Abstract

We present a method for the calibration of a spatially phase-shifted digital speckle pattern interferometer (SPS–DSPI), which was designed and built for the purpose of testing the James Webb space telescope (JWST) optical structures and related technology development structures. The need to measure dynamic deformations of large, diffuse structures to nanometer accuracy at cryogenic temperature is paramount in the characterization of a large diameter space and terrestrial based telescopes. The techniques described herein apply to any situation, in which high accuracy measurement of diffuse structures are required. The calibration of the instrument is done using a single-crystal silicon gauge. The gauge has four islands of different heights that change in a predictable manner as a function of temperature. The SPS–DSPI is used to measure the relative piston between the islands as the temperature of the gauge is changed. The measurement results are then compared with the theoretical changes in the height of the gauge islands. The maximum deviation of the measured rate of change of the relative piston in nm∕K from the expected value is 3.3%.

© 2007 Optical Society of America

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References

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  1. K. Creath, "Phase-shifting speckle interferometry," Appl. Opt. 24, pp. 3053-3058 (1985).
    [CrossRef] [PubMed]
  2. H. Steinbichler and J. Gutjahr, U.S. Patent No. 5,155,363A (1990).
  3. B. Saif, "Simultaneous phase-shifted digital speckle pattern interferometry," Ph.D. dissertation (University of Arizona, 2004).
  4. P. Sabelhaus and J. Decker, "An overview of the James Webb space telescope (JWST) project," Proc. SPIE 5487, 550-563 (2004).
    [CrossRef]
  5. C. Atkinson, S. Texter, R. Hellekson, K. Patton, R. Keski-Kuha, and L. Feinberg, "Status of the JWST optical telescope element," Proc. SPIE 6265, 62650T (2006).
    [CrossRef]
  6. J. Arenberg, L. Gilman, N. Abbruzze, J. Reuter, K. Anderson, J. Jahic, J. Yacoub, H. Padilla, C. Atkinson, D. Moon, K. Patton, P. May, J. York, T. Messer, S. Backovsky, J. Tucker, C. Harvey, M. Bluth, B. Eegholm, B. Zukowski, B. Saif, R. Keski-Kuha, P. Blake, J. Kegley, and K. Russell, "The JWST backplane stability test article: a critical technology demonstration," Proc. SPIE 6265, 62650Q (2006).
    [CrossRef]
  7. M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, "Dynamic phase-shifting electronic speckle pattern interferometer," in Optical Manufacturing and Testing VI, H. P. Stahl, ed., Proc. SPIE 5869, 58691B (2005).
  8. M. Bluth, "CTE Model," SAI-TM-2865, Technical memorandum, not published (2005).

2006

C. Atkinson, S. Texter, R. Hellekson, K. Patton, R. Keski-Kuha, and L. Feinberg, "Status of the JWST optical telescope element," Proc. SPIE 6265, 62650T (2006).
[CrossRef]

J. Arenberg, L. Gilman, N. Abbruzze, J. Reuter, K. Anderson, J. Jahic, J. Yacoub, H. Padilla, C. Atkinson, D. Moon, K. Patton, P. May, J. York, T. Messer, S. Backovsky, J. Tucker, C. Harvey, M. Bluth, B. Eegholm, B. Zukowski, B. Saif, R. Keski-Kuha, P. Blake, J. Kegley, and K. Russell, "The JWST backplane stability test article: a critical technology demonstration," Proc. SPIE 6265, 62650Q (2006).
[CrossRef]

2004

P. Sabelhaus and J. Decker, "An overview of the James Webb space telescope (JWST) project," Proc. SPIE 5487, 550-563 (2004).
[CrossRef]

1985

Appl. Opt.

Proc. SPIE

P. Sabelhaus and J. Decker, "An overview of the James Webb space telescope (JWST) project," Proc. SPIE 5487, 550-563 (2004).
[CrossRef]

C. Atkinson, S. Texter, R. Hellekson, K. Patton, R. Keski-Kuha, and L. Feinberg, "Status of the JWST optical telescope element," Proc. SPIE 6265, 62650T (2006).
[CrossRef]

J. Arenberg, L. Gilman, N. Abbruzze, J. Reuter, K. Anderson, J. Jahic, J. Yacoub, H. Padilla, C. Atkinson, D. Moon, K. Patton, P. May, J. York, T. Messer, S. Backovsky, J. Tucker, C. Harvey, M. Bluth, B. Eegholm, B. Zukowski, B. Saif, R. Keski-Kuha, P. Blake, J. Kegley, and K. Russell, "The JWST backplane stability test article: a critical technology demonstration," Proc. SPIE 6265, 62650Q (2006).
[CrossRef]

Other

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, "Dynamic phase-shifting electronic speckle pattern interferometer," in Optical Manufacturing and Testing VI, H. P. Stahl, ed., Proc. SPIE 5869, 58691B (2005).

M. Bluth, "CTE Model," SAI-TM-2865, Technical memorandum, not published (2005).

H. Steinbichler and J. Gutjahr, U.S. Patent No. 5,155,363A (1990).

B. Saif, "Simultaneous phase-shifted digital speckle pattern interferometry," Ph.D. dissertation (University of Arizona, 2004).

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Figures (8)

Fig. 1
Fig. 1

Schematic block diagram of the SPS-DSPI.

Fig. 2
Fig. 2

CRA mounted on a copper plate: area 1 has a height of 2   mm , area 2 has a height of 59   mm , and area 4 has a height of 63   mm with respect to area 3. The diameter of structure is 8 in. The material is single crystal silicon with well-defined and uniform CTE, 2.55 × 10 6 , at ambient temperature.

Fig. 3
Fig. 3

Flow chart for the software for processing CRA data. The baseline criteria used is a fixed time interval.

Fig. 4
Fig. 4

Raw data plot. The y axis shows the relative piston in nm between the highest and the lowest CRA islands as a function of temperature, which is changed from 292 to 300   K . The 6 × imaging lens is used.

Fig. 5
Fig. 5

Relative piston between the highest and the lowest islands on the CRA as a function of temperature. Excerpt of the raw measurements, for a long baseline period of 7 min. The dots represent measured relative piston, the dashed line shows the fitted slope using all the relative piston measurements. The solid line shows the fitted slope excluding the relative measurements during the bulge period. The scatter changes during the baseline period.

Fig. 6
Fig. 6

Fringe mosaic for a baseline period (7 min start to end). The size of each of the figures is 500 pixels wide × 500 pixels high. The pictures are numbered left to right, top to bottom. The bulge period starts at picture 2 and ends at picture 6. The correlation in time is seen between the bulge in the raw data plot and the low number of fringes on the CRA.

Fig. 7
Fig. 7

Slope plot for 6 × lens measurement at 15.1   m distance from SPS–DSPI. Rebaselining is done every 7 min. The resulting relative piston between the island surfaces of the CRA can be found from integration of the relative piston change over the temperature interval. The mean slope is shown as the dotted line, the expected slope from the model is shown as the solid line.

Fig. 8
Fig. 8

Calibration results obtained with the 6 × lens at 15.1   m distance, in vacuum. The relative piston between the highest and the lowest island was measured.

Tables (1)

Tables Icon

Table 1 List of Calibration Measurements Performed on the CRA in Vacuum, at 15.1 m away from the SPS–DSPI a

Equations (12)

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tan   ϕ i = ( I i , 4 I i ,2 ) / ( I i ,1 I i ,3 ) ,
tan   ϕ f = ( I f , 4 I f ,2 ) / ( I f ,1 I f ,3 ) ,
tan ( ϕ i ϕ f ) = ( tan   ϕ i tan   ϕ f ) / ( 1 + tan   ϕ i   tan   ϕ f ) ,
tan ( ϕ i ϕ f ) = ( I i , 4 I i , 2 ) ( I f ,1 I f ,3 ) ( I f , 4 I f ,2 ) ( I i ,1 I i , 3 ) ( I i ,1 I i ,3 ) ( I f ,1 I f ,3 ) + ( I i , 4 I i ,2 ) ( I f , 4 I f ,2 ) .
ϕ f ϕ i = arctan [ n ( Δ I f 42 n Δ I i 13 n ) ( Δ I f 13 n Δ I i 42 n ) n ( Δ I f 13 n Δ I i 13 n + Δ I f 42 n Δ I i 42 n ) ] ,
Δ I f 42 = I f , 4 I f ,2 , etc .
R = M v ,
M = [ x i 2 x i x i n ] ,
R = [ ( y i x i ) y i ] ,
resid = y ( m 0 x + y 0 ) .
m σ = M 1 ( stddev ( resid ) 2 ) ,
mean_slope = ( slopes j m σ j ) ( 1 m σ j ) ,

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