Abstract

Testing of aspherics by means of computer-generated holograms (CGHs) is well known. To perform a quasi-absolute test of rotationally symmetric aspheric surfaces, two wave fronts must be encoded in the CGH. Both the null lens and a spherical lens have to be stored. This enables successive measurements of the aspheric and of a cat’s-eye position without changing the object arm of the interferometer. Two possibilities for encoding both wave fronts have been investigated. A first-order approximation for estimating the influence of disturbing diffraction orders is given.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 197–202.
  2. G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1976), Vol. 13.
    [CrossRef]
  3. A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
    [CrossRef]
  4. D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
  5. J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” Patent-OffenlegungsschriftAZ 198 20 785.9 (17April1998).
  6. N. Lindlein, “Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics,” Appl. Opt. 40, 2698–2708 (2001).
    [CrossRef]
  7. W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
    [CrossRef]
  8. E. Carcolé, M. S. Millán, J. Campos, “Derivation of weighting coefficients for multiplexed phase-diffractive elements,” Opt. Lett. 20, 2360–2362 (1995).
    [CrossRef] [PubMed]

2001 (1)

1995 (1)

1976 (1)

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

1975 (1)

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 197–202.

Campos, J.

Carcolé, E.

Fercher, A. F.

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

Lindlein, N.

Millán, M. S.

Schulz, G.

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1976), Vol. 13.
[CrossRef]

Schwider, J.

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1976), Vol. 13.
[CrossRef]

J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” Patent-OffenlegungsschriftAZ 198 20 785.9 (17April1998).

Welford, W. T.

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 197–202.

Appl. Opt. (1)

Opt. Acta (1)

A. F. Fercher, “Computer-generated holograms for testing optical elements: error analysis and error compensation,” Opt. Acta 23, 347–365 (1976).
[CrossRef]

Opt. Commun. (1)

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

Opt. Lett. (1)

Other (4)

D. Malacara, ed., Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

J. Schwider, “Absolutprüfung von asphärischen Flächen unter Zuhilfenahme von diffraktiven Normalelementen und planen sowie sphärischen Referenzflächen,” Patent-OffenlegungsschriftAZ 198 20 785.9 (17April1998).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 197–202.

G. Schulz, J. Schwider, “Interferometric testing of smooth surfaces,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1976), Vol. 13.
[CrossRef]

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 (9)

Fig. 1
Fig. 1

Schematic setup of the interferometer for testing aspherics by use of a null-lens system.

Fig. 2
Fig. 2

Schematic of the three positions for the absolute measurement of spherical surfaces.

Fig. 3
Fig. 3

Ray-tracing scheme of the setup used for the derivation. Here, the surface is R = U.

Fig. 4
Fig. 4

Efficiencies of a superposed wave-front CGH for orders m = -2, …, 3. The sum of the efficiencies for m = 1 and m = 0 is also shown.

Fig. 5
Fig. 5

Ratio of the output intensities for a superposed wave-front CGH as a function of the relative input weight.

Fig. 6
Fig. 6

Schematic of a sliced aperture CGH with two alternately encoded phase functions.

Fig. 7
Fig. 7

Efficiencies of a sliced wave-front CGH for orders m = 0 for A and B. The efficiencies of the higher orders |m| = 1 and |m| = 2 do not differ for A and B. The sum of the efficiencies for m A = 0 and m B = 0 is also shown.

Fig. 8
Fig. 8

Ratio of the output intensities for a sliced wave-front CGH as a function of relative window width.

Fig. 9
Fig. 9

Comparison of efficiency η1 and average efficiency η0,2 of a superposed wave-front CGH. The efficiencies of orders m = 0 and m = 2 are also shown.

Equations (30)

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

W1x, y=WRx, y+WSx, y+Px, y,
W2x, y=WRx, y+WSx, y+P-x, -y,
W3x, y=WRx, y+1/2WSx, y+WS-x, -y,
Px, y=1/2W1x, y+W2-x, -y-W3x, y-W3-x, -y.
W3x, y=WRx, y+1/2WSx, y+WS-x, -y,
W1x, y=WRx, y+WSx, y+Px, y,
W2x, y=WRx, y+WSx, y+Qx, y.
Px, y=W1x, y-W2x, y+Qx, y.
ares expiΦ=aA expiϕA+aB expiϕB.
expiΦ=m=-m=+ am expimϕA+1-mϕB.
λνxx+2Δx, y+2Δy=m+m-2kϕA-ϕBx+2dx, ym-1m-1k2×ϕA-ϕBx2ϕA-ϕBx2+ϕA-ϕBy2ϕA-ϕBxy,
λνyx+2Δx, y+2Δy=m+m-2kϕA-ϕBy+2dx, ym-1m-1k2×ϕA-ϕBx2ϕA-ϕBxy+ϕA-ϕBy2ϕA-ϕBy2,
Δx=dx, ykm-1ϕA-ϕBx,
Δy=dx, ykm-1ϕA-ϕBy.
hAx, y=combxp * rectxwAHAx, y,
h˜Au, v=pwAcombupsincuwA * H˜Au, v.
expiΦA,mx, y=expiϕAx, y+msx,
λνxx+2Δx, y+2Δy=1kϕU+ϕV-2ϕRx+m+ms+2dx, yk2ms+ϕU-ϕRx2ϕV-ϕRx2+ϕU-ϕRy2ϕV-ϕRxy,
λνyx+2Δx, y+2Δy=1kϕU+ϕV-2ϕRy+2dx, yk2ms+ϕU-ϕRx2ϕV-ϕRxy+ϕU-ϕRy2ϕV-ϕRy2,
Δx=dx, ykϕU-ϕRx+ms,
Δy=dx, ykϕU-ϕRy.
aA,m=wApsincmwAp.
λνxx, y=m+m-2kϕDx,
λνyx, y=m+m-2kϕDy,
λνxx, y=m+m-2kϕCx+c,
λνyx, y=m+m-2kϕCy,
λνxx, y=2dm-1m-1k2ϕCx+c×2ϕCx2+ϕCy2ϕCxy,
λνyx, y=2dm-1m-1k2ϕCx+c×2ϕCxy+ϕCy2ϕCy2.
λνxx, y=1k-ϕDx+m+ms, λνyx, y=-1kϕDy.
λνxx, y=-1kϕCx+cx-m+ms,

Metrics