Abstract

This paper presents a simultaneous multi-segmented mirror orientation test system (SMOTS) using localized sheared images. A CMOS camera captures images of reflected 2D sinusoidal patterns from the test mirrors as their orientation changes. Surface orientation is measured to within 0.8 µrad (0.16 arcseconds) for a flat mirror. In addition, we measure the variation of seven mirror segments simultaneously. Furthermore, SMOTS is applied to measure the orientation of two concave mirrors with an accuracy of 2.7 µrad (0.56 arcseconds). The measurement time for seven segments is 0.07 s. This technique can monitor the mirror segment orientation in an open/closed-loop for various optical setups.

© 2017 Optical Society of America

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References

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2016 (1)

2014 (1)

2013 (1)

J. M. Oschmann, M. Clampin, and H. MacEwen, “Special Section Guest Editorial: Space Telescopes,” Opt. Eng. 52(9), 091801 (2013).
[Crossref]

2012 (2)

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

2010 (1)

2008 (1)

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

2005 (1)

2003 (1)

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

2002 (1)

2001 (1)

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

2000 (1)

J. S. Fender, “Future trends in large space optics,” Proc. SPIE 4013, 682–686 (2000).
[Crossref]

1998 (1)

1997 (3)

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Local Piston Detection of a Segmented Mirror Telescope with Curvature Sensing of Wavefronts Affected by Atmospheric Turbulence. Numerical Simulations,” NATO ASI Ser., Ser. C 501, 355–358 (1997).

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” Proc. SPIE 2871, 613–616 (1997).
[Crossref]

X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, “High accuracy, wide range, rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36(25), 6190–6195 (1997).
[Crossref] [PubMed]

1980 (1)

Angel, R. P.

Bouchez, A.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Burge, J. H.

Cao, Y.

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

Chanan, G.

Chen, D.

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

Choi, H.

Clampin, M.

J. M. Oschmann, M. Clampin, and H. MacEwen, “Special Section Guest Editorial: Space Telescopes,” Opt. Eng. 52(9), 091801 (2013).
[Crossref]

Dai, X.

Dekens, F.

Dierickx, P.

Dohlen, K.

Farahani, A.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Fender, J. S.

J. S. Fender, “Future trends in large space optics,” Proc. SPIE 4013, 682–686 (2000).
[Crossref]

Filgueira, J.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Fuensalida, J. J.

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Local Piston Detection of a Segmented Mirror Telescope with Curvature Sensing of Wavefronts Affected by Atmospheric Turbulence. Numerical Simulations,” NATO ASI Ser., Ser. C 501, 355–358 (1997).

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” Proc. SPIE 2871, 613–616 (1997).
[Crossref]

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

Greivenkamp, J. E.

Huang, Z.

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

Jacoby, G.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Johns, M.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Kim, D. W.

Kirkman, D.

Li, L.

Liu, Y.

Long, X.

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Lu, M.

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

MacEwen, H.

J. M. Oschmann, M. Clampin, and H. MacEwen, “Special Section Guest Editorial: Space Telescopes,” Opt. Eng. 52(9), 091801 (2013).
[Crossref]

Mast, T.

McCarthy, P.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Michaels, S.

Montoya, L.

Nelson, J.

Oschmann, J. M.

J. M. Oschmann, M. Clampin, and H. MacEwen, “Special Section Guest Editorial: Space Telescopes,” Opt. Eng. 52(9), 091801 (2013).
[Crossref]

Parks, R. E.

Platt, B. C.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Raybould, K.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Rodriguez-Ramos, J. M.

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Local Piston Detection of a Segmented Mirror Telescope with Curvature Sensing of Wavefronts Affected by Atmospheric Turbulence. Numerical Simulations,” NATO ASI Ser., Ser. C 501, 355–358 (1997).

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” Proc. SPIE 2871, 613–616 (1997).
[Crossref]

Sasaki, O.

Shack, R.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Shectman, S.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Sheehan, M.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Southwell, W. H.

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

Su, P.

Suzuki, T.

Troy, M.

Trumper, I.

Wang, L.

Wu, F.

Wu, Y.

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

Yaitskova, N.

Yuan, J.

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Zhao, W.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

NATO ASI Ser., Ser. C (1)

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Local Piston Detection of a Segmented Mirror Telescope with Curvature Sensing of Wavefronts Affected by Atmospheric Turbulence. Numerical Simulations,” NATO ASI Ser., Ser. C 501, 355–358 (1997).

Opt. Eng. (1)

J. M. Oschmann, M. Clampin, and H. MacEwen, “Special Section Guest Editorial: Space Telescopes,” Opt. Eng. 52(9), 091801 (2013).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

Y. Wu, Y. Cao, Z. Huang, M. Lu, and D. Chen, “Improved composite Fourier transform profilometry,” Opt. Laser Technol. 44(7), 2037–2042 (2012).
[Crossref]

Proc. SPIE (4)

J. S. Fender, “Future trends in large space optics,” Proc. SPIE 4013, 682–686 (2000).
[Crossref]

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

R. Gilmozzi and J. Spyromilio, “The 42m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[Crossref]

J. M. Rodriguez-Ramos and J. J. Fuensalida, “Piston detection of a segmented mirror telescope using a curvature sensor: preliminary results with numerical simulations,” Proc. SPIE 2871, 613–616 (1997).
[Crossref]

Rev. Sci. Instrum. (1)

J. Yuan and X. Long, “CCD-area-based autocollimator for precision small-angle measurement,” Rev. Sci. Instrum. 74(3), 1362–1365 (2003).
[Crossref]

Other (1)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (John Wiley and Sons, 1978), Chap. 7.

Supplementary Material (3)

NameDescription
» Visualization 1       SMOTS measurement for seven hexagonal segments
» Visualization 2       SMOTS measurement with and without perturbation compensation
» Visualization 3       SMOTS measurement for two concave mirrors

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Figures (16)

Fig. 1
Fig. 1 Schematic SMOTS configuration (left) and the image of two-dimensionally multiplexed sinusoidal pattern captured by camera (right).
Fig. 2
Fig. 2 Comparison between the test methods of the (a) simultaneous multi-segmented mirror orientation test system (SMOTS) and (b) Shack-Hartmann wavefront sensor (SHWS).
Fig. 3
Fig. 3 Experimental SMOTS setup and picture of segmented target mirror used in experiments. The tilt angle θ of a segment causes the sinusoidal pattern to shift.
Fig. 4
Fig. 4 Fourier analysis steps for sheared pattern calculation.
Fig. 5
Fig. 5 Sign convention for SMOTS; The FFT amplitude has ambiguity of the shift direction. This direction issue is resolved by using the sign of the imaginary part.
Fig. 6
Fig. 6 Comparison between the direct and sheared pattern analysis methods. The same phase shift is applied to (a) single frequency and (b) mixed frequency case. The red arrow shows the nominal frequency of the reference pattern (x-axis) and its calculated phase value (y-axis). (Note: Since the numerical implementation of fast Fourier transform defined in a finite and discrete domain, the phase angle is defined in the entire frequency range. This can be suppressed by applying a threshold outside the expected frequency range, but it is presented without such treatment in this plot. The spikes in the plot represent the 2π jumps in the arctangent calculation.)
Fig. 7
Fig. 7 Reverse-raytracing spot diagram footprints at the screen for the Zemax modeled highly defocused (left), focused (middle), and highly aberrated (right) imaging cases. (Note: Only the outer bounds of the ray distribution are plotted here to distinguish shifted cases.)
Fig. 8
Fig. 8 (a) A schematic reverse Zemax model (showing only three field points) for the linearity check simulating a defocused sinusoidal pattern case. (b) The error in the calculated angle is plotted as a function of input mirror tilting angle for the five field points.
Fig. 9
Fig. 9 (a) A schematic reverse Zemax model (showing only three field points) for the linearity check simulating an aberrated sinusoidal pattern case. (b) The error in the calculated angle is plotted as a function of input mirror tilting angle for the five field points.
Fig. 10
Fig. 10 (a) A schematic reverse Zemax model for the linearity check simulating multiple mirror segments. (b) The error in the calculated angle is plotted as a function of input mirror tilting angle for the three segments.
Fig. 11
Fig. 11 Large dynamic range with large step size measurement comparison (left) between SMOTS and autocollimator for a flat mirror tilted up to ~1400 µrad. The difference between the two measurements (right) shows less than 0.8 µrad RMS errors. (Note: The error bars represents ± 1 σ standard deviation for 30 data measurements.)
Fig. 12
Fig. 12 The small dynamic range with fine step size measurement comparison (left) between SMOTS and autocollimator for a flat mirror tilted up to ~1400 µrad. The difference between the two measurements (right) shows less than 0.8 µrad RMS errors. (Note: The error bars represent ± 1 σ standard deviation for 30 data measurements.)
Fig. 13
Fig. 13 A snapshot image of the seven hexagonal segments in SMOTS detector showing the over-layered seven digital apertures and calculated instantaneous tip-tilt. The ~15 Hz real-time measurement result is present in Visualization 1.
Fig. 14
Fig. 14 (left) Simultaneous orientation measurement plot of the seven hexagonal segments using SMOTS. An environmental perturbation was introduced around 12 and 15 s duration. (right) Time sequence snapshots of the seven segments orientation for the perturbed case and the compensated case [Visualization 2].
Fig. 15
Fig. 15 The tilt measurement comparison (left) and the difference (right) between SMOTS and autocollimator for a concave mirror tilted up to ~800 µrad. (Note: The error bars represents ± 1 σ standard deviation for 30 data measurements.)
Fig. 16
Fig. 16 Picture of the target using two concave mirrors (left) and one frame of measured SMOTS data showing the orientations of the mirrors (right) [Visualization 3].

Equations (6)

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Initial pattern frequency bin: FT( f( x ) )=F( f )
Shifted pattern frequency bin: FT( f ( x+Δ ) )= e i2πΔ F(f)
Sheared pattern frequency bin:FT[ f( x+Δ )  f( x ) ]=FT( f( x+Δ ) )FT( f( x ) ) =( e i2πΔ  1) F( f )
Δ= 1 2π arccos[ 1 1 2 ( [ FT( f( x+Δ ) )FT( f( x ) ) ] 2 F ( f ) 2 ) ]
x f =  x i +Pixel pitch in physical units × number of pixels for one period × shifted phase (Δ) 
θ= 1 2 ( arctan( ( x i x 0 ) z d ) arctan( ( x f x 0 ) z d ) )

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