Abstract

We present simulated results on piston detection applying the classical Ronchi test to a segmented surface. We have found that a piston error in a test segment, induces a change in the transversal aberration, that can be analyzed by mutually comparing the fringes frequency in each segment. We propose that the piston term of the segmented surface can be recovered by geometrically relating the change in transversal aberration with the piston term. To test this, we have simulated some ronchigrams for a known piston error, and we have been able to recover this term for a dynamic range comprised among 57nm and 550 µm. For piston errors >550µm a change in the transversal aberration can be appreciated and measured in the ronchigrams although these large pistons are now classical defocusings. Thus we have demonstrated that the Ronchi test can be an alternative method for the piston detection with a large dynamic range.

© 2004 Optical Society of America

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References

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  2. V. Orlov, ???Co-phasing of segmented Mirror telescopes,??? (Large Ground based telescopes projects and instrumentation, Workshop, Leiden 2000), pp. 391-396.
  3. V. Voitsekhovich S. Bara and V.G. Orlov, ???Co-phasing of segmented telescopes: A new approach to piston measurements,??? A & A, 382, 746-751, (2002).
  4. Weiyao Zou, ???New phasing algorithm for large segmented telescope mirrors,??? Opt. Eng. 41, 2338-2344,(2002).
    [CrossRef]
  5. Achim Shumacher, Nicholas Devaney and Luzuma Montoya, ???Phasing segmented mirrors: a modification of the Keck narrow-band technique and its application to extremely large telescopes,??? Appl. Opt. 41, 1297-1307, (2002).
    [CrossRef]
  6. R. Díaz-Uribe, A. Jiménez-Hernádez, ???Phased measurement for segmented optics with 1D diffraction patterns,??? Opt. Express 12, 1192-1204, (2004), <a href="http:/www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1192">http:/www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1192</a>
    [CrossRef] [PubMed]
  7. G. Chanan M. Troy and E. Sirko, ???Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared,??? Appl. Opt. 38, 704-713, (1999).
    [CrossRef]
  8. G. Chanan M. Troy F. Dekens S. Michaels J. Nelson T. Mast D. Kirkman, ???Phasing the mirror segments of the Keck Telescopes: the broadband phasing algorithm,??? Appl. Opt. 37, 140-155, (1998).
    [CrossRef]
  9. G. Chanan C. Ohara M. Troy, ???Phasing the mirror segments of the Keck Telescopes II: the narrow-band phasing algorithm,??? Appl. Opt. 37, 140-155, (2000).
    [CrossRef]
  10. J. Salinas, E. Luna, L. Salas, A. Cornejo, I. Cruz and V. Garcia, ???The Classical Ronchi test for piston detection,??? in Large Ground, Based Telescopes, Jacobus M. Oschmann, Larry M. Stepp, eds., Proc. SPIE 4837, 758-763 (2003).
  11. J. Salinas-Luna,???Cofaseo de una superficie segmentada,??? PHD thesis, INAOE, Puebla, México, (2002).
  12. Javier Salinas-Luna, Esteban Luna-Aguilar & Alejandro Cornejo-Rodríguez, ???Detección de pistón por polarimetría,??? Rev. Mex. de Fís. (to be published).
  13. D. Malacara, Optical Shop testing, ???Ronchi test,??? (Academic Press 1992), Chap 9.
  14. J.Bai, Shangyi Cheng Guoguang Yang , ???Phase Alignment of segmented mirrors using a digital wavefront interferometer,??? Opt. Eng. 36, 2355-2357 (1997).
    [CrossRef]
  15. Hecht-Zajac, OPTICA, ??ptica geométrica, teoría paraxial, (Addison Wensley Longman, 1998).
  16. H.H. Hopkins, Wave Theory of Aberrations, Wave and Ray Aberrations, (the Clarendon Press, 1950).
  17. Edward L. O??? Neill, Introduction to Statistical Optics, The Geometrical theory of aberrations, (Dover Publications, 1992).
  18. E. Luna, S. Zazueta and L. Gutiérrez, ???An innovative method for the alignment of astronomical telescopes,??? PASP, 113:379-384, (2001).
    [CrossRef]
  19. IAUNAM, OAN , Apdo. Postal 877, Ensenada B. C. México, c.p. 22830 and Javier Salinas-Luna et al. are preparing a manuscript to be called ???The classical Ronchi test for piston detection:experimental part.???

A & A (1)

V. Voitsekhovich S. Bara and V.G. Orlov, ???Co-phasing of segmented telescopes: A new approach to piston measurements,??? A & A, 382, 746-751, (2002).

Appl. Opt. (4)

Opt. Eng. (2)

J.Bai, Shangyi Cheng Guoguang Yang , ???Phase Alignment of segmented mirrors using a digital wavefront interferometer,??? Opt. Eng. 36, 2355-2357 (1997).
[CrossRef]

Weiyao Zou, ???New phasing algorithm for large segmented telescope mirrors,??? Opt. Eng. 41, 2338-2344,(2002).
[CrossRef]

Opt. Express (1)

PASP (1)

E. Luna, S. Zazueta and L. Gutiérrez, ???An innovative method for the alignment of astronomical telescopes,??? PASP, 113:379-384, (2001).
[CrossRef]

Proc. SPIE (1)

J. Salinas, E. Luna, L. Salas, A. Cornejo, I. Cruz and V. Garcia, ???The Classical Ronchi test for piston detection,??? in Large Ground, Based Telescopes, Jacobus M. Oschmann, Larry M. Stepp, eds., Proc. SPIE 4837, 758-763 (2003).

Rev. Mex. de Fís. (1)

Javier Salinas-Luna, Esteban Luna-Aguilar & Alejandro Cornejo-Rodríguez, ???Detección de pistón por polarimetría,??? Rev. Mex. de Fís. (to be published).

Other (8)

D. Malacara, Optical Shop testing, ???Ronchi test,??? (Academic Press 1992), Chap 9.

Hecht-Zajac, OPTICA, ??ptica geométrica, teoría paraxial, (Addison Wensley Longman, 1998).

H.H. Hopkins, Wave Theory of Aberrations, Wave and Ray Aberrations, (the Clarendon Press, 1950).

Edward L. O??? Neill, Introduction to Statistical Optics, The Geometrical theory of aberrations, (Dover Publications, 1992).

J. Salinas-Luna,???Cofaseo de una superficie segmentada,??? PHD thesis, INAOE, Puebla, México, (2002).

D.J. Shroeder, Astronomical Optics, Multiple-Aperture telescopes (Academic Press, 1987).

V. Orlov, ???Co-phasing of segmented Mirror telescopes,??? (Large Ground based telescopes projects and instrumentation, Workshop, Leiden 2000), pp. 391-396.

IAUNAM, OAN , Apdo. Postal 877, Ensenada B. C. México, c.p. 22830 and Javier Salinas-Luna et al. are preparing a manuscript to be called ???The classical Ronchi test for piston detection:experimental part.???

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Figures (10)

Fig. 1.
Fig. 1.

Geometrical relationship between the transversal aberration TA(x), and the piston term δf , for a meridional view.

Fig. 2.
Fig. 2.

Some examples of center of fringes loci of ronchigrams for spherical segmented surfaces when, a) the source is off-axis in the -x direction (perpendicular to fringes) farther larger than 3.0 cm, to show better this effect, 9 fringes are observed, b) the source is off-axis in the +y direction 8 λ (parallel to fringes), as can be seen the ronchigram has diminished its frequency, of 9 to 7 bright fringes, c) the ronchigram has a combination of the two off-axis positions of the source mentioned. In all cases the piston term is maintained in 10 λ.

Fig. 3.
Fig. 3.

Center of fringes loci in the ronchigrams of a) an ellipse rotated about its major axis, with conic constant K=-0.5, b) an ellipse rotated about its minor axis, k=1 and c)a hyperboloid, K=-1.5, d) a parabolic segmented mirror(k=-1), with a segment center off-axis 20 mm (20000 µm), e) a parabolic segmented primary mirror. In this ronchigram the curved fringes means that the spherical aberration is present, f) for a segmented surface with a parabolic segment and spherical segment. This is an example in which is not possible to correct the piston term by the sphericity presence in one of the segments, g) a ideal spherical segmented surface, h) a spherical segmented surface with random noise of 30%. The ronchigram is very degraded by air turbulence. In all cases a Ronchi ruling of 500 lines per inch was used, the piston term is maintained in 30 λ and the source position was placed close to curvature radius.

Fig. 4.
Fig. 4.

Ronchigrams comparison for, a) a monolithic mirror and b) a segmented surface with piston error.

Fig. 5.
Fig. 5.

Ronchigrams to show that the addition of a constant sagitta generates different piston errors in a segmented surface of 30 λ for the wavelength of a) 414 nm (blue color of argon laser), b) 532 nm (green color of a diode laser), c) 632.8 nm (red color of He-Ne laser) and d) 1.2 µm, and for a piston error of e) 30 λ in z direction and f)-30 λ in -z direction. All this cases from the point of view of geometric optics.

Fig. 6.
Fig. 6.

Detection Range for a ruling of 500 lines per inch. a) Minimum piston error detected of 0.09λ (≈57nm), b) the maximum change in frequency detected was for a piston term of 550 µm, and c) ronchigram with high change in frequency in the test segment of the order of 2 millimeters(≈2000 µm) in the vertex plane of the surface. In the image plane this term does not piston, it is now a defocusing.

Fig. 7.
Fig. 7.

Ronchigrams of the central maximums in different cases of piston for a reference wavelength, (λ) of 632.8 nm, and without diffraction effects. a1) 550 µm, 7 fringes a2) 550 µm, 3 fringes, b1) 100 λ, 7 fringes b2)100 λ, 3 fringes c1)50 λ, 7 fringes c2) 50 λ, 3 fringes and d1) 40 λ, 7 fringes d2)40 λ, 3 fringes.

Fig. 8.
Fig. 8.

e1) 30 λ, 7 fringes e2) 30 λ, 3 fringes, f1) 20 λ, 7 fringes f2)20 λ, 3 fringes g1)10 λ, 7 fringes g2) 10 λ, 3 fringes and h1) λ, 7 fringes h2) λ, 3 fringes.

Fig. 9.
Fig. 9.

i1) 0.5 λ, 7 fringes i2) 0.5 λ, 3 fringes, j1) 0.4 λ, 7 fringes j2) 0.4 λ, 3 fringes k1) 0.3 λ, 7 fringes k2) 0.3 λ, 3 fringes and l1) 0.2 λ, 7 fringes l2) 0.2 λ, 3 fringes.

Fig. 10.
Fig. 10.

m1) 0.1 λ, 7 fringes m2) 0.1 λ, 3 fringes, n1) 0.09 λ, 7 fringes n2) 0.09 λ, 3 fringes o1) ideal co-phasing, 7 fringes o2) ideal co-phasing, 3 fringes.

Tables (3)

Tables Icon

Table 1. The R R + 2 δ f factor as a function of the piston displacement.

Tables Icon

Table 2. The G constant behavior for the center of fringes loci for a segmented surface ronchigram 7 bright fringes, the piston term was 10 λ (λ=632.8nm). The G constant is the same in each central maximum of the fringes on the surface.

Tables Icon

Table 3. Results for ideal piston detection with the classical Ronchi test by means center of fringes loci in ronchigrams with a Ronchi ruling of 500 and 1000 lines per inch in 7 bright fringes and with random noise of 10%. T 1 are the coordinates of the +1 order(fringe) and are maintained without change for reference. The coordinates of T 2 are varying until they equal T 1.

Equations (23)

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1 s o + 1 s i = 2 R .
1 s o + 1 s i = 2 R ,
s o = R + δ f ,
s i = R ( R + δ f ) R + 2 δ f .
R R + 2 δ f 1 .
W ( x , y ) = A ( x 2 + y 2 ) 2 + By ( x 2 + y 2 ) + C ( x 2 + 3 y 2 ) + D ( x 2 + y 2 ) ;
W ( x , y ) = TA ( S ) R ;
W x = 2 Dx .
T 1 = R W x = 2 RDx .
x R = T 1 Δ F .
T 1 = x Δ F R .
D = Δ F 2 R 2 ,
x R = 1 2 T 1 Δ F .
T 1 = 2 x Δ F R .
x R = 1 2 T 2 Δ F + δ f ,
T 2 = 2 x ( Δ F + δ f ) R .
Δ T = 2 δ f x R ,
δ f = R 2 Δ T x .
G = Δ T x ,
δ f = R 2 G .
ESC = f T 2 .
f = 25.4 mm NLP ,
δ f = R 2 Δ T ( ESC ) T 1

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