Abstract

What we believe to be a new technique for the fabrication of a penta prism (PP) with high accuracy right angle deviation of the incident beam is presented. We derive simple formulas relating to the error in right angle deviation (∈) with the errors in 45° (β) and 90° (δ) angles of a PP, and we determine from the angle (r) between the plane wavefronts reflected from the right angled surfaces (external Fresnel reflection on the entrance surface and internal Fresnel reflection on the exit surface) of a PP and the angular error (δ) between the same surfaces. The error in right angle deviation is determined from the measurement of r using an autocollimator and a Fizeau interferometer, and is corrected to a high order of accuracy during the final stage of polishing one of the slanted surfaces of the PP. A new technique to determine the magnitude and direction of the small values of r is proposed and verified. The result for a PP is presented.

© 2007 Optical Society of America

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References

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  1. S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
    [CrossRef]
  2. P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).
  3. W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
    [CrossRef]
  4. R. B. Hooker, "Automatic wavefront sensor," Appl. Opt. 12, 865-871 (1973).
    [CrossRef] [PubMed]
  5. P. R. Yoder, "High precision 10-cm aperture penta and roof penta mirror assemblies," Appl. Opt. 10, 2231-2234 (1971).
    [CrossRef] [PubMed]
  6. O. Prakash and R. S. Ram, "Measurement of the angle of deviation of a penta prism," J. Opt. 26, 137-139 (1995).
    [CrossRef]
  7. S. M. Rao, "Method for measurement of the angles of a penta prism," Opt. Eng. 37, 1368-1371 (1998).
    [CrossRef]
  8. R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
    [CrossRef]
  9. A. S. DeVany, "Reduplication of a penta prism angle using master angle prisms and plano-interferometer," Appl. Opt. 10, 1371-1375 (1971).
    [CrossRef] [PubMed]
  10. H. S. Rana and N. B. Mullet, "Fabrication challenges in large prisms," Proc. SPIE 4411, 140-141 (2002).
    [CrossRef]
  11. A. S. DeVany, "Correcting glass angles of a prism," Appl. Opt. 16, 2019-2020 (1977).
  12. M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23.
  13. M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 30-34.

2007 (1)

P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).

2005 (2)

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
[CrossRef]

2002 (1)

H. S. Rana and N. B. Mullet, "Fabrication challenges in large prisms," Proc. SPIE 4411, 140-141 (2002).
[CrossRef]

1998 (1)

S. M. Rao, "Method for measurement of the angles of a penta prism," Opt. Eng. 37, 1368-1371 (1998).
[CrossRef]

1995 (2)

S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
[CrossRef]

O. Prakash and R. S. Ram, "Measurement of the angle of deviation of a penta prism," J. Opt. 26, 137-139 (1995).
[CrossRef]

1992 (2)

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23.

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 30-34.

1977 (1)

1973 (1)

1971 (2)

Bergeson, S.

R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
[CrossRef]

Burge, J.

P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).

Chen, C. Y.

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

DeVany, A. S.

Durfee, D. S.

R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
[CrossRef]

Hooker, R. B.

Jark, W.

S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
[CrossRef]

Lee, T. X.

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

Liu, C. H.

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

Mallic, P. C. V.

P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).

Mullet, N. B.

H. S. Rana and N. B. Mullet, "Fabrication challenges in large prisms," Proc. SPIE 4411, 140-141 (2002).
[CrossRef]

Murty, M. V. R. K.

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 30-34.

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23.

Olson, R.

R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
[CrossRef]

Paul, J.

R. Olson, J. Paul, S. Bergeson, and D. S. Durfee, "Self-referenced prism deflection measurement schemes with microradian precision," Appl. Opt. 22, 4639-4647 (2005).
[CrossRef]

Prakash, O.

O. Prakash and R. S. Ram, "Measurement of the angle of deviation of a penta prism," J. Opt. 26, 137-139 (1995).
[CrossRef]

Qian, S.

S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
[CrossRef]

Ram, R. S.

O. Prakash and R. S. Ram, "Measurement of the angle of deviation of a penta prism," J. Opt. 26, 137-139 (1995).
[CrossRef]

Rana, H. S.

H. S. Rana and N. B. Mullet, "Fabrication challenges in large prisms," Proc. SPIE 4411, 140-141 (2002).
[CrossRef]

Rao, S. M.

S. M. Rao, "Method for measurement of the angles of a penta prism," Opt. Eng. 37, 1368-1371 (1998).
[CrossRef]

Sun, C. C.

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

Sun, W. S.

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

Takacs, P. Z.

S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
[CrossRef]

Yoder, P. R.

Zhao, C.

P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).

Appl. Opt. (5)

J. Mod. Opt. (1)

W. S. Sun, T. X. Lee, C. C. Sun, C. H. Liu, and C. Y. Chen, "Design of miniature HD-DVD optical pick-up head using a penta prism," J. Mod. Opt. 52, 775-789 (2005).
[CrossRef]

J. Opt. (1)

O. Prakash and R. S. Ram, "Measurement of the angle of deviation of a penta prism," J. Opt. 26, 137-139 (1995).
[CrossRef]

Opt. Eng. (2)

S. M. Rao, "Method for measurement of the angles of a penta prism," Opt. Eng. 37, 1368-1371 (1998).
[CrossRef]

P. C. V. Mallic, C. Zhao, and J. Burge, "Measurement of a 2 meter flat using a penta prism scanning system," Opt. Eng. 46, 023602 (2007).

Proc. SPIE (1)

H. S. Rana and N. B. Mullet, "Fabrication challenges in large prisms," Proc. SPIE 4411, 140-141 (2002).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Qian, W. Jark, and P. Z. Takacs, "The penta-prism LTP: a long-trace-profiler with stationary optical head and moving penta-prism," Rev. Sci. Instrum. 36, 2562-2569 (1995).
[CrossRef]

Other (2)

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 22-23.

M. V. R. K. Murty, "Newton, Fizeau, and Haidinger interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 30-34.

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Figures (10)

Fig. 1
Fig. 1

Ray paths corresponding to single pass and backreflected components in a PP.

Fig. 2
Fig. 2

Single pass ray deviation in a PP.

Fig. 3
Fig. 3

Right angle testing with a FI.

Fig. 4
Fig. 4

Fizeau fringes for the right angle.

Fig. 5
Fig. 5

Fizeau fringes from the right angle for the determination of the sign of δ.

Fig. 6
Fig. 6

Resultant wedge and fringe direction for combinations of ω x and ω y . (OA), (OA′), (OB), and (OB′) represent the resultant wedge directions for the orthogonal pairs ( ω x , ω y ) , ( ω x , ω y ) , ( ω x , ω y ) , and ( ω x , ω y ) , respectively. F 1 F 1 indicates the fringe direction for ( ω x , ω y ) and ( ω x , ω y ) . F 2 F 2 shows the fringe direction for ( ω x , ω y ) and ( ω x , ω y ) .

Fig. 7
Fig. 7

Setup for determining ∈ from the measurement of r using a FI.

Fig. 8
Fig. 8

Fizeau fringes obtained due to the interference of plane wavefronts reflected from the entrance and exit surfaces of the PP.

Fig. 9
Fig. 9

Fizeau fringes for the 100.0 mm diameter wedge plate (horizontal fringes) and for the combination (inclined fringes).

Fig. 10
Fig. 10

Fizeau fringes for the 50.0 mm diameter wedge plate.

Equations (14)

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

( 2 i 1 + 2 i 2 + ϕ ) = π ,
( i 1 + i 2 ) = ( 45 ° + β ) .
ϕ = ( 90 ° 2 β ) .
AQX 1 = ( 90 ° + 2 β δ ) .
i 1 = ( 90 ° AQX 1 ) = ( δ 2 β ) .
n sin ( δ 2 β ) = sin r 1 ,
r 1 = n ( δ 2 β ) .
θ = [ ( π / 2 ) + ( n 1 ) δ 2 n β ] .
= [ θ ( π / 2 ) ] = [ ( n 1 ) δ 2 n β ] .
ν = ( 90 ° + 4 β 2 δ ) .
r = n i 2 = n ( 2 δ 4 β ) .
= [ ( r / 2 ) δ ] .
ω = ( ω x 2 + ω y 2 ) ,
tan α = ( ω y / ω x ) .

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