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Influence of Earth's Curvature and Atmospheric Refraction on Leveling01:26

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During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance.
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Optical refractive inverse weak value tiltmeter.

Garrett K Josemans, Benjamin A Baldwin, John E Gray

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    Summary
    This summary is machine-generated.

    This study enhances the optical weak value amplification (WVA) model, demonstrating its use as a sensitive tiltmeter. Laboratory measurements confirm a high tilt sensitivity and signal-to-noise ratio increase.

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    Area of Science:

    • Optics and Photonics
    • Quantum Measurement

    Background:

    • The optical weak value amplification (WVA) technique, introduced in 1989, offers potential for enhanced measurement sensitivity.
    • Understanding the pointer behavior in WVA devices is crucial for optimizing their performance.

    Purpose of the Study:

    • To present an expanded mathematical model for optical WVA devices.
    • To investigate the impact of incidence angle on pointer behavior within WVA regions.
    • To demonstrate the novel application of a birefringence-based WVA device as a sensitive tiltmeter.

    Main Methods:

    • Developed an expanded mathematical model for optical WVA devices.
    • Modeled pointer behavior concerning the incidence angle of a birefringent crystal.
    • Conducted laboratory measurements to validate the model and assess tiltmeter performance.

    Main Results:

    • Achieved a tilt sensitivity of approximately 0.58 m/rad.
    • Demonstrated an amplification factor of 390 times compared to nonamplified refraction.
    • Observed an increase in signal-to-noise ratio (SNR) of approximately 110 times over shot noise.

    Conclusions:

    • The expanded mathematical model accurately describes WVA device behavior.
    • Birefringence-based WVA devices can be effectively utilized as highly sensitive tiltmeters.
    • The study validates the practical application of WVA for precision measurements.