Abstract

A diffractive grazing-incidence interferometer for the test of cylindrical lenses is described. Besides surface aberrations from the ideal shape, the interferometer allows for the simultaneous determination of the relative position and orientation of surfaces to another. The measurement principle as well as a classification of deviation types is given. Measurement results for planar concave lenses are presented.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Sturm, H.-G. Treusch, P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” in Lasers in Material Processing, L. H. Beckmann, ed., Proc. SPIE3097, 717–726 (1997).
  2. R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
    [CrossRef]
  3. J. M. Geary, “Testing cylindrical lenses,” Opt. Eng. 26, 1219–1224 (1987).
    [CrossRef]
  4. D. Malacara, Optical Shop Testing (Wiley, New York, 1991).
  5. A. J. MacGovern, J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10, 619–624 (1971).
    [CrossRef] [PubMed]
  6. N. Abramson, “The interferoscope: a new type of interferometer with variable fringe separation,” Optik (Stuttgart) 30, 56–71 (1969).
  7. K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to nonoptical surfaces,” J. Phys. E 6, 1045–1048 (1973).
    [CrossRef]
  8. T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
    [CrossRef]
  9. S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: experiment,” Appl. Opt. 38, 121–125 (1999).
    [CrossRef]
  10. H. Nürge, J. Schwider, “Testing of cylindrical lenses by grazing incidence interferometry,” Optik 111, 545–555 (2000).
  11. D. W. Robinson, G. T. Reid, eds., Interferogram Analysis (Institute of Physics Publishing, London, 1993).
  12. Axicons, also known as conical lenses, are rotationally symmetric prisms. They can be used to convert a parallel light beam into a conical beam. Configured binary diffractive structures, axicons are DOEs with equidistant circular grooves.
  13. R. Schreiner, “Interferometric shape measurement of rough surfaces at grazing incidence,” Opt. Eng. 41, 1570–1576 (2002).
    [CrossRef]
  14. J. Schneider, K. Mantel, R. Schreiner, N. Lindlein, J. Schwider, “Compensation for anamorphotic distortion in grazing-incidence interferometry testing planar specimens,” Appl. Opt. 42, 4480–4487 (2003).
    [CrossRef] [PubMed]
  15. K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
    [CrossRef] [PubMed]
  16. G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
    [CrossRef]
  17. M. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533–537 (1970).
    [CrossRef] [PubMed]
  18. E. W. Young, “Optimal removal of all mislocation effects in interferometric tests,” in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE661, 116–124 (1986).
    [CrossRef]
  19. The centration measurement equipment for cylindrical lenses was developed by AGFA.

2003 (1)

2002 (1)

R. Schreiner, “Interferometric shape measurement of rough surfaces at grazing incidence,” Opt. Eng. 41, 1570–1576 (2002).
[CrossRef]

2000 (1)

H. Nürge, J. Schwider, “Testing of cylindrical lenses by grazing incidence interferometry,” Optik 111, 545–555 (2000).

1999 (1)

1998 (1)

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

1995 (1)

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

1989 (1)

1987 (1)

J. M. Geary, “Testing cylindrical lenses,” Opt. Eng. 26, 1219–1224 (1987).
[CrossRef]

1973 (1)

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to nonoptical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

1971 (1)

1970 (1)

1969 (1)

N. Abramson, “The interferoscope: a new type of interferometer with variable fringe separation,” Optik (Stuttgart) 30, 56–71 (1969).

Abramson, N.

N. Abramson, “The interferoscope: a new type of interferometer with variable fringe separation,” Optik (Stuttgart) 30, 56–71 (1969).

Beach, R. J.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Benett, W. J.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Birch, K. G.

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to nonoptical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Blümel, T.

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

Brinkmann, S.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: experiment,” Appl. Opt. 38, 121–125 (1999).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

Burow, R.

Carlson, N. W.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Dresel, T.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: experiment,” Appl. Opt. 38, 121–125 (1999).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

Elssner, K.-E.

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

K.-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989).
[CrossRef] [PubMed]

Emanuel, M. A.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Freitas, B. L.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Geary, J. M.

J. M. Geary, “Testing cylindrical lenses,” Opt. Eng. 26, 1219–1224 (1987).
[CrossRef]

Green, F. J.

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to nonoptical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Grzanna, J.

Kafka, R.

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

Lindlein, N.

Loosen, P.

V. Sturm, H.-G. Treusch, P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” in Lasers in Material Processing, L. H. Beckmann, ed., Proc. SPIE3097, 717–726 (1997).

MacGovern, A. J.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1991).

Mantel, K.

Nürge, H.

H. Nürge, J. Schwider, “Testing of cylindrical lenses by grazing incidence interferometry,” Optik 111, 545–555 (2000).

Rimmer, M.

Schneider, J.

Schreiner, R.

J. Schneider, K. Mantel, R. Schreiner, N. Lindlein, J. Schwider, “Compensation for anamorphotic distortion in grazing-incidence interferometry testing planar specimens,” Appl. Opt. 42, 4480–4487 (2003).
[CrossRef] [PubMed]

R. Schreiner, “Interferometric shape measurement of rough surfaces at grazing incidence,” Opt. Eng. 41, 1570–1576 (2002).
[CrossRef]

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: experiment,” Appl. Opt. 38, 121–125 (1999).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

Schulz, G.

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

Schwider, J.

J. Schneider, K. Mantel, R. Schreiner, N. Lindlein, J. Schwider, “Compensation for anamorphotic distortion in grazing-incidence interferometry testing planar specimens,” Appl. Opt. 42, 4480–4487 (2003).
[CrossRef] [PubMed]

H. Nürge, J. Schwider, “Testing of cylindrical lenses by grazing incidence interferometry,” Optik 111, 545–555 (2000).

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: experiment,” Appl. Opt. 38, 121–125 (1999).
[CrossRef]

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

Skidmore, J. A.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Solarz, R. W.

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

Spolaczyk, R.

Sturm, V.

V. Sturm, H.-G. Treusch, P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” in Lasers in Material Processing, L. H. Beckmann, ed., Proc. SPIE3097, 717–726 (1997).

Treusch, H.-G.

V. Sturm, H.-G. Treusch, P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” in Lasers in Material Processing, L. H. Beckmann, ed., Proc. SPIE3097, 717–726 (1997).

Vogel, A.

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

Wyant, J. C.

Young, E. W.

E. W. Young, “Optimal removal of all mislocation effects in interferometric tests,” in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE661, 116–124 (1986).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am A (1)

T. Dresel, S. Brinkmann, R. Schreiner, J. Schwider, “Testing of rod objects by grazing incidence interferometry: theory,” J. Opt. Soc. Am A 15, 2921–2928 (1998).
[CrossRef]

J. Phys. E (1)

K. G. Birch, F. J. Green, “Oblique incidence interferometry applied to nonoptical surfaces,” J. Phys. E 6, 1045–1048 (1973).
[CrossRef]

Opt. Commun. (1)

G. Schulz, T. Blümel, R. Kafka, K.-E. Elssner, A. Vogel, “Calibration of an interferometer for testing cylindrical surfaces,” Opt. Commun. 117, 512–520 (1995).
[CrossRef]

Opt. Eng. (2)

J. M. Geary, “Testing cylindrical lenses,” Opt. Eng. 26, 1219–1224 (1987).
[CrossRef]

R. Schreiner, “Interferometric shape measurement of rough surfaces at grazing incidence,” Opt. Eng. 41, 1570–1576 (2002).
[CrossRef]

Optik (1)

H. Nürge, J. Schwider, “Testing of cylindrical lenses by grazing incidence interferometry,” Optik 111, 545–555 (2000).

Optik (Stuttgart) (1)

N. Abramson, “The interferoscope: a new type of interferometer with variable fringe separation,” Optik (Stuttgart) 30, 56–71 (1969).

Other (7)

D. Malacara, Optical Shop Testing (Wiley, New York, 1991).

V. Sturm, H.-G. Treusch, P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” in Lasers in Material Processing, L. H. Beckmann, ed., Proc. SPIE3097, 717–726 (1997).

R. J. Beach, M. A. Emanuel, B. L. Freitas, J. A. Skidmore, N. W. Carlson, W. J. Benett, R. W. Solarz, “Applications of microlens-conditioned laser diode arrays” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Montamedi, L. Beiser, eds., Proc. SPIE2383, 283–297 (1995).
[CrossRef]

D. W. Robinson, G. T. Reid, eds., Interferogram Analysis (Institute of Physics Publishing, London, 1993).

Axicons, also known as conical lenses, are rotationally symmetric prisms. They can be used to convert a parallel light beam into a conical beam. Configured binary diffractive structures, axicons are DOEs with equidistant circular grooves.

E. W. Young, “Optimal removal of all mislocation effects in interferometric tests,” in Optical Testing and Metrology, C. P. Grover, ed., Proc. SPIE661, 116–124 (1986).
[CrossRef]

The centration measurement equipment for cylindrical lenses was developed by AGFA.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Cylindrical lenses in a large variety of dimensions and numerical apertures have to be characterized. Two examples are shown.

Fig. 2
Fig. 2

Example of a positional deviation. In contrast to the ideal lens (left), the defective lens has convex surfaces that are not properly aligned (right).

Fig. 3
Fig. 3

Measurement principle.

Fig. 4
Fig. 4

Typical DOE structure used to test a biconcave lens.

Fig. 5
Fig. 5

Principle of determination of the positional deviation for a wedge error. Angles Φ1 and Φ2 can be calculated by a least-squares fit of the misalignment functionals to the measured phase and yield the wedge angle Φ1 − Φ2.

Fig. 6
Fig. 6

Classification of the positional deviations. There are five different error classes possible for a general rod object.

Fig. 7
Fig. 7

(a) The tilted upper surface of the lens does not exhibit a positional deviation, as the rotation of a concave surface about its symmetry axis does not lead to wave aberrations. (b) In another state of alignment the same lens now shows a centering and a thickness error.

Fig. 8
Fig. 8

Cutoff error.

Fig. 9
Fig. 9

The cutoff error may be determined by appropriate combination of two measurements, the second one taken with the lens in a flipped position.

Fig. 10
Fig. 10

Misalignment aberrations can be uniquely separated for a symmetrical domain, i.e., a symmetrical interferogram. Left, domain for a planar surface; right, domain for a cylindrical surface.

Fig. 11
Fig. 11

The three detectable positional deviations for a planar concave lens.

Fig. 12
Fig. 12

Result of measurement of a planar concave lens with a 220-mm radius of curvature. Contour plots of the surface deviations show peak to valley values of 40.2 µm for the upper planar surface (left), 7.3 µm for the planar rear surface (middle), and 6.8 µm for the cylindrical front surface (right). The positional deviations are illustrated. The difference in the contour lines is 2 µm (upper surface), 0.5 µm (rear surface), and 0.5 µm (front surface).

Tables (3)

Tables Icon

Table 1 Detectable Positional Deviations for Cylindrical Lenses

Tables Icon

Table 2 Wedge Errors (°) of a Series of Three Planar Concave Lenses

Tables Icon

Table 3 Torsion Errors (°) of a Series of Three Planar Concave Lenses

Equations (9)

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

Φ meas = Φ obj + Φ mis + Φ sys .
Φ mis = 2 k ( n ̂ · d ) ( ê · n ̂ ) ,
d = T + Ω × r .
Φ mis ( x , y ) = i T i M T i i Ω j M Ω j .
M Ω y = 4 π λ eff z , M Ω z = 4 π λ eff y .
M T x = 4 π λ eff cos φ , M T y = 4 π λ eff sin φ , M Ω x = 4 π λ eff z sin φ , M Ω y = 4 π λ eff z cos φ .
z 0 z 1 d z φ 0 φ 1 d φ M T i ( φ , z ) M T j ( φ , z ) , z 0 z 1 d z φ 0 φ 1 d φ M T i ( φ , z ) M Ω j ( φ , z ) , z 0 z 1 d z φ 0 φ 1 d φ M Ω i ( φ , z ) M Ω j ( φ , z )
Δ W ~ sin 2 u Δ d u 2 Δ d
Δ W ~ sin u Δ l u Δ l

Metrics