Abstract

For the application of autocollimation spectroscopy [Z. Phys. D 18, 249–255 (1991)] a pulsed dye laser that is emerging from a focus (diameter, 1 mm; divergence, 30 mrad) has to be reflected back in itself with high precision. The difference Δθ between the mean angles of the counterpropagating laser beams has to be less than 1 × 10−6 rad. Using a paraxial approximation, we show that a cat’s eye fulfills the needs best. An adjustment procedure together with additional calibration equipment (CCD arrays and quadrant diodes) for the device is presented. Accounting for the uncertainties of the adjustment and using ray tracing, we show that Δθ ≤ 5 × 10−7 rad can be achieved.

© 1995 Optical Society of America

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References

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  1. A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
    [CrossRef]
  2. D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
    [CrossRef]
  3. D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
    [CrossRef]
  4. J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
    [CrossRef]
  5. A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
    [CrossRef]
  6. W. Shaomin, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 25, pp. 279–348.
    [CrossRef]
  7. L. H. Tanner, “Camera testing by use of speckle patterns,” Appl. Opt. 13, 2026–2035 (1974).
    [CrossRef] [PubMed]
  8. H. Meyer, Optische Glasfilter (Schott Glaswerke, Mainz, 1987), pp. 133.

1991 (1)

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

1990 (1)

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

1989 (1)

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

1988 (1)

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

1986 (1)

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

1974 (1)

Gassen, J.

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Georgiadis, A. P.

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Helmcke, J.

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

Ishikawa, J.

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

Kremer, L.

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

Meyer, H.

H. Meyer, Optische Glasfilter (Schott Glaswerke, Mainz, 1987), pp. 133.

Morinaga, A.

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

Müller, D.

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Pape, A.

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Pross, H.-J.

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

Riehle, F.

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

Ronchi, L.

W. Shaomin, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 25, pp. 279–348.
[CrossRef]

Scheuer, F.

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

Sens, J. C.

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Shaomin, W.

W. Shaomin, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 25, pp. 279–348.
[CrossRef]

Sträter, H. D.

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

Sträter, H.-D.

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Tanner, L. H.

von Brentano, P.

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. Morinaga, F. Riehle, J. Ishikawa, J. Helmcke, “A Ca optical frequency standard: frequency stabilization by means of nonlinear Ramsey resonances,” Appl. Phys. B 48, 165–171 (1989).
[CrossRef]

Europhys. Lett. (1)

D. Müller, J. Gassen, L. Kremer, H.-J. Pross, F. Scheuer, H.-D. Sträter, P. von Brentano, A. Pape, J. C. Sens, “Lamb shift measurement in hydrogenlike phosphorus,” Europhys. Lett. 5, 503–507 (1988).
[CrossRef]

Opt. Commun. (1)

J. Gassen, D. Müller, P. von Brentano, A. P. Georgiadis, “A high power dye laser pumped by a crowbar mode flashlamp,” Opt. Commun. 76, 131–137 (1990).
[CrossRef]

Phys. Lett. A (1)

A. P. Georgiadis, D. Müller, H.-D. Sträter, J. Gassen, P. von Brentano, J. C. Sens, A. Pape, “Measurement of the Lamb shift in hydrogenic sulfur by laser spectroscopy,” Phys. Lett. A 115, 108–110 (1986).
[CrossRef]

Z. Phys. D (1)

D. Müller, J. Gassen, F. Scheuer, H. D. Sträter, P. von Brentano, “Autocollimation spectroscopy for fast hydrogenic ions,” Z. Phys. D 18, 249–255 (1991).
[CrossRef]

Other (2)

W. Shaomin, L. Ronchi, “Principles and design of optical arrays,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 25, pp. 279–348.
[CrossRef]

H. Meyer, Optische Glasfilter (Schott Glaswerke, Mainz, 1987), pp. 133.

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Figures (8)

Fig. 1
Fig. 1

Deviation Δθ of an autocollimator with tilted concave mirror. z, optical axis.

Fig. 2
Fig. 2

Deviation Δθ of an autocollimator with lateral displaced corner cube.

Fig. 3
Fig. 3

Deviation Δθ of an autocollimator with tilted plane mirror.

Fig. 4
Fig. 4

Adjustment errors of the autocollimator. ΔH, distance between the principal planes; x, distance between lens and object minus focal length; y, distance between lens and mirror minus focal length; h, lateral position of the lens with respect to the optical axis; β, tilt angle of the mirror; α, tilt angle of the lens.

Fig. 5
Fig. 5

Optical setup necessary for a Lamb-shift measurement by use of the autocollimation spectroscopy. With the beam steerer the laser beam can be reflected into all directions. The focal lengths are confirmed to the dimension of the experiment: fL1 = 1200 mm, f = 200 mm.

Fig. 6
Fig. 6

Deviation Δθ for single rays calculated by the ray-tracing method. The position of incidence rin is variated in the range of ±0.7 mm. Top: All adjustment errors are zero; the wavelength is 633 nm. Bottom: All adjustment errors as given in Table 2; the wavelength is 735 nm.

Fig. 7
Fig. 7

Typical beam profile of the dye laser used with Rhodamine 6G.

Fig. 8
Fig. 8

Deviation of the dye laser profile as given in Fig. 7 without divergence. The position rin and the angle θin of incidence are varied. The dashed line gives the deviation Δθ mean over the angle distribution.

Tables (4)

Tables Icon

Table 1 Comparison of Three Types of Autocollimators with Analogous Displacements of Optical Elements in Paraxial Approximationa

Tables Icon

Table 2 Summary of the Errors of Adjustment as Defined in Fig. 4a

Tables Icon

Table 3 Measured Beam Parameters and Their Errors

Tables Icon

Table 4 Paraxial Error of the Reflector for the Dye Laser

Equations (12)

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r = ( r θ 1 1 ) = ( lateral position angle to optical axis 1 1 ) .
r out = ( r out θ out 1 1 ) = M × r in = ( A B 0 ^ 1 ^ ) × ( r in θ in 1 1 ) ,
M = 1 f 2 [ 2 x y - f 2 2 x ( x y - f 2 ) - 2 h ( x y - f 2 ) ( 2 β f - 4 α ) ( x y - f 2 ) 2 y 2 x y - f 2 - 2 h y y ( 2 β f - 4 α ) 0 0 1 0 0 0 0 1 ] .
( r in + r out θ in + θ out ) = ( δ r pic δ θ pic ) = ( 2 x y / f 2 2 x 2 y / f 2 - 2 x 2 y / f 2 2 x y / f 2 ) × ( r in θ in ) ( 2 x θ in 2 y / f 2 r in ) .
δ r off = ( 1 - x y / f 2 ) ( 2 h - 2 β f + 4 α ) ,
δ θ off = - y / f 2 ( 2 h - 2 β f + 4 α ) - δ r off y / f 2 .
Δ θ = δ θ pic + δ θ off ;
δ r off = R pinhole f L 2 / f O .
β = 0.105 × 10 - 3 rad ,
δ θ off = 0.037 × 10 - 6 rad = 0.037 μ rad .
Δ θ = ( - 11.95 × r in / mm - 0.03 ) μ rad .
Δ θ = 0.47 μ rad .

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