Abstract

Applying the iterative triangulation stitching algorithm, we provide an experimental demonstration by testing a Φ120mm flat mirror, a Φ1450mm off-axis parabolic mirror and a convex hyperboloid mirror. By comparing the stitching results with the self-examine subaperture, it shows that the reconstruction results are in consistent with that of the subaperture testing. As all the experiments are conducted with a 5-dof adjustment platform with big adjustment errors, it proves that using the above mentioned algorithm, the subaperture stitching can be easily performed without a precise positioning system. In addition, with the algorithm, we accomplish the coordinate unification between the testing and processing that makes it possible to guide the processing by the stitching result.

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References

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  1. J. G.  Thunen, O. Y.  Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1983).
    [CrossRef]
  2. W. W.  Chow, G. N.  Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8(9), 468–470 (1983).
    [CrossRef] [PubMed]
  3. T. W.  Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
    [CrossRef]
  4. A.  Kulawiec, P.  Murphy, M. D.  Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512-1–765512-4 (2010).
    [CrossRef]
  5. C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
    [CrossRef]
  6. P.  Su, J. H.  Burge, R. E.  Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49(1), 21–31 (2010).
    [CrossRef] [PubMed]
  7. P. Su, Absolute Measurements of Large Mirrors (The University Of Arizona 2008).
  8. D.  Liu, Y.  Yang, C.  Tian, Y.  Luo, L.  Wang, “Practical methods for retrace error correction in nonnull aspheric testing,” Opt. Express 17(9), 7025–7035 (2009).
    [CrossRef] [PubMed]
  9. M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
  10. P. F.  Zhang, H.  Zhao, X.  Zhou, J. J.  Li, “Sub-aperture stitching interferometry using stereovision positioning technique,” Opt. Express 18(14), 15216–15222 (2010).
    [CrossRef] [PubMed]
  11. M.  Novak, C.  Zhao, J. H.  Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 1–8 (2008).
    [CrossRef]
  12. C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
    [CrossRef]
  13. S. Y.  Chen, S. Y.  Li, Y. F.  Dai, L. Y.  Ding, S. Y.  Zeng, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16(7), 4760–4765 (2008).
    [CrossRef] [PubMed]

2012 (1)

C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
[CrossRef]

2010 (3)

2009 (1)

2008 (2)

2006 (1)

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

1994 (1)

M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).

1986 (1)

T. W.  Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
[CrossRef]

1983 (2)

J. G.  Thunen, O. Y.  Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1983).
[CrossRef]

W. W.  Chow, G. N.  Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8(9), 468–470 (1983).
[CrossRef] [PubMed]

Bray, M.

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

Burge, J. H.

P.  Su, J. H.  Burge, R. E.  Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Opt. 49(1), 21–31 (2010).
[CrossRef] [PubMed]

M.  Novak, C.  Zhao, J. H.  Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 1–8 (2008).
[CrossRef]

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

Chen, S. Y.

Chow, W. W.

Dai, Y. F.

Ding, L. Y.

Fee, C. M.

C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
[CrossRef]

Kulawiec, A.

A.  Kulawiec, P.  Murphy, M. D.  Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512-1–765512-4 (2010).
[CrossRef]

Kwon, O. Y.

J. G.  Thunen, O. Y.  Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1983).
[CrossRef]

Lawrence, G. N.

Li, J. J.

Li, S. Y.

Liu, D.

Luo, Y.

Marco, M. D.

A.  Kulawiec, P.  Murphy, M. D.  Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512-1–765512-4 (2010).
[CrossRef]

Murphy, P.

C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
[CrossRef]

A.  Kulawiec, P.  Murphy, M. D.  Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512-1–765512-4 (2010).
[CrossRef]

Novak, M.

M.  Novak, C.  Zhao, J. H.  Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 1–8 (2008).
[CrossRef]

Okada, K.

M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).

Otsubo, M.

M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).

Parks, R. E.

Sprowl, R. A.

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

Stuhlinger, T. W.

T. W.  Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
[CrossRef]

Su, P.

Supranowitz, C.

C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
[CrossRef]

Thunen, J. G.

J. G.  Thunen, O. Y.  Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1983).
[CrossRef]

Tian, C.

Tsujiuchi, J.

M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).

Wang, L.

Yang, Y.

Zeng, S. Y.

Zhang, P. F.

Zhao, C.

M.  Novak, C.  Zhao, J. H.  Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 1–8 (2008).
[CrossRef]

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

Zhao, H.

Zhou, X.

Appl. Opt. (1)

Opt. Eng. (1)

M.  Otsubo, K.  Okada, J.  Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (6)

M.  Novak, C.  Zhao, J. H.  Burge, “Distortion mapping correction in aspheric null testing,” Proc. SPIE 7063, 1–8 (2008).
[CrossRef]

C.  Zhao, R. A.  Sprowl, M.  Bray, J. H.  Burge, “Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique,” Proc. SPIE 6293, 1–9 (2006).
[CrossRef]

T. W.  Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
[CrossRef]

A.  Kulawiec, P.  Murphy, M. D.  Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512-1–765512-4 (2010).
[CrossRef]

C.  Supranowitz, C. M.  Fee, P.  Murphy, “Asphere metrology using variable optical null technology,” Proc. SPIE 8416, 841604-1– 841604-5 (2012).
[CrossRef]

J. G.  Thunen, O. Y.  Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1983).
[CrossRef]

Other (1)

P. Su, Absolute Measurements of Large Mirrors (The University Of Arizona 2008).

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Figures (28)

Fig. 1
Fig. 1

Flow chart of subaperture stitching algorithm.

Fig. 2
Fig. 2

Calculation in the overlapping area. (a) sketch of the projection on the X-Y plane; (b) sketch of Delaunay triangulation.

Fig. 3
Fig. 3

Schematic diagram of calculation with the stitching factor.

Fig. 4
Fig. 4

The configuration for alignment and correction of mapping distortion.

Fig. 5
Fig. 5

Experimental setup.

Fig. 6
Fig. 6

Measured subapertures.

Fig. 7
Fig. 7

Full aperture testing result.

Fig. 8
Fig. 8

Stitching result with traditional algorithm.

Fig. 9
Fig. 9

Stitching result with iterative algorithm.

Fig. 10
Fig. 10

Residual map between traditional algorithm and full aperture testing result.

Fig. 11
Fig. 11

Residual map between iterative algorithm and full aperture testing result.

Fig. 12
Fig. 12

Experimental setup.

Fig. 13
Fig. 13

Measured subapertures.

Fig. 14
Fig. 14

Stitching result.

Fig. 15
Fig. 15

Testing result around the target.

Fig. 16
Fig. 16

Stitching result after replacing the data in the targets.

Fig. 17
Fig. 17

Measuring arm testing.

Fig. 18
Fig. 18

Surface map after different processing cycles.

Fig. 19
Fig. 19

Self-examine subaperture map and residual map.

Fig. 20
Fig. 20

Experimental setup.

Fig. 21
Fig. 21

Subaperture design.

Fig. 22
Fig. 22

Measured subapertures.

Fig. 23
Fig. 23

Extra aberrations to the central subaperture (PV 0.431λ, RMS 0.116λ).

Fig. 24
Fig. 24

Extra aberrations to the off-axis subaperture (PV 0.656λ, RMS 0.169λ).

Fig. 25
Fig. 25

stitching result.

Fig. 26
Fig. 26

Stitching result after replacing the data in the targets.

Fig. 27
Fig. 27

Three Coordinate Measuring.

Fig. 28
Fig. 28

Self-examine subaperture map and residual map.

Tables (2)

Tables Icon

Table 1 Coordinates of targets in the testing and processing coordinate system respectively.

Tables Icon

Table 2 Coordinates of targets in the testing and processing coordinate system respectively.

Equations (24)

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

( x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 )( a b d )=( z 1 z 2 z 3 )
z=axbyd
Φ i ' (x,y)= Φ i (x,y)+ k=1 L a ik f k (x,y)
{ f 1 (x,y)=x; f 2 (x,y)=y; f 3 (x,y)=1.
min= i=1...N j=1..N ji ij [( Φ i (x,y)+ k=1 L a ik f k (x,y) )( Φ j (x,y)+ k=1 L a jk f k (x,y) )] 2
P=QR
{ 1kL; 1jN1.
P (j1)k = i=1 ij N ij f k (x,y)( Φ j (x,y) Φ i (x,y))
{ 1 k ' L; 1lN1.
Q ((j1)k)((l1) k ' ) ={ i=1 ij N ij f k (x,y) f k ' (x,y) , j=l; jl f k (x,y) f k ' (x,y) , jl.
R (j1)k = a jk
{ x 1 = x 2 +dx+Δx; y 1 = y 2 +dy+Δy.
z= z 1 X P X O2 X O1 X O2 + z 2 X P X O1 X O2 X O1
{ X P =( x p , y p ) X O1 =( x O1 , y O1 ) X O2 =( x O2 , y O2 )
z= w k z k
w k = X P X O1 X P X O(k1) X P X O(k+1) X P X ON X Ok X O1 X Ok X O(k1) X Ok X O(k+1) X Ok X ON
z= w k z k w k
[ X i Y i 1 ]=T[ x y 1 ]
T=[ scosθ ssinθ t x ssinθ scosθ t y 0 0 1 ]
[ X i ' Y i ' ]=[ x i scosθ y i ssinθ+ t x x i ssinθ+ y i scosθ+ t y ]
i=1 N ( ( X i ' X i ) 2 + ( Y i ' Y i ) 2 )
s=1.0117, t x =-680.25, t y =-729.1934, θ=0 .9110 °
r R 2F 55.8mm
s=0.1258, t x =64.8861mm, t y =64.9580mm, θ=0.0745°.

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