Abstract

Rather than measuring aberrations across the field to quantify the alignment of an optical system, we show how a single, on-axis measurement of the pupil mapping can be used to measure the off-axis performance of the system and determine the state of alignment. In this paper we show how the Abbe sine condition can be used to relate the mapping between the entrance and exit pupils to image aberrations that have linear field dependence. This mapping error then can be used to measure the linear astigmatism caused by the misalignment. Additionally, we present experimental results from the sine condition test on a simple system.

© 2011 Optical Society of America

Full Article  |  PDF Article

Corrections

Sara Lampen, Matthew Dubin, and James H. Burge, "Implementation of sine condition test to measure optical system misalignments: erratum," Appl. Opt. 52, 8518-8518 (2013)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-35-8518

References

  • View by:
  • |
  • |
  • |

  1. E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv Mikrosk. 9, 413–418(1873).
    [CrossRef]
  2. L. Mertz, “Geometrical design for aspheric reflecting systems,” Appl. Opt. 18, 4182–4186 (1979).
    [CrossRef] [PubMed]
  3. J. H. Burge and R. P. Angel, “Wide-field telescope using spherical mirrors,” Proc. SPIE 5174, 83–92 (2003).
    [CrossRef]
  4. R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).
  5. M. Shibuya, “Exact sine condition in the presence of spherical aberration,” Appl. Opt. 31, 2206–2210 (1992).
    [CrossRef] [PubMed]
  6. C. Zhao and J. H. Burge, “Criteria for correction of quadratic field-dependent aberrations,” J. Opt. Soc. Am. A 19, 2313–2321 (2002).
    [CrossRef]
  7. 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]
  8. B. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
    [CrossRef]
  9. L. Noethe, “Final alignment of the VLT,” Proc. SPIE 4003, 382–390 (2000).
    [CrossRef]
  10. H. Lee, “Optimal collimation of misaligned optical systems by concentering primary field aberrations,” Opt. Express 18, 19249–19262 (2010).
    [CrossRef] [PubMed]
  11. R. Tessieres, Analysis for Alignment of Optical Systems(University of Arizona, 2003).
  12. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
    [PubMed]
  13. M. Mansuripur, Classical Optics and Its Applications, 1st ed. (Cambridge University, 2002).
  14. R. K. Luneburg, Mathematical Theory of Optics, 1st ed.(University of California, 1964).
  15. H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambridge University, 1970).
  16. R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–151 (1980).
  17. P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” Publ. Astron. Soc. Pac. 123, 812–832 (2011).
    [CrossRef]
  18. T. Schmid, K. P. Thompson, and J. P. Rolland, “Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes,” Appl. Opt. 49, D131–D144 (2010).
    [CrossRef] [PubMed]

2011 (1)

P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” Publ. Astron. Soc. Pac. 123, 812–832 (2011).
[CrossRef]

2010 (3)

2003 (1)

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

2002 (1)

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]

1992 (1)

1980 (1)

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–151 (1980).

1979 (1)

1873 (1)

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

Abbe, E.

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv Mikrosk. 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]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambridge University, 1970).

Burge, J. 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]

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

C. Zhao and J. H. Burge, “Criteria for correction of quadratic field-dependent aberrations,” J. Opt. Soc. Am. A 19, 2313–2321 (2002).
[CrossRef]

Kingslake, R.

R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Lee, H.

Levinson, R. S.

P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” Publ. Astron. Soc. Pac. 123, 812–832 (2011).
[CrossRef]

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]

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics, 1st ed.(University of California, 1964).

Mansuripur, M.

M. Mansuripur, Classical Optics and Its Applications, 1st ed. (Cambridge University, 2002).

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]

Rolland, J. P.

Schechter, P. L.

P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” Publ. Astron. Soc. Pac. 123, 812–832 (2011).
[CrossRef]

Schmid, T.

Shack, R. V.

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–151 (1980).

Shibuya, M.

Tessieres, R.

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

Thompson, K.

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–151 (1980).

Thompson, K. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

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]

C. Zhao and J. H. Burge, “Criteria for correction of quadratic field-dependent aberrations,” J. Opt. Soc. Am. A 19, 2313–2321 (2002).
[CrossRef]

Appl. Opt. (3)

Archiv Mikrosk. (1)

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

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Proc. SPIE (4)

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–151 (1980).

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]

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]

Publ. Astron. Soc. Pac. (2)

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

P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” Publ. Astron. Soc. Pac. 123, 812–832 (2011).
[CrossRef]

Other (6)

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

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

M. Mansuripur, Classical Optics and Its Applications, 1st ed. (Cambridge University, 2002).

R. K. Luneburg, Mathematical Theory of Optics, 1st ed.(University of California, 1964).

H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambridge University, 1970).

R. Kingslake, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

(a) General illustration of an axisymmetric optical system with finite conjugates: O, object point; I, conjugate image point; B, point on entrance pupil (EP); C, point on exit pupil (XP) conjugate to B; ε o , off-axis object point; ε i , conjugate off-axis image point; S ^ o , unit vector pointing from O to B; θ o , angle of S ^ o with respect to the axis; S ^ i , unit vector from I to C; θ i , angle of S ^ i with respect to the axis. (b) Close-up of object space: Δ D , exact scalar path difference between O and ε o ; Δ d , approximate scalar path difference.

Fig. 2
Fig. 2

Illustration of how the pupil mapping error found using Eq. (8) can be used to find the linearly field dependent aberrations of an optical system.

Fig. 3
Fig. 3

Field dependence of W Coma (top row) and pupil dependence of W Coma (bottom row).

Fig. 4
Fig. 4

(a)–(c) Full field spot diagrams of linear astigmatism shown through focus, plots without annotations originally seen in [7]. (d) Close-up of the spots from plot (b) to show the linear nature of the field dependence.

Fig. 5
Fig. 5

Field dependence of W LA (top row) and pupil dependence of W LA (bottom row).

Fig. 6
Fig. 6

Illustration of Eq. (8). Step 1, quiver plot representation of the form of pupil mapping error from linear astigmatism. Step 2, projection of pupil mapping error onto the observation vectors and the resulting form of astigmatisms.

Fig. 7
Fig. 7

Sketch of the general measurement approach to convert the angular mapping of θ o and θ i into a spatial mapping.

Fig. 8
Fig. 8

Diagram of the alternative measurement explanation, which uses a grating to create two beams that act as the two test beams used in interferometry. (a) The optical system under the test axis is aligned to the point source and test grating. (b) The optical system under test is tilted with respect to the point source and test grating Close-up of object space showing θ o from Fig. 7 (object space inset) and close-up of image space showing θ i from Fig. 7 (image space inset).

Fig. 9
Fig. 9

Illustration of the SCTest experimental setup on a single lens as well as the layout of the ZEMAX model of the experimental system.

Fig. 10
Fig. 10

Picture of experimental system illustrated in Fig. 9. The order selection aperture is not pictured.

Fig. 11
Fig. 11

Images of interferogram. Interference of (a) first orders, (b) third orders, (c) fifth orders.

Tables (1)

Tables Icon

Table 1 Measured and Predicted Data in Pairs of Orders as a Function of Zernike Standard Polynomials

Equations (12)

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

W o ( x EP , y EP ) = O B ¯ ( x EP , y EP ) ε o B ¯ ( x EP , y EP ) = Δ D ( x EP , y EP ) .
W o ( x EP , y EP ) Δ d = S ^ o ε o = ε o , x x EP R o + ε o , y y EP R o ,
x EP = m x x XP + f x ( x XP , y XP ) , y EP = m y y XP + f y ( x XP , y XP ) ,
W o ( x EP , y EP ) = W I ( x XP , y XP ) , ε o , x x EP R o + ε o , y y EP R o = ε o , x R o [ m x x XP + f x ( x XP , y XP ) ] + ε o , y R o [ m y y XP + f y ( x XP , y XP ) ] .
ε o , x x EP R o + ε o , y y EP R o = 1 m [ ε i , x x XP R i + ε i , y y XP R i ] + 1 R o [ ε o , x f x ( x XP , y XP ) + ε o , y f y ( x XP , y XP ) ] .
x EP R o = | S ^ o , x | sin θ o , x , y EP R o = | S ^ o , y | sin θ o , y ,
W PME = ( ε o , x sin θ o , x + ε o , y sin θ o , y ) 1 m ( ε i , x sin θ i , x + ε i , y sin θ i , y ) .
W PME = S ^ o ε o 1 m S ^ i ε i .
W Coma = C ( H x Z 8 + H y Z 7 ) ,
Z 7 = ( 3 ρ 3 2 ρ ) sin θ , Z 8 = ( 3 ρ 3 2 ρ ) cos θ .
W LA = C ( H x Z 6 + H y Z 5 ) ,
Z 5 = ρ 2 sin 2 θ , Z 6 = ρ 2 cos 2 θ .

Metrics