Abstract

We observe a non-complementary dark-space produced when two Ronchi-grams, at zero-phase and π -phase, are overlapped and use these dark spaces to quantify Ronchi-grams. Diffraction and multiple beam interference effects narrow the Ronchi fringes created with a coherent point source illumination and prevent accurate determination of the geometrical fringe edges. The dark spaces created when the intensity of two Ronchi grams is added allow assessing the geometrical edge at the dark space middle providing a way to reduce measurement errors. We re-construct the wavefront deformation in a test beam with a 35-term Zernike polynomial. Experimental results are presented.

© 2009 Optical Society of America

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References

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  1. V. Ronchi, "Forty Years of History of a Grating Interferometer," Appl. Opt. 3, 437-451 (1964).
    [CrossRef]
  2. T. Yatagai, "Fringe scanning Ronchi test for aspherical surfaces," Appl. Opt. 23, 3676-3679 (1984).
    [CrossRef] [PubMed]
  3. J. Castro-Ramos, and J. Sasian, "Automatic phase shifting Ronchi tester with a square Ronchi ruling," Proc. SPIE 5532, 199-210 (2004).
    [CrossRef]
  4. There are many different versions, but we adopted one. J. C. Wyant and K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, XI, (Academic Press, Inc.1992).
  5. ZEMAX Optical Design Program, ZEMAX Development Corporation, www.zemax.com.

2004

J. Castro-Ramos, and J. Sasian, "Automatic phase shifting Ronchi tester with a square Ronchi ruling," Proc. SPIE 5532, 199-210 (2004).
[CrossRef]

1984

1964

Castro-Ramos, J.

J. Castro-Ramos, and J. Sasian, "Automatic phase shifting Ronchi tester with a square Ronchi ruling," Proc. SPIE 5532, 199-210 (2004).
[CrossRef]

Ronchi, V.

Sasian, J.

J. Castro-Ramos, and J. Sasian, "Automatic phase shifting Ronchi tester with a square Ronchi ruling," Proc. SPIE 5532, 199-210 (2004).
[CrossRef]

Yatagai, T.

Appl. Opt.

Proc. SPIE

J. Castro-Ramos, and J. Sasian, "Automatic phase shifting Ronchi tester with a square Ronchi ruling," Proc. SPIE 5532, 199-210 (2004).
[CrossRef]

Other

There are many different versions, but we adopted one. J. C. Wyant and K. Creath, "Basic Wavefront Aberration Theory for Optical Metrology," in Applied Optics and Optical Engineering, XI, (Academic Press, Inc.1992).

ZEMAX Optical Design Program, ZEMAX Development Corporation, www.zemax.com.

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Figures (2)

Fig. 1.
Fig. 1.

Ronchi-grams with (a) 0-phase and (b) π-phase. (c) Combined image of Ronchi-grams (a) and (b).

Fig. 2.
Fig. 2.

Ronchi test setup for measuring transverse ray aberrations in a beam.

Tables (1)

Tables Icon

Table 1. Best fit Zernike coefficients for spherical aberration for several grating positions Z along the optical axis. The coefficients are in unit of wavelengths. a 3: focus, a 8: primary spherical aberration, and a 15, a 24, a 35: higher order spherical aberrations.

Equations (9)

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TRA = 2 m ± 1 4 p
ε ( i ) x = 2 F / # k = 1 35 a k Z ( i ) k x
ε ( i ) y = 2 F / # k = 1 35 a k Z ( i ) k y
χ = i = 1 N x ( ε ( i ) x , exp ε ( i ) x , thry ) 2 + i = 1 N y ( ε ( i ) y , exp ε ( i ) y , thry ) 2
A ZZ T = 1 2 F / # E Z T
A = ( a 1 a 2 a 35 ) ,
E = ( ε x ( 1 ) ε x ( 2 ) ε x ( N x ) ε y ( 1 ) ε y ( 2 ) ε y ( N y ) ) ,
Z = ( Z ( 1 ) 1 x Z ( 2 ) 1 x Z ( N x ) 1 x Z ( 1 ) 1 y Z ( 2 ) 1 y Z ( N y ) 1 y Z ( 1 ) 2 x Z ( 2 ) 2 x Z ( N x ) 2 x Z ( 1 ) 2 y Z ( 2 ) 2 y Z ( N y ) 2 y Z ( 1 ) 34 x Z ( 2 ) 34 x Z ( N x ) 34 x Z ( 1 ) 34 y Z ( 2 ) 34 y Z ( N y ) 34 x Z ( 1 ) 35 x Z ( 2 ) 35 x Z ( N x ) 35 x Z ( 1 ) 35 y Z ( 2 ) 35 y Z ( N y ) 35 y )
A = 1 2 F / # E Z T ( Z Z T ) 1

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