L. Kremer, D. Budelsky, D. Platte, and P. von Brentano, "Autocollimator for spectroscopy of broad resonances with pulsed lasers," Appl. Opt. 34, 4827-4834 (1995)
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.
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Comparison of Three Types of Autocollimators with Analogous Displacements of Optical Elements in Paraxial Approximationa
System
Misalignment of Reflector
Displacement of Lens
Δθ
Δr (mm)
Concave mirror
Tilt α = 10−4 rad
—
2α = 2 × 10−4
2αR = 0.2
(R = 200 mm)
Displacement h = 0.01 mm
—
2h/R = 10−4
2h = 0.04
Corner cube
Displacement h = 0.01 mm
0
2h/f = 10−4
0
(f = 200 mm)
0
h = 0.1 mm
2h/f = 10−3
0
Cat’s eye
Tilt β = 10−4 rad
0
0
2βf = 0.04
(f = 200 mm)
0
h = 0.1 mm
0
2h = 0.2
Only the cat’s eye is angular insensitive enough against displacements of all elements. Because of the vanishing positional error of the corner cube, it is difficult to measure the angular deviation at the reference plane. For the application under question the angular displacement is much more important than the positional. This results in further investigations only for the cat’s eye.
Table 2
Summary of the Errors of Adjustment as Defined in Fig. 4a
The second column contains the contribution to the errors, the third column contains their values as determined during adjustment, and the fourth column contains the total value for the errors as a statistical sum of the third row. δθoff and β are calculated paraxial.
Table 3
Measured Beam Parameters and Their Errors
Beam Parameters
Error
Intensity of the spot
0.5%
Center position of the spot
5 μm (dye laser), 5 μm(He–Ne laser)
Spot radius
5 μm
Table 4
Paraxial Error of the Reflector for the Dye Laser
Error
Error Contribution
Value
Sum
Unit
x, y
Adjustment
0.1
−0.2(1)
mm
Chromatic aberration
−0.2
rout
Position determination He–Ne laser
0.005
0.027
mm
Position determination dye laser
0.005
Additional neutral-density filter
0.025
θout
= rout/fL5
0.54
mrad
rin
≈ −rout + δroff
0.037
mm
δθpic
≈ 2riny/f2
0.54
μrad
δθoff
= δroffy/f2
−0.075
μrad
Δθ
= Δθpic + δθoff
0.465
μrad
Tables (4)
Table 1
Comparison of Three Types of Autocollimators with Analogous Displacements of Optical Elements in Paraxial Approximationa
System
Misalignment of Reflector
Displacement of Lens
Δθ
Δr (mm)
Concave mirror
Tilt α = 10−4 rad
—
2α = 2 × 10−4
2αR = 0.2
(R = 200 mm)
Displacement h = 0.01 mm
—
2h/R = 10−4
2h = 0.04
Corner cube
Displacement h = 0.01 mm
0
2h/f = 10−4
0
(f = 200 mm)
0
h = 0.1 mm
2h/f = 10−3
0
Cat’s eye
Tilt β = 10−4 rad
0
0
2βf = 0.04
(f = 200 mm)
0
h = 0.1 mm
0
2h = 0.2
Only the cat’s eye is angular insensitive enough against displacements of all elements. Because of the vanishing positional error of the corner cube, it is difficult to measure the angular deviation at the reference plane. For the application under question the angular displacement is much more important than the positional. This results in further investigations only for the cat’s eye.
Table 2
Summary of the Errors of Adjustment as Defined in Fig. 4a
The second column contains the contribution to the errors, the third column contains their values as determined during adjustment, and the fourth column contains the total value for the errors as a statistical sum of the third row. δθoff and β are calculated paraxial.
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