric delay is generally divided into hydrostatic and wet parts, each of which is the product of the zenith delay and the corresponding mapping function dependency on elevation angle (Bohm & Schuh 2013). In nuSolve , the zenith hydrostatic delay (ZHD) is modeled as a function of the surface pressure, and the zenith wet delay (ZWD) is calculated with the relative humidity and temperature at the surface (Saastamoinen 1972; Davis et al. 1985). However, the uncertainty of ZWD model is far larger than ZHD model due to high spatial and temporal variability and unpredictability of the amount of water vapor. Therefore, the residual ZWD is then parameterized as a PWL function of time (e.g., the interval of 30 min in this experiment) in the data analysis. We compared the solutions with two different sets of priori ZHD+ZWD: one using meteorological data (pressure, relative humidity, temperature) from the station's log files and the other using a constant value from the standard model in nuSolve . The use of meteorological data resulted in increased weighted root-mean-squares (WRMS) of the post-fitting residuals from ∼ 12 ps to ∼ 15 ps with K band data. In this experiment, the temperature or water vapor content at the KVN site, including their temporal changes, might not accurately reflect the conditions of the air masses above. Therefore, we did not adopt the KVN meteorological data in the following analysis.  \nThe KVN system provides the greatest spanned frequency range yet used to calibrate the ionosphere. The ionospheric delays of single K band or Q band geodetic observations were usually calibrated using the global vertical total electron content (TEC) map derived from global navigation satellite system (GNSS) observations provided by the International GNSS Service (IGS) with a temporal resolution of 120 minutes (Lanyi et al. 2010; Charlot et al. 2020). We also tested the regional vertical TEC map provided by the Korea Astronomy and Space Science Institute GNSS network (KASINet) (Jeong et al. 2022), which has a temporal resolution of 5 minutes and includes observing data from co-located GNSS stations at each KVN site. The differential slant TEC (dTEC) for KVN derived with either IGS or KASINet TEC maps is only a few TEC units (TECU), except for the noon time. One TECU corresponds to an ionospheric delay  \nFigure 5. The closure group delay, closure delay rate, and closure phase in the KVN triangle baseline (KTN-KUS-KYS), with different frequency bands represented by dots of different colors. Up panels: closure group delay without/with FPT; Middle panels: closure delay rate without/with FPT; and Bottom panels: closure phase without/with FPT. The 43 GHz result is not presented and has large uncertainties due to the low SNR issues on KUS station.  \n<!-- image -->  \nTable 4. Geodetic results  \nof 2.5 ps, 0.6 ps, 0.15 ps, and 0.07 ps at 22 GHz, 43 GHz, 88 GHz, and 132 GHz, respectively. Consequently, the ionospheric delays in our KVN observations are at the 10 ps level for the K band and are negligible for the Q, W, and D bands.  \nWith the single KTN-KYS baseline, the post-fit delay residuals have a WRMS of 13.2 ps at K band and 11.6 ps at Q band. This discrepancy could potentially stem from reduced ionospheric effects at the Q band. For the W and D bands, larger WRMS values are observed due to relatively larger delay uncertainties. The utilization of either GNSS TEC maps or dual-band VLBI combinations did not yield noticeable improvements in WRMS with this data, likely due to the negligible ionospheric effects on the short baselines. Notably, considering that global vertical ionospheric effects typically vary from a few to dozens of TECUs (Nothnagel 2019), the multi-band KVN system holds promise for obtaining ionospheric-free delays across the entire broad bandwidth from 20 to over 100 GHz with long baselines in the near future.", '4.3. Geodetic results': 'We performed a comparative analysis of WRMS post-fit delay residuals (pfdr) and estimated baseline lengths, as detailed in Table 4 and Figure 6, considering various frequency bands and the presence or absence of FPT. The baseline lengths estimated and reported in Table 4 are consistent with their respective uncertainties.  \nThe post-fit delay residuals exhibit a WRMS of 12.4 ps at K band and 11.8 ps at Q band. When employing FPT, there is no noticeable difference in WRMS at K and Q bands. This suggests that the impact of atmospheric phase fluctuations at K and Q bands, particularly for baselines of less than 500 km and 2-minute scans, is minimal. This finding aligns with the similar closure group delays observed in Figure 5 and Table 3. Notably, the delay accuracy at the Q band is similar with that at the K band, and the slightly smaller WRMS at the Q band may be attributed to reduced ionospheric effects.  \nIn the case of W and D bands, the visibility phases are significantly affected by atmospheric turbulence. As depicted in Figure 3, FPT enhances fringe SNR, leading to an additional 100 delay observables at the D band. It is worth noting that the W band already boasts a very high detection rate ( ∼ 95%). Additionally, FPT reduced systematic errors in group delay and delay rate. The WRMS of the post-fitting residuals decreased from 25.0 ps to 20.5 ps at the W band and from 39.3 ps to 27.6 ps at the D band. This indicates that the errors introduced by atmospheric phase fluctuations contributing to the WRMS are ∼ 14 ps for the W band and ∼ 28 ps for the D band in this experiment. This finding aligns with the effects observed in closure group delays in Figure 5 and Table 3. The baseline lengths can be different at 4 mm between without and with FPT. And using FPT, the baseline lengths at W and D bands are generally closer to that of the K band. Therefore, calibration for atmospheric phase fluctuations is necessary in geodetic VLBI at millimeter wavebands.  \nThe source positions estimated in geodetic analysis for this experiment achieve milliarcsecond precision, posing challenges in investigating sub-milliarcsecond frequency-dependent position offsets. Nevertheless, this can be achieved with multiple epochs, extended baselines, and/or including the SFPR method.  \nFigure 6. Post-fitting residuals at different bands  \n<!-- image -->', '5. CONCLUSION AND OUTLOOK': "We have successfully conducted the first simultaneous geodetic and astrometric VLBI experiment at 22/43/88/132 GHz with KVN. Our achievement includes a high detection rate of approximately 95% at the W band and about 70% at the D band. Moreover, we have obtained competitive accuracy when compared to traditional centimeter wavebands, with the WRMS of the post-fitting residuals measuring 12.4 ps at K band, 11.8 ps at Q band, 20.5 ps at W band, and  \n27.6 ps at D band. This experiment demonstrates that the millimeter waveband can be used for geodetic applications with high precision.  \nFor the first time, we introduced the FPT method to geodetic VLBI analysis, an approach for calibrating atmospheric phase fluctuations. Our results demonstrated that FPT improves fringe detection and enhances the accuracy of delay measurements at the W and D bands. We found that atmospheric phase fluctuations, prevalent with baselines under 500 km and 2-minute scans, contribute to errors of approximately 14 ps at the W band and 28 ps at the D band. These fluctuations represent a major error source in millimeter-wave geodetic VLBI and can be effectively mitigated through the FPT method for general sources. It is important to emphasize that FPT proves highly beneficial for geodetic mm-VLBI observations. This extends beyond merely detecting weaker sources, encompassing the precise measurement of frequency-dependent offsets in source positions at millimeter wavebands (Rioja & Dodson 2011).  \nThe challenges we previously believed regarding geodetic VLBI at the millimeter waveband might be surmountable. The high detection rate at 22/43/88/132 GHz for 82 sources has encouraged us to complete an all-sky distributed source catalog for geodetic VLBI and mm-VLBI studies in astrophysics (e.g., Dodson et al. 2017). The number of detectable ICRF sources at K/Q/W bands is expected to exceed several hundred with KVN (Xu et al. 2024). Typical mm-VLBI observations (above 80 GHz) require reference pointing scans to ensure accurate antenna pointing. In this experiment, such scans were not implemented due to the lack of support in SKED . Nevertheless, the results were satisfactory, owing to the high pointing accuracy of KVN. Further efforts to incorporate reference pointing scans into geodetic mm-VLBI scheduling are currently underway. The precision of group delay with broad bandwidth synthesis from 20 to 100 GHz with KVN can be comparable to or better than VGOS, as demonstrated by a fringe in Xu et al. (2024). The KVN phase-cal system is also being tested to determine the delay and phase offsets among different bands and monitor the effect of changes in ambient temperature on components of the signal chain. While the current KVN baseline is relatively short and limits our ability to explore the ionosphere, source structure, and frequency-dependent offsets in source positions, it's worth noting that simultaneous tri-band (K/Q/W) receivers are undergoing global development (e.g., Dodson et al. 2023). We anticipate that we will have access to longer baselines in the coming years, enabling more comprehensive investigations in these areas as mentioned in Section 1.", 'A. SOURCE CATALOG': 'The 82 sources used in this experiment are listed in Table 5.  \nTable 5 . 82 sources for geodetic VLBI at K/Q/W/D band  \nXu et al.  \nTable 5 (continued)  \nTable 5 continued on next page', 'REFERENCES': 'Akiyama, K., Algaba, J.-C., An, T., et al. 2022, Galaxies,  \n10, 113, doi: 10.3390/galaxies10060113  \nAnderson, J. M., & Xu, M. H. 2018, Journal of Geophysical  \nResearch (Solid Earth), 123, 10,162,  \ndoi: 10.1029/2018JB015550  \nAstropy Collaboration, Robitaille, T. P., Tollerud, E. J.,  \net al. 2013, A&A, 558, A33,  \ndoi: 10.1051/0004-6361/201322068  \nBlackburn, L., Chan, C.-k., Crew, G. B., et al. 2019, ApJ, 882, 23, doi: 10.3847/1538-4357/ab328d  \nSovers, O. J., Fanselow, J. L., & Jacobs, C. S. 1998, Reviews of Modern Physics, 70, 1393, doi: 10.1103/RevModPhys.70.1393 Walker, R. 2022, The sched user manual Whitney, A. R., Cappallo, R., Aldrich, W., et al. 2022, HOPS: Haystack Observatory Postprocessing System, Astrophysics Source Code Library, record ascl:2205.019. http://ascl.net/2205.019 Xu, M. H., Anderson, J. M., Heinkelmann, R., et al. 2021a, Journal of Geodesy, 95, 51,  \ndoi: 10.1007/s00190-021-01496-7  \nXu, M. H., Heinkelmann, R., Anderson, J. M., et al. 2016, AJ, 152, 151, doi: 10.3847/0004-6256/152/5/151 Xu, M. H., Savolainen, T., Anderson, J. M., et al. 2022, A&A, 663, A83, doi: 10.1051/0004-6361/202140840 Xu, S., Jung, T., & Byun, D.-Y. 2024, Geodetic and Astrometric VLBI at K/Q/W/D Bands with the KVN, Zenodo, doi: 10.5281/zenodo.10902979  \nXu, S., Jike, T., Jung, T., et al. 2021b, in 25th European VLBI Group for Geodesy and Astrometry Working Meeting, ed. R. Haas, Vol. 25, 71-73'}