Abstract

A method for null-testing fast convex aspheric optical surfaces is presented. The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid. Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape. Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method. Numerical simulations show that it is possible to detect surface departures as small as 5 µm.

© 2000 Optical Society of America

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References

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  1. E. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.
  2. A. Offner, D. Malacara, “Null tests using compensators,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 427–454.
  3. D. G. Bruns, “Null test for hyperbolic convex mirrors,” Appl. Opt. 22, 12–13 (1983).
    [CrossRef] [PubMed]
  4. G. N. Lawrence, R. D. Day, “Interferometric characterization of full spheres: data reduction techniques,” Appl. Opt. 26, 4875–4882 (1987).
    [CrossRef] [PubMed]
  5. It can be shown, within the paraxial approximation, that the shape of an object imaged onto a plane surface corresponds to an elongated ellipsoid. Although this shape is difficult to build, a cylinder can reasonably approximate it. See I. E. Funes-Maderey, “Videoqueratometría de campo plano” (“Flat field videokeratometry”), B.A. thesis, (Universidad Nacional Autónoma de México, México, 1998).
  6. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Appendix 1: An Optical Surface and Its Characteristics.
  7. R. Díaz-Uribe, A. Cornejo-Rodriguez, J. Pedraza-Contreras, O. Cardona-Nunez, A. Cordero-Davila, “Profile measurement of a conic surface, using a He–Ne laser and a nodal bench,” Appl. Opt. 24, 2612–2615 (1985).
    [CrossRef]
  8. R. Díaz-Uribe, J. Pedraza-Contreras, O. Cardona-Nunez, A. Cordero-Davila, A. Cornejo-Rodriguez, “Cylindrical lenses: testing and radius of curvature measurement,” Appl. Opt. 25, 1707–1709 (1986).
    [CrossRef] [PubMed]
  9. R. Díaz-Uribe has prepared a paper titled “Medium-precision null-screen testing of off-axis parabolic mirrors for segmented primary telescope optics: the Large Millimetric Telescope,” Appl. Opt. 39, 2790–2804 (2000).

2000

1987

1986

1985

1983

Bruns, D. G.

Cardona-Nunez, O.

Cordero-Davila, A.

Cornejo-Rodriguez, A.

Day, R. D.

Díaz-Uribe, R.

Funes-Maderey, I. E.

It can be shown, within the paraxial approximation, that the shape of an object imaged onto a plane surface corresponds to an elongated ellipsoid. Although this shape is difficult to build, a cylinder can reasonably approximate it. See I. E. Funes-Maderey, “Videoqueratometría de campo plano” (“Flat field videokeratometry”), B.A. thesis, (Universidad Nacional Autónoma de México, México, 1998).

Ghozeil, E.

E. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

Lawrence, G. N.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Appendix 1: An Optical Surface and Its Characteristics.

A. Offner, D. Malacara, “Null tests using compensators,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 427–454.

Offner, A.

A. Offner, D. Malacara, “Null tests using compensators,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 427–454.

Pedraza-Contreras, J.

Appl. Opt.

Other

E. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

A. Offner, D. Malacara, “Null tests using compensators,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 427–454.

It can be shown, within the paraxial approximation, that the shape of an object imaged onto a plane surface corresponds to an elongated ellipsoid. Although this shape is difficult to build, a cylinder can reasonably approximate it. See I. E. Funes-Maderey, “Videoqueratometría de campo plano” (“Flat field videokeratometry”), B.A. thesis, (Universidad Nacional Autónoma de México, México, 1998).

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), Appendix 1: An Optical Surface and Its Characteristics.

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Figures (7)

Fig. 1
Fig. 1

Layout of the testing configuration.

Fig. 2
Fig. 2

Variables involved in the calculation of the null screen. The lens in front of the stop is not included to keep the drawing simple.

Fig. 4
Fig. 4

(a) Flat-printed screen (plane) for use in the testing of the hemisphere (distances in millimeters). (b) The screen after it is inserted into an acrylic cylinder. (c) The resultant image of the screen after reflection on the test surface. Note that the corners of the square image almost reach the edge of the hemisphere. (d) The screen image when the surface is decentered (i.e., laterally displaced along the x axis). (e) The screen image for a defocused surface that is further away from the surface than the design distance b. (f) The screen image for a defocused surface that is closer to the surface that the design distance b.

Fig. 5
Fig. 5

(a) Flat-printed screen (plane) for the testing of the parabolic surface (distances in millimeters). (b) The same screen inserted into an acrylic cylinder (the largest one). The small cylinder with the screen for testing the hemisphere is in the foreground between two other cylinders. (c) The resultant image of the screen after reflection on the parabolic surface. In this case the fastening ring blocks the corners of the square image. (d) Image of the screen for a combination of x and y decentering. (e) Image of the screen for defocusing closer to the surface than the design distance b. (f) Image of the screen for defocusing further away from the surface than the design distance b.

Fig. 6
Fig. 6

Numerically simulated image of the screen when the hemisphere is slightly deformed into an ellipsoidal surface by a change in the conic constant from k = 0 to k = -0.06. The departure from a perfect square grid is clearly evident. Smaller changes in the value of k may not yield such evident changes in the image.

Fig. 7
Fig. 7

Departures in the distance ΔP [see Eq. (7)] of the grid image points from a perfect square grid as functions of the conic constant k. The rms, the maximum, and the minimum values are shown. Data for the hemisphere are shown.

Tables (2)

Tables Icon

Table 1 Design Parameters for the Null Screen to Test the Hemisphere (Surface 1)

Tables Icon

Table 2 Design Parameters for the Null Screen to Test the Parabolic Surface (Surface 2)

Equations (11)

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z=cs21+1-k+1c2s21/2,
ξ=abQ+r-a2r2-ρ2bbQ+2r1/2a2Q+ρ2 ρ,
z2=ξρ a-b,
ρ3=R,
z3=aξ2+aQz2-r2-2Qz2-rρξ+aQz2-ar-ρξ2-ρQz2-r2+2ξρξ+aQz2-ar×-R+ξ+z2,
b=aD2 d-β,
β=D28rfor Q=0rQ1-1-QD24r21/2for Q0.
D=8 rad2+2a21/2
ρ=n2+m21/2l,  tan ϕ=mn
X=Rϕ,  Y=z3ρ,
ΔP=x-x2+y-y21/2.

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