The use of atmospheric dispersion in optical distance measurement

Owens, James C.

doi:10.1007/bf02525701

Cited by 10 publications

(6 citation statements)

References 11 publications

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“…In addition to describing the ray tracing procedure we (1) give examples of differences between Ds and D, (2) indicate errors associated with the dual zenith angle method for height difference determination, and (3) demonstrate from both theory and the ray-tracing calculations through real atmospheres that a systematic error in multiwavelength measurements results from neglecting the physical path length difference between the two light beams (of different wavelength) through the dispersive atmosphere. • Owens [1968] cites results from a technical report by Thayer that indicate similar limitations to the use of a dual-color system, as derived here. Huggett and Slater [1977] give equations for, and field measurements made in California with, a three-wavelength instrument.…”

Section: Ray Tracingsupporting

confidence: 61%

“…The dual-color distance-measuring instrument accounts for the refractive index along the line on the basis of dispersion [Owens, 1968;Bouricius and Earnshaw, 1974;Slater and Huggett, 1976;Huggett and Slater, 1977]. The approach assumes that the physical path is the same for each beam, allowing one to obtain the difference in refractive index from the difference in optical path length.…”

Section: Dual-color Lasermentioning

confidence: 99%

“…This correction term resulting from AS seems to have been analyzed by Thayer [Owens, 1968] and is incorporated in the determination of gb -•ir, and therefore ti and the line length. Using a similar form of ( (Table 3).…”

Section: Asm-asnb = St(rib-•ir) (20)mentioning

confidence: 99%

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Distance corrections for single‐ and dual‐color lasers by ray tracing

Berg¹,

Carter²

1980

J. Geophys. Res.

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The appendix is available with entire article on microfiche. Order from the American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document J80‐007; $1.00. Payment must accompany order. The physical arc length difference between the red and blue beam of a dual‐color laser generates an error term in determining Δn (and thus n, the refractive index, and D, the line length). Numerical ray trace examples and theoretical approximations show the resulting relative error ΔD/D to increase as D2. The error reaches 1 part in 108 (107) at D of 12 (40) km, respectively, through an atmospheric structure of a line with Δh ≅ 2000 m. Error reduction by a factor of nearly 10 is possible by using the pressure, temperature, and humidity of both endpoints to calculate n or, to a lesser degree, by assuming a standard coefficient of refraction k. Two lines, approximately 30 km each, with Δh of 2000 and 3000 m, were sampled by helicopter on the island of Maui through an inversion layer. The two ray trace lengths were compared to standard reductions. Hypothetical shorter and longer lines through the same atmospheric structures and elevation difference Δh are also reduced by both methods. Length differences from the two methods appear at 10−7 level for lines longer than 60 km and depend on the sharpness of the temperature inversion. The dual zenith angle method of determining Δh would yield errors of the order of 60 cm for the real line.

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Section: Ray Tracingsupporting

confidence: 61%

Section: Dual-color Lasermentioning

confidence: 99%

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Distance corrections for single‐ and dual‐color lasers by ray tracing

Berg¹,

Carter²

1980

J. Geophys. Res.

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“…Alternatively, the two-colour method proposed by Bender and Owens1516 can realize air refractive index correction without precise knowledge of environmental parameters31718192021. The basic principle of the method is to employ lights with two different wavelengths to measure the same geometrical distance D and thus obtain two optical distances D 1 and D 2 .…”

mentioning

confidence: 99%

Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs

Takáhashi

Arai

et al. 2013

Sci Rep

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Optical frequency combs have become an essential tool for distance metrology, showing great advantages compared with traditional laser interferometry. However, there is not yet an appropriate method for air refractive index correction to ensure the high performance of such techniques when they are applied in air. In this study, we developed a novel heterodyne interferometry technique based on two-colour frequency combs for air refractive index correction. In continuous 500-second tests, a stability of 1.0 × 10−11 was achieved in the measurement of the difference in the optical distance between two wavelengths. Furthermore, the measurement results and the calculations are in nearly perfect agreement, with a standard deviation of 3.8 × 10−11 throughout the 10-hour period. The final two-colour correction of the refractive index of air over a path length of 61 m was demonstrated to exhibit an uncertainty better than 1.4 × 10−8, which is the best result ever reported without precise knowledge of environmental parameters.

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“…Atmospheric parameters such as the temperature, pressure, humidity, and possibly the CO 2 content are measured to calculate the refractive index using the Edlén equation 6 , 7 , However, it is difficult to get an accurate distribution of these parameters along the optical path, especially at long distances and with a moving stage 8 . Nevertheless, the influence of the turbulence of the atmosphere can be corrected using the two-color method proposed by Bender and Owens 9 , 10 , which is widely used in optical frequency combs 11 – 14 and laser interferometers 15 – 18 . This method measures a geometric distance, L , with both wavelength λ 1 and λ 2 , to obtain two optical distances, L λ 1 and L λ 2 , and gives the geometric distance L = L λ 1 − A ( L λ 2 − L λ 1 ), where A is the so-called A-coefficient in two-color method that represents the dispersion relation for air refractive indices at two wavelengths.The conventional two-color method eliminated the influence of the atmosphere, yet simultaneously enlarged the uncertainties in measured optical distances, Δ L λ 1 and Δ L λ 2 , because of the stability of the laser wavelength, thermal expansion and the optical thermal drift 19 .…”

Section: Introductionmentioning

confidence: 99%

Two-color heterodyne laser interferometry for long-distance stage measurement with correction of uncertainties in measured optical distances

Liu

Bayanheshig

et al. 2017

Sci Rep

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We designed a new system that eliminates deviations by correcting uncertainty in optical distance measurements in the laser two-color heterodyne interferometer. In simulations, eliminating the uncertainty from the atmosphere, the deviation in the uncertainty of the optical distance was 50 times greater with the two-color method than with the one-color method. Adding a correction arm reduces the deviation caused by the uncertainties in measured optical distances. The uncertainty in the measured path length is reduced to 20 nm over a path length of 1500 mm, giving a relative uncertainty of 1.34 × 10−8.

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The use of atmospheric dispersion in optical distance measurement

Cited by 10 publications

References 11 publications

Distance corrections for single‐ and dual‐color lasers by ray tracing

Distance corrections for single‐ and dual‐color lasers by ray tracing

Extremely high-accuracy correction of air refractive index using two-colour optical frequency combs

Two-color heterodyne laser interferometry for long-distance stage measurement with correction of uncertainties in measured optical distances

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