Abstract

In this paper, we propose the use of a reflective spatial light modulator (RSLM) controlled by a PC, instead of a metal plate with holes, to produce the interference patterns in Chalmers interferometric test. The main advantage of the proposed method is that with an RSLM, it is possible to test and obtain an interference pattern for any zone of a surface or lens by opening two appropriate apertures. This increases the accuracy of the results and reduces the time required to obtain them.

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References

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  1. L. C. Martin, “The testing of optical instruments, and the study of their performance,” in Technical Optics (Pitman, 1959), 285–286.
  2. M. Antonieta Zuloaga Garmendia, Chalmers Test. Masters in Science thesis, Instituto Nacional de Astrofísica, Óptica y Electrónica, México (1994).
  3. F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
    [CrossRef]
  4. F. Granados Agustin and A. Cornejo Rodriguez, “Generalización del método de mediciones interferométricas múltiples en pruebas de superficies ópticas,” Rev. Mex. Fis.45(2), 132–139 (1999).
  5. J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” in Optical Fabrication, Testing, and Metrology, R. Geyl, D. Rimmer, L. Wang, eds., Proc. SPIE 5252, 264 (2004).
  6. J. Kacperski and M. Kujawinska, “Active, LCoS based laser interferometer for microelements studies,” Opt. Express14(21), 9664–9678 (2006).
    [CrossRef] [PubMed]
  7. C. Gardner and A. H. Bennett, “A modified Hartmann test based on interference,” J. Opt. Soc. Am.11(4), 441–452 (1925).
    [CrossRef]
  8. F. A. Jenkins and H. E. White, “Interference of two beams of light,” in Fundamentals of Optics (McGraw Hill, 1981), 261–266.
  9. M. Born and E. Wolf, “Elements of the theory of interference and interferometers,” in Principles of Optics (Cambridge, 1999), 286–292.
  10. H. Guenther and D. H. Liebenberg, “Automatic techniques for analyzing nulled interferograms,” in Optical Interferograms Reduction and Interpretation, R. C. Moore eds (ASTM, Philadelphia, 1978), 34–35.
  11. M. V. Mantravadi and D. Malacara, “Newton, Fizeau and Haidiger interferometers,” in Optical Shop Testing, D. Malacara ed. (A. John Wiley & Sons, 2007), 12–13.

2006

2004

F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
[CrossRef]

1999

F. Granados Agustin and A. Cornejo Rodriguez, “Generalización del método de mediciones interferométricas múltiples en pruebas de superficies ópticas,” Rev. Mex. Fis.45(2), 132–139 (1999).

1925

Bennett, A. H.

Cornejo Rodriguez, A.

F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
[CrossRef]

F. Granados Agustin and A. Cornejo Rodriguez, “Generalización del método de mediciones interferométricas múltiples en pruebas de superficies ópticas,” Rev. Mex. Fis.45(2), 132–139 (1999).

Fausto Escobar Romero, J.

F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
[CrossRef]

Gardner, C.

Granados Agustin, F.

F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
[CrossRef]

F. Granados Agustin and A. Cornejo Rodriguez, “Generalización del método de mediciones interferométricas múltiples en pruebas de superficies ópticas,” Rev. Mex. Fis.45(2), 132–139 (1999).

Kacperski, J.

Kujawinska, M.

J. Opt. Soc. Am.

Opt. Express

Opt. Rev.

F. Granados Agustin, J. Fausto Escobar Romero, and A. Cornejo Rodriguez, “Testing parabolic surface with annular subaperture interferograms,” Opt. Rev.11(2), 82–86 (2004).
[CrossRef]

Rev. Mex. Fis.

F. Granados Agustin and A. Cornejo Rodriguez, “Generalización del método de mediciones interferométricas múltiples en pruebas de superficies ópticas,” Rev. Mex. Fis.45(2), 132–139 (1999).

Other

J. Liesener and H. J. Tiziani, “Interferometer with dynamic reference,” in Optical Fabrication, Testing, and Metrology, R. Geyl, D. Rimmer, L. Wang, eds., Proc. SPIE 5252, 264 (2004).

F. A. Jenkins and H. E. White, “Interference of two beams of light,” in Fundamentals of Optics (McGraw Hill, 1981), 261–266.

M. Born and E. Wolf, “Elements of the theory of interference and interferometers,” in Principles of Optics (Cambridge, 1999), 286–292.

H. Guenther and D. H. Liebenberg, “Automatic techniques for analyzing nulled interferograms,” in Optical Interferograms Reduction and Interpretation, R. C. Moore eds (ASTM, Philadelphia, 1978), 34–35.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau and Haidiger interferometers,” in Optical Shop Testing, D. Malacara ed. (A. John Wiley & Sons, 2007), 12–13.

L. C. Martin, “The testing of optical instruments, and the study of their performance,” in Technical Optics (Pitman, 1959), 285–286.

M. Antonieta Zuloaga Garmendia, Chalmers Test. Masters in Science thesis, Instituto Nacional de Astrofísica, Óptica y Electrónica, México (1994).

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Figures (12)

Fig. 1
Fig. 1

Diagram of the Chalmers test.

Fig. 2
Fig. 2

Selection of open holes with different positions, separations, and size.

Fig. 3
Fig. 3

Geometry of wavefront propagation in the Young’s experiment.

Fig. 4
Fig. 4

Experimental diagram of the proposed method.

Fig. 5
Fig. 5

(a) Interference pattern produced by two squares of size 554 µm, aligned at 45° and separated by 1088 µm; (b) interference pattern produced by two circles of size 408 µm, separated by 1360 µm, and with vertical alignment; (c) interference pattern produced by two circles of size 1360 µm, separated by 2720 µm, and with vertical alignment.

Fig. 6
Fig. 6

(a) Interference with squares of size 20 pixels (272 µm), separated by 50 pixels (680 µm).(b) Amplification of the interferogram of the eighth order of diffraction.

Fig. 7
Fig. 7

(a) Interference with squares of size 40 pixels (544 µm), separated by 50 pixels (680 µm). (b) Amplification of the interferogram of the seventh order of diffraction.

Fig. 8
Fig. 8

Experimental setup.

Fig. 9
Fig. 9

Selection of the wavefront.

Fig. 10
Fig. 10

Interferogram test of mirror with 5 deformations.

Fig. 11
Fig. 11

Mesh location of interferograms.

Fig. 12
Fig. 12

(a) Interference with vertical oriented squares of size 40 pixels (544 µm) and separated by 40 pixels (544 µm) in zone 31; (b) interference with squares of size 40 pixels (544 µm) and separated by 40 pixels (544 µm) in zone 107; (c) interference with squares of size 40 pixels (544 µm) and separated by 40 pixels (544 µm) in zone 85.

Tables (2)

Tables Icon

Table1 Results obtained with different sizes and separations of aperture squares in the RSLM.

Tables Icon

Table 2 Derived error for the three tested zones of the spherical mirror.

Equations (6)

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

I= I 1 + I 2 ±2 I 1 I 2 cosδ,
I 1 = E 1 2 I 2 = E 2 2 .
δ= 2π λ Δ= 2π λ ( BP ¯ AP ¯ ),
Δ=asinα=a h d .
h=λ d a .
surfaceerror=Es= ΔS( λ 2 ) S ,

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