Frequency Standard Contributions to Limitations on the Signal-to-Noise Ratio in Very Long Baseline Interferometric (VLBI) Observations

Eric Burt; Geoff Bower; Joe Lazio; Marin Anderson; Sonia Hernandez; Todd Ely

arxiv: 2508.19123 · v2 · submitted 2025-08-26 · 🌌 astro-ph.IM

Frequency Standard Contributions to Limitations on the Signal-to-Noise Ratio in Very Long Baseline Interferometric (VLBI) Observations

Eric Burt , Todd Ely , Geoff Bower , Joe Lazio , Marin Anderson , Sonia Hernandez This is my paper

Pith reviewed 2026-05-18 20:56 UTC · model grok-4.3

classification 🌌 astro-ph.IM

keywords VLBIfrequency standardssignal-to-noise ratiocoherence functionultra-stable oscillatorhydrogen maseroptical local oscillatorspace-based interferometry

0 comments

The pith

The coherence function alone does not determine frequency standard viability in VLBI, and a derived clock-limited signal-to-noise expression shows only the USO and hydrogen maser work for high-frequency observations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that relying on the coherence function C(T) alone is not enough to judge if a frequency standard will work well in VLBI observations. The authors derive a new expression focused on the clock's effect on the signal-to-noise ratio of the visibility measurements. Testing this on real devices finds the ultra-stable oscillator suitable only for short times at high frequencies, the hydrogen maser better but possibly too bulky for space, and optical local oscillators as a strong candidate for longer integrations. This helps narrow options for frequency standards needed in space-based VLBI to get sharper images of distant objects like black holes.

Core claim

The paper's core claim is that the usual coherence time metric does not suffice to determine frequency standard performance in VLBI, so they derive an expression for the clock-limited signal-to-noise ratio in VLBI visibilities. When this expression is evaluated using the specifications of actual frequency standards, only the ultra-stable oscillator and hydrogen maser prove viable for high-frequency VLBI, with the former restricted to integration times of 30 seconds at 90 GHz, 10 seconds at 230 GHz, 5 seconds at 345 GHz, and none at 630 GHz. The hydrogen maser allows longer times but may be too large for space applications, while the optical local oscillator from emerging optical clock techon

What carries the argument

The derived expression for the clock-limited VLBI visibility signal-to-noise ratio, which incorporates frequency standard stability to set observation viability limits.

If this is right

Only the USO and hydrogen maser are viable for upcoming high-frequency VLBI.
USO integration times are limited to 30s at 90 GHz, 10s at 230 GHz, 5s at 345 GHz, and not viable at 630 GHz.
The hydrogen maser may have prohibitive size for space missions.
Optical local oscillators show promise with viable times of over 100s at 90 GHz, 60s at 230 GHz, 40s at 345 GHz, and 22s at 630 GHz.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Space VLBI mission planners will need to focus on compact high-stability frequency references to enable longer coherent integrations.
The S/N expression approach could be applied to assess other noise sources limiting interferometric performance.
Progress in optical clock miniaturization for space may directly expand the feasible parameter space for high-resolution black hole imaging.

Load-bearing premise

The published performance metrics of the evaluated frequency standards accurately represent their behavior under the specific VLBI integration conditions and space environment assumed in the derived S/N expression.

What would settle it

A VLBI observation at 230 GHz using an ultra-stable oscillator over 10 seconds that achieves a visibility signal-to-noise ratio significantly above the value predicted by the clock-limited expression would challenge the derived limits.

Figures

Figures reproduced from arXiv: 2508.19123 by Eric Burt, Geoff Bower, Joe Lazio, Marin Anderson, Sonia Hernandez, Todd Ely.

**Figure 2.** Figure 2: Schematic representation of two VLBI antennas and their relationship to a source ( Thompson et al., 2017, figure 3.1). The vector between the two antennas is 𝑫> measured in wavelengths or 𝑫 measured in meters. Note that both 𝒔 and 𝒔𝟎 as depicted in the figure are unit vectors and will be represented as 𝒔] and 𝒔]𝟎 in the text to avoid confusion. The source is projected onto the spherical surface determined … view at source ↗

read the original abstract

Since its observation in 2019, the first image of a super-massive black hole using Very Long Baseline Interferometry (VLBI) with an Earth-scale baseline has generated much scientific and public interest, including the possible extension of the baseline into space to obtain higher image resolution. Operating one or more VLBI nodes in space will require the use of frequency standards that are space qualified, greatly reducing the number of options available. The coherence function C(T) is the metric usually used to determine the viability of a frequency standard. Here we show that C(T) is a useful but not sufficient metric for gauging frequency standard performance in VLBI and instead derive an expression for the clock-limited VLBI visibility S/N. We evaluate this expression for real frequency standards and find only the Ultra-Stable Oscillator (USO) and hydrogen maser to be viable for upcoming high-frequency VLBI with the USO only useful for very limited integration times (30s at 90 GHz, 10s at 230 GHz, 5s at 345 GHz, and not viable at 630 GHz). The maser extends these, but may have prohivitive size for a space mission. We also evaluate emerging frequency standard technologies and find the Optical Local Oscillator portion of optical clocks to be very promising (conservatively >100s at 90 GHz, 60s at 230 GHz, 40s at 345 GHz, and 22s at 630 GHz) when accounting for both performance and potential operation in space.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper derives a clock-limited VLBI S/N expression that improves on C(T) alone and applies it to real standards, but the viability numbers rest on ground-test specs without space adjustments.

read the letter

The main point is that the authors derive an S/N formula for VLBI visibility amplitude that incorporates clock phase noise directly, rather than stopping at the usual coherence function C(T). They then plug published performance numbers for USOs, hydrogen masers, and optical local oscillators into that expression and report concrete integration-time limits at 90–630 GHz. Only the USO and maser come out as viable under current specs, with the USO restricted to very short times and the maser flagged for possible size problems; the optical LO looks promising on paper for longer integrations. That mapping from Allan deviation or phase noise to S/N at millimeter wavelengths is the concrete output a mission planner could use right away. The derivation itself appears to follow standard timing relations and cites the relevant VLBI literature without obvious circularity. The evaluations use external published clock data rather than fitting to VLBI observations, which keeps the logic clean on that front. The soft spot is the direct insertion of lab-measured stabilities into the formula without any scaling for space conditions. Thermal cycling, radiation, vibration, or microgravity can shift oscillator performance, and because the S/N expression is monotonic in the stability parameter, even modest degradation would move the reported time limits and change which standards look acceptable. The paper notes the space-qualification requirement in the introduction but does not model those effects or cite adjusted figures. The size comment on the maser is also left qualitative. This is aimed at people designing or proposing space VLBI nodes for black-hole imaging or other high-resolution work. A reader who needs to set coherent integration times or compare oscillator options will get usable numbers from the evaluations. The underlying thinking is clear and the application is timely, so the paper deserves a serious referee to check the derivation steps and press on the space-environment assumptions.

Referee Report

1 major / 3 minor

Summary. The paper claims that the coherence function C(T) is a useful but insufficient metric for frequency standard performance in VLBI and derives an expression for the clock-limited VLBI visibility S/N. Numerical evaluation of this expression using published performance data for real frequency standards (USO, hydrogen maser, optical local oscillator) shows that only the USO and hydrogen maser are viable for upcoming high-frequency VLBI (90–630 GHz), with the USO limited to very short integration times (30 s at 90 GHz, 10 s at 230 GHz, 5 s at 345 GHz, none at 630 GHz); the maser extends these but may be too large for space, while optical local oscillators appear promising (>100 s at 90 GHz down to 22 s at 630 GHz) when considering both performance and space operability.

Significance. If the derived S/N expression holds and the evaluations are robust, the work supplies a more precise, quantitative tool than C(T) for selecting frequency standards in space VLBI missions aimed at higher-resolution black-hole imaging. The explicit derivation and concrete numerical predictions for specific frequencies and standards constitute a practical contribution. The manuscript also correctly identifies that C(T) alone does not capture the full S/N impact.

major comments (1)

[§4] §4 (Evaluation of frequency standards and integration-time limits): The reported viability thresholds and integration-time limits are obtained by direct insertion of ground-based Allan-deviation or phase-noise figures into the derived S/N expression. No corrections or sensitivity analysis are provided for space-specific effects (thermal cycling, radiation, vibration, microgravity). Because the S/N expression is monotonic in the clock-stability parameter, any unaccounted degradation scales the quantitative conclusions (e.g., the 30 s / 10 s / 5 s limits for the USO and the >100 s / 60 s / 40 s / 22 s figures for the optical local oscillator). This assumption is load-bearing for the central claim that only USO and maser are viable while optical oscillators are promising.

minor comments (3)

[Abstract] Abstract: typo “prohivitive” should read “prohibitive”.
[§4] The manuscript should add explicit references or table entries for the exact published Allan-deviation values and frequency ranges used in the numerical evaluations.
[Figures] Figure captions and axis labels for S/N versus integration time should state the assumed VLBI parameters (baseline length, frequency, bandwidth) to allow direct reproduction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the utility of the derived clock-limited S/N expression. We address the single major comment on §4 below and agree that additional discussion of space effects strengthens the work. The revised manuscript will incorporate a sensitivity analysis and explicit caveats.

read point-by-point responses

Referee: [§4] §4 (Evaluation of frequency standards and integration-time limits): The reported viability thresholds and integration-time limits are obtained by direct insertion of ground-based Allan-deviation or phase-noise figures into the derived S/N expression. No corrections or sensitivity analysis are provided for space-specific effects (thermal cycling, radiation, vibration, microgravity). Because the S/N expression is monotonic in the clock-stability parameter, any unaccounted degradation scales the quantitative conclusions (e.g., the 30 s / 10 s / 5 s limits for the USO and the >100 s / 60 s / 40 s / 22 s figures for the optical local oscillator). This assumption is load-bearing for the central claim that only USO and maser are viable while optical oscillators are promising.

Authors: We acknowledge that the referee's point is correct and that our quantitative limits are based on published ground-test or laboratory figures. For the USO and hydrogen maser, space-qualified hardware has flown on prior missions with stability performance that is typically within a factor of ~2 of ground values; we will cite those mission results explicitly. For optical local oscillators the technology is still maturing, so space-specific degradation data are not yet available in the literature. We will revise §4 to add a new subsection that (1) summarizes known space-environment impacts on each technology class, (2) states that the tabulated integration times are therefore upper-bound estimates, and (3) presents a simple sensitivity analysis showing how the S/N-limited integration times scale for assumed degradation factors of 2× and 5× in Allan deviation. This makes the load-bearing assumption transparent without altering the core derivation or the comparative ranking of the standards. revision: yes

Circularity Check

0 steps flagged

Derivation of S/N expression independent of evaluated clock data

full rationale

The paper first argues that the coherence function C(T) is useful but insufficient for VLBI frequency standard assessment, then derives an expression for clock-limited VLBI visibility S/N. This derivation is presented as following from standard interferometric visibility and phase stability relations. The evaluation step then inserts externally published Allan deviation or phase noise figures for USO, hydrogen maser, and optical local oscillator devices. No equation in the provided abstract or description reduces the derived S/N back to a fitted parameter taken from the same VLBI data, and no self-citation is invoked as the sole justification for the central formula. The chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The evaluations rely on external published performance data for the frequency standards.

pith-pipeline@v0.9.0 · 5828 in / 1140 out tokens · 25539 ms · 2026-05-18T20:56:16.211645+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We evaluate this expression for real frequency standards and find only the Ultra-Stable Oscillator (USO) and hydrogen maser to be viable... derive an expression for the clock-limited VLBI visibility S/N
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The coherence function C(T) is the metric usually used... instead derive an expression for the clock-limited VLBI visibility S/N

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · 1 internal anchor

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Ultra stable oscillator (USO) for deep space exploration

a. Comparison of clock-imposed limitations on S/N for 3 pure noise types and no fringe rate correction: white frequency (red), flicker frequency (green), random walk noise (blue) and white phase (black). In each case the hypothetical single-clock Allan deviation was taken to be 1×10−13 at 1 second. b. Same simulation with an accumulation period of 0.4 s a...

work page 2011
[2]

Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz

Clock-limited Visibility S/N calculated numerically for: Hydrogen maser (red), a USO (blue) and a hypothetical clock with an Allan Deviation of 1×10−13√𝜏⁄ (dashed black) for reference. Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz. In each graph the threshold value of 20 described in the text (b...

work page 2024
[3]

Modeled S/N limit imposed by high performance hydrogen masers at 345 GHz (red) and real visibility data at 345 GHz taken by the EHT consortium over several baselines including the SMA and ALMA (black dots). 4.2 Signal to Noise Limits for Currently Available Space Clocks Space VLBI limits the choices of frequency standard to those that have been flight-qua...

work page 2017
[4]

Space-qualified rubidium atomic frequency standard clocks,

would be the ideal choice. However, it has been challenging to achieve the same maser performance in space as on the ground. In addition, the hydrogen maser has a relatively high SWaP and may not be feasible for some missions. There are two types of masers: active and passive. Active means that the atoms themselves emit radiation at the clock frequency to...

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[5]

Figure 13 shows the results of simulating clock-limited S/N from equations (38) - (42) for the currently operating high-performance space clocks

Allan deviation of currently operating high-performance space clocks: USO (purple), GPS Rubidium Atomic Frequency Standard or RAFS (blue), Galileo Passive Hydrogen Maser or 10-14 10-13 10-12 10-11Allan Deviation 0.11101001000Time (s) USORadioastron PHMcold Rb RAFS manuscript submitted to Radio Science PHM (black), Radioastron active hydrogen maser (red), ...

work page 2006
[6]

Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz

Clock-limited Visibility S/N calculated numerically for: the Radioastron hydrogen maser (red), a USO (purple), a laser-cooled rubidium space clock (green), the Galileo passive hydrogen maser (black), and the GPS rubidium atomic frequency standard (blue). Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630...

work page 2017
[7]

warm-cell optical clock

For instance, at 345 GHz, the maximum integration time for which the S/N limit stays above the threshold of 20 goes from about 4 s for two USO’s to about 5.5 s for a maser and a USO. This analysis suggests that a USO reference in space combined with a maser reference on the ground may be viable, even at 345 GHz, as long as a total integration time of less...

work page 2010
[8]

The OLO is significantly better than the iodine clock and the ACES maser on short time scales, but crosses over iodine at about 20 seconds and the maser at about 100 seconds

Here, all of these standards are equal to or better than a maser, so unlike the case of the USO above, we assume that the ground component would also use the same clock. The OLO is significantly better than the iodine clock and the ACES maser on short time scales, but crosses over iodine at about 20 seconds and the maser at about 100 seconds. Space qualif...

work page 2024
[9]

Each trace corresponds to the coherence function for the indicated VLBI frequency

𝐶345(𝑇) (black) for a visibility with a USO at one node (space) and a hydrogen maser at the other (ground). Each trace corresponds to the coherence function for the indicated VLBI frequency. Superimposed is the coherence efficiency defined in the text for each VLBI frequency and this visibility (red dots). The normally accepted coherence value of 0.92 for...

work page 2017
[10]

#+𝜈AB. Under these conditions the exponential is very nearly linear over the band and can be treated as a constant evaluated at the center frequency, 𝜈=𝜈

to include “weakly” stationary noise types, by which we mean noise with zero mean, but potentially time-dependent variances. Substituting yields 𝐸[𝑒𝑖Φ(𝑡)]=∫1𝜎Φ(𝑡)√2𝜋+∞−∞ 𝑒−Φ(𝑡)22𝜎Φ(𝑡)2⁄cosΦ(𝑡)𝑑Φ (A6) Note that there is no contribution from the imaginary term since it is odd in Φ so only the real term is retained. Performing the integration gives 𝐸[𝑒𝑖Φ(𝑡)]...

work page 1979
[11]

flicker floor

with independent increments 𝐸[Φ(𝑠′)2]=𝑞𝑅𝑊𝑠′=2𝜂𝑠′ 𝐸[Φ(𝑠)2]=𝑞𝑅𝑊𝑠=2𝜂𝑠 𝐸[Φ(𝑠)Φ(𝑠′)]=𝐸[Φ(𝑠)2]+𝐸[Φ(𝑠)(Φ(𝑠′)−Φ(𝑠))] =𝐸[Φ(𝑠)2]+𝐸[Φ(𝑠)]𝐸[Φ(𝑠′)−Φ(𝑠)] =𝑞𝑅𝑊min(𝑠,𝑠′)=2𝜂min(𝑠,𝑠′) (A29) Turning to 𝐸[cosΦ(𝑠)cosΦ(𝑠′)] this can be computed from its definition (for instance, see Equation 3-103 in Maybeck (1979)) using manuscript submitted to Radio Science 𝐸[cosΦ(𝑠)cosΦ(𝑠′)...

work page 1979
[12]

Copyright to be transferred to the journal within 10 days of acceptance

All rights reserved. Copyright to be transferred to the journal within 10 days of acceptance. Data Availability The software used to simulate the clock-limited VLBI visibility S/N in this article is Caltech proprietary software that can be made available to researchers with a license. Please contact the authors for information on obtaining a license to th...

work page doi:10.1051/0004-6361/202347932 2024
[13]

https://doi.org/10.3847/1538-4357/ac7c1d Burt, E., Prestage, J., Tjoelker, R., Enzer, D., Kuang, D., Murphy, D., et al. (2021). Demonstration of a trapped-ion atomic clock in space. Nature, 595(7865), 43-47. https://doi.org/10.1038/s41586-021-03571-7 manuscript submitted to Radio Science Campbell, G. K., & Phillips, W. D. (2011). Ultracold atoms and preci...

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https://doi.org/10.1086/660156 Droz, F., Mosset, P., Wang, Q., Rochat, P., Belloni, M., Gioia, M., et al. (2009). Space passive hydrogen maser-performances and lifetime data. Paper presented at the 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum. https://doi.org/10.1109/FREQ.2009.5168208 Fortier, T...

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https://doi.org/10.1038/s41467-018-05219-z Margolis, H. (2010). Optical frequency standards and clocks. Contemporary Physics, 51(1), 37-58. https://doi.org/10.1080/00107510903257616 Maybeck, P. S. (1979). Stochastic models, estimation, and control volume 1 (Vol. 1): Elsevier. ISBN: 978-0-12-480701-3 Middleton, D. (1987). Introduction to statistical commun...

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https://doi.org/10.48550/arXiv.2410.07453 Riehle, F. (2006). Frequency standards: Basics and applications: John Wiley & Sons. ISBN 3-527-40230-6 manuscript submitted to Radio Science Rioja, M., Dodson, R., Asaki, Y., Hartnett, J., & Tingay, S. (2012). The impact of frequency standards on coherence in vlbi at the highest frequencies. The Astronomical Journ...

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High Precision Astrometric Millimeter VLBI Using a New Method for Atmospheric Calibration

https://doi.org/10.1088/0004-6256/144/4/121 Rioja, M. J., & Dodson, R. (2011). High precision astrometric millimeter vlbi using a new method for atmospheric calibration. arXiv preprint arXiv:1101.2051. https://doi.org/10.1088/0004-6256/141/4/114 Rioja, M. J., Dodson, R., & Asaki, Y. (2023). The transformational power of frequency phase transfer methods fo...

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https://doi.org/10.3390/galaxies11010016 Rogers, A., & Moran Jr, J. (1981). Coherence limits for very-long-baseline interferometry. IEEE Transactions on Instrumentation and Measurement. https://doi.org/10.1109/TIM.1981.6312409 Rogers, A. E. (1988). Atmospheric limits: A review of the effect of path length variations on the coherence and accuracy of vlbi. ...

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https://doi.org/10.1109/TUFFC.2004.1324399 Sasao, T., & Fletcher, A. B. (2008). Introduction to vlbi systems. In Lecture Notes for KVN Students based on Ajou University lecture notes (2 ed.). Space-qualified rubidium atomic frequency standard clocks. Retrieved from https://www.excelitas.com/product/space-qualified-rubidium-atomic-frequency-standard-clocks...

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https://vremya-ch.com/index.php/en/progects-en/spaceapplications-en/vch-1010-en-2/index.html

https://doi.org/10.3847/1538-3881/aa99e0 Vremya space hydrogen maser (2011). https://vremya-ch.com/index.php/en/progects-en/spaceapplications-en/vch-1010-en-2/index.html

work page doi:10.3847/1538-3881/aa99e0 2011

[1] [1]

Ultra stable oscillator (USO) for deep space exploration

a. Comparison of clock-imposed limitations on S/N for 3 pure noise types and no fringe rate correction: white frequency (red), flicker frequency (green), random walk noise (blue) and white phase (black). In each case the hypothetical single-clock Allan deviation was taken to be 1×10−13 at 1 second. b. Same simulation with an accumulation period of 0.4 s a...

work page 2011

[2] [2]

Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz

Clock-limited Visibility S/N calculated numerically for: Hydrogen maser (red), a USO (blue) and a hypothetical clock with an Allan Deviation of 1×10−13√𝜏⁄ (dashed black) for reference. Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz. In each graph the threshold value of 20 described in the text (b...

work page 2024

[3] [3]

Modeled S/N limit imposed by high performance hydrogen masers at 345 GHz (red) and real visibility data at 345 GHz taken by the EHT consortium over several baselines including the SMA and ALMA (black dots). 4.2 Signal to Noise Limits for Currently Available Space Clocks Space VLBI limits the choices of frequency standard to those that have been flight-qua...

work page 2017

[4] [4]

Space-qualified rubidium atomic frequency standard clocks,

would be the ideal choice. However, it has been challenging to achieve the same maser performance in space as on the ground. In addition, the hydrogen maser has a relatively high SWaP and may not be feasible for some missions. There are two types of masers: active and passive. Active means that the atoms themselves emit radiation at the clock frequency to...

work page 2019

[5] [5]

Figure 13 shows the results of simulating clock-limited S/N from equations (38) - (42) for the currently operating high-performance space clocks

Allan deviation of currently operating high-performance space clocks: USO (purple), GPS Rubidium Atomic Frequency Standard or RAFS (blue), Galileo Passive Hydrogen Maser or 10-14 10-13 10-12 10-11Allan Deviation 0.11101001000Time (s) USORadioastron PHMcold Rb RAFS manuscript submitted to Radio Science PHM (black), Radioastron active hydrogen maser (red), ...

work page 2006

[6] [6]

Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630 GHz

Clock-limited Visibility S/N calculated numerically for: the Radioastron hydrogen maser (red), a USO (purple), a laser-cooled rubidium space clock (green), the Galileo passive hydrogen maser (black), and the GPS rubidium atomic frequency standard (blue). Each graph shows results for a different VLBI frequency: a) 90 GHz, b) 230 GHz, c) 345 GHz, and d) 630...

work page 2017

[7] [7]

warm-cell optical clock

For instance, at 345 GHz, the maximum integration time for which the S/N limit stays above the threshold of 20 goes from about 4 s for two USO’s to about 5.5 s for a maser and a USO. This analysis suggests that a USO reference in space combined with a maser reference on the ground may be viable, even at 345 GHz, as long as a total integration time of less...

work page 2010

[8] [8]

The OLO is significantly better than the iodine clock and the ACES maser on short time scales, but crosses over iodine at about 20 seconds and the maser at about 100 seconds

Here, all of these standards are equal to or better than a maser, so unlike the case of the USO above, we assume that the ground component would also use the same clock. The OLO is significantly better than the iodine clock and the ACES maser on short time scales, but crosses over iodine at about 20 seconds and the maser at about 100 seconds. Space qualif...

work page 2024

[9] [9]

Each trace corresponds to the coherence function for the indicated VLBI frequency

𝐶345(𝑇) (black) for a visibility with a USO at one node (space) and a hydrogen maser at the other (ground). Each trace corresponds to the coherence function for the indicated VLBI frequency. Superimposed is the coherence efficiency defined in the text for each VLBI frequency and this visibility (red dots). The normally accepted coherence value of 0.92 for...

work page 2017

[10] [10]

#+𝜈AB. Under these conditions the exponential is very nearly linear over the band and can be treated as a constant evaluated at the center frequency, 𝜈=𝜈

to include “weakly” stationary noise types, by which we mean noise with zero mean, but potentially time-dependent variances. Substituting yields 𝐸[𝑒𝑖Φ(𝑡)]=∫1𝜎Φ(𝑡)√2𝜋+∞−∞ 𝑒−Φ(𝑡)22𝜎Φ(𝑡)2⁄cosΦ(𝑡)𝑑Φ (A6) Note that there is no contribution from the imaginary term since it is odd in Φ so only the real term is retained. Performing the integration gives 𝐸[𝑒𝑖Φ(𝑡)]...

work page 1979

[11] [11]

flicker floor

with independent increments 𝐸[Φ(𝑠′)2]=𝑞𝑅𝑊𝑠′=2𝜂𝑠′ 𝐸[Φ(𝑠)2]=𝑞𝑅𝑊𝑠=2𝜂𝑠 𝐸[Φ(𝑠)Φ(𝑠′)]=𝐸[Φ(𝑠)2]+𝐸[Φ(𝑠)(Φ(𝑠′)−Φ(𝑠))] =𝐸[Φ(𝑠)2]+𝐸[Φ(𝑠)]𝐸[Φ(𝑠′)−Φ(𝑠)] =𝑞𝑅𝑊min(𝑠,𝑠′)=2𝜂min(𝑠,𝑠′) (A29) Turning to 𝐸[cosΦ(𝑠)cosΦ(𝑠′)] this can be computed from its definition (for instance, see Equation 3-103 in Maybeck (1979)) using manuscript submitted to Radio Science 𝐸[cosΦ(𝑠)cosΦ(𝑠′)...

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Copyright to be transferred to the journal within 10 days of acceptance

All rights reserved. Copyright to be transferred to the journal within 10 days of acceptance. Data Availability The software used to simulate the clock-limited VLBI visibility S/N in this article is Caltech proprietary software that can be made available to researchers with a license. Please contact the authors for information on obtaining a license to th...

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https://doi.org/10.1086/660156 Droz, F., Mosset, P., Wang, Q., Rochat, P., Belloni, M., Gioia, M., et al. (2009). Space passive hydrogen maser-performances and lifetime data. Paper presented at the 2009 IEEE International Frequency Control Symposium Joint with the 22nd European Frequency and Time forum. https://doi.org/10.1109/FREQ.2009.5168208 Fortier, T...

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High Precision Astrometric Millimeter VLBI Using a New Method for Atmospheric Calibration

https://doi.org/10.1088/0004-6256/144/4/121 Rioja, M. J., & Dodson, R. (2011). High precision astrometric millimeter vlbi using a new method for atmospheric calibration. arXiv preprint arXiv:1101.2051. https://doi.org/10.1088/0004-6256/141/4/114 Rioja, M. J., Dodson, R., & Asaki, Y. (2023). The transformational power of frequency phase transfer methods fo...

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https://doi.org/10.1109/TUFFC.2004.1324399 Sasao, T., & Fletcher, A. B. (2008). Introduction to vlbi systems. In Lecture Notes for KVN Students based on Ajou University lecture notes (2 ed.). Space-qualified rubidium atomic frequency standard clocks. Retrieved from https://www.excelitas.com/product/space-qualified-rubidium-atomic-frequency-standard-clocks...

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https://doi.org/10.3847/1538-3881/aa99e0 Vremya space hydrogen maser (2011). https://vremya-ch.com/index.php/en/progects-en/spaceapplications-en/vch-1010-en-2/index.html

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