Abstract

By taking a new look at an old concept, we have shown in our previous work how the Abbe sine condition can be used to measure linearly field-dependent aberrations in order to verify the alignment of optical systems. In this paper, we expand on this method and discuss the design choices involved in implementing the sine condition test (SCTest). Specifically, we discuss the two illumination options for the test: point source with a grating or flat-panel display, and we discuss the tradeoffs of the two approaches. Additionally, experimental results are shown using a flat-panel display to measure linearly field-dependent aberrations. Last, we elaborate on how to implement the SCTest on more complex optical systems, such as a three-mirror anastigmat and a double Gauss imaging lens system.

© 2013 Optical Society of America

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References

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  1. E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv fuer mikroskopische Anatomie 9, 413–418 (1873).
    [CrossRef]
  2. L. Mertz, “Geometrical design for aspheric reflecting systems,” Appl. Opt. 18, 4182–4186 (1979).
    [CrossRef]
  3. J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
    [CrossRef]
  4. J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
    [CrossRef]
  5. S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011).
    [CrossRef]
  6. B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
    [CrossRef]
  7. L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
    [CrossRef]
  8. H. Lee, “Optimal collimation of misaligned optical systems by concentering primary field aberrations,” Opt. Express 18, 19249–19262 (2010).
    [CrossRef]
  9. R. Tessieres, Analysis for Alignment of Optical Systems (University of Arizona, 2003).
  10. D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley-Interscience, 2007).
  11. S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
    [CrossRef]
  12. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).
  13. A. Offner, “Catoptric anastigmatic afocal optical system,” U.S. patent, 3674334 (4July1972).
  14. R. Orr, Alignment of a Three Mirror Anastigmat (University of Arizona, 2011).

2012 (1)

S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
[CrossRef]

2011 (1)

2010 (2)

H. Lee, “Optimal collimation of misaligned optical systems by concentering primary field aberrations,” Opt. Express 18, 19249–19262 (2010).
[CrossRef]

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
[CrossRef]

2003 (1)

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
[CrossRef]

2000 (1)

L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
[CrossRef]

1996 (1)

B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

1979 (1)

1873 (1)

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv fuer mikroskopische Anatomie 9, 413–418 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv fuer mikroskopische Anatomie 9, 413–418 (1873).
[CrossRef]

Angel, R. P.

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
[CrossRef]

Burge, J. H.

S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
[CrossRef]

S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011).
[CrossRef]

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
[CrossRef]

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
[CrossRef]

Dubin, M.

S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
[CrossRef]

S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

Lampen, S.

S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
[CrossRef]

S. Lampen, M. Dubin, and J. H. Burge, “Implementation of sine condition test to measure optical system misalignments,” Appl. Opt. 50, 6391–6398 (2011).
[CrossRef]

Lee, H.

Lu, S. H.

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
[CrossRef]

McLeod, B.

B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

Mertz, L.

Noethe, L.

L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
[CrossRef]

Offner, A.

A. Offner, “Catoptric anastigmatic afocal optical system,” U.S. patent, 3674334 (4July1972).

Orr, R.

R. Orr, Alignment of a Three Mirror Anastigmat (University of Arizona, 2011).

Tessieres, R.

R. Tessieres, Analysis for Alignment of Optical Systems (University of Arizona, 2003).

Zhao, C.

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
[CrossRef]

Appl. Opt. (2)

Archiv fuer mikroskopische Anatomie (1)

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv fuer mikroskopische Anatomie 9, 413–418 (1873).
[CrossRef]

Opt. Express (1)

Proc. SPIE (4)

L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
[CrossRef]

J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
[CrossRef]

J. H. Burge, C. Zhao, and S. H. Lu, “Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems,” Proc. SPIE 7652, 765219 (2010).
[CrossRef]

S. Lampen, M. Dubin, and J. H. Burge, “Use of a flat panel display for measurement of sine condition violations,” Proc. SPIE 8491, 84910F (2012).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

Other (5)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

A. Offner, “Catoptric anastigmatic afocal optical system,” U.S. patent, 3674334 (4July1972).

R. Orr, Alignment of a Three Mirror Anastigmat (University of Arizona, 2011).

R. Tessieres, Analysis for Alignment of Optical Systems (University of Arizona, 2003).

D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley-Interscience, 2007).

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Figures (11)

Fig. 1.
Fig. 1.

General illustration of an optical system with finite conjugates. O, object point; I, conjugate image point; B, point on EP; C, point on XP conjugate to B; εo, off-axis object point; εi, conjugate off-axis image point; S^o, unit vector pointing from O to B; θo, angle of S^o with respect to the axis; S^i, unit vector from I to C; θi, angle of S^i with respect to the axis. Text and image from [5].

Fig. 2.
Fig. 2.

Illustration of the two approaches to implementing the SCTest. (a) Coherent approach: a grating is used to diffract the light from a coherent point source that propagates though the UUT and interferes at the analyzer plane [5]. (b) Display approach: an electronic display is imaged onto the analyzer grating, creating a Moiré pattern with the grating. The example ray bundles shown represent the imaging of the SCTest and are examples of only a few of the many rays present in the real system. Similar to [11].

Fig. 3.
Fig. 3.

(a) Abridged layout of display approach showing the planes conjugate to the source. See Fig. 2 for complete annotations. (b) Beam footprint at imaging-system aperture plane when imaging-system aperture and test aperture footprint are aligned. Centroid of beam located at ideal reference point. (c) Beam footprint passed when apertures are misaligned. Centroid of beam decentered from ideal reference point.

Fig. 4.
Fig. 4.

Comparison between on-axis images and extended-source images to show removal of coherent artifacts. Same gray-scale mapping used for all images. (a) Average of on-axis measurements taken when the source was on-axis at the first position of the analyzer grating during phase shifting. (b) Average of all measurements taken at the first position of the analyzer grating to synthesize a coherent source to remove coherent noise. (c) Close-up of coherent noise in (a). (d) Close-up of same section in (b) to show the reduction in coherent noise.

Fig. 5.
Fig. 5.

Comparison between extended source phase and point source phase. (a) Phase measured with on-axis point source. (b) Phase measured with extended source, where the extended source was created by averaging images taken at different point source locations in object space. (c) Difference between the extended-source phase measurement and the on-axis phase measurement. The rings in the data are a result of the coherent noise that was reduced by using an extended source. (d)–(f) Close-up of the same section in (a)–(c).

Fig. 6.
Fig. 6.

Picture of SCTest experimental setup used to measure sensitivity of UUT alongside illustration of model from Fig. 2(b) [11].

Fig. 7.
Fig. 7.

Images of the Moiré pattern formed when the display was imaged onto the analyzer grating by the UUT. (a) Moiré pattern formed when display lines and analyzer are in horizontal orientation to measures the linearly field dependence in the vertical direction. At the analyzer plane, the image of the display consists of 105.8 line pairs across the height of the display, versus the 95.3 line pairs across the same section of the analyzer grating. (b) Display lines and analyzer in vertical orientations. The image of the display consists of 141.1 line pairs across the width of the image, while the analyzer has 126.9 line pairs over that same distance. (c) Sample of map after unwrapping, composite of Z4-Z22. The scale of the map is the same as (a) and (b). The circular mask was applied to fit the Zernike standard polynomials.

Fig. 8.
Fig. 8.

Tilt sensitivities of the UUT shown in Fig. 6. Blue measurement points are experimental data shown with ±2σ error bars. Solid red lines are the tilt sensitivity of the Zemax model shown in Fig. 2. (a) Linear astigmatism in vertical direction. (b) Linear astigmatism in horizontal direction [11].

Fig. 9.
Fig. 9.

Layout of the implementation of the SCTest to verify the alignment of an afocal TMA. For the display approach, a flat-panel is placed at the EP, and the order selection aperture is replaced by the test aperture. [11].

Fig. 10.
Fig. 10.

(a) Layout model of generic double Gauss, 28° field showing the EP and XP locations inside the system. (b) Implementing the SCTest by shifting the stop outside the double Gauss system. For the display approach, a flat-panel is placed at the EP, and the order selection aperture is replaced by a test aperture. Similar to [11].

Fig. 11.
Fig. 11.

Implementing the SCTest on double Gauss optical system by re-imaging the pupils outside the system. See parts (c) and (d) for labels. (a) Illustration of the system from the projection grating to EP. (b) Illustration of the system from the EP to analyzer grating. (c) Full implementation of SCTest on double Gauss system. (d) Model showing how the SCTest can be used to verify the alignment of auxiliary optics before testing the alignment of the double Gauss. Similar to [11].

Equations (2)

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Wo(xEP,yEP)Δd=S^o·εo,
WPME=Wo(xEP,yEP)Wi(xXP,yXP)=S^o·εo1mS^i·εi,

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