Abstract

Prisms have been needlessly neglected as components used in modern optical design. In optical throughput, stray light, flexibility, and in their ability to be used in direct-view geometry, they excel over gratings. Here we show that even their well-known weak dispersion relative to gratings has been overrated by designing doublet and double Amici direct-vision compound prisms that have 14° and 23° of dispersion across the visible spectrum, equivalent to 800 and 1300lines/mm gratings. By taking advantage of the multiple degrees of freedom available in a compound prism design, we also show prisms whose angular dispersion shows improved linearity in wavelength. In order to achieve these designs, we exploit the well-behaved nature of prism design space to write customized algorithms that optimize directly in the nonlinear design space. Using these algorithms, we showcase a number of prism designs that illustrate a performance and flexibility that goes beyond what has often been considered possible with prisms.

© 2011 Optical Society of America

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References

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2011 (2)

2010 (1)

2009 (2)

S. E. Holland, W. F. Kolbe, and C. J. Bebek, “Device design for a 12.3-megapixel, fully depleted, back-illuminated, high-voltage compatible charge-coupled device,” IEEE Trans. Electron Devices 56, 2612–2622 (2009).
[CrossRef]

Y.-J. Lin, K.-M. Chen, and S.-T. Wu, “Broadband and polarization-independent beam steering using dielectrophoresis-tilted prism,” Opt. Express 17, 8651–8656 (2009).
[CrossRef] [PubMed]

2008 (1)

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

2007 (2)

Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. 32, 3525–3527 (2007).
[CrossRef] [PubMed]

P. J. Bos, H. Garcia, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasures and imaging applications: solving the singularity problem in the two-prism design,” Opt. Eng. 46, 113001 (2007).
[CrossRef]

2006 (1)

2005 (1)

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

2003 (2)

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038–1047 (2003).
[CrossRef]

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

2002 (1)

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

1999 (1)

1997 (1)

C. G. Wynne, “Atmospheric dispersion in very large telescopes with adaptive optics,” Mon. Not. R. Astron. Soc. 285, 130–134(1997).

1995 (1)

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165–179 (1995).
[CrossRef]

1976 (1)

N. V. Sheinis, “Design of a wedge scanner,” Sov. J. Opt. Technol. 43, 473 (1976).

1975 (1)

E. N. Goncharenko and G. N. Repinskii, “The design of achromatic wedges,” Sov. J. Opt. Technol. 42, 445–448(1975).

1970 (1)

1963 (1)

1959 (1)

1952 (1)

1900 (1)

C. G. Abbott, J. Fowle, and E. Frederick, “A prism of uniform dispersion,” Astrophys. J. 11, 135–139 (1900).
[CrossRef]

1886 (1)

G. D. Liveing and J. Dewar, “Note on a new form of direct vision spectroscope,” Proc. R. Soc. London 41, 449–452 (1886).
[CrossRef]

1881 (3)

F. Fuchs, “Vorschläge zur construction einiger optischer vorichtungen [Proposals for construction of some optical devices],” Z. Instrumentenkd. 1, 326–329(1881), in German.

K. W. Zenger, “Ueber ein neues spectroskop mit gerader durchsicht [On a new direct view spectroscope],” Z. Instrumentenkd. 1, 263–266 (1881), in German.

W. Wernicke, “Neues Flüssigkeitsprisma für Spectralapparate [A new liquid prism for spectroscopes],” Z.Instrumentenkd. 1, 353–357 (1881), in German.

1879 (2)

A. Riccó, “Combinazioni spettroscopiche a visione diretta [Combinations for direct vision spectroscopy],” Mem. Soc. Astron. Ital. 8, 21–34 (1879), in Italian.

A. Thollon, “Spectroscopes à vision directe et a grande dispersion [Direct vision spectroscopes with large dispersion],” J. Phys. Theor. Appl. 8, 73–77 (1879), in French.
[CrossRef]

1878 (2)

A. Thollon, “Nouveau spectroscope [A new spectroscope],” J. Phys. Theor. Appl. 7, 141–148 (1878), in French.
[CrossRef]

A. Thollon, “Théorie du nouveau spectroscope à vision directe [Theory of the new direct vision spectroscope],” C.R. Hebd. Seances Acad. Sci. 86, 595–598 (1878), in French.

1873 (1)

H. Emsmann, “Ein spectroskop à vision directe mit nur einem prisma [A direct vision spectroscope with a single prism],” Ann. Phys. 150, 636–640 (1873), in German.

1872 (1)

P. G. Tait, “On anomalous spectra, and on a simple direct-vision spectroscope,” Proc. R. Soc. Edinburgh 7, 410–414(1872).

1871 (1)

J. Browning, “Note on the use of compound prisms,” Mon. Not. R. Astron. Soc. 31, 203–205 (1871).

1866 (1)

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Annali del Reale Museo di Fisica e Storia Naturale di Firenze 1, 1–20 (1866), in Italian.

1865 (1)

A. S. Herschel, “Direct vision spectroscopes by double internal reflection,” Intellectual Observer 7, 444–447 (1865).

1864 (1)

J. P. Gassiot, “Description of a train of eleven sulphide-of-carbon prisms arranged for spectrum analysis,” Proc. R. Soc. London 13, 183–185 (1864).
[CrossRef]

1863 (1)

G. B. Donati, “Memorie astronomiche,” Mon. Not. R. Astron. Soc. 23, 100–107 (1863).

1862 (2)

P. J. C. Janssen, “Note sur trois spectroscopes [Note on three spectroscopes],” C.R. Hebd. Seances Acad. Sci. 55, 576–578 (1862), in French.

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Nuovo Cimento 15, 292–304 (1862), in Italian.
[CrossRef]

Abbott, C. G.

C. G. Abbott, J. Fowle, and E. Frederick, “A prism of uniform dispersion,” Astrophys. J. 11, 135–139 (1900).
[CrossRef]

Bebek, C. J.

S. E. Holland, W. F. Kolbe, and C. J. Bebek, “Device design for a 12.3-megapixel, fully depleted, back-illuminated, high-voltage compatible charge-coupled device,” IEEE Trans. Electron Devices 56, 2612–2622 (2009).
[CrossRef]

Bittner, R.

R. Bittner, Y. Delclaud, G. Cerutti-Maori, and J.-Y. Labandibar, “Spectra apparatus of the concentric type having a Fery prism,” U. S. patent 5,781,290 (14 July 1998).

Blechinger, F.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165–179 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 452–453.

Bos, P. J.

P. J. Bos, H. Garcia, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasures and imaging applications: solving the singularity problem in the two-prism design,” Opt. Eng. 46, 113001 (2007).
[CrossRef]

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038–1047 (2003).
[CrossRef]

Brodzik, A. K.

Browning, J.

J. Browning, “Note on the use of compound prisms,” Mon. Not. R. Astron. Soc. 31, 203–205 (1871).

Cerutti-Maori, G.

R. Bittner, Y. Delclaud, G. Cerutti-Maori, and J.-Y. Labandibar, “Spectra apparatus of the concentric type having a Fery prism,” U. S. patent 5,781,290 (14 July 1998).

Chen, K.-M.

Chevrette, P.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Churilovskii, V. N.

V. N. Churilovskii, Raschet Prizmennykh System [The Design of Prism Systems] (Leningrad, 1933), in Russian.

Conn, G. K. T.

Curatu, E.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Delclaud, Y.

R. Bittner, Y. Delclaud, G. Cerutti-Maori, and J.-Y. Labandibar, “Spectra apparatus of the concentric type having a Fery prism,” U. S. patent 5,781,290 (14 July 1998).

Deming, R. W.

Dereniak, E. L.

E. L. Dereniak and T. D. Dereniak, Geometric and Trigonometric Optics (Cambridge University, 2008), pp.347–350.
[CrossRef]

Dereniak, T. D.

E. L. Dereniak and T. D. Dereniak, Geometric and Trigonometric Optics (Cambridge University, 2008), pp.347–350.
[CrossRef]

Dewar, J.

G. D. Liveing and J. Dewar, “Note on a new form of direct vision spectroscope,” Proc. R. Soc. London 41, 449–452 (1886).
[CrossRef]

Dohi, T.

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

Donati, G. B.

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Annali del Reale Museo di Fisica e Storia Naturale di Firenze 1, 1–20 (1866), in Italian.

G. B. Donati, “Memorie astronomiche,” Mon. Not. R. Astron. Soc. 23, 100–107 (1863).

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Nuovo Cimento 15, 292–304 (1862), in Italian.
[CrossRef]

Doucet, M.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Duncan, B. D.

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038–1047 (2003).
[CrossRef]

Ebizuka, N.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Emsmann, H.

H. Emsmann, “Ein spectroskop à vision directe mit nur einem prisma [A direct vision spectroscope with a single prism],” Ann. Phys. 150, 636–640 (1873), in German.

Ewing, W. S.

J. M. Mooney, W. S. Ewing, and R. J. Nelson, “Multi-band direct vision prism,” U. S. patent 6,935,757 (30 August 2005).

Fowle, J.

C. G. Abbott, J. Fowle, and E. Frederick, “A prism of uniform dispersion,” Astrophys. J. 11, 135–139 (1900).
[CrossRef]

Frederick, E.

C. G. Abbott, J. Fowle, and E. Frederick, “A prism of uniform dispersion,” Astrophys. J. 11, 135–139 (1900).
[CrossRef]

Fuchs, F.

F. Fuchs, “Vorschläge zur construction einiger optischer vorichtungen [Proposals for construction of some optical devices],” Z. Instrumentenkd. 1, 326–329(1881), in German.

Gao, L.

Garcia, H.

P. J. Bos, H. Garcia, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasures and imaging applications: solving the singularity problem in the two-prism design,” Opt. Eng. 46, 113001 (2007).
[CrossRef]

Gassiot, J. P.

J. P. Gassiot, “Description of a train of eleven sulphide-of-carbon prisms arranged for spectrum analysis,” Proc. R. Soc. London 13, 183–185 (1864).
[CrossRef]

Goncharenko, E. N.

E. N. Goncharenko and G. N. Repinskii, “The design of achromatic wedges,” Sov. J. Opt. Technol. 42, 445–448(1975).

Greivenkamp, J. E.

J. E. Greivenkamp, Field Guide to Geometrical Optics(SPIE, 2004), p. 1.
[CrossRef]

Groom, D. E.

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

Hagen, N.

Harnisch, B.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165–179 (1995).
[CrossRef]

Herschel, A. S.

A. S. Herschel, “Direct vision spectroscopes by double internal reflection,” Intellectual Observer 7, 444–447 (1865).

Herzberger, M.

Holland, S. E.

S. E. Holland, W. F. Kolbe, and C. J. Bebek, “Device design for a 12.3-megapixel, fully depleted, back-illuminated, high-voltage compatible charge-coupled device,” IEEE Trans. Electron Devices 56, 2612–2622 (2009).
[CrossRef]

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

Hu, Z.

Iye, M.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Janssen, P. J. C.

P. J. C. Janssen, “Note sur trois spectroscopes [Note on three spectroscopes],” C.R. Hebd. Seances Acad. Sci. 55, 576–578 (1862), in French.

Kajino, F.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kawabata, K. S.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kester, R. T.

Kim, D.

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

Kim, K.

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

Kobayashi, E.

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

Kolbe, W. F.

S. E. Holland, W. F. Kolbe, and C. J. Bebek, “Device design for a 12.3-megapixel, fully depleted, back-illuminated, high-voltage compatible charge-coupled device,” IEEE Trans. Electron Devices 56, 2612–2622 (2009).
[CrossRef]

Kunkel, B.

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165–179 (1995).
[CrossRef]

Labandibar, J.-Y.

R. Bittner, Y. Delclaud, G. Cerutti-Maori, and J.-Y. Labandibar, “Spectra apparatus of the concentric type having a Fery prism,” U. S. patent 5,781,290 (14 July 1998).

Lacoursière, J.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

LeMaster, D. A.

D. A. LeMaster, “Design and model verification of an infrared chromotomographic imaging system,” Master’s thesis (Air Force Institute of Technology, 2004).

Lin, Y.-J.

Liveing, G. D.

G. D. Liveing and J. Dewar, “Note on a new form of direct vision spectroscope,” Proc. R. Soc. London 41, 449–452 (1886).
[CrossRef]

Lockyer, J. N.

J. N. Lockyer, The Spectroscope and its Applications(Macmillan, 1873).

Matsumiya, K.

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

McClure, N. R.

Mooney, J. M.

A. K. Brodzik and J. M. Mooney, “Convex projections algorithm for restoration of limited-angle chromotomographic images,” J. Opt. Soc. Am. A 16, 246–257 (1999).
[CrossRef]

J. M. Mooney, W. S. Ewing, and R. J. Nelson, “Multi-band direct vision prism,” U. S. patent 6,935,757 (30 August 2005).

Murty, M. V. R. K.

Narasimham, A. L.

Nelson, R. J.

J. M. Mooney, W. S. Ewing, and R. J. Nelson, “Multi-band direct vision prism,” U. S. patent 6,935,757 (30 August 2005).

Palaio, N. P.

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

Repinskii, G. N.

E. N. Goncharenko and G. N. Repinskii, “The design of achromatic wedges,” Sov. J. Opt. Technol. 42, 445–448(1975).

Ricard, B.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Riccó, A.

A. Riccó, “Combinazioni spettroscopiche a visione diretta [Combinations for direct vision spectroscopy],” Mem. Soc. Astron. Ital. 8, 21–34 (1879), in Italian.

Rollins, A. M.

Sato, S.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Savard, M.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Schellen, H.

H. Schellen, Spectrum Analysis in its Application to Terrestrial Substances and the Physical Constitution of the Heavenly Bodies (Appleton, 1872), p.82, translated by J. Lassell and C. Lassell.

Secchi, P. A.

P. A. Secchi, Le Stelle [The Stars] (Dumolard, 1877), in Italian.

Sergan, V.

P. J. Bos, H. Garcia, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasures and imaging applications: solving the singularity problem in the two-prism design,” Opt. Eng. 46, 113001 (2007).
[CrossRef]

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038–1047 (2003).
[CrossRef]

Sheinis, N. V.

N. V. Sheinis, “Design of a wedge scanner,” Sov. J. Opt. Technol. 43, 473 (1976).

Smith, W.

W. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill Professional, 2007), pp.126–128.

Stephens, R. E.

Stigler, R. D.

R. D. Stigler, “Non-deviating prism with continuously variable dispersion,” U. S. patent 5,610,771 (11 March 1997).

Stover, R. J.

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

Tait, P. G.

P. G. Tait, “On anomalous spectra, and on a simple direct-vision spectroscope,” Proc. R. Soc. Edinburgh 7, 410–414(1872).

Thibault, S.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Thollon, A.

A. Thollon, “Spectroscopes à vision directe et a grande dispersion [Direct vision spectroscopes with large dispersion],” J. Phys. Theor. Appl. 8, 73–77 (1879), in French.
[CrossRef]

A. Thollon, “Nouveau spectroscope [A new spectroscope],” J. Phys. Theor. Appl. 7, 141–148 (1878), in French.
[CrossRef]

A. Thollon, “Théorie du nouveau spectroscope à vision directe [Theory of the new direct vision spectroscope],” C.R. Hebd. Seances Acad. Sci. 86, 595–598 (1878), in French.

Tkaczyk, T. S.

Tyrrell, H. J. V.

Verreault, S.

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Wei, M.

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

Wernicke, W.

W. Wernicke, “Neues Flüssigkeitsprisma für Spectralapparate [A new liquid prism for spectroscopes],” Z.Instrumentenkd. 1, 353–357 (1881), in German.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 452–453.

Wu, S.-T.

Wynne, C. G.

C. G. Wynne, “Atmospheric dispersion in very large telescopes with adaptive optics,” Mon. Not. R. Astron. Soc. 285, 130–134(1997).

Yokota, H.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Zenger, K. W.

K. W. Zenger, “Ueber ein neues spectroskop mit gerader durchsicht [On a new direct view spectroscope],” Z. Instrumentenkd. 1, 263–266 (1881), in German.

Ann. Phys. (1)

H. Emsmann, “Ein spectroskop à vision directe mit nur einem prisma [A direct vision spectroscope with a single prism],” Ann. Phys. 150, 636–640 (1873), in German.

Annali del Reale Museo di Fisica e Storia Naturale di Firenze (1)

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Annali del Reale Museo di Fisica e Storia Naturale di Firenze 1, 1–20 (1866), in Italian.

Appl. Opt. (5)

Astrophys. J. (1)

C. G. Abbott, J. Fowle, and E. Frederick, “A prism of uniform dispersion,” Astrophys. J. 11, 135–139 (1900).
[CrossRef]

C.R. Hebd. Seances Acad. Sci. (2)

A. Thollon, “Théorie du nouveau spectroscope à vision directe [Theory of the new direct vision spectroscope],” C.R. Hebd. Seances Acad. Sci. 86, 595–598 (1878), in French.

P. J. C. Janssen, “Note sur trois spectroscopes [Note on three spectroscopes],” C.R. Hebd. Seances Acad. Sci. 55, 576–578 (1862), in French.

IEEE Trans. Electron Devices (2)

S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully depleted, back-illuminated charge-coupled devices fabricated on high-resistivity silicon,” IEEE Trans. Electron Devices 50, 225–238 (2003).
[CrossRef]

S. E. Holland, W. F. Kolbe, and C. J. Bebek, “Device design for a 12.3-megapixel, fully depleted, back-illuminated, high-voltage compatible charge-coupled device,” IEEE Trans. Electron Devices 56, 2612–2622 (2009).
[CrossRef]

Intellectual Observer (1)

A. S. Herschel, “Direct vision spectroscopes by double internal reflection,” Intellectual Observer 7, 444–447 (1865).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. Theor. Appl. (2)

A. Thollon, “Spectroscopes à vision directe et a grande dispersion [Direct vision spectroscopes with large dispersion],” J. Phys. Theor. Appl. 8, 73–77 (1879), in French.
[CrossRef]

A. Thollon, “Nouveau spectroscope [A new spectroscope],” J. Phys. Theor. Appl. 7, 141–148 (1878), in French.
[CrossRef]

Mem. Soc. Astron. Ital. (1)

A. Riccó, “Combinazioni spettroscopiche a visione diretta [Combinations for direct vision spectroscopy],” Mem. Soc. Astron. Ital. 8, 21–34 (1879), in Italian.

Mon. Not. R. Astron. Soc. (3)

J. Browning, “Note on the use of compound prisms,” Mon. Not. R. Astron. Soc. 31, 203–205 (1871).

G. B. Donati, “Memorie astronomiche,” Mon. Not. R. Astron. Soc. 23, 100–107 (1863).

C. G. Wynne, “Atmospheric dispersion in very large telescopes with adaptive optics,” Mon. Not. R. Astron. Soc. 285, 130–134(1997).

Nuovo Cimento (1)

G. B. Donati, “Intorno alle strie degli spettri stellari [On lines in stellar spectra],” Nuovo Cimento 15, 292–304 (1862), in Italian.
[CrossRef]

Opt. Eng. (2)

B. D. Duncan, P. J. Bos, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasure applications,” Opt. Eng. 42, 1038–1047 (2003).
[CrossRef]

P. J. Bos, H. Garcia, and V. Sergan, “Wide-angle achromatic prism beam steering for infrared countermeasures and imaging applications: solving the singularity problem in the two-prism design,” Opt. Eng. 46, 113001 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. Annu. Conf. Eng. Med. Biol. (1)

K. Kim, D. Kim, K. Matsumiya, E. Kobayashi, and T. Dohi, “Wide FOV wedge prism endoscope,” Proc. Annu. Conf. Eng. Med. Biol. 6, 5758–5761 (2005).

Proc. R. Soc. Edinburgh (1)

P. G. Tait, “On anomalous spectra, and on a simple direct-vision spectroscope,” Proc. R. Soc. Edinburgh 7, 410–414(1872).

Proc. R. Soc. London (2)

J. P. Gassiot, “Description of a train of eleven sulphide-of-carbon prisms arranged for spectrum analysis,” Proc. R. Soc. London 13, 183–185 (1864).
[CrossRef]

G. D. Liveing and J. Dewar, “Note on a new form of direct vision spectroscope,” Proc. R. Soc. London 41, 449–452 (1886).
[CrossRef]

Proc. SPIE (3)

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, “Novel direct vision prism and Wollaston prism assembly for diffraction limit applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

F. Blechinger, B. Harnisch, and B. Kunkel, “Optical concepts for high resolution imaging spectrometers,” Proc. SPIE 2480, 165–179 (1995).
[CrossRef]

J. Lacoursière, M. Doucet, E. Curatu, M. Savard, S. Verreault, S. Thibault, P. Chevrette, and B. Ricard, “Large-deviation achromatic Risley prisms pointing systems,” Proc. SPIE 4773, 123–131 (2002).
[CrossRef]

Sov. J. Opt. Technol. (2)

E. N. Goncharenko and G. N. Repinskii, “The design of achromatic wedges,” Sov. J. Opt. Technol. 42, 445–448(1975).

N. V. Sheinis, “Design of a wedge scanner,” Sov. J. Opt. Technol. 43, 473 (1976).

Z. Instrumentenkd. (2)

K. W. Zenger, “Ueber ein neues spectroskop mit gerader durchsicht [On a new direct view spectroscope],” Z. Instrumentenkd. 1, 263–266 (1881), in German.

F. Fuchs, “Vorschläge zur construction einiger optischer vorichtungen [Proposals for construction of some optical devices],” Z. Instrumentenkd. 1, 326–329(1881), in German.

Z.Instrumentenkd. (1)

W. Wernicke, “Neues Flüssigkeitsprisma für Spectralapparate [A new liquid prism for spectroscopes],” Z.Instrumentenkd. 1, 353–357 (1881), in German.

Other (16)

R. Bittner, Y. Delclaud, G. Cerutti-Maori, and J.-Y. Labandibar, “Spectra apparatus of the concentric type having a Fery prism,” U. S. patent 5,781,290 (14 July 1998).

J. E. Greivenkamp, Field Guide to Geometrical Optics(SPIE, 2004), p. 1.
[CrossRef]

R. D. Stigler, “Non-deviating prism with continuously variable dispersion,” U. S. patent 5,610,771 (11 March 1997).

E. L. Dereniak and T. D. Dereniak, Geometric and Trigonometric Optics (Cambridge University, 2008), pp.347–350.
[CrossRef]

V. N. Churilovskii, Raschet Prizmennykh System [The Design of Prism Systems] (Leningrad, 1933), in Russian.

H. Schellen, Spectrum Analysis in its Application to Terrestrial Substances and the Physical Constitution of the Heavenly Bodies (Appleton, 1872), p.82, translated by J. Lassell and C. Lassell.

J. N. Lockyer, The Spectroscope and its Applications(Macmillan, 1873).

P. A. Secchi, Le Stelle [The Stars] (Dumolard, 1877), in Italian.

http://www.owlnet.rice.edu/~tt3/.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 452–453.

The actual optimization algorithm used in our design code is SciPy’s fmin function, which uses a Nelder–Mead simplex algorithm. Many other algorithms were tested and work equally well, with fmin being the fastest among them.

D. A. LeMaster, “Design and model verification of an infrared chromotomographic imaging system,” Master’s thesis (Air Force Institute of Technology, 2004).

J. M. Mooney, W. S. Ewing, and R. J. Nelson, “Multi-band direct vision prism,” U. S. patent 6,935,757 (30 August 2005).

ZEMAX Development Corp., www.zemax.com.

http://www.us.schott.com/advanced_optics/english/our_products/materials/data_tools/.

W. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill Professional, 2007), pp.126–128.

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Figures (13)

Fig. 1
Fig. 1

Ray trace through a simple prism. The ray is incident at an angle θ 0 from the optical axis (dashed); θ 1 , θ 1 , θ 2 , and θ 2 are the angles of incidence and refraction on the first and second prism interfaces, and θ 3 is the angle of the deviated ray with respect to the axis. The prism shown here has an apex angle α = 60 ° and is oriented such that the front and back faces of the prism have angles β = 15 ° and γ = 45 ° with respect to the optical axis. The prism has an index of refraction n = 1.5 , a height h, and an axial thickness t. For the ray traced here, θ 0 = 30 ° and θ 3 = 7.4 ° , such that δ = 37.4 ° . Using the sign convention, θ 1 and θ 1 are positive quantities, while θ 2 and θ 2 are negative. The quantity Δ y is the beam displacement.

Fig. 2
Fig. 2

Incident beam width w is transformed into an exiting beam width w . The minimum prism height h min and minimum prism axial thickness t min are constrained by the beam width, prism geometry and angle of incidence.

Fig. 3
Fig. 3

A ray trace through a doublet compound prism, where the second element is assumed to be oriented symmetrically with respect to the normal to the optical axis. The system shown here has prism apex angles α 1 = 60 ° and α 2 = 40 ° , indices of refraction n 1 = 1.5 and n 2 = 1.8 , height h, axis-to-apex height h 0 , beam displacement Δ y , and axial thicknesses t 1 and t 2 . The input ray has angle θ 0 = 10 ° , such that δ = 0.4 ° .

Fig. 4
Fig. 4

Doublet prism design space, showing contour plots of a, the central deviation δ ¯ ( α 1 , α 2 ) , and b, the difference of the dispersion Δ ( α 1 , α 2 ) from the target value Δ * = 1 ° for a 400– 700 nm spectral range and glass choices of BK7 and SF6. The dashed blue lines indicate the ( α 1 , α 2 ) values required to meet either the δ ¯ * = 0 design target (for direct-vision) or the Δ * = 1 ° target, while the red solid lines indicate prism angles satisfying linear Eq. (5). A design satisfies both targets where the two curves meet, and the gray background indicates the valid design space, outside of which total internal reflections occur at one of the prism interfaces.

Fig. 5
Fig. 5

Design parameters of a nondeviating N-LAK34/N-SF66 prism doublet as a function of the target dispersion. The α 1 and α 2 curves proceed in an approximately parabolic curves until about 14.6 ° , beyond which the system can no longer achieve the target values. In this case, the limit is reached as the front face of the prism approaches the grazing angle to the incident beam (i.e., θ 1 approaches 90 ° ).

Fig. 6
Fig. 6

Typical angular dispersion curve for a prism disperser (left axis) and the corresponding dispersion gradient (right axis). A detector array placed at the focal plane of a lens will provide a uniformly sampled spectrum if the dispersion gradient is constant across the spectrum. For the case shown here, the sampling will be 10 × finer in the blue end of the spectrum than in the red.

Fig. 7
Fig. 7

Two prism designs from Table 1, design 1a (for improved dispersion linearity) and 1b (for a compact system). Both designs have δ ¯ * = 0 and Δ * = 1 ° . The rays are drawn for the central wavelength, λ ¯ . Note that both prisms show some negative beam displacement.

Fig. 8
Fig. 8

As the prism is rotated, the deviation angle δ steers the field of view (with half-angle θ 0 ) through a wider “field of regard” (with half-angle δ + θ 0 ).

Fig. 9
Fig. 9

Dispersion, in millidegrees, of the achromatized beam deviation designs 1b–5b from Table 2.

Fig. 10
Fig. 10

Raytrace through a double Amici prism: the first and third elements are identical, and the second element is oriented symmetrically with respect to the normal to the optical axis. The system shown here has prism apex angles α 1 = 70 ° and α 2 = 60 ° , indices of refraction n 1 = 1.5 and n 2 = 1.8 , height h, and axial thicknesses t 1 and t 2 . The input ray has angle θ 0 = 15 ° , such that δ = 30 ° . For this setup, the beam displacement Δ y is nearly zero.

Fig. 11
Fig. 11

Double Amici prism design space, showing contour plots of (a) the deviation δ and (b) the dispersion Δ for a 400– 700 nm spectral range, and for a fused silica/N-LASF31A/fused silica glass triplet, with (a)  δ ¯ * = 0 and (b)  Δ * = 2 ° . As in Fig. 4, the dashed blue line indicates ( α 1 , α 2 ) designs meeting target values, the red solid lines indicate designs using linear Eq. (5), and the gray background indicates the valid design space.

Fig. 12
Fig. 12

(a) Design parameters of a nondeviating N-LAK34/N-SF66 double Amici prism as a function of the target dispersion. The kink in the curves occurs at Δ * = 23.5 ° , beyond which the system can no longer achieve the target values. The vertical bar at the right side of the plot indicates the design configuration whose layout is shown in (b).

Fig. 13
Fig. 13

Layout, dispersion, and dispersion gradient for prism designs 1b and 1c from Table 3. The rays drawn in the prism layouts are for the central wavelength, λ ¯ . The dashed line in (a) is the best-fit linear portion of 1b’s dispersion curve. The gradient curves in (b) indicate that the spectral sampling rate in the blue end of the spectrum will be 6 × (design 1b) or 10 × (design 1c) that in the red end due to dispersion NL.

Tables (3)

Tables Icon

Table 1 Best Performing Doublet Prisms for Design Targets δ ¯ * = 0 and Δ * = 1 ° ( 400 nm λ 700 nm , θ 0 = 0 ) a

Tables Icon

Table 2 Achromatic Beam Deviation: the Best Performing Doublet Prisms (for θ 0 = 0 ), Listed in Order of (a) Compactness or (b) Dispersion Chromaticity, Where Chromaticity C is Defined by Eq. (13) a

Tables Icon

Table 3 Best Performing Double Amici Prisms for Design Targets δ ¯ * = 0 and Δ * = 4 ° ( 400 nm λ 700 nm , θ 0 = 0 ) a

Equations (26)

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

θ 1 = θ 0 β , θ 2 = arcsin ( n sin θ 2 ) , θ 1 = arcsin ( 1 n sin θ 1 ) , θ 3 = θ 2 + γ , θ 2 = θ 1 α , } ,
δ = θ 0 θ 3 = θ 1 θ 2 α .
Δ = δ ( λ min ) δ ( λ max ) δ max δ min .
δ = θ 0 γ arcsin ( n sin ( arcsin ( 1 n sin ( θ 0 β ) ) α ) ) ,
δ = ( n 1 ) α ,
t min = h 0 ( tan γ tan β ) , Δ y min = h 0 sin ( α ) sin ( θ 1 + β ) cos ( β ) cos ( θ 2 ) , h min = max { h 0 , h 0 + Δ y } , w = w cos ( θ 2 ) / cos ( θ 1 ) ,
δ ( λ ) = δ 1 ( λ ) + δ 2 ( λ ) = ( n 1 ( λ ) 1 ) α 1 + ( n 2 ( λ ) 1 ) α 2 ,
Δ = δ 1 ( λ ¯ ) V 1 + δ 2 ( λ ¯ ) V 2 ,
δ ¯ 1 = δ ¯ 2 = Δ ( 1 V 2 1 V 1 ) 1 ,
α 1 = Δ n ¯ 1 1 ( 1 V 1 1 V 2 ) 1 ,
α 2 = Δ n ¯ 2 1 ( 1 V 2 1 V 1 ) 1 .
δ ( n 1 ( λ ) , n 2 ( λ ) , α 1 , α 2 , θ 0 ) ,
θ 1 = θ 0 β 1 , θ 3 = θ 2 α 2 , θ 1 = arcsin ( 1 n 1 sin θ 1 ) , θ 3 = arcsin ( n 2 sin θ 3 ) , θ 2 = θ 1 α 1 , θ 4 = θ 3 + 1 2 α 2 , θ 2 = arcsin ( n 1 n 2 sin θ 2 ) , } ,
M = ( δ ¯ δ ¯ * ) 2 + ( Δ Δ * ) 2 ,
NL = | d 2 δ d λ 2 | d λ .
M = ( δ ¯ δ ¯ * ) 2 + ( Δ Δ * ) 2 + w nl NL ,
SSR = max { | d δ d λ | } / min { | d δ d λ | } .
Θ = i = 1 I { 0 , θ i < θ limit ( θ limit θ i ) 2 , θ i > θ limit .
t 1 = h 0 ( tan γ 1 tan β 1 ) , t 2 = 2 ( h h 0 ) tan β 2 ,
M chr = ( δ ¯ δ * ) 2 + C + Θ ,
C = | max { δ ( λ ) } min { δ ( λ ) } |
δ ¯ = 2 δ ¯ 1 + δ ¯ 2 = 2 ( n ¯ 1 1 ) α 1 + ( n ¯ 2 1 ) α 2 , Δ = 2 δ ¯ 1 V 1 + δ ¯ 2 V 2 .
α 1 = Δ 2 ( n ¯ 1 1 ) ( 1 V 1 1 V 2 ) 1 , α 2 = Δ n ¯ 2 1 ( 1 V 2 1 V 1 ) 1 .
θ 1 = θ 0 β 1 , θ 3 = arcsin ( n 2 n 1 sin θ 3 ) , θ 1 = arcsin ( 1 n 1 sin θ 1 ) , θ 4 = θ 3 α 1 , θ 2 = θ 1 α 1 , θ 4 = arcsin ( n 1 sin θ 4 ) , θ 2 = arcsin ( n 1 n 2 sin θ 2 ) , θ 5 = θ 4 β 1 θ 3 = θ 2 α 2 , }
α 2 2 = arcsin ( n ¯ 1 n ¯ 2 sin ( α 1 + arcsin ( 1 n ¯ 1 sin β 1 ) ) ) .
n ¯ 2 = 2 n ¯ 1 1 .

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