Abstract

An interferometer with a Fresnel zone plate located in the center of curvature of a concave mirror was studied. Attention was paid to the unique features of the interference field, which has a special point at which the path difference is equal to zero, thereby allowing for the observation of Newton-type fringes in white and quasi-monochromatic light. The conditions necessary for reducing the instrumental error to values less than λ/20 were determined. Methods for suppressing noise and destructive interference patterns were also found. Metrological tests were carried out, and they proved the possibility of using this interferometer for industrial testing of spherical and parabolic mirrors.

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References

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    [CrossRef]
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    [CrossRef]
  5. A. W. Lohmann, "An interferometer with a zone plate as beam-splitter," Opt. Acta 32, 1465-1462 (1985).
    [CrossRef]
  6. T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
    [CrossRef]
  7. A. G. Poleshchuk, E. G. Churin, and A. E. Matochkin, "Common pass interferometer with off-axis computer generated hologram," in Diffractive Optics 2001, Vol. 30 of EOS Topical Meeting Digest Series (European Optical Society, 2001), pp. 60-61.
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    [CrossRef] [PubMed]
  9. V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
    [CrossRef]
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  16. G. A. Lenkova, "Special features of intensity distribution in diffraction spectrum of amplitude-phase gratings," Optoelectron. Instrum. Data Proc. 5, 14-26 (1992).
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    [CrossRef]
  19. G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. I. Interference in imaginary plates," Opt. Spektrosk. 22, 800-809 (1967; in Russian).
  20. G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. II. Practical circuits," Opt. Spektrosk. 23, 312-317 (1967; in Russian).

2003 (1)

V. P. Koronkevich and G. A. Lenkova, "Instrumental error of diffraction interferometers," Optoelectron. Instrum. Data Proc. 39, 23-33 (2003).

2002 (1)

V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
[CrossRef]

1998 (1)

V. P. Koronkevich, V. P. Korolkov, and A. G. Poleshchuk, "Laser technologies in diffractive optics," Optoelectron. Instrum. Data Proc. 6, 5-21 (1998).

1995 (2)

G. A. Lenkova, "The effect of phase profile depth on intensity distribution in diffraction orders of a bifocal element," Optoelectron. Instrum. Data Proc. 5, 15-22 (1995).

T. Nomura, K. Kamiya, H. Miyashiro, K. Yoshikawa, and H. Tashiro, "Method to obtain a clear fringe pattern with a zone-plate interferometer," Appl. Opt. 34, 2187-2193 (1995).
[CrossRef] [PubMed]

1992 (2)

G. A. Lenkova, "Special features of intensity distribution in diffraction spectrum of amplitude-phase gratings," Optoelectron. Instrum. Data Proc. 5, 14-26 (1992).

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

1989 (1)

J. Huand, N. Ohyama, and T. Honda, "A null test of conic surfaces in zone plate interferometer," Opt. Commun. 72, 17-21 (1989).
[CrossRef]

1985 (1)

A. W. Lohmann, "An interferometer with a zone plate as beam-splitter," Opt. Acta 32, 1465-1462 (1985).
[CrossRef]

1976 (1)

Yu. V. Kolomijtsev, "Interferometers" (Mashinostroenie , Moscow, 1976), in Russian.

1974 (1)

1972 (2)

1967 (2)

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. I. Interference in imaginary plates," Opt. Spektrosk. 22, 800-809 (1967; in Russian).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. II. Practical circuits," Opt. Spektrosk. 23, 312-317 (1967; in Russian).

1960 (1)

1952 (1)

A. N. Zakharyevskii, "Interferometers" (GIOM , Moscow, 1952), in Russian.

Churin, E. G.

A. G. Poleshchuk, E. G. Churin, and A. E. Matochkin, "Common pass interferometer with off-axis computer generated hologram," in Diffractive Optics 2001, Vol. 30 of EOS Topical Meeting Digest Series (European Optical Society, 2001), pp. 60-61.

Guan, H.

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

Hariharan, P.

Honda, T.

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

J. Huand, N. Ohyama, and T. Honda, "A null test of conic surfaces in zone plate interferometer," Opt. Commun. 72, 17-21 (1989).
[CrossRef]

Huand, J.

J. Huand, N. Ohyama, and T. Honda, "A null test of conic surfaces in zone plate interferometer," Opt. Commun. 72, 17-21 (1989).
[CrossRef]

Ichioka, Y.

Kamiya, K.

Kawamoto, Y.

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

Kolomijtsev, Yu. V.

Yu. V. Kolomijtsev, "Interferometers" (Mashinostroenie , Moscow, 1976), in Russian.

Korolkov, V. P.

V. P. Koronkevich, V. P. Korolkov, and A. G. Poleshchuk, "Laser technologies in diffractive optics," Optoelectron. Instrum. Data Proc. 6, 5-21 (1998).

Koronkevich, V. P.

V. P. Koronkevich and G. A. Lenkova, "Instrumental error of diffraction interferometers," Optoelectron. Instrum. Data Proc. 39, 23-33 (2003).

V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
[CrossRef]

V. P. Koronkevich, V. P. Korolkov, and A. G. Poleshchuk, "Laser technologies in diffractive optics," Optoelectron. Instrum. Data Proc. 6, 5-21 (1998).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. I. Interference in imaginary plates," Opt. Spektrosk. 22, 800-809 (1967; in Russian).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. II. Practical circuits," Opt. Spektrosk. 23, 312-317 (1967; in Russian).

Lenkova, G. A.

V. P. Koronkevich and G. A. Lenkova, "Instrumental error of diffraction interferometers," Optoelectron. Instrum. Data Proc. 39, 23-33 (2003).

V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
[CrossRef]

G. A. Lenkova, "The effect of phase profile depth on intensity distribution in diffraction orders of a bifocal element," Optoelectron. Instrum. Data Proc. 5, 15-22 (1995).

G. A. Lenkova, "Special features of intensity distribution in diffraction spectrum of amplitude-phase gratings," Optoelectron. Instrum. Data Proc. 5, 14-26 (1992).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. II. Practical circuits," Opt. Spektrosk. 23, 312-317 (1967; in Russian).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. I. Interference in imaginary plates," Opt. Spektrosk. 22, 800-809 (1967; in Russian).

Lohmann, A. W.

Maksutov, D. D.

D. D. Maksutov, "Optics in astronomy" (Nauka , Leningrad, 1979), in Russian.

Malacara, D.

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

Matochkin, A. E.

V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
[CrossRef]

A. G. Poleshchuk, E. G. Churin, and A. E. Matochkin, "Common pass interferometer with off-axis computer generated hologram," in Diffractive Optics 2001, Vol. 30 of EOS Topical Meeting Digest Series (European Optical Society, 2001), pp. 60-61.

Miyashiro, H.

Nomura, T.

Ohyama, N.

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

J. Huand, N. Ohyama, and T. Honda, "A null test of conic surfaces in zone plate interferometer," Opt. Commun. 72, 17-21 (1989).
[CrossRef]

Poleshchuk, A. G.

V. P. Koronkevich, V. P. Korolkov, and A. G. Poleshchuk, "Laser technologies in diffractive optics," Optoelectron. Instrum. Data Proc. 6, 5-21 (1998).

A. G. Poleshchuk, E. G. Churin, and A. E. Matochkin, "Common pass interferometer with off-axis computer generated hologram," in Diffractive Optics 2001, Vol. 30 of EOS Topical Meeting Digest Series (European Optical Society, 2001), pp. 60-61.

Sen, D.

Smart, R. N.

Tashiro, H.

Yamaguchi, M.

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

Yoshikawa, K.

Young, M.

Zakharyevskii, A. N.

A. N. Zakharyevskii, "Interferometers" (GIOM , Moscow, 1952), in Russian.

Appl. Opt. (3)

GIOM (1)

A. N. Zakharyevskii, "Interferometers" (GIOM , Moscow, 1952), in Russian.

J. Opt. Soc. Am. (2)

Mashinostroenie (1)

Yu. V. Kolomijtsev, "Interferometers" (Mashinostroenie , Moscow, 1976), in Russian.

Nauka (1)

D. D. Maksutov, "Optics in astronomy" (Nauka , Leningrad, 1979), in Russian.

Opt. Acta (1)

A. W. Lohmann, "An interferometer with a zone plate as beam-splitter," Opt. Acta 32, 1465-1462 (1985).
[CrossRef]

Opt. Commun. (1)

J. Huand, N. Ohyama, and T. Honda, "A null test of conic surfaces in zone plate interferometer," Opt. Commun. 72, 17-21 (1989).
[CrossRef]

Opt. Spektrosk. (2)

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. I. Interference in imaginary plates," Opt. Spektrosk. 22, 800-809 (1967; in Russian).

G. A. Lenkova and V. P. Koronkevich, "Interferometers with double beam transmission. II. Practical circuits," Opt. Spektrosk. 23, 312-317 (1967; in Russian).

Optoelectron. Instrum. Data Proc. (4)

V. P. Koronkevich and G. A. Lenkova, "Instrumental error of diffraction interferometers," Optoelectron. Instrum. Data Proc. 39, 23-33 (2003).

V. P. Koronkevich, V. P. Korolkov, and A. G. Poleshchuk, "Laser technologies in diffractive optics," Optoelectron. Instrum. Data Proc. 6, 5-21 (1998).

G. A. Lenkova, "Special features of intensity distribution in diffraction spectrum of amplitude-phase gratings," Optoelectron. Instrum. Data Proc. 5, 14-26 (1992).

G. A. Lenkova, "The effect of phase profile depth on intensity distribution in diffraction orders of a bifocal element," Optoelectron. Instrum. Data Proc. 5, 15-22 (1995).

Proc. SPIE (2)

V. P. Koronkevich, G. A. Lenkova, and A. E. Matochkin, "Zone plate interferometer for testing the spherical surfaces," Proc. SPIE 4900, 654-658 (2002).
[CrossRef]

T. Honda, Y. Kawamoto, H. Guan, M. Yamaguchi, and N. Ohyama, "Zone-plate null interferometer for measuring aspherical mirror with large aperture," Proc. SPIE 1720, 305-310 (1992).
[CrossRef]

Other (2)

A. G. Poleshchuk, E. G. Churin, and A. E. Matochkin, "Common pass interferometer with off-axis computer generated hologram," in Diffractive Optics 2001, Vol. 30 of EOS Topical Meeting Digest Series (European Optical Society, 2001), pp. 60-61.

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

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Figures (10)

Fig. 1
Fig. 1

Optical scheme of the diffraction interferometer: 6, entrance pupil; A 1 , A 2 , intermediate exit pupils; [ 0 , + 1 ] , exit pupils [ 0 , + 1 ] and [ + 1 , 0 ] . See text for further details.

Fig. 2
Fig. 2

Interference field at the interferometer output near the diaphragm [see (3) in Fig. 1].

Fig. 3
Fig. 3

Cross sections of the field in the plane of the exit pupils: (a)–(c), bright spots at the center are exit pupils of operating fringes [ 0 , + 1 ] + [ + 1 , 0 ] ; (d)–(f) operating fringes on the pupils (at the center of the field) and fringes [ + 1 , - 1 ] + [ - 1 , + 1 ] (background).

Fig. 4
Fig. 4

Interference field in the plane of the exit port: (a)–(c), spherical mirror ( ( R = 350.718 mm ; diameter, 64 mm ); (d)–(f), parabolic mirror ( R = 1499.7 mm ; diameter, 150 mm ).

Fig. 5
Fig. 5

Interferograms obtained with a semiconductor laser ( λ = 650 nm ) for a mirror with R = 781.3 mm , D = 120 mm , (a) f = 50 mm , (b) f = 25 mm .

Fig. 6
Fig. 6

Results of the parabola testing ( R = 1499.7 mm , D = 150 mm ) : 1, calculated curve describing the deviation of the ideal parabolic surface from the nearest sphere; 2, curve built on the results obtained with the diffraction interferometer; 3, curve corresponding to aberrations of the tested surface. See text for discussion of points 4 and 5.

Fig. 7
Fig. 7

Interferograms recorded by the Zygo device (a), (c) (e) and by the diffraction interferometer (b), (d), (f). (a)–(d) spherical surface; (e), (f), parabolic surface.

Fig. 8
Fig. 8

(a) Three-beam and (b) two-beam interference bands observed by using the modified scheme of the diffraction interferometer.

Fig. 9
Fig. 9

Optical scheme of the diffraction interferometer used for testing mirrors with central apertures. See text for further details.

Fig. 10
Fig. 10

Interferograms produced by (a), (b) the diffraction interferometer and (c) the Zygo interferometer.

Equations (10)

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S 2 = f R / ( R + f ) ,
S 3 = f R / ( R - f ) ,
r n 2 = f n λ + ( n λ ) 2 / 4 ,
k = - e 2 .
δ m = - u 4 { [ 1 / R ( R - S 2 ) ] [ 1 / 2 R - 1 / 4 ( R - S 2 ) ] - ( 1 + k ) / 4 R 3 } ,
δ m = ( u 4 / 4 R 3 ) [ k + ( f / R ) 2 ] .
δ p = ( 3 u 4 / 4 R 3 ) ( f / R ) 2 .
δ = δ m + δ p = ( u 4 / 4 R 3 ) [ k + 4 ( f / R ) 2 ] .
δ 0 = - ( u 2 / 8 R 3 ) [ k + 4 ( f / R ) 2 ] ( H 2 - u 2 ) .
h = 2.008 λ / [ 2 π ( n - 1 ) ] ,

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