Abstract

An analytical expression is derived for the tilt introduced into a wave front by a Dove prism with manufacturing errors in the prism’s base angles and pyramidal angle. We found that the tilt decreases when the base angles are increased above the values of traditional design. The increase in the length-aperture ratio of a prism is detrimental to the prism’s performance. However, a Dove prism with a widened aperture increases throughput and maintains a manageable prism weight for implementation in a rotational shearing interferometer. Thus we propose a Dove prism designed with a widened aperture to increase throughput in a rotational shearing interferometer and with larger base angles to minimize the wave-front tilt introduced by manufacturing errors. Experimental results implemented in a rotational shearing interferometer demonstrate the feasibility of this design.

© 2003 Optical Society of America

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References

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  1. M. S. Scholl, “Signal generated by an extra-solar-system planet detected by a rotating rotationally shearing interferometer,” J. Opt. Soc. Am. A 13, 1584–1592 (1996).
    [CrossRef]
  2. M. S. Scholl, G. Paez, “Simulated interferometric patterns generated by a nearby star-planet system and detected by a rotational shearing interferometer,” J. Opt. Soc. Am. A 16, 2019–2024 (1999).
    [CrossRef]
  3. R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
    [CrossRef]
  4. M. Strojnik Scholl, G. Paez, “Cancellation of star-light generated by a nearby star-planet system upon detection with a rotationally-shearing interferometer,” Infrared Phys. Technol. 40, 357–365 (1999).
    [CrossRef]
  5. M. Strojnik, G. Paez, “Testing the aspherical surfaces with the differential rotational-shearing interferometer,” in Fabrication Testing of Aspheres, A. Lindquist, M. Piscotty, J. S. Taylor, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1999), pp. 119–123.
  6. M. Strojnik, G. Paez, “Mathematical theory of differential rotational shearing interferometry: asymmetrical aberrations,” in Interferometry 99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 335–346 (1999).
    [CrossRef]
  7. J. L. Flores, G. Paez, M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010–6018 (1999).
    [CrossRef]
  8. W. Vaughan, “Dove prisms, properties and problems,” Opt. Spectra 15, 68–69 (1981).
  9. H. Z. Sar-El, “Revised Dove prism formulas,” Appl. Opt. 30, 375–376 (1991).
    [CrossRef] [PubMed]
  10. S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
    [CrossRef]
  11. D. E. Grant, “Dove prism viewer for investigation of space error in color matching,” J. Opt. Soc. Am. 47, 256 (1957).
    [CrossRef]
  12. E. G. Paek, J. Y. Choe, T. K. Oh, J. H. Hong, T. Y. Chang, “Nonmechanical image rotation with an acousto-optic Dove prism,” Opt. Lett. 22, 1195–1197 (1997).
    [CrossRef] [PubMed]
  13. J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
    [CrossRef]
  14. C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).
  15. D. Baker, “Field-widened interferometers for Fourier spectroscopy,” in Spectrometric Techniques, G. A. Vanasse, ed. (Academic, New York, 1977), Vol. 1, Chap. 2.
  16. M. V. R. K. Murty, E. C. Hagerott, “Rotational-shearing interferometry,” Appl. Opt. 5, 615–619 (1966).
    [CrossRef] [PubMed]
  17. J. Sandoval Gonzalez, G. Paez, M. Strojnik, “Optomechanical design of a prism rotator,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik, B. F. Andresen, eds., Proc. SPIE4486, 170–180 (2001).
    [CrossRef]
  18. E. C. Kintner, R. M. Sillitto, “Edge-ringing in partially coherent imaging,” Opt. Acta 24, 591–605 (1977).
    [CrossRef]
  19. E. C. Kintner, “Edge-ringing and Fresnel diffraction,” Opt. Acta 22, 235–241 (1975).
    [CrossRef]
  20. J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
    [CrossRef]
  21. E. C. Kintner, “Polarization control in optical-fiber gyroscopes,” Opt. Lett. 6, 154–156 (1981).
    [CrossRef] [PubMed]
  22. E. C. Kintner, “Method for the calculation of partially coherent imagery,” Appl. Opt. 17, 2747–2753 (1978).
    [CrossRef] [PubMed]
  23. T. Lian, M. Chang, “New types of reflecting prism assembly,” Opt. Eng. 35, 3427–3431 (1996).
    [CrossRef]
  24. S. K. Gupta, R. Hradaynath, “Angular tolerance on Dove prisms,” Appl. Opt. 22, 3146–3147 (1983).
    [CrossRef] [PubMed]
  25. R. H. Ginsberg, “Image rotation,” Appl. Opt. 33, 8105–8108 (1994).
    [CrossRef]
  26. E. J. Galvez, C. D. Holmes, “Geometric phase of optical rotators,” J. Opt. Soc. Am. A 16, 1981–1985 (1999).
    [CrossRef]
  27. R. E. Hopkins, “Mirror and prism systems,” in Military Standardization Handbook 141 (Defense Supply Agency, Washington, D.C., 1962), pp. 13-1–13-25.
  28. M. Strojnik, G. Paez, “Radiometry,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 18, pp. 649–699.
  29. G. Paez, M. Strojnik, J. Garcia-Marquez, “On performance evaluation of future telescopes,” J. Mod. Opt. (to be published).
  30. D. M. Alloin, J. M. Mariotti, Diffraction Limited Imaging with Very Large Telescopes, NATO ASI Ser. C274 (1990).
  31. G. Paez, M. Strojnik, “Telescopes,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 8, pp. 207–261.

2000 (1)

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

1999 (4)

1997 (1)

1996 (2)

1994 (1)

1991 (1)

1983 (1)

1981 (2)

E. C. Kintner, “Polarization control in optical-fiber gyroscopes,” Opt. Lett. 6, 154–156 (1981).
[CrossRef] [PubMed]

W. Vaughan, “Dove prisms, properties and problems,” Opt. Spectra 15, 68–69 (1981).

1978 (2)

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

E. C. Kintner, “Method for the calculation of partially coherent imagery,” Appl. Opt. 17, 2747–2753 (1978).
[CrossRef] [PubMed]

1977 (1)

E. C. Kintner, R. M. Sillitto, “Edge-ringing in partially coherent imaging,” Opt. Acta 24, 591–605 (1977).
[CrossRef]

1975 (1)

E. C. Kintner, “Edge-ringing and Fresnel diffraction,” Opt. Acta 22, 235–241 (1975).
[CrossRef]

1966 (1)

1965 (1)

J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

1957 (1)

Alloin, D. M.

D. M. Alloin, J. M. Mariotti, Diffraction Limited Imaging with Very Large Telescopes, NATO ASI Ser. C274 (1990).

Armitage, J. D.

J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Baker, D.

D. Baker, “Field-widened interferometers for Fourier spectroscopy,” in Spectrometric Techniques, G. A. Vanasse, ed. (Academic, New York, 1977), Vol. 1, Chap. 2.

Bracewell, R. N.

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

Cha, K. H.

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

Chang, M.

T. Lian, M. Chang, “New types of reflecting prism assembly,” Opt. Eng. 35, 3427–3431 (1996).
[CrossRef]

Chang, T. Y.

Choe, J. Y.

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

E. G. Paek, J. Y. Choe, T. K. Oh, J. H. Hong, T. Y. Chang, “Nonmechanical image rotation with an acousto-optic Dove prism,” Opt. Lett. 22, 1195–1197 (1997).
[CrossRef] [PubMed]

Flores, J. L.

Galvez, E. J.

Garcia-Marquez, J.

G. Paez, M. Strojnik, J. Garcia-Marquez, “On performance evaluation of future telescopes,” J. Mod. Opt. (to be published).

Ginsberg, R. H.

Grant, D. E.

Gupta, S. K.

Hagerott, E. C.

Holmes, C. D.

Hong, J. H.

Hopkins, R. E.

R. E. Hopkins, “Mirror and prism systems,” in Military Standardization Handbook 141 (Defense Supply Agency, Washington, D.C., 1962), pp. 13-1–13-25.

Hradaynath, R.

Im, J. Y.

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

Kang, C. G.

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

Kintner, E. C.

E. C. Kintner, “Polarization control in optical-fiber gyroscopes,” Opt. Lett. 6, 154–156 (1981).
[CrossRef] [PubMed]

E. C. Kintner, “Method for the calculation of partially coherent imagery,” Appl. Opt. 17, 2747–2753 (1978).
[CrossRef] [PubMed]

E. C. Kintner, R. M. Sillitto, “Edge-ringing in partially coherent imaging,” Opt. Acta 24, 591–605 (1977).
[CrossRef]

E. C. Kintner, “Edge-ringing and Fresnel diffraction,” Opt. Acta 22, 235–241 (1975).
[CrossRef]

Lee, S. H.

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

Lian, T.

T. Lian, M. Chang, “New types of reflecting prism assembly,” Opt. Eng. 35, 3427–3431 (1996).
[CrossRef]

Lohmann, A.

J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Mariotti, J. M.

D. M. Alloin, J. M. Mariotti, Diffraction Limited Imaging with Very Large Telescopes, NATO ASI Ser. C274 (1990).

Murty, M. V. R. K.

Oh, T. K.

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

E. G. Paek, J. Y. Choe, T. K. Oh, J. H. Hong, T. Y. Chang, “Nonmechanical image rotation with an acousto-optic Dove prism,” Opt. Lett. 22, 1195–1197 (1997).
[CrossRef] [PubMed]

Paek, E. G.

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

E. G. Paek, J. Y. Choe, T. K. Oh, J. H. Hong, T. Y. Chang, “Nonmechanical image rotation with an acousto-optic Dove prism,” Opt. Lett. 22, 1195–1197 (1997).
[CrossRef] [PubMed]

Paez, G.

J. L. Flores, G. Paez, M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010–6018 (1999).
[CrossRef]

M. S. Scholl, G. Paez, “Simulated interferometric patterns generated by a nearby star-planet system and detected by a rotational shearing interferometer,” J. Opt. Soc. Am. A 16, 2019–2024 (1999).
[CrossRef]

M. Strojnik Scholl, G. Paez, “Cancellation of star-light generated by a nearby star-planet system upon detection with a rotationally-shearing interferometer,” Infrared Phys. Technol. 40, 357–365 (1999).
[CrossRef]

M. Strojnik, G. Paez, “Testing the aspherical surfaces with the differential rotational-shearing interferometer,” in Fabrication Testing of Aspheres, A. Lindquist, M. Piscotty, J. S. Taylor, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1999), pp. 119–123.

M. Strojnik, G. Paez, “Mathematical theory of differential rotational shearing interferometry: asymmetrical aberrations,” in Interferometry 99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 335–346 (1999).
[CrossRef]

G. Paez, M. Strojnik, “Telescopes,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 8, pp. 207–261.

M. Strojnik, G. Paez, “Radiometry,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 18, pp. 649–699.

G. Paez, M. Strojnik, J. Garcia-Marquez, “On performance evaluation of future telescopes,” J. Mod. Opt. (to be published).

J. Sandoval Gonzalez, G. Paez, M. Strojnik, “Optomechanical design of a prism rotator,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik, B. F. Andresen, eds., Proc. SPIE4486, 170–180 (2001).
[CrossRef]

Ryu, C. S.

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

Sandoval Gonzalez, J.

J. Sandoval Gonzalez, G. Paez, M. Strojnik, “Optomechanical design of a prism rotator,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik, B. F. Andresen, eds., Proc. SPIE4486, 170–180 (2001).
[CrossRef]

Sar-El, H. Z.

Scholl, M. S.

Sillitto, R. M.

E. C. Kintner, R. M. Sillitto, “Edge-ringing in partially coherent imaging,” Opt. Acta 24, 591–605 (1977).
[CrossRef]

Strojnik, M.

J. L. Flores, G. Paez, M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010–6018 (1999).
[CrossRef]

M. Strojnik, G. Paez, “Mathematical theory of differential rotational shearing interferometry: asymmetrical aberrations,” in Interferometry 99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 335–346 (1999).
[CrossRef]

M. Strojnik, G. Paez, “Testing the aspherical surfaces with the differential rotational-shearing interferometer,” in Fabrication Testing of Aspheres, A. Lindquist, M. Piscotty, J. S. Taylor, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1999), pp. 119–123.

J. Sandoval Gonzalez, G. Paez, M. Strojnik, “Optomechanical design of a prism rotator,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik, B. F. Andresen, eds., Proc. SPIE4486, 170–180 (2001).
[CrossRef]

M. Strojnik, G. Paez, “Radiometry,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 18, pp. 649–699.

G. Paez, M. Strojnik, J. Garcia-Marquez, “On performance evaluation of future telescopes,” J. Mod. Opt. (to be published).

G. Paez, M. Strojnik, “Telescopes,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 8, pp. 207–261.

Strojnik Scholl, M.

M. Strojnik Scholl, G. Paez, “Cancellation of star-light generated by a nearby star-planet system upon detection with a rotationally-shearing interferometer,” Infrared Phys. Technol. 40, 357–365 (1999).
[CrossRef]

Tang, X.

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

Vaughan, W.

W. Vaughan, “Dove prisms, properties and problems,” Opt. Spectra 15, 68–69 (1981).

Wyatt, C. L.

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).

Yi, S. Y.

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

Appl. Opt. (6)

Infrared Phys. Technol. (1)

M. Strojnik Scholl, G. Paez, “Cancellation of star-light generated by a nearby star-planet system upon detection with a rotationally-shearing interferometer,” Infrared Phys. Technol. 40, 357–365 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nature (London) (1)

R. N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature (London) 274, 780–781 (1978).
[CrossRef]

Opt. Acta (3)

E. C. Kintner, R. M. Sillitto, “Edge-ringing in partially coherent imaging,” Opt. Acta 24, 591–605 (1977).
[CrossRef]

E. C. Kintner, “Edge-ringing and Fresnel diffraction,” Opt. Acta 22, 235–241 (1975).
[CrossRef]

J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965).
[CrossRef]

Opt. Eng. (2)

J. Y. Im, E. G. Paek, X. Tang, J. Y. Choe, T. K. Oh, “Experimental nonmechanical image rotation to 20 angles using an acousto-optic Dove prism,” Opt. Eng. 39, 2909–2914 (2000).
[CrossRef]

T. Lian, M. Chang, “New types of reflecting prism assembly,” Opt. Eng. 35, 3427–3431 (1996).
[CrossRef]

Opt. Lett. (2)

Opt. Spectra (1)

W. Vaughan, “Dove prisms, properties and problems,” Opt. Spectra 15, 68–69 (1981).

Other (11)

S. Y. Yi, C. S. Ryu, S. H. Lee, K. H. Cha, C. G. Kang, “A rotational robust fingerprint recognition system by using Dove prisms,” in Optical Pattern Recognition IX, D. P. Casasent, T. Chao, eds., Proc. SPIE3386, 222–230 (1998).
[CrossRef]

M. Strojnik, G. Paez, “Testing the aspherical surfaces with the differential rotational-shearing interferometer,” in Fabrication Testing of Aspheres, A. Lindquist, M. Piscotty, J. S. Taylor, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1999), pp. 119–123.

M. Strojnik, G. Paez, “Mathematical theory of differential rotational shearing interferometry: asymmetrical aberrations,” in Interferometry 99: Techniques and Technologies, M. Kujawinska, M. Takeda, eds., Proc. SPIE3744, 335–346 (1999).
[CrossRef]

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).

D. Baker, “Field-widened interferometers for Fourier spectroscopy,” in Spectrometric Techniques, G. A. Vanasse, ed. (Academic, New York, 1977), Vol. 1, Chap. 2.

J. Sandoval Gonzalez, G. Paez, M. Strojnik, “Optomechanical design of a prism rotator,” in Infrared Spaceborne Remote Sensing IX, M. Strojnik, B. F. Andresen, eds., Proc. SPIE4486, 170–180 (2001).
[CrossRef]

R. E. Hopkins, “Mirror and prism systems,” in Military Standardization Handbook 141 (Defense Supply Agency, Washington, D.C., 1962), pp. 13-1–13-25.

M. Strojnik, G. Paez, “Radiometry,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 18, pp. 649–699.

G. Paez, M. Strojnik, J. Garcia-Marquez, “On performance evaluation of future telescopes,” J. Mod. Opt. (to be published).

D. M. Alloin, J. M. Mariotti, Diffraction Limited Imaging with Very Large Telescopes, NATO ASI Ser. C274 (1990).

G. Paez, M. Strojnik, “Telescopes,” in Handbook of Optical Engineering, D. Malacara, B. Thompson, eds. (Marcel Dekker, New York, 2001), Chap. 8, pp. 207–261.

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Figures (15)

Fig. 1
Fig. 1

RSI implemented in a Mach-Zehnder configuration, which may be used to detect extrasolar planets or to test optical systems without rotational symmetry. BSs, beam splitters.

Fig. 2
Fig. 2

A Dove prism rotates a wave front about the optical axis. When a Dove prism is rotated by an angle φ, the wave front is inverted and rotated by 2φ.

Fig. 3
Fig. 3

A Dove prism with manufacturing errors introduces tilt and displacement into the rotated wave front. The tilt introduced into the wave front is δ, and d is the lateral displacement at z o .

Fig. 4
Fig. 4

Error in base angles. The prism with manufacturing errors Δα1 and Δα2 introduces tilt δ into a wave front.

Fig. 5
Fig. 5

Dove prisms display smaller tilt for the same base angle errors when they are designed with large values of base angle α (fused silica, n = 1.4572, λ = 632.8 nm).

Fig. 6
Fig. 6

A Dove prism suffers pyramidal error when angle θ p is different from zero. This angle represents a slight inclination of the normal to the reflecting and refracting surfaces with respect to the vertical plane of symmetry.

Fig. 7
Fig. 7

Dove prisms display smaller tilt for the pyramidal angle errors when they are designed with large values of base angle α (fused silica, n = 1.4572, λ = 632.8 nm).

Fig. 8
Fig. 8

Exact ray trace using vector formulation, showing that tilts introduced by pyramidal-angle error and base-angle error are along two orthogonal directions. Total tilt is obtained by vector addition.

Fig. 9
Fig. 9

Prism length L decreases with index of refraction. The length of the Dove prism is shorter by 23% when the prism is made from a material with a refractive index of 1.9 (Optical glass LaSFN9) than the length of fused silica with n = 1.457.

Fig. 10
Fig. 10

Throughput is increased by use of a widened aperture, without increasing the prism length. In a traditional prism with a square aperture, aperture side A is equal to side D.

Fig. 11
Fig. 11

A short, widened prism rotates a rectangular entrance pupil. A wave front with large diameter may be tested by rotation of the prism by a scanning angle.

Fig. 12
Fig. 12

A RSI in a Mach-Zehnder configuration that incorporates a rectangular aperture may be used to test a complete circular wave front by rotation of the Dove prisms at the same time. Subapertures are tested sequentially by rotation of one prism by φ and the other by φ + φ in increments of Δφ = 2[sin-1(D/ A) - φ/2]. BSs, beam splitters.

Fig. 13
Fig. 13

Two Dove prisms fabricated with optical glass SFN64 and index of refraction 1.701 (λ = 632.8 nm), with a rectangular aperture of dimensions D = 15 ± 0.1 mm, A = 80 ± 0.1 mm, and L = 87 ± 0.1 mm. The prism base angle is 65° ± 20″.

Fig. 14
Fig. 14

RSI in the Mach-Zehnder configuration, with the shear incorporated by a rotated Dove prism with the rectangular aperture. In this setup we are testing an achromatic lens (f = 300 mm, d = 42 mm) located at a distance from the laser source equal to the lens’s focal length and employing a microscope objective and a spatial filter (not shown).

Fig. 15
Fig. 15

Interferogram recorded with the CCD camera at the image plane in Fig. 14, with a shearing angle of 20° (Dove prism rotated by 10°). Nearly straight tilt fringes indicate that the lens has some combination of astigmatism and coma. The shape of the image field depends on the Dove prism’s aperture and on the magnitude of the shear angle.

Tables (2)

Tables Icon

Table 1 Representative Prism Parameters and Their Tolerances

Tables Icon

Table 2 Worst-Case Performance of Dove Prism

Equations (5)

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

δ=α+Δα2-arcosn sinΔα1-Δα2+arcsin1ncosα+Δα1.
δ=2θpn2-cos2α1/2-sinαcosα.
δtotal=δpyramid2+δbase21/2.
d=n-1nβL.
L=Dsin2α1+n2-cos2α1/2+sinαn2-cos2α1/2-sinα.

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