Abstract

A new technique for external measurement of dihedral right angles is presented. An expanded, collimated, and linearly polarized He–Ne laser beam (632.8nm) from a Fizeau interferometer is launched into a cyclic path optical configuration (CPOC) in which the counterpropagating p and s polarization components traverse the same optical path in opposite directions. A right-angled component (RAC), with its plane surfaces forming the right angle, is set to externally reflect the counterpropagating p and s components of the CPOC in nearly the same directions but with a lateral separation. In a plane normal to the right-angle edge of the RAC, the laterally separated collimated beams have angular separation, which is equal to twice the error in the dihedral right angle. Another CPOC setup is used to recombine the beams by reducing the lateral shear to zero. Error in right angle is calculated from the spacing of the resulting two-beam Fizeau fringes. Methods for overcoming the restriction of measurement accuracy due to beam aperture limitation and the effects of the positional tilt of the RAC have been discussed. Results of validation experiments are presented.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. J. E. Ludman and C. Wards, “Angle measurements of scanners by interferometry,” Proc. SPIE 299, 106-111 (1981).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2008 (2)

2006 (1)

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

2005 (1)

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

2003 (1)

1997 (1)

S. M. Rao, “Method for measurement of the angles of the 90-45-45 deg⁡ and 60-30-90 deg⁡ prisms,” Opt. Eng. 36, 198-200(1997).
[CrossRef]

1992 (1)

1991 (1)

D. Malacara and R. F. Hernandez, “Simple test for the 90 degree angle in prisms,” Proc. SPIE 1332, 36-40 (1991).
[CrossRef]

1990 (1)

A. Saxena and L. Yeswanth, “Low cost method for sub arc second testing of a right angle prism,” Opt. Eng. 29, 1516-1520(1990).
[CrossRef]

1982 (1)

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65-71 (1982).

1981 (1)

J. E. Ludman and C. Wards, “Angle measurements of scanners by interferometry,” Proc. SPIE 299, 106-111 (1981).

1977 (1)

1968 (1)

K. Yoshihara, “On the triangular path interferometer,” Jpn. J. Appl. Phys. 7, 529-535 (1968).
[CrossRef]

Ai, C.

Burke, J.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

Chatterjee, S.

Creath, K.

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. Robinson, ed. (IOP Publishing, 1993), pp. 94-140.

DeVany, A. S.

A. S. DeVany, Master Optical Techniques (Wiley, 1981), Ch. 12, pp. 158-159.

Dligatch, S.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Ge, Z.

Gross, M.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Hernandez, R. F.

D. Malacara and R. F. Hernandez, “Simple test for the 90 degree angle in prisms,” Proc. SPIE 1332, 36-40 (1991).
[CrossRef]

Kujawinska, M.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, D. Robinson, ed. (IOP Publishing, 1993), pp. 145-193.

Kumar, Y. P.

Leistner, A.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Ludman, J. E.

J. E. Ludman and C. Wards, “Angle measurements of scanners by interferometry,” Proc. SPIE 299, 106-111 (1981).

Malacara, D.

D. Malacara and R. F. Hernandez, “Simple test for the 90 degree angle in prisms,” Proc. SPIE 1332, 36-40 (1991).
[CrossRef]

Murty, M. V. R. K.

M. V. R. K. Murty, “Newton, Fizeau and Haidinger inteferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23, 30-34.

Nemati, B.

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

Netterfield, R. P.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Oreb, B.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

Platt, B.

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

Rao, S. M.

S. M. Rao, “Method for measurement of the angles of the 90-45-45 deg⁡ and 60-30-90 deg⁡ prisms,” Opt. Eng. 36, 198-200(1997).
[CrossRef]

Saxena, A.

A. Saxena and L. Yeswanth, “Low cost method for sub arc second testing of a right angle prism,” Opt. Eng. 29, 1516-1520(1990).
[CrossRef]

Scarborough, J. B.

J. B. Scarborough, Numerical Mathematical Analysis (Oxford & IBH, 1966), Ch. 17, pp. 510-511.

Seckold, J. A.

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Smith, K.

Takeda, M.

Thomas, D.

Wards, C.

J. E. Ludman and C. Wards, “Angle measurements of scanners by interferometry,” Proc. SPIE 299, 106-111 (1981).

Wyant, J.

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65-71 (1982).

Wyant, J. C.

Yeswanth, L.

A. Saxena and L. Yeswanth, “Low cost method for sub arc second testing of a right angle prism,” Opt. Eng. 29, 1516-1520(1990).
[CrossRef]

Yoshihara, K.

K. Yoshihara, “On the triangular path interferometer,” Jpn. J. Appl. Phys. 7, 529-535 (1968).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

K. Yoshihara, “On the triangular path interferometer,” Jpn. J. Appl. Phys. 7, 529-535 (1968).
[CrossRef]

Laser Focus (1)

J. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65-71 (1982).

Opt. Eng. (2)

S. M. Rao, “Method for measurement of the angles of the 90-45-45 deg⁡ and 60-30-90 deg⁡ prisms,” Opt. Eng. 36, 198-200(1997).
[CrossRef]

A. Saxena and L. Yeswanth, “Low cost method for sub arc second testing of a right angle prism,” Opt. Eng. 29, 1516-1520(1990).
[CrossRef]

Proc. SPIE (4)

D. Malacara and R. F. Hernandez, “Simple test for the 90 degree angle in prisms,” Proc. SPIE 1332, 36-40 (1991).
[CrossRef]

J. E. Ludman and C. Wards, “Angle measurements of scanners by interferometry,” Proc. SPIE 299, 106-111 (1981).

J. Burke, B. Oreb, B. Platt, and B. Nemati, “Precision metrology of dihedral angle error in prisms and corner cubes for the space interferometry mission,” Proc. SPIE 5869, 225-235(2005).

B. Oreb, J. Burke, R. P. Netterfield, J. A. Seckold, A. Leistner, M. Gross, and S. Dligatch, “Development of precision double corner cubes for the space inteferometer mission,” Proc. SPIE 6292, 1-13 (2006).

Other (5)

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. Robinson, ed. (IOP Publishing, 1993), pp. 94-140.

M. Kujawinska, “Spatial phase measurement methods,” in Interferogram Analysis, D. Robinson, ed. (IOP Publishing, 1993), pp. 145-193.

M. V. R. K. Murty, “Newton, Fizeau and Haidinger inteferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23, 30-34.

J. B. Scarborough, Numerical Mathematical Analysis (Oxford & IBH, 1966), Ch. 17, pp. 510-511.

A. S. DeVany, Master Optical Techniques (Wiley, 1981), Ch. 12, pp. 158-159.

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Figures (12)

Fig. 1
Fig. 1

Optical schematic of a CPOC-based setup for the external measurement of dihedral right angles. RDS, rotating diffuser screen; IL, imaging lens.

Fig. 2
Fig. 2

Ray paths in a CPOC. Identical counterpropagating ray paths for an incident angle i 0 are shown with a single arrow. Ray paths for a different incident angle ( i 0 + δ i ) are shown with multiple arrows.

Fig. 3
Fig. 3

Plan view of CPOC-1 arrangement on a PPBP.

Fig. 4
Fig. 4

Fizeau fringes for ε = 12 arc sec .

Fig. 5
Fig. 5

Direction of air wedge formed between emergent plane wavefronts for positive values of δ.

Fig. 6
Fig. 6

Directions of the resultant wedge and that of associated Fizeau fringes for possible directions of ω x and ω y .

Fig. 7
Fig. 7

Fizeau fringes for ω x = ± 7 and ω y = ± 8.5 arc sec .

Fig. 8
Fig. 8

Angular misalignment of the RAC, a 90 ° 45 ° prism, with respect to the counterpropagating collimated beams in CPOC-1. R represents right-angle edge. (a) Top view of the RAC (rays are shown by arrows) (b) Side view of the RAC (dot at the center shows the projection for the central ray of the counterpropagating beams). (c) Front view of the RAC with tilted R (rays are shown by arrows).

Fig. 9
Fig. 9

Tilted Fizeau fringes.

Fig. 10
Fig. 10

Single tilted fringe over the full field.

Fig. 11
Fig. 11

Fizeau fringes obtained using setup shown in Fig. 1 (a) because of beams reflected externally from the right-angled surfaces of a prism. Tilt in the fringes is due to orthogonal pair ( ω x , ω r y ). (b) Change in fringe orientation with ω a + 7.3 arc sec . (c) Change in fringe orientation with ω a 7.3 arc sec .

Fig. 12
Fig. 12

Plot of ε r versus ω a for a range of values of ω x (0.1, 0.2, 0.3, 0.4 arc sec ) and ω ry (5, 10.0 15.0 arc sec ).

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ω = ( ω x 2 + ω y 2 ) 1 / 2 ,
tan α = ( ω y / ω x ) .
[ ω r y / ( ω x + ω a ) ] = tan α 1 ,
[ ω r y / ( ω x ω a ) ] = tan α 2 ,
ω x = ω a [ ( tan α 2 + tan α 1 ) / ( tan α 2 tan α 1 ) ] .
Δ ω x = [ ( δ ω x δ α 1 ) 2 ( Δ α 1 ) 2 + ( δ ω x δ α 2 ) 2 ( Δ α 2 ) 2 + ( δ ω x δ ω a ) 2 ( Δ ω a ) 2 ] 1 2 ,
( δ ω x / δ α 1 ) = ( 2 ω a tan α 2 sec 2 α 1 ) / ( tan α 2 tan α 1 ) 2 ,
( δ ω x / δ α 2 ) = ( 2 ω a tan α 1 sec 2 α 2 ) / ( tan α 2 tan α 1 ) 2 ,
( δ ω x / δ ω a ) = ( tan α 2 + tan α 1 ) / ( tan α 2 tan α 1 ) .

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