Common-path design criteria for laser datum based measurement of small angle deviations and laser autocollimation method in compliance with the criteria with high accuracy and stability

Fan Zhu; Jiubin Tan; Jiwen Cui

doi:10.1364/OE.21.011391

1. Introduction

Laser datum based measurement of small angle deviations is widely used for calibration of machine tools, alignment of precision instruments during assembly, measurement of large-scale structures deformations, etc. High measurement accuracy and stability of small angle deviations are increasingly important as manufacturing technology and scientific research develop fast. However, laser beam drifts resulting from laser generation mechanism and instability of beam transmission medium commonly occur during laser datum based measurement, and they are always coupled with the small angle deviations being measured, and so, small angle deviations cannot be measured with high accuracy and stability, especially over a long measurement distance.

Laser beam drift resulting from laser generation mechanism measures from 0.2 arcsec to 20 arcsec, and it is the main drift in laser datum based measurement of small angle deviations. Much work has been done on the laser beam drift [1–6]. However, the methods proposed are mainly focused on the applications in which a laser beam is used as a linear datum for the measurement of straightness or coaxiality. There are few such methods suitable for the measurement of small angle deviations. S. C. Irick et al. used a reference beam method for the long trace profiler to detect the laser beam drift and the deviations of the optical head when the local slope of a surface profile is being measured [7]. S. Qian et al. introduced six non-tilted reference beam methods to improve the measurement accuracy [8]. K. Li et al. proposed a method using common-path compensation for the angular drift of measurement beam to improve the measurement stability and resolution [9]. The laser beam drift resulting from laser generation mechanism can be well compensated by using these methods. However, the reference and measurement beams used in these methods transmits along different beam paths after being split by the beam splitter, which leads to the difference in the drifts of reference and measurement beams resulting from the instability of air medium along the beam paths. Therefore, the beam drift resulting from the instability of air medium cannot be compensated using these methods.

Laser beam is usually transmitted in air medium, and the fluctuations of local temperature, air pressure, humidity, content of carbon dioxide, and airflow etc. of air medium lead to the angular drift of laser beam. Researches have shown that the angular drift resulting from the instability of air medium can be 0.02 arcsec, even under the condition of constant temperature, vibration isolated and beam path shielded. Moreover, the drift resulting from the instability of air medium varies with the transmission distance of laser beam, and this makes it very difficult to improve the measurement accuracy and stability of small angle deviations over a long measurement distance.

Several technical methods have been applied to diminish the drift resulting from the instability of air medium. One commonly used method is to make a measurement using a short and shielded beam path, but it cannot be applied in some applications where a long beam path is needed, such as the straightness measurement of a long guide way. The air-blowing method can be used to change the spectrum of air flow along the beam path into a high-frequency band which can then be filtered using a low-pass filter to diminish the effect of air flow on the measurement stability, but it cannot be applied when the small angle deviation varies in high frequency [10]. The method of monitoring the parameters of air medium to compensate the drift, which is mentioned and studied in [11], needs to arrange multiple sensors along the beam path, so both the apparatus and the compensation process are sophisticated. Moreover, the random fluctuation of air medium exists everywhere along the beam path, and the compensation can only be done over several sections of the path, which deteriorates the compensation effect. The common-path compensation method utilizes a reference beam which is transmitted on common path with the measurement beam. The common-path transmission promises that the drifts of the reference and measurement beams resulting from the instability of air medium are exactly the same, so that the drifts can be well compensated [12–15]. The common-path compensation method is most suitable for the drift resulting from the instability of air medium. C. Yin et al. gave their novel comprehension of common-path principle and some examples to illustrate how to judge whether a measurement scheme is in compliance with common-path principle or not [16]. However, how to design a system with common-path beam drift detection and compensation in laser datum based measurement of small angle deviations, or what criteria should be satisfied when designing such a system has not been discussed yet.

Therefore, criteria for the design of a system with common-path beam drift detection and compensation in laser datum based precision measurement of small angle deviations are proposed to guide the implementation of common-path principle in dealing with laser beam drifts resulting from laser generation mechanism and instability of beam transmission medium. A laser autocollimation method is designed in compliance with the criteria for the measurement of small angle deviations with high accuracy and stability, especially over a long measurement distance.

2. Common-path design criteria

A measurement system should be designed in compliance with the common-path principle so that the drifts resulting from laser generation mechanism and instability of beam transmission medium can be accurately detected and compensated, especially over a long measurement distance. The followings are the criteria which a common-path design must comply with.

(1) The drifts of measurement and reference beams should be the same when they enter into the measurement system, which guarantees that the reference and measurement beams have the same initial drift derived from their respective laser sources. The optimal case is that these two beams come from the same laser source.
(2) The reference beam should be transmitted along the common path with the measurement beam in the whole measurement process, which guarantees the reference and measurement beams have the same drift resulting from the instability of beam transmission medium along the beam path, which is crucial for the detection and compensation of this kind of drift. This also guarantees both the reference and measurement beams pass through almost the same group of optic components, so the effect of thermal deformation of mechanical structures and optical components can also be compensated.
(3) The reference beam should have some characteristics different from those of the measurement beam so that these characteristics can be used to separate the two beams from the common path transmission for detection at the receiving end.
(4) The reference and measurement beams should have different sensitivities to the small angle deviations being measured, which guarantees the beam drifts can be abstracted from the couple of the drifts and the small angle deviations being measured, and then used for compensation.

3. Laser autocollimation method in compliance with the criteria

A laser autocollimation method is designed in compliance with the criteria, which is shown in Fig. 1. The laser beam collimated by collimating lens 6 is directed to combination reflector 12 with p-polarization (a linear polarization parallel to the horizontal), and split into a reference beam and a measurement beam by combination reflector 12. The reference and measurement beams are reflected back from combination reflector 12 to collimating lens 6 through a common path with their polarizations perpendicular to each other. The reference and measurement beams are separated by secondary PBS 5 at the receiving end and received by QPD 3 and PSD 4 respectively.

Fig. 1 Schematic diagram of laser autocollimation method. 1.single-mode optical fiber(SMOF); 2.object plane; 3.QPD; 4.PSD; 5.secondary PBS; 6.collimating lens; 7.primary PBS; 8.beam splitting target reflector(BSTR); 8(a).semi-reflective film; 8(b).first reflective surface; 8(c).second reflective surface; 9.half-wave plate; 10.45° tilted mirror; 11.BS; 12.combination reflector.

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Combination reflector 12 is a crucial unit for this laser autocollimation method. It is comprised of primary PBS 7, BSTR 8, half-wave plate 9, and 45° tilted mirror 10. BSTR 8 is a right-angle prism with half of its slope coated with semi-reflective film and the other half remains intentionally uncoated.

When a collimated laser beam with p-polarization is directed to combination reflector 12, it totally passes through primary PBS 7 and split into a reflected beam and a transmitted beam by the semi-reflective film of BSTR 8. Both of the reflected beam and the transmitted beam have the same p-polarization with the incident collimated laser beam. So the reflected beam totally passes through PBS 7 again and goes back to collimating lens 6.

On the other hand, the transmitted beam with p-polarization at the semi-reflective film is reflected by the two perpendicular reflective surfaces of BSTR 8 and directed to half-wave plate 9. As shown in Fig. 2(c), the slow axis of half-wave plate 9 is adjusted at 45° to the horizontal, so the resulting polarization of the beam is linear with its direction at 90° to the horizontal (which is s-polarization) after it passes through half-wave plate 9. The beam is then reflected to primary PBS 7 by 45° tilted mirror 10. The beam is totally reflected by primary PBS 7 due to its s-polarization, and goes back to collimating lens 6 along the common path with the beam reflected from the semi-reflective film of BSTR 8.

Fig. 2 Principle of combination reflector. (a)deflections of measurement and reference beams with angular drift of incident laser beam; (b) deflections of measurement and reference beams with small angle deviation of combination reflector; (c) variations of polarizations of measurement and reference beams.

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The principle of combination reflector 12 is analyzed using the transmission matrix of a plane mirror at every reflective surface of the reflector. The equation of the reflecting surface of a plane mirror in the xyz coordinate system and its transmission matrix R can be expressed as [17]

A x + B y + C z + D = 0

R = [\begin{matrix} 1 - 2 A^{2} / F^{2} & - 2 A B / F^{2} & - 2 A C / F^{2} \\ - 2 A B / F^{2} & 1 - 2 B^{2} / F^{2} & - 2 B C / F^{2} \\ - 2 A C / F^{2} & - 2 B C / F^{2} & 1 - 2 C^{2} / F^{2} \end{matrix}]

where,

F = \sqrt{A^{2} + B^{2} + C^{2}}

, and

A / F

,

B / F

,

C / F

are the direction cosines of the normal of the plane.

When the laser beam collimated by collimating lens 6 is directed along axis z and combination reflector 12 is set right against the direction of the collimated laser beam, as shown in Fig. 2(a), transmission matrix R₁ of the semi-reflective film, R₂ of the first reflective surface of BSTR 8, R₃ of the second reflective surface of BSTR 8, R₄ of the 45° tilted mirror 10, and R₅ of the reflective film of primary PBS 7 can be expressed as

\begin{array}{l} R_{1} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & - 1 \end{matrix}], R_{2} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], R_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], \\ \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} R_{4} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], R_{5} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}] \end{array}

Direction cosine A₁ of the incident collimated laser beam at the semi-reflective film with an angular drift α in y-z plane can be expressed as

A_{1} = [\begin{matrix} 0 \\ - \sin α \\ \cos α \end{matrix}]

Direction cosine A₂ of the beam reflected by the semi-reflective film of BSTR 8 is

A_{2} = R_{1} A_{1} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & - 1 \end{matrix}] • [\begin{matrix} 0 \\ - \sin α \\ \cos α \end{matrix}] = [\begin{matrix} 0 \\ - \sin α \\ - \cos α \end{matrix}]

Direction cosine A₃ of the beam transmitted through the semi-reflective film of BSTR 8 and reflected sequentially from the first reflective surface of BSTR 8, the second reflective surface of BSTR 8, 45° tilted mirror 10, and the reflective film of primary PBS 7 can be expressed as

A_{3} = R_{5} R_{4} R_{3} R_{2} A_{1} = [\begin{matrix} 0 \\ \sin α \\ - \cos α \end{matrix}]

It can be seen from Eqs. (5) and (6) that the two beams reflected back from combination reflector 12 to collimating lens 6 have the same magnitude of drift with the laser beam collimated by collimating lens 6.

When combination reflector 12 has a rotation of angle θ in y-z plane, as shown in Fig. 2(b), transmission matrix R₁′ of the semi-reflective film, R₂′ of the first reflective surface of BSTR 8, R₃′ of the second reflective surface of BSTR 8, R₄′ of the 45° tilted mirror 10, and R₅′ of the reflective film of primary PBS 7 can be expressed as

\begin{array}{l} R_{1}' = [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos (2 θ) & - \sin (2 θ) \\ 0 & - \sin (2 θ) & - \cos (2 θ) \end{matrix}], R_{2}' = [\begin{matrix} 1 & 0 & 0 \\ 0 & - \sin (2 θ) & - \cos (2 θ) \\ 0 & - \cos (2 θ) & \sin (2 θ) \end{matrix}], \\ R_{3}' = [\begin{matrix} 1 & 0 & 0 \\ 0 & \sin (2 θ) & \cos (2 θ) \\ 0 & \cos (2 θ) & - \sin (2 θ) \end{matrix}], R_{4}' = [\begin{matrix} 1 & 0 & 0 \\ 0 & - \sin (2 θ) & - \cos (2 θ) \\ 0 & - \cos (2 θ) & \sin (2 θ) \end{matrix}], \\ \begin{matrix} \begin{matrix} \begin{matrix}  \end{matrix} \end{matrix} \end{matrix} R_{5}' = [\begin{matrix} 1 & 0 & 0 \\ 0 & - \sin (2 θ) & - \cos (2 θ) \\ 0 & - \cos (2 θ) & \sin (2 θ) \end{matrix}] \end{array}

Direction cosine A₂′ of the beam reflected from the semi-reflective film of BSTR 8 can be written as

A_{2}' = R_{1}' A_{1} = [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos (2 θ) & - \sin (2 θ) \\ 0 & - \sin (2 θ) & - \cos (2 θ) \end{matrix}] • [\begin{matrix} 0 \\ - \sin α \\ \cos α \end{matrix}] = [\begin{matrix} 0 \\ - \sin (2 θ + α) \\ - \cos (2 θ + α) \end{matrix}]

Direction cosine A₃′ of the beam transmitted through the semi-reflective film of BSTR 8 and reflected sequentially from the first reflective surface of BSTR 8, the second reflective surface of BSTR 8, 45° tilted mirror 10, and the reflective film of primary PBS 7 can be given by

A_{3}' = R_{5}' R_{4}' R_{3}' R_{2}' A_{1} = [\begin{matrix} 0 \\ \sin α \\ - \cos α \end{matrix}]

By comparing direction cosines A₂′ and A₃′ of the two beams in y direction, it can be seen that after the rotation of combination reflector 12 the directional changes of the two beams are

β = - (2 θ + α), γ = α

It can be seen from Eq. (10) that the direction of the beam reflected from the semi-reflective film varies with both the angular drift of incident collimated laser beam and the rotation of combination reflector 12, while the direction of the beam transmitted through the semi-reflective film and reflected from sequential reflective surfaces varies only with the angular drift of incident collimated laser beam. So the beam reflected from the semi-reflective film can be used as the measurement beam for the measurement of small angle deviations, and the beam transmitted through the semi-reflective film and reflected from sequential reflective surfaces can be used as the reference beam for the detection of the angular drift of incident collimated laser beam. The reference and measurement beams are reflected back to collimating lens 6 along a common path, so the drifts of the two beams resulting from the instability of beam transmission medium are exactly the same, which provides a fine compensation for this kind of drift. The reference beam with s-polarization and the measurement beam with p-polarization are separated by secondary PBS 5 and received by their own detectors respectively at the receiving end.

The directional change of the reference beam, which consists of the beam drifts resulting from laser generation mechanism and instability of air medium, can be obtained using spot displacement Δ₂ detected by QPD 3 and focal length f of collimating lens 6. The directional change of reference beam can be expressed as

γ + φ = \frac{Δ_{2}}{f}

where γ is the drift resulting from laser generation mechanism and φ is the drift resulting from the instability of beam transmission medium.

The directional change of the measurement beam, which consists of small angle deviation θ of combination reflector 12, drift γ resulting from laser generation mechanism and drift φ resulting from the instability of air medium, can be obtained using the spot displacement Δ₁ detected by PSD 3 and focal length f of collimating lens 6. The directional change of measurement beam can be expressed as

2 θ + γ + φ = \frac{Δ_{1}}{f}

It can be seen from Eqs. (11) and (12) that small angle deviation θ of combination reflector 12 can be given by

θ = \frac{Δ_{1} - Δ_{2}}{2 f}

It can be seen by checking against the criteria proposed in section 2 that the measurement and reference beams used in this laser autocollimation method come from the same laser source, which satisfies the first criterion. The measurement and reference beams are transmitted along the common path with their polarizations perpendicular to each other, which satisfies the second and third criteria. The measurement and reference beams have the same sensitivity to the drift resulting from laser generation mechanism and the drift resulting from the instability of air medium, but they have different sensitivities to the small angle deviation of the combination reflector due to the unique characteristics of the combination reflector, which satisfies the fourth criterion.

4. Effects of assembly errors of combination reflector

The combination reflector is assembled by several optic components, so the fabrication and assembly errors of the combination reflector are inevitable. The sequential reflective surfaces from which the reference beam is reflected can be seemed as a right-angle prism and a parallel mirror pair, as shown in Figs. 3(a) and 3(b). If the right-angle prism and the parallel mirror pair have no errors, the direction of the reference beam should remain unchanged after the reference beam passes through them.

Fig. 3 Directional changes of reference beam after passing through a parallel mirror pair and a right-angle prism. (a) parallel mirror pair; (b) right-angle prism; (c) parallel mirror pair with error δ₂ ; (b) right-angle prism with error δ₁.

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If there is a small fabrication error δ₁ of the right angle prism and a small assembly error δ₂ of the parallel mirror pair, as shown in Figs. 3(c) and 3(d), transmission matrix R₃′′ of the second reflective surface of BSTR 8 and R₄′′ of 45° tilted mirror 10 after combination reflector 12 rotates with angle θ can be expressed as

R_{3}'' = [\begin{matrix} 1 & 0 & 0 \\ 0 & \sin (2 θ + 2 δ_{1}) & \cos (2 θ + 2 δ_{1}) \\ 0 & \cos (2 θ + 2 δ_{1}) & - \sin (2 θ + 2 δ_{1}) \end{matrix}]

R_{4}'' = [\begin{matrix} 1 & 0 & 0 \\ 0 & - \sin (2 θ + 2 δ_{2}) & - \cos (2 θ + 2 δ_{2}) \\ 0 & - \cos (2 θ + 2 δ_{2}) & \sin (2 θ + 2 δ_{2}) \end{matrix}]

Direction cosine A₃′ of the reference beam after passing through them can then be given by

A_{3}' = R_{5}' R_{4}'' R_{3}'' R_{2}' A_{1} = [\begin{matrix} 0 \\ \sin (α - 2 δ_{1} + 2 δ_{2}) \\ - \cos (α - 2 δ_{1} + 2 δ_{2}) \end{matrix}]

It can be seen from Eq. (16) that directional change γ′ of the reference beam in direction y can be given by

γ' = α - 2 δ_{1} + 2 δ_{2}

It can be seen by comparing Eqs. (10) and (17) that the fabrication and assembly errors δ₁ and δ₂ of the combination reflector can be brought into the directional change of the reference beam. However, errors δ₁ and δ₂ are constants since the combination reflector is an assembly, so the errors bring only a constant deflection of reference beam. The direction of reference beam varies only with the angular drift of the incident collimated laser beam and both fabrication and assembly errors have no effect on it at all. So the combination reflector is quite compatible with the fabrication and assembly errors, which is very important for practical applications of the combination reflector.

5. Experiments and results

5.1 Consistency test of drifts of reference and measurement beams

A combination reflector and an experimental setup shown in Fig. 4 have been built for the verification of the consistency of the drifts of reference and measurement beams. An incident collimated laser beam is reflected from a rotary angle reflector to the combination reflector along a shielded beam path to avoid the effect of air flow, and is then split into a measurement beam and a reference beam by the combination reflector. The two beams are reflected by a BS and focused by a focusing lens after it returns from the combination reflector. The two beams are separated by a PBS at the receiving end and received by a QPD and a PSD respectively.

Fig. 4 Setup for consistency test of the drifts of reference and measurement beams.

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The rotary angle reflector is used to change the direction of incident collimated laser beam to simulate the angular drift of the beam. The rotary angle reflector is rotated in steps. The directional changes of reference and measurement beams are monitored by QPD and PSD. The rotation steps of the rotary angle reflector and the corresponding directional changes of reference and measurement beams are shown in Fig. 5. It can be seen that the directions of reference and measurement beams have consistent directional changes with the direction of the incident collimated beam.

Fig. 5 Directional changes of reference and measurement beams with incident collimated laser beam. (a) directional changes of incident collimated laser beam; (b) directional changes of reference and measurement beams.

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In order to verify the consistency of drifts resulting from the instability of air medium, the shielding pipe along the beam path is taken off, and an air fan is used to generate air flow on the path. The outputs of QPD and PSD are sampled simultaneously at a sample interval of 100 milliseconds for two hours. A contrast of drifts between reference and measurement beams resulting from the instability of air medium in two hours and five minutes are shown in Figs. 6(a) and 6(b) respectively. It can be seen through comparison that the two beams have nearly consistent drifts resulting from the air flow.

Fig. 6 Contrast of drifts between reference and measurement beams resulting from the instability of air medium. (a) drifts in two hours; (b) drifts in two minutes.

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5.2 Stability test of laser autocollimation system

An experimental laser autocollimation system is built up based on the combination reflector for measurement of small angle deviations at a long measurement distance. The experimental setup is placed on a granite stage in a clean room with constant temperature and vibration isolated. The combination reflector is placed at a distance of two meters in front of the collimating lens to verify the stability of the system over a long measurement distance. The drifts of measurement and reference beams according to Eqs. (11) and (12) and the results after compensation according to Eq. (13) are shown in Fig. 7. The drift of measurement beam is 0.173 arcsec in two hours and 0.105 arcsec in ten minutes. The correlation coefficients representing the consistency of the drifts of measurement and reference beams is 90.2% in two hours and 95.7% in ten minutes, which indicates that there is a residual drift after compensation. As shown in Figs. 7(c) and 7(d), the stability of the laser autocollimation system after compensation is 0.020 arcsec in two hours and 0.016 arcsec in ten minutes, which means that the laser autocollimation system has very high measurement stability over a long measurement distance, and so, it is very suitable for some applications such as the straightness measurement of a long ultra-precision guide way, or the alignment of aircraft assemblies.

Fig. 7 Stability test of laser autocollimation system. (a) drifts of measurement and reference beams in two hours; (b) drifts of measurement and reference beams in ten minutes; (c) stability of the system in two hours; (d) stability of the system in ten minutes.

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5.3 Calibration of laser autocollimation system

The laser autocollimation system is calibrated using a laser angle interferometer. As shown in Fig. 8, an arm is rotated with a precision rotary table, and the rotation is monitored using a laser angle interferometer. The combination reflector is mounted on the arm and rotated with it in steps of 5 arcsec. Output θ given out by the laser autocollimation system according to Eq. (13) and the output θ_s of the laser angle interferometer are read out simultaneously. The output θ is fitted to the polynomials of θ_s of degree 10. The fitted curve and the output of the laser angle interferometer are shown in Fig. 9(a), and the residuals between them are shown in Fig. 9(b). The PV value of the residuals is 0.013 arcsec over the range of ± 1190 arcsec.

Fig. 8 Setup for calibration of laser autocollimation system.

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Fig. 9 Calibration results of laser autocollimation system. (a) output of laser angle interferometer and fitted curve of output of laser autocollimation system; (b) residuals of fitted curve and output of laser angle interferometer.

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5.4 Straightness measurement of two-meter-long air bearing slide

As an example of its typical applications, the straightness of a two-meter-long air bearing slide is measured using the laser autocollimation system. The straightness is also measured simultaneously using another two commercial autocollimators for comparison with the laser autocollimation system. The resolution and accuracy of one commercial autocollimator is 0.01 arcsec and ± 0.1 arcsec respectively, and the other one is 0.005 arcsec and ± 0.01 arcsec.

The slide moves continuously from one end to the other end with its position given out by a grating ruler. While the slide is moving, the outputs of the laser autocollimation system and the two commercial autocollimators are sampled simultaneously at a sample interval of 100 milliseconds. The outputs are plotted in Fig. 10(a), and the straightness measurement results calculated by using the outputs are plotted in Fig. 10(b). It can be seen from Fig. 10(a) that the drifts of the two commercial autocollimators resulting from the instability of air medium along the beam path become much more significant as the beam path becomes longer with the slide moving away, and the outputs of the laser autocollimation system with compensation are much less affected, which confirms that the laser autocollimation system with compensation for the beam drifts resulting from laser generation mechanism and instability of air medium has a high measurement stability and a strong anti-interference capability.

Fig. 10 Straightness measurement of slide. (a) outputs of two commercial autocollimators and laser autocollimation system; (b) straightness results according to the outputs.

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6. Conclusions

It can be seen from the presentation above that, the criteria for common-path design proposed in this paper can be used as the guidance for implementation of common-path principle in dealing with the laser beam drifts resulting from laser generation mechanism and the instability of beam transmission medium in laser datum based measurement of small angle deviations. The laser autocollimation method designed in compliance with the criteria has an accuracy of 0.013 arcsec over the range of ± 1190 arcsec and a stability of 0.020 arcsec in two hours and 0.016 arcsec in ten minutes over a measurement distance of two meters. It can therefore be concluded that the criteria and the laser autocollimation method can be effectively used for measurement of small angle deviations with high accuracy and stability, especially over a long measurement distance.

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Common-path design criteria for laser datum based measurement of small angle deviations and laser autocollimation method in compliance with the criteria with high accuracy and stability

Abstract

1. Introduction

2. Common-path design criteria

3. Laser autocollimation method in compliance with the criteria

4. Effects of assembly errors of combination reflector

5. Experiments and results

5.1 Consistency test of drifts of reference and measurement beams

5.2 Stability test of laser autocollimation system

5.3 Calibration of laser autocollimation system

5.4 Straightness measurement of two-meter-long air bearing slide

6. Conclusions

References and links

Cited By

Figures (10)

Equations (17)

Optics Express