Abstract

A new method for testing both refractive and reflective optical components using beam deflection is presented. For a beam with a 80-μm waist, 1-μrad deflections are detectable from a reflecting test surface. This corresponds to an average height resolution in the reflecting surface of eight-tenths of an angstrom over the dimensions of the beam.

© 1986 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  2. B. Kelley, “Lateral-Effect Photodiodes,” Laser Focus 12, 38 (Mar.1976).
  3. J. T. Verdeyen, Laser Electronics (Prentice-Hall), Englewood Cliffs, NJ, 1981, Chap. 14.
  4. A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.
  5. J. M. Bennett, “Measurement of the rms Roughness, Autocovariance Function, and Other Statistical Properties of Optical Surfaces using a FECO Scanning Interferometer,” Appl. Opt. 15, 2705 (1976).
    [CrossRef] [PubMed]
  6. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975, Sec. 9.12.

1976 (2)

Bennett, J. M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975, Sec. 9.12.

Kelley, B.

B. Kelley, “Lateral-Effect Photodiodes,” Laser Focus 12, 38 (Mar.1976).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics (Prentice-Hall), Englewood Cliffs, NJ, 1981, Chap. 14.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.

Appl. Opt. (1)

Laser Focus (1)

B. Kelley, “Lateral-Effect Photodiodes,” Laser Focus 12, 38 (Mar.1976).

Other (4)

J. T. Verdeyen, Laser Electronics (Prentice-Hall), Englewood Cliffs, NJ, 1981, Chap. 14.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 6.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975, Sec. 9.12.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the beam deflection apparatus. Lens L1 forms a waist on the test component. TC1 is a reflective surface, and TC2 is a refractive component. Both components if ideal retroreflect the beam. A beam splitter BS extracts the beam, and the telescope, which consists of the objective lens L2 and eyepiece L3, magnifies angular deviations in the beam due to defects in the test component. Detector D senses deflections of the beam.

Fig. 2
Fig. 2

Optical system for increasing the scan distance.

Fig. 3
Fig. 3

Output of the lock-in amplifier for seven displacements of the beam, each of which corresponds to a 5 μrad change in slope of the test surface. The beam waist on the test surface is 0.47 mm. See text for other parameters.

Fig. 4
Fig. 4

Output of the lock-in amplifier for four displacements of the beam, each of which corresponds to a 1-μrad change in slope of the test surface. The beam waist on the test surface is 80 μm. See text for other parameters.

Fig. 5
Fig. 5

Lock-in output for a 2-mm scan across the test surface: (a) 0.47-mm waist on the test surface; (b) 80-μm waist.

Fig. 6
Fig. 6

Lock-in output for a 9-mm horizontal scan across the refractive component of Fig. 1. The three traces correspond to three vertical beam positions on the refractive component, each separated by 0.5 mm.

Fig. 7
Fig. 7

Lock-in output vs time for a stationary corner cube. Each scan is for 100 s. See text for other parameters.

Equations (7)

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γ = f o f e + δ f e ,
Z = ( f o + f e ) f e f o - ( f e f o ) 2 Z .
slope = x ( R 2 + x 2 ) 1 / 2 x R ,
D ( x ) = 2 C ( M , l ) d y d x ,
y ( x ) = ½ C - 1 ( M , l ) D ( x ) d x .
w m = w 1 f e f o [ 1 + Z 1 4 + R 1 2 Z 1 2 ( Z 1 2 + R 1 2 ) 2 - 2 Z 1 2 ( Z 1 2 + R 1 2 ) 2 ] , Z m = ( f o + f e ) f o f e - f e 2 R 1 Z 1 2 f o 2 ( Z 1 2 + R 1 2 ) ,
Z m ( f o + f e ) f o f e - f e 2 f o 2 Z , w m f e f o π ω o 3 λ Z .

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