Abstract

Current metrology tools have limitations when measuring rough aspherical surfaces with 1–2 μm root mean square roughness; thus, the surface cannot be shaped accurately by grinding. To improve the accuracy of grinding, the scanning long-wave optical test system (SLOTS) has been developed to measure rough aspherical surfaces quickly and accurately with high spatial resolution and low cost. It is a long-wave infrared deflectometry device consisting of a heated metal ribbon and an uncooled thermal imaging camera. A slope repeatability of 13.6 μrad and a root-mean-square surface accuracy of 31 nm have been achieved in the measurements of two 4 inch spherical surfaces. The shape of a rough surface ground with 44 μm grits was also measured, and the result matches that from a laser tracker measurement. With further calibration, SLOTS promises to provide robust guidance through the grinding of aspherics.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. J. W. Goodman, “Introduction to Fourier Optics,” 3rd ed. (Roberts & Company, 2005), p. 45.
  15. C. Zhao and J. H. Burge, “Orthonormal vector polynomials in a unit circle, part I: basis set derived from gradients of Zernike polynomials,” Opt. Express 15, 18014 (2007).
    [CrossRef]
  16. C. Zhao and J. H. Burge, “Orthonormal vector polynomials in a unit circle, part II: completing the basis set,” Opt. Express 16, 6586–6591 (2008).
    [CrossRef]
  17. C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
    [CrossRef]

2012 (1)

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

2011 (1)

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

2010 (1)

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

2008 (1)

2007 (1)

2004 (1)

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

2002 (1)

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wave front sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

1995 (1)

D. Anderson and J. Burge, “Swing-arm profilometry of aspherics,” Proc. SPIE 2536, 169–179 (1995).
[CrossRef]

1983 (1)

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 13–24 (1983).
[CrossRef]

1980 (2)

Anderson, D.

D. Anderson and J. Burge, “Swing-arm profilometry of aspherics,” Proc. SPIE 2536, 169–179 (1995).
[CrossRef]

Angel, R. P.

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

Burge, J.

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

D. Anderson and J. Burge, “Swing-arm profilometry of aspherics,” Proc. SPIE 2536, 169–179 (1995).
[CrossRef]

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

Burge, J. H.

Copland, J.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wave front sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Faber, C.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

Ghozeil, I.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, 3rd ed. (Wiley-Interscience, 2007), pp. 361–397.

Goodman, J. W.

J. W. Goodman, “Introduction to Fourier Optics,” 3rd ed. (Roberts & Company, 2005), p. 45.

Hahn, R.

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 13–24 (1983).
[CrossRef]

Hausler, G.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Häusler, G.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

Hayslett, C.

Johnson, J.

J. Johnson, “Characterization of optical surface grinding using bond and loose abrasives,” Ph.D. dissertation (University of Arizona, 2011).

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

Krobot, R.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

Kwon, O.

Malacara-Doblado, D.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, 3rd ed. (Wiley-Interscience, 2007), pp. 361–397.

Martin, B.

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

Miller, S.

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

Neal, D.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wave front sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Neal, D. R.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wave front sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 275–316.

Olesch, E.

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

Park, W. H.

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

Parks, R.

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

Parks, R. E.

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

Ritter, R.

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 13–24 (1983).
[CrossRef]

Southwell, W. H.

Su, P.

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

Su, T.

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

Wang, L.

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

Warner, S.

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

Wyant, J.

Zhao, C.

C. Zhao and J. H. Burge, “Orthonormal vector polynomials in a unit circle, part II: completing the basis set,” Opt. Express 16, 6586–6591 (2008).
[CrossRef]

C. Zhao and J. H. Burge, “Orthonormal vector polynomials in a unit circle, part I: basis set derived from gradients of Zernike polynomials,” Opt. Express 15, 18014 (2007).
[CrossRef]

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

Zobrist, T.

T. Zobrist, “Application of laser tracker technology for measuring optical surfaces,” Ph.D. dissertation (University of Arizona, 2009).

Appl. Opt. (2)

O. Kwon, J. Wyant, and C. Hayslett, “Rough surface interferometry at 10.6 μm,” Appl. Opt. 19, 1862–1869 (1980).

P. Su, R. E. Parks, L. Wang, R. P. Angel, and J. H. Burge, “Software configurable optical test system-computerized reverse Hartmann test,” Appl. Opt. 49, 366–376 (2010).

J. Opt. Soc. Am. (1)

Opt. Express (2)

Opt. Lasers Eng. (1)

R. Ritter and R. Hahn, “Contribution to analysis of the reflection grating method,” Opt. Lasers Eng. 4, 13–24 (1983).
[CrossRef]

Proc. SPIE (5)

M. C. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[CrossRef]

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann wave front sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

D. Anderson and J. Burge, “Swing-arm profilometry of aspherics,” Proc. SPIE 2536, 169–179 (1995).
[CrossRef]

T. Su, W. H. Park, R. Parks, P. Su, and J. Burge, “Scanning long-wave optical test system: a new ground optical surface slope test system,” Proc. SPIE 8126, 81260E (2011).
[CrossRef]

C. Faber, E. Olesch, R. Krobot, and G. Häusler, “Deflectometry challenges interferometry: the competition gets tougher!” Proc. SPIE 8493, 84930R (2012).
[CrossRef]

Other (6)

J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 275–316.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann–Shack, and other screen tests,” in Optical Shop Testing, 3rd ed. (Wiley-Interscience, 2007), pp. 361–397.

J. Johnson, “Characterization of optical surface grinding using bond and loose abrasives,” Ph.D. dissertation (University of Arizona, 2011).

J. W. Goodman, “Introduction to Fourier Optics,” 3rd ed. (Roberts & Company, 2005), p. 45.

B. Martin, J. Burge, S. Miller, S. Warner, and C. Zhao, “Fabrication and testing of 8.4 m off-axis segments for the giant Magellan telescope,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OWD6.

T. Zobrist, “Application of laser tracker technology for measuring optical surfaces,” Ph.D. dissertation (University of Arizona, 2009).

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Figures (20)

Fig. 1.
Fig. 1.

Comparison between the wire test and the SLOTS test. (a) Wire test and (b) SLOTS test. The light travels in the opposite direction as in the wire test. The heated ribbon is the source, and the camera is put where the point source would be in the wire test. The solid lines represent the rays that pass through the camera aperture, while the dotted lines indicate the rays that miss. Local surface slope is calculated with the coordinates of the aperture, reflection points, and ribbon.

Fig. 2.
Fig. 2.

Abstract setup in 3D coordinates where wx and wy are the surface slopes and xm and ym are the coordinates on the mirror surface; W is the designed surface height function, xc and yc are the coordinates of the camera pinhole, xs and ys are the ribbon coordinates, zm2s and zm2c are the Z-direction distances from the mirror vertex to the illumination plane and camera pinhole, respectively, dm2s and dm2c are the distances from the point on the mirror surface to the source and camera pinhole, respectively.

Fig. 3.
Fig. 3.

SLOTS test of a spherical mirror modeled in Zemax. The light path is reversed in the model compared to a real SLOTS test. A spherical mirror generates concentrated spot diagram, therefore, the ribbon is able to illuminate the entire surface at once.

Fig. 4.
Fig. 4.

SLOTS test of a parabolic mirror modeled in Zemax. The spot diagram is more diverse; therefore, the ribbon only illuminates part of the surface at one position. The ribbon covers the whole spot diagram by scanning. The mirror image is from [9].

Fig. 5.
Fig. 5.

Ribbon can illuminate the same detector pixel from a region. Two sets of rays show the conjugation between the detector and the mirror.

Fig. 6.
Fig. 6.

Intensity profile of a single detector pixel. Each dot represents a readout value of the same pixel when the ribbon is at position xi. When the ribbon is within in the illumination region, this detector pixel is illuminated. The shape of the plot is determined by the setup, see Section 2.C.

Fig. 7.
Fig. 7.

Mirror pixel is the image of a detector pixel. (a) In first-order optics, the mirror pixel is a square with sharp edges. (b) When the camera point spread function (PSF) is considered, the mirror pixel is the convolution of the PSF and the geometrical image. The PSF in this plot is as aberration-free Airy disk.

Fig. 8.
Fig. 8.

Schematic of the radiometry model. The light emerging from the source image is modulated by the mirror pixel before it goes to the camera aperture. In the plot, dΩ is the differential solid angle extended by a small area on the source from the camera aperture, A is the area of the camera aperture.

Fig. 9.
Fig. 9.

Throughput of a detector pixel versus the ribbon position. In the model the test mirror is flat, the mirror pixel size is 2×2mm, the camera aperture diameter is 2 mm, the source and the camera are 500 mm away from the mirror, and the width of the source is 2 mm.

Fig. 10.
Fig. 10.

Test setup of a concave surface. (a) Ribbon is imaged onto the camera aperture. The solid angle is extended by the detector pixel from the source image. (b) Aperture and the ribbon image seen by the detector. Aw is the area of the source image within the camera aperture.

Fig. 11.
Fig. 11.

Two prototypes of SLOTS. (a) Prototype A. An electrically heated tungsten ribbon serves as the source. Two linear stages and a rotary stage make up the scanning system. The camera is an uncooled thermal imaging camera. (b) Prototype B. A system prepared to test the primary of ATST. Due to the large spot size of the mirror, the tungsten ribbon and linear stage are much longer than those in prototype A. Instead of two linear stages, prototype B has a single linear stage mounted on a rotary stage.

Fig. 12.
Fig. 12.

Right-angle-shaped reflector of prototype B. The back-radiated light is reflected away from the test setup.

Fig. 13.
Fig. 13.

Measured ground mirror with 1.6 m radius of curvature. The surface rms roughness is about 1.2 μm.

Fig. 14.
Fig. 14.

(a) One of the raw images from the SLOTS test. Because the surface is spherical, the ribbon is able to illuminate the entire mirror at once. (b) Centroids map (zoomed in) and (c) slope map.

Fig. 15.
Fig. 15.

Measured polished surface with 1.9 m radius of curvature.

Fig. 16.
Fig. 16.

Measured slope maps. (a) and (b) are the raw slope maps in x and y direction respectively (averaged 30 measurements). The unit is radian. (c) and (d) are the slope maps after the Zernike gradient polynomial fitting and with the first 10 terms removed. The unit is an e-5 radian.

Fig. 17.
Fig. 17.

(a) Comparison of the surface maps from SLOTS and (b) that from an interferometer. The first 10 Zernike terms are removed from the two surface maps. The difference (c) is a subtraction of the two maps [6].

Fig. 18.
Fig. 18.

Very rough surface ground with 44 μm loose abrasive grits. The surface has a radius of curvature of 16 m. The diameter of the surface is 406 mm.

Fig. 19.
Fig. 19.

Test setup alignment. A small, thin, flat mirror was attached to the center of the test surface with a drop of water. An HeNe laser shot a beam from in front of the camera to the flat mirror. The test surface was tip-tilted until the reflected laser beam pointed at the center of the scan system.

Fig. 20.
Fig. 20.

(a) Measured surface maps from SLOTS and (b) laser tracker of the 44 μm grits ground surface. Tilt and power were removed from both measurements. The agreement of feature shape and magnitude proves that SLOTS is able to guide the fabrication process in a very early stage.

Tables (3)

Tables Icon

Table 1. Uncommon Specs of the Two Prototypes

Tables Icon

Table 2. Main Procedure of the SLOTS Test

Tables Icon

Table 3. Measurement Parameters and Results of the Measurement of the 1.6 m Ground Mirror

Equations (5)

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

wx(xm,ym)=xmxsdm2s+xmxcdm2czm2sW(xm,ym)dm2s+zm2cW(xm,ym)dm2c,wy(xm,ym)=ymysdm2s+ymycdm2czm2sW(xm,ym)dm2s+zm2cW(xm,ym)dm2c,
wx(xm,ym)=12(xmxszm2s+xmxczm2c),wy(xm,ym)=12(ymyszm2s+ymyczm2c).
xs=ixiIiiIi.
Φ=r·L·A·Ω=r·L·A·ribbon imageF(mirror pixel)dΩ,
Φ=r·L·Aw·Ωp.

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