Abstract

A pseudoscopic (inverted depth) image made with spiral diffracting elements intermediated by a pinhole is explained by its symmetry properties. The whole process is made under common white light illumination and allows the projection of images. The analysis of this projection demonstrates that the images of two objects pointing away longitudinally have the main features of standard pseudoscopic image points. An orthoscopic (normal depth) image has also been obtained with the breaking of the symmetry conditions.

© 2008 Optical Society of America

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References

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  1. W. C. Sweatt, “Achromatic triplet using holographic optical elements,” Appl. Opt. 16, 1390-1391 (1977).
    [CrossRef] [PubMed]
  2. I. Weingärtner and K.-J. Rosenbruch, “Chromatic correction of two- and three-element holographic imaging systems,” Opt. Acta 29, 519-529 (1982).
    [CrossRef]
  3. J. J. Lunazzi, “Holoprojection of images by a double diffraction process,” presented at XIV Encontro Nacional de Física da Matéria Condensada, Caxambu-Minas Gerais, Brazil, May 7-11, 1991.
  4. J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit,” Opt. Express 10, 1368-1373 (2002).
    [PubMed]
  5. J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit: critical point properties,” J. Opt. Soc. Am. A 23, 1021-1026 (2006).
    [CrossRef]
  6. J. J. Lunazzi and D. S. F. Magalhães, “Diffractive imaging with bidimensional elements: first experimental results,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 127.
  7. J. J. Lunazzi and D. S. F. Magalhães, “Pseudoscopic white-light imaging by means of two bi-dimensional diffracting elements and a pinhole,” Proc. SPIE 5622, 1463-1468 (2004).
    [CrossRef]
  8. D. S. F. Magalhães, “Estudo de imagens por dupla difração com seleção de luz branca e elementos definidos bidimensionalmente,” M.Sc. thesis (Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 2005), http: // www.ifi.unicamp.br/ccjdr/teses/apresentacao.php3?filename=IF419.
  9. J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
    [CrossRef]
  10. J. J. Lunazzi and D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.
  11. J. J. Lunazzi and N. I. R. Rivera, “Orthoscopic imaging in a double diffraction process with slit,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 344-344.
  12. E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
    [CrossRef]
  13. N. I. R. Rivera, “Imagem por dupla difracao com luz branca sem elementos intermediários,” Ph.D. thesis (Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas, 2007), http://webbif.ifi.unicamp.br/teses/apresentacao.php?filename=IF284.
  14. M. C. Hutley, Diffraction Gratings (Academic, 1982), pp. 23-26.
  15. J. J. Lunazzi, “3D photography by holography,” Opt. Eng. (Bellingham) 29, 9-14 (1990).
    [CrossRef]
  16. J. J. Lunazzi, “Holophotography with a diffraction grating,” Opt. Eng. (Bellingham) 29, 15-18 (1990).
    [CrossRef]

2006 (1)

2004 (1)

J. J. Lunazzi and D. S. F. Magalhães, “Pseudoscopic white-light imaging by means of two bi-dimensional diffracting elements and a pinhole,” Proc. SPIE 5622, 1463-1468 (2004).
[CrossRef]

2003 (1)

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
[CrossRef]

2002 (1)

1991 (1)

E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
[CrossRef]

1990 (2)

J. J. Lunazzi, “3D photography by holography,” Opt. Eng. (Bellingham) 29, 9-14 (1990).
[CrossRef]

J. J. Lunazzi, “Holophotography with a diffraction grating,” Opt. Eng. (Bellingham) 29, 15-18 (1990).
[CrossRef]

1982 (1)

I. Weingärtner and K.-J. Rosenbruch, “Chromatic correction of two- and three-element holographic imaging systems,” Opt. Acta 29, 519-529 (1982).
[CrossRef]

1977 (1)

Ferrari, J. A.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
[CrossRef]

Frins, E. M.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
[CrossRef]

Gaggioli, N. G.

E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
[CrossRef]

Garbusi, E.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
[CrossRef]

Hogert, E. N.

E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, 1982), pp. 23-26.

Lunazzi, J. J.

J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit: critical point properties,” J. Opt. Soc. Am. A 23, 1021-1026 (2006).
[CrossRef]

J. J. Lunazzi and D. S. F. Magalhães, “Pseudoscopic white-light imaging by means of two bi-dimensional diffracting elements and a pinhole,” Proc. SPIE 5622, 1463-1468 (2004).
[CrossRef]

J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit,” Opt. Express 10, 1368-1373 (2002).
[PubMed]

J. J. Lunazzi, “Holophotography with a diffraction grating,” Opt. Eng. (Bellingham) 29, 15-18 (1990).
[CrossRef]

J. J. Lunazzi, “3D photography by holography,” Opt. Eng. (Bellingham) 29, 9-14 (1990).
[CrossRef]

J. J. Lunazzi and N. I. R. Rivera, “Orthoscopic imaging in a double diffraction process with slit,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 344-344.

J. J. Lunazzi, “Holoprojection of images by a double diffraction process,” presented at XIV Encontro Nacional de Física da Matéria Condensada, Caxambu-Minas Gerais, Brazil, May 7-11, 1991.

J. J. Lunazzi and D. S. F. Magalhães, “Diffractive imaging with bidimensional elements: first experimental results,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 127.

J. J. Lunazzi and D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.

Magalhães, D. S. F.

J. J. Lunazzi and D. S. F. Magalhães, “Pseudoscopic white-light imaging by means of two bi-dimensional diffracting elements and a pinhole,” Proc. SPIE 5622, 1463-1468 (2004).
[CrossRef]

D. S. F. Magalhães, “Estudo de imagens por dupla difração com seleção de luz branca e elementos definidos bidimensionalmente,” M.Sc. thesis (Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 2005), http: // www.ifi.unicamp.br/ccjdr/teses/apresentacao.php3?filename=IF419.

J. J. Lunazzi and D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.

J. J. Lunazzi and D. S. F. Magalhães, “Diffractive imaging with bidimensional elements: first experimental results,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 127.

Rebollo, M. A.

E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
[CrossRef]

Rivera, N. I. R.

J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit: critical point properties,” J. Opt. Soc. Am. A 23, 1021-1026 (2006).
[CrossRef]

J. J. Lunazzi and N. I. R. Rivera, “Pseudoscopic imaging in a double diffraction process with a slit,” Opt. Express 10, 1368-1373 (2002).
[PubMed]

N. I. R. Rivera, “Imagem por dupla difracao com luz branca sem elementos intermediários,” Ph.D. thesis (Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas, 2007), http://webbif.ifi.unicamp.br/teses/apresentacao.php?filename=IF284.

J. J. Lunazzi and N. I. R. Rivera, “Orthoscopic imaging in a double diffraction process with slit,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 344-344.

Rosenbruch, K.-J.

I. Weingärtner and K.-J. Rosenbruch, “Chromatic correction of two- and three-element holographic imaging systems,” Opt. Acta 29, 519-529 (1982).
[CrossRef]

Sweatt, W. C.

Weingärtner, I.

I. Weingärtner and K.-J. Rosenbruch, “Chromatic correction of two- and three-element holographic imaging systems,” Opt. Acta 29, 519-529 (1982).
[CrossRef]

Appl. Opt. (1)

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

Opt. Acta (1)

I. Weingärtner and K.-J. Rosenbruch, “Chromatic correction of two- and three-element holographic imaging systems,” Opt. Acta 29, 519-529 (1982).
[CrossRef]

Opt. Eng. (Bellingham) (2)

J. J. Lunazzi, “3D photography by holography,” Opt. Eng. (Bellingham) 29, 9-14 (1990).
[CrossRef]

J. J. Lunazzi, “Holophotography with a diffraction grating,” Opt. Eng. (Bellingham) 29, 15-18 (1990).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

E. N. Hogert, M. A. Rebollo, and N. G. Gaggioli, “Alignment and/or tilting measurement by means of conical diffraction phenomena,” Opt. Laser Technol. 23, 341-344 (1991).
[CrossRef]

Phys. Rev. E (1)

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619 (2003).
[CrossRef]

Proc. SPIE (1)

J. J. Lunazzi and D. S. F. Magalhães, “Pseudoscopic white-light imaging by means of two bi-dimensional diffracting elements and a pinhole,” Proc. SPIE 5622, 1463-1468 (2004).
[CrossRef]

Other (7)

D. S. F. Magalhães, “Estudo de imagens por dupla difração com seleção de luz branca e elementos definidos bidimensionalmente,” M.Sc. thesis (Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 2005), http: // www.ifi.unicamp.br/ccjdr/teses/apresentacao.php3?filename=IF419.

J. J. Lunazzi and D. S. F. Magalhães, “Photographing by means of a diffractive axicon,” http://arxiv.org/pdf/physics/0701234.

J. J. Lunazzi and N. I. R. Rivera, “Orthoscopic imaging in a double diffraction process with slit,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 344-344.

N. I. R. Rivera, “Imagem por dupla difracao com luz branca sem elementos intermediários,” Ph.D. thesis (Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas, 2007), http://webbif.ifi.unicamp.br/teses/apresentacao.php?filename=IF284.

M. C. Hutley, Diffraction Gratings (Academic, 1982), pp. 23-26.

J. J. Lunazzi, “Holoprojection of images by a double diffraction process,” presented at XIV Encontro Nacional de Física da Matéria Condensada, Caxambu-Minas Gerais, Brazil, May 7-11, 1991.

J. J. Lunazzi and D. S. F. Magalhães, “Diffractive imaging with bidimensional elements: first experimental results,” in Proceedings of XXVII Encontro Nacional de Física da Matéria Condensada, Poços de Caldas, MG, Brasil (May 4-8, 2004), Vol. 1, pp. 127.

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Figures (13)

Fig. 1
Fig. 1

General view of the optical system and the decomposing of the imaging process through a family of planes corresponding to circular symmetry.

Fig. 2
Fig. 2

Image formation of two object points A and B.

Fig. 3
Fig. 3

Ray tracing for the image of a point white-light object.

Fig. 4
Fig. 4

Ray-tracing scheme for the normal depth image.

Fig. 5
Fig. 5

B 1 and B 2 are images of the objects B 1 and B 2 , all of them belonging to planes PI and PII.

Fig. 6
Fig. 6

Experimental setup of a double diffraction system with a pinhole.

Fig. 7
Fig. 7

Light distribution reaching the pinhole P.

Fig. 8
Fig. 8

Photos of the objects F 1 and F 2 used to obtain the pseudoscopic image.

Fig. 9
Fig. 9

Schematic view of the apparatus of image formation.

Fig. 10
Fig. 10

F 2 at left; image of F 2 ( F 2 ) at right. The defocus of the image of F 1 is visible.

Fig. 11
Fig. 11

F 1 at left; image of F 1 ( F 1 ) at right. The defocus of the image of F 2 is visible as a spectral dispersion.

Fig. 12
Fig. 12

(a) Photograph of the halogen lamp employed as object. (b) Orthoscopic image of the object obtained in our system.

Fig. 13
Fig. 13

Dashed lines represent the slit position in (a) double-diffracted images for the plane grating case, (b) double-diffracted images for the circular grating case.

Tables (4)

Tables Icon

Table 1 Experimental Checking of the Pseudoscopic Image a

Tables Icon

Table 2 Comparison between Experimental and Calculated Values of the Image Distance (mm)

Tables Icon

Table 3 Calculated Values of the Horizontal Image Extension (mm)

Tables Icon

Table 4 Vertical Extension of the Image (mm)

Equations (11)

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

sin θ i sin θ d = λ ν sin ϕ ,
X 1 X ( X 1 X ) 2 + Z 2 + X 1 X 1 2 + Z R 2 = λ v v ,
X 2 X ( X 2 X ) 2 + Z 2 + X 2 X 2 2 + Z R 2 = λ a v .
X 1 X 1 2 + Z R 2 + X i X 1 ( X i X 1 ) 2 + Z i 2 = λ v v ,
X 2 X 2 2 + Z R 2 + X i X 2 ( X i X 2 ) 2 + Z i 2 = λ a v .
X 1 X 1 2 + Z R 2 + X i X 1 ( X i X 1 ) 2 + Z i 2 = λ v v ,
X 2 X 2 2 + Z R 2 + X i X 2 ( X i X 2 ) 2 + Z i 2 = λ a v .
α = arctan ( h X ) .
X 1 , 2 cos α X 2 + h 2 ( X 1 , 2 cos α X 2 + h 2 ) 2 + Z 2 + X 1 , 2 cos α ( X 1 , 2 cos α ) 2 + Z R 2 = λ a , v v ,
X 1 , 2 cos α ( X 1 , 2 cos α ) 2 + Z R 2 + X 1 , 2 cos α X i ( X 1 , 2 cos α X i ) 2 + Z i 2 = λ a , v v .
h = X i sin α ,

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