Abstract

Focal plane testing methods such as the Shack–Hartmann wavefront sensor and phase-shifting deflectometry are valuable tools for optical testing. In this study, we propose a novel wavefront slope testing method that uses a scanning galvo laser, in which a single-mode Gaussian beam scans the pupils of the tested optics in the system. In addition, the ray aberration is reconstructed by the four-step phase-shifting measurement by modulating the angular domain. The measured wavefront is verified by a Fizeau interferometer in terms of Zernike polynomials.

© 2015 Optical Society of America

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References

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  1. I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 361–397.
  2. J. Ares, T. Mancebo, and S. Bara, “Position and displacement sensing with Shack–Hartmann wave-front sensors,” Appl. Opt. 39, 1511–1520 (2000).
    [Crossref]
  3. J. Z. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [Crossref]
  4. M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
    [Crossref]
  5. T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
    [Crossref]
  6. C. Liang and J. Sasian, “Geometrical optics modeling of the grating-slit test,” Opt. Express 15, 1738–1744 (2007).
    [Crossref]
  7. J. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. XI, pp. 2–34.
  8. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [Crossref]
  9. M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
    [Crossref]
  10. B. Saleh and M. Teich, “Beam optics,” in Fundamentals of Photonics (1991), pp. 80–93.
  11. H. Schreiber, J. Bruning, and J. Greivenkamp, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 557–629.

2008 (1)

M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
[Crossref]

2007 (1)

2004 (2)

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

2000 (1)

1994 (1)

1980 (1)

Ares, J.

Bara, S.

Bille, J. F.

Bothe, T.

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

Bruning, J.

H. Schreiber, J. Bruning, and J. Greivenkamp, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 557–629.

Creath, K.

J. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. XI, pp. 2–34.

Ghozeil, I.

I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 361–397.

Goelz, S.

Greivenkamp, J.

H. Schreiber, J. Bruning, and J. Greivenkamp, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 557–629.

Grimm, B.

Hausler, G.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Jueptner, W.

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

Kaminski, J.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Knauer, M.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Li, W.

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

Liang, C.

Liang, J. Z.

Mancebo, T.

Miller, J.

M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
[Crossref]

Niesten, M.

M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
[Crossref]

Saleh, B.

B. Saleh and M. Teich, “Beam optics,” in Fundamentals of Photonics (1991), pp. 80–93.

Sasian, J.

Schreiber, H.

H. Schreiber, J. Bruning, and J. Greivenkamp, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 557–629.

Southwell, W. H.

Sprague, R.

M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
[Crossref]

Teich, M.

B. Saleh and M. Teich, “Beam optics,” in Fundamentals of Photonics (1991), pp. 80–93.

von Kopylow, C.

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

Wyant, J.

J. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. XI, pp. 2–34.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Opt. Express (1)

Proc. SPIE (3)

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

T. Bothe, W. Li, C. von Kopylow, and W. Jueptner, “High-resolution 3D shape measurement on specular surfaces by fringe reflection,” Proc. SPIE 5457, 411–422 (2004).
[Crossref]

M. Niesten, R. Sprague, and J. Miller, “Scanning laser beam displays,” Proc. SPIE 7001, 70010E (2008).
[Crossref]

Other (4)

B. Saleh and M. Teich, “Beam optics,” in Fundamentals of Photonics (1991), pp. 80–93.

H. Schreiber, J. Bruning, and J. Greivenkamp, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 557–629.

J. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Academic, 1992), Vol. XI, pp. 2–34.

I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (2007), pp. 361–397.

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Figures (12)

Fig. 1.
Fig. 1. Relation between the ray and the wavefront aberration.
Fig. 2.
Fig. 2. Schematic diagram of the laser projector [9].
Fig. 3.
Fig. 3. Centroid of the spot position in relation to time.
Fig. 4.
Fig. 4. Defining the transverse ray aberration in the system.
Fig. 5.
Fig. 5. Measurement principle of the system.
Fig. 6.
Fig. 6. System setup for the optical tests.
Fig. 7.
Fig. 7. Measurement process.
Fig. 8.
Fig. 8. Four intensity frames in each orthogonal direction are captured in one of the laboratory lenses. The fringe pattern hints at the existence of a spherical aberration.
Fig. 9.
Fig. 9. (a) Original angular maps in two orthogonal directions. (b) Angular maps after phase unwrapping in two orthogonal directions.
Fig. 10.
Fig. 10. Transverse ray aberration map on the normalized pupil coordinates in two orthogonal directions.
Fig. 11.
Fig. 11. Wavefront aberration on the normalized pupil coordinates.
Fig. 12.
Fig. 12. Setup of the Fizeau interferometer with the ball retro-reflective method.

Tables (2)

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Table 1. Description of Lenses

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Table 2. Comparison of Measurement Results

Equations (11)

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TA x ( x , y ) = r W ( x , y ) x ,
TA x ( ρ x , ρ y ) = r h W ( ρ x , ρ y ) ρ x = 2 F # W ( ρ x , ρ y ) ρ x .
TA ( ρ x , ρ y ) = 2 F # C d [ Z ( ρ x , ρ y ) ] .
U ( ρ , z ) = A 1 j z 0 ( 2 z 0 / k ) 1 / 2 W ( z ) e { ( ρ 2 W 2 ( z ) ) j [ k z + k ρ 2 2 R ( z ) tan 1 ( z z 0 ) ] } ,
I ( ρ , z ) = | U ( ρ , z ) | 2 = I ( z ) e [ 2 ρ 2 W 2 ( z ) ] .
W 0 ( z ) = M ( z , f ) W 0 .
W ( z ) = M W 0 [ 1 + ( M 2 × ( z f ) + f M 2 × z 0 ) 2 ] 1 / 2 .
I A ( α , β ) = I 0 [ 1 + γ cos ( 2 π P α + 0 β ) ] .
I A ( ρ x , ρ y ) I 0 [ 1 + γ cos ( 2 π P L ρ x + 0 ρ y ) ] .
I B ( ε x , ε y ) = 1 M × I 0 [ 1 + γ cos ( 2 π P L ρ x ( ε x , ε y ) ) ] .
ε x = TA x ( ρ x , ρ y ) 2 ( F / # ) × δ .

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