Abstract

A new technique for precise focal-length measurements with a hologram is presented. This technique is widely applicable and is particularly useful for measuring large, slow lenses. In diffraction, the Fresnel-zone plate hologram emulates the reflective properties of a convex spherical mirror for use during transmission null tests of an optic by use of a phase-shifting interferometer. The hologram is written lithographically and therefore offers a higher degree of precision at a lower cost than its spherical mirror counterpart. A hologram offers the additional benefit of easy characterization by use of the same interferometer employed in examining the test optic. Better than ±0.01% precision is achieved during measurement of a 9-m focal-length lens by use of a 150-mm aperture interferometer.

© 2003 Optical Society of America

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References

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  1. B. Howland, A. F. Proll, “Apparatus for the accurate determination of flange focal distance,” Appl. Opt. 11, 1247–1251 (1970).
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    [CrossRef] [PubMed]
  3. B. J. Pernick, B. Hyman, “Least-squares technique for determining principal plane location and focal length,” Appl. Opt. 26, 2938–2939 (1987).
  4. C.-W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
    [CrossRef]
  5. R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 50–55 (1990).
  6. M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
    [CrossRef]
  7. K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).
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    [CrossRef] [PubMed]
  9. J. Z. Malacara, “Angle, distance, curvature, and focal length measurements,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 715–741.
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  11. J. E. Grievenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 501–598.
  12. Veeco Metrology Group, Optical Profilers and Laser Interferometers, 2650 East Elvira Road, Tucson, Ariz. 85706-7123, http://www.veeco.com
  13. K. Creath, “WYKO systems for optical metrology,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 111–114 (1987).
    [CrossRef]
  14. E. Hecht, Optics, 3rd ed. (Addison Wesley Longman, Menlo Park, Calif., 1998), pp. 476–488.
  15. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999), pp. 413–417.
  16. G. R. Fowles, Introduction to Modern Optics (Dover, New York, 1989), pp. 125–129.
  17. D. S. Goodman, “General principles of geometric optics,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, Inc., N. Y., 1995), Vol. 1, pp. 1.68–1.69.

1989 (1)

C.-W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

1987 (2)

1985 (1)

1980 (1)

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

1970 (1)

B. Howland, A. F. Proll, “Apparatus for the accurate determination of flange focal distance,” Appl. Opt. 11, 1247–1251 (1970).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999), pp. 413–417.

Bruning, J. H.

J. E. Grievenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 501–598.

Chang, C.-W.

C.-W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Creath, K.

K. Creath, “WYKO systems for optical metrology,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 111–114 (1987).
[CrossRef]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Dover, New York, 1989), pp. 125–129.

Freischlad, K. R.

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

Gerchman, M. C.

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Glatt, I.

Goodman, D. S.

D. S. Goodman, “General principles of geometric optics,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, Inc., N. Y., 1995), Vol. 1, pp. 1.68–1.69.

Grievenkamp, J. E.

J. E. Grievenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 501–598.

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison Wesley Longman, Menlo Park, Calif., 1998), pp. 476–488.

Howland, B.

B. Howland, A. F. Proll, “Apparatus for the accurate determination of flange focal distance,” Appl. Opt. 11, 1247–1251 (1970).

Hunter, G. C.

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Hyman, B.

Jain, N. K.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 50–55 (1990).

Kafri, O.

Kaiser, W.

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

Küchel, M.

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

Kumar, H.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 50–55 (1990).

Malacara, J. Z.

J. Z. Malacara, “Angle, distance, curvature, and focal length measurements,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 715–741.

Mayer, M.

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

Murata, K.

Nakano, Y.

Pernick, B. J.

Proll, A. F.

B. Howland, A. F. Proll, “Apparatus for the accurate determination of flange focal distance,” Appl. Opt. 11, 1247–1251 (1970).

Shannon, R. R.

R. R. Shannon, The Art and Science of Optical Design (Cambridge University Press, Cambridge, UK, 1997), pp. 170–173.

Sirohi, R. S.

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 50–55 (1990).

Su, D. C.

C.-W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Wiedmann, W.

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999), pp. 413–417.

Appl. Opt. (4)

Opt. Commun. (1)

C.-W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Opt. Eng. (1)

M. C. Gerchman, G. C. Hunter, “Differential technique for accurately measuring the radius of curvature of long radius concave optical surfaces,” Opt. Eng. 19, 843–848 (1980).
[CrossRef]

Other (11)

K. R. Freischlad, M. Küchel, W. Wiedmann, W. Kaiser, M. Mayer, “High-precision interferometric testing of spherical mirrors with long radius of curvature,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 8–17 (1990).

R. S. Sirohi, H. Kumar, N. K. Jain, “Focal length measurement using diffraction at a grating,” in Optical Testing and Metrology III, C. P. Grover, ed., Proc. SPIE1332, 50–55 (1990).

J. Z. Malacara, “Angle, distance, curvature, and focal length measurements,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 715–741.

R. R. Shannon, The Art and Science of Optical Design (Cambridge University Press, Cambridge, UK, 1997), pp. 170–173.

J. E. Grievenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, Second Edition, D. Malacara, ed. (Wiley, N. Y., 1992), pp. 501–598.

Veeco Metrology Group, Optical Profilers and Laser Interferometers, 2650 East Elvira Road, Tucson, Ariz. 85706-7123, http://www.veeco.com

K. Creath, “WYKO systems for optical metrology,” in Interferometric Metrology, N. A. Massie, ed., Proc. SPIE816, 111–114 (1987).
[CrossRef]

E. Hecht, Optics, 3rd ed. (Addison Wesley Longman, Menlo Park, Calif., 1998), pp. 476–488.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999), pp. 413–417.

G. R. Fowles, Introduction to Modern Optics (Dover, New York, 1989), pp. 125–129.

D. S. Goodman, “General principles of geometric optics,” in Handbook of Optics, 2nd ed., M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, Inc., N. Y., 1995), Vol. 1, pp. 1.68–1.69.

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental setup for measuring BFD of a test lens by retroreflecting a PSI test beam with a spherical mirror to produce a null fringe. (b) A similar setup to that of Fig. 1(a), which has the spherical mirror replaced with a reflective Fresnel-zone hologram.

Fig. 2
Fig. 2

Experimental method for testing the diffractive radius of curvature of the Fresnel hologram. The hologram is translated axially on a precision slide between the cat’s-eye position and a rear location that also produces a null fringe in the PSI.

Fig. 3
Fig. 3

Geometric diagram useful for determining the Fresnel-zone (i.e., hologram ring) boundary locations that give a desired diffractive radius of curvature.

Fig. 4
Fig. 4

Example plot of residual Zernike wave-front focus (i.e., focal power) in waves at 632.8 nm versus axial location of hologram during radius of curvature testing. Data is taken at smaller distance intervals near the zero crossing of Zernike focus.

Fig. 5
Fig. 5

Interferograms showing wave-front measurement data before and after subtraction of a background interferogram that exhibits hologram substrate shape. Note that the interferogram after background subtraction better exhibits the circular symmetry expected from a measurement of wave-front focus.

Fig. 6
Fig. 6

Example plot of residual Zernike wave-front focus (i.e., focal power) in waves at 632.8 nm versus axial location of hologram [i.e., τ of Fig. 1(b)] during lens BFD testing.

Equations (5)

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sag  y2/2R.
Δsag  -y2/2R2 ΔR,
rn=ρn2-R21/2,
2ρn-2R=nλ/2.
background focal power = Δϕϕlenst-12.

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