Abstract

To fully interpret the Ronchigram, a good automatic phase reduction algorithm is necessary. A new phase reduction algorithm, originally designed for interferometry test of large optics, is presented for the Ronchi test. Due to the common path property, only two Ronchigrams shifted by π/2 are necessary for the reproducing phase. Accuracy can be better than one-thirtieth of the grating space. Methods are suggested for finding spherical aberration and astigmatism without integrating the phase using the Ronchi test. Tests of results using the new algorithm show good agreement with typical interferometry tests.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Yatagi, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt. 23, 3676–3679 (1984).
    [CrossRef]
  2. K. Omura, T. Yatagi, “Phase Measuring Ronchi Test,” Appl. Opt. 27, 523–528 (1988).
    [CrossRef] [PubMed]
  3. R. Angel, D. Wan, “A New Algorithm for Rapid Automatic Reduction of Test Interferograms,” Workshop on Optical Fabrication and Testing (Optical Society of America, Seattle, 1986).
  4. Der-Shen Wan, “Optics for Large Telescope,” Ph.D. Dissertation, University of Arizona (1987).
  5. R. Angel, private communication (1987).
  6. S. Toyooka, M. Tominaga, “Spatial Fringe Scanning for Optical Phase Measurement,” Optics Commun. 51, 68–70 (1984).
    [CrossRef]
  7. A. Cornejo-Rodriguez, in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978), pp. 311–314.
  8. J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), p. 60.

1988 (1)

1984 (2)

S. Toyooka, M. Tominaga, “Spatial Fringe Scanning for Optical Phase Measurement,” Optics Commun. 51, 68–70 (1984).
[CrossRef]

T. Yatagi, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt. 23, 3676–3679 (1984).
[CrossRef]

Angel, R.

R. Angel, D. Wan, “A New Algorithm for Rapid Automatic Reduction of Test Interferograms,” Workshop on Optical Fabrication and Testing (Optical Society of America, Seattle, 1986).

R. Angel, private communication (1987).

Cornejo-Rodriguez, A.

A. Cornejo-Rodriguez, in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978), pp. 311–314.

Gaskill, J.

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), p. 60.

Omura, K.

Tominaga, M.

S. Toyooka, M. Tominaga, “Spatial Fringe Scanning for Optical Phase Measurement,” Optics Commun. 51, 68–70 (1984).
[CrossRef]

Toyooka, S.

S. Toyooka, M. Tominaga, “Spatial Fringe Scanning for Optical Phase Measurement,” Optics Commun. 51, 68–70 (1984).
[CrossRef]

Wan, D.

R. Angel, D. Wan, “A New Algorithm for Rapid Automatic Reduction of Test Interferograms,” Workshop on Optical Fabrication and Testing (Optical Society of America, Seattle, 1986).

Wan, Der-Shen

Der-Shen Wan, “Optics for Large Telescope,” Ph.D. Dissertation, University of Arizona (1987).

Yatagi, T.

Appl. Opt. (2)

Optics Commun. (1)

S. Toyooka, M. Tominaga, “Spatial Fringe Scanning for Optical Phase Measurement,” Optics Commun. 51, 68–70 (1984).
[CrossRef]

Other (5)

A. Cornejo-Rodriguez, in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978), pp. 311–314.

J. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), p. 60.

R. Angel, D. Wan, “A New Algorithm for Rapid Automatic Reduction of Test Interferograms,” Workshop on Optical Fabrication and Testing (Optical Society of America, Seattle, 1986).

Der-Shen Wan, “Optics for Large Telescope,” Ph.D. Dissertation, University of Arizona (1987).

R. Angel, private communication (1987).

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 (32)

Fig. 1
Fig. 1

Illustration of intensity phase conversion, where the solid line represents intensity and the dashed line represents the true phase.

Fig. 2
Fig. 2

Toggling algorithm.

Fig. 3
Fig. 3

Flow chart of the new phase reduction algorithm.

Fig. 4
Fig. 4

Setup for Ronchi test for measuring a concave surface.

Fig. 5
Fig. 5

Fringe visibility vs shear over the wavefront.

Fig. 6
Fig. 6

Ronchigrams with π/2 shifted phase.

Fig. 7
Fig. 7

Normalized Ronchigram.

Fig. 8
Fig. 8

Intensity of a row: dotted–dashed line, original intensity; dashed line, averaged intensity; and solid line, normalized intensity.

Fig. 9
Fig. 9

Reduced phase of one Ronchigram with tilt removed; eight-bit gray level represents 2π (one wave).

Fig. 10
Fig. 10

Phase due to average of two π/2 shifted Ronchigrams, eight bit gray level representing 2π (one wave).

Fig. 11
Fig. 11

Algorithm error shown in Fig. 10, ranging from ± one-thirtieth to ± one-fiftieth of the grating space.

Fig. 12
Fig. 12

Ronchigram of a f/1.8 parabola near the center of vertex curvature.

Fig. 13
Fig. 13

Ronchigrams with ruling moved one mm toward the mirror from the position of Fig. 12.

Fig. 14
Fig. 14

Phase map of the Ronchigram shown in Fig. 13 with tilt removed; eight-bit gray level represents 3.5 waves.

Fig. 15
Fig. 15

Phase of the central row in Fig. 14 showing the transverse spherical aberration.

Fig. 16
Fig. 16

Phase of one column in Fig. 14 (x = −0.62).

Fig. 17
Fig. 17

Phase of central column in Fig. 14 (x = 0).

Fig. 18
Fig. 18

Phase of one column in Fig. 14 (x = 0.62); dashed line shows a fitted quadratic curve.

Fig. 19
Fig. 19

Difference of phase at y = 0.68 and at y = 0 for various columns.

Fig. 20
Fig. 20

Wavefront profile showing difference between a parabola and a sphere; eight-bit gray level represents 19 μm.

Fig. 21
Fig. 21

Departure from a standard parobola of the central row shown in Fig. 20 with some defocus.

Fig. 22
Fig. 22

Departure from a standard parabola of the central row without defocus; solid line represents the results of the Ronchi test and the dashed line represents a interferometry null test fitted by Zernike polynomials to the fourth-order.

Fig. 23
Fig. 23

Setup of a reflective null test.

Fig. 24
Fig. 24

Interferogram of a f/1.8 parabola obtained by null reflective test.

Fig. 25
Fig. 25

Interferogram of a spherical surface obtained from Fizeau interferometer.

Fig. 26
Fig. 26

Ronchigram of the spherical surface with the same orientation as in the interferometry test.

Fig. 27
Fig. 27

Phase of the Ronchigram shown in Fig. 26; eight-bit gray level represents 1.5 waves.

Fig. 28
Fig. 28

Phase of the central column shown in Fig. 27; its slope was used for checking the coefficient of the 2xy term.

Fig. 29
Fig. 29

Ronchigram of the spherical surface rotated by 45°.

Fig. 30
Fig. 30

Phase of the Ronchigram shown in Fig. 29; eight-bit gray level represents 1.5 waves.

Fig. 31
Fig. 31

Phase of the central column shown in Fig. 30; its slope was used for checking the coefficient of the x2y2 term.

Fig. 32
Fig. 32

Phase of the central row shown in Fig. 27; spherical aberration is found by the vertical difference between the phase curve and the dashed line.

Tables (1)

Tables Icon

Table I Zernike Polynomials Fitting of Fig. 25

Equations (8)

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

I ( x , y ) = a ( x , y ) - b ( x , y ) cos [ ϕ ( x , y ) ] ,
E = ϕ - π ( 1 - cos ϕ ) / 2.
E = n = 1 sin ( 2 n ϕ ) / n ( 2 n - 1 ) ( 2 n + 1 ) = sin ( 2 ϕ ) / 3 + sin ( 4 ϕ ) / 30 + sin ( 6 ϕ ) / 105 +
I norm = ( I - I min ) / ( I max - I min ) ,
rect ( x a ) comb ( x d ) * rect ( x 0.5 d ) ,
r h x W ( x , y ) = r h ( W 40 ( 4 x 3 + 4 x y 2 ) + 2 W 20 x ) = n d ,
r h x ( Z 6 2 x y ) 0.6328 / d ,
r h x ( Z 13 6 ( x 2 + y 2 ) 2 ) 0.6328 / d .

Metrics