Abstract

Modern optical systems achieve incredible resolution and require more thorough testing. We present a method of evaluating and displaying the modulation transfer function (MTF) of a lens over its full rectangular field of view. The method consists of utilizing commercially available MTF test stations to gather data as well as custom software to plot the results. Critically, these measurements allow the characterization of misaligned systems with much higher accuracy than the typical three- or five-field-point MTF measurements yield. Examples are provided of both well-centered and poorly centered systems.

© 2017 Optical Society of America

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Corrections

18 July 2017: A correction was made to Ref. 26.


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References

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    [Crossref]
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  24. “Optics and photonics–Optical transfer function–Definitions and mathematical relationships,” .
  25. “Optics and photonics–Optical transfer function–Principles and procedures of measurement,” .
  26. “Optics and optical instruments–accuracy of optical transfer function (OTF) measurement,” .
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    [Crossref]
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  34. E. Granger and K. Cupery, “An optical merit function (SQF), which correlates with subjective image judgements,” Photogr. Sci. Eng. 15, 221–230 (1972).
  35. B. O. Hultgren, “Subjective quality factor revisited: a unification of objective sharpness measures,” Proc. SPIE 1249, 12–22 (1990).
    [Crossref]

2014 (1)

2012 (1)

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012).
[Crossref]

2011 (1)

2005 (1)

1990 (2)

B. O. Hultgren, “Subjective quality factor revisited: a unification of objective sharpness measures,” Proc. SPIE 1249, 12–22 (1990).
[Crossref]

P. T. Carellas and S. D. Fantone, “Why measure MTF?” Opt. Photon. News 1(6), 27–29 (1990).
[Crossref]

1988 (1)

1986 (1)

K. P. Thompson, “Beyond optical design interaction between the lens designer and the real world,” Proc. SPIE 0554, 426–438 (1986).
[Crossref]

1982 (1)

1980 (1)

K. P. Thompson, “A graphic approach to the analysis of perturbed optical systems,” Proc. SPIE 0237, 127–134 (1980).
[Crossref]

1972 (1)

E. Granger and K. Cupery, “An optical merit function (SQF), which correlates with subjective image judgements,” Photogr. Sci. Eng. 15, 221–230 (1972).

1965 (3)

1964 (2)

1963 (1)

F. Scott, R. M. Scott, and R. V. Shack, “The use of edge gradients in determining modulation transfer functions,” Photogr. Sci. Eng. 7, 64–68 (1963).

1956 (1)

H. H. Hopkins, “The frequency response of optical systems,” Proc. Phys. Soc. London Sect. B 69, 562–576 (1956).
[Crossref]

1948 (4)

O. Schade, “Electro-optical characteristics of television systems. Introduction and part I: characteristics of vision and visual systems,” RCA Rev. 9, 5–37 (1948).

O. Schade, “Electro-optical characteristics of television systems,part II: electro-optical specifications for television systems,” RCA Rev. 9, 245–286 (1948).

O. Schade, “Electro-optical characteristics of television systems,part III: electro-optical characteristics of camera systems,” RCA Rev. 9, 491 (1948).

O. Schade, “Electro-optical characteristics of television systems,part IV: correlation and evaluation of electro-optical characteristics of imaging systems,” RCA Rev. 9, 653–686 (1948).

1934 (1)

F. Zernike, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica 1, 689–704 (1934).
[Crossref]

Arnison, M. R.

Barakat, R.

Carellas, P. T.

P. T. Carellas and S. D. Fantone, “Why measure MTF?” Opt. Photon. News 1(6), 27–29 (1990).
[Crossref]

Cupery, K.

E. Granger and K. Cupery, “An optical merit function (SQF), which correlates with subjective image judgements,” Photogr. Sci. Eng. 15, 221–230 (1972).

Deller, C. A.

DeVries, G.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Fantone, S. D.

P. T. Carellas and S. D. Fantone, “Why measure MTF?” Opt. Photon. News 1(6), 27–29 (1990).
[Crossref]

Fienup, J. R.

Fleig, J. F.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Fletcher, P. A.

Forbes, G. W.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Granger, E.

E. Granger and K. Cupery, “An optical merit function (SQF), which correlates with subjective image judgements,” Photogr. Sci. Eng. 15, 221–230 (1972).

Hopkins, H. H.

H. H. Hopkins, “The frequency response of optical systems,” Proc. Phys. Soc. London Sect. B 69, 562–576 (1956).
[Crossref]

Houston, A.

Hultgren, B. O.

B. O. Hultgren, “Subjective quality factor revisited: a unification of objective sharpness measures,” Proc. SPIE 1249, 12–22 (1990).
[Crossref]

Koliopoulos, C. L.

Larkin, K. G.

Lawrence, G. N.

Liu, Y.-M.

Malacara, D.

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

Marchand, E. W.

Masaoka, K.

Miladinovic, D.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Morgan-Mar, D. P.

Murphy, P. E.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Nishida, Y.

O’Donohue, S.

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

Rolland, J. P.

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012).
[Crossref]

Schade, O.

O. Schade, “Electro-optical characteristics of television systems,part II: electro-optical specifications for television systems,” RCA Rev. 9, 245–286 (1948).

O. Schade, “Electro-optical characteristics of television systems,part III: electro-optical characteristics of camera systems,” RCA Rev. 9, 491 (1948).

O. Schade, “Electro-optical characteristics of television systems,part IV: correlation and evaluation of electro-optical characteristics of imaging systems,” RCA Rev. 9, 653–686 (1948).

O. Schade, “Electro-optical characteristics of television systems. Introduction and part I: characteristics of vision and visual systems,” RCA Rev. 9, 5–37 (1948).

Scott, F.

F. Scott, R. M. Scott, and R. V. Shack, “The use of edge gradients in determining modulation transfer functions,” Photogr. Sci. Eng. 7, 64–68 (1963).

Scott, R. M.

F. Scott, R. M. Scott, and R. V. Shack, “The use of edge gradients in determining modulation transfer functions,” Photogr. Sci. Eng. 7, 64–68 (1963).

Shack, R. V.

F. Scott, R. M. Scott, and R. V. Shack, “The use of edge gradients in determining modulation transfer functions,” Photogr. Sci. Eng. 7, 64–68 (1963).

Sugawara, M.

Tatian, B.

Thompson, K.

Thompson, K. P.

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012).
[Crossref]

K. P. Thompson, “Beyond optical design interaction between the lens designer and the real world,” Proc. SPIE 0554, 426–438 (1986).
[Crossref]

K. P. Thompson, “A graphic approach to the analysis of perturbed optical systems,” Proc. SPIE 0237, 127–134 (1980).
[Crossref]

K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. thesis (University of Arizona, 1980).

Yamashita, T.

Zernike, F.

F. Zernike, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica 1, 689–704 (1934).
[Crossref]

Appl. Opt. (3)

J. Opt. Soc. Am. (5)

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

Opt. Express (1)

Opt. Photon. News (2)

K. P. Thompson and J. P. Rolland, “Freeform optical surfaces: a revolution in imaging optical design,” Opt. Photon. News 23(6), 30–35 (2012).
[Crossref]

P. T. Carellas and S. D. Fantone, “Why measure MTF?” Opt. Photon. News 1(6), 27–29 (1990).
[Crossref]

Photogr. Sci. Eng. (2)

F. Scott, R. M. Scott, and R. V. Shack, “The use of edge gradients in determining modulation transfer functions,” Photogr. Sci. Eng. 7, 64–68 (1963).

E. Granger and K. Cupery, “An optical merit function (SQF), which correlates with subjective image judgements,” Photogr. Sci. Eng. 15, 221–230 (1972).

Physica (1)

F. Zernike, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica 1, 689–704 (1934).
[Crossref]

Proc. Phys. Soc. London Sect. B (1)

H. H. Hopkins, “The frequency response of optical systems,” Proc. Phys. Soc. London Sect. B 69, 562–576 (1956).
[Crossref]

Proc. SPIE (3)

K. P. Thompson, “A graphic approach to the analysis of perturbed optical systems,” Proc. SPIE 0237, 127–134 (1980).
[Crossref]

K. P. Thompson, “Beyond optical design interaction between the lens designer and the real world,” Proc. SPIE 0554, 426–438 (1986).
[Crossref]

B. O. Hultgren, “Subjective quality factor revisited: a unification of objective sharpness measures,” Proc. SPIE 1249, 12–22 (1990).
[Crossref]

RCA Rev. (4)

O. Schade, “Electro-optical characteristics of television systems. Introduction and part I: characteristics of vision and visual systems,” RCA Rev. 9, 5–37 (1948).

O. Schade, “Electro-optical characteristics of television systems,part II: electro-optical specifications for television systems,” RCA Rev. 9, 245–286 (1948).

O. Schade, “Electro-optical characteristics of television systems,part III: electro-optical characteristics of camera systems,” RCA Rev. 9, 491 (1948).

O. Schade, “Electro-optical characteristics of television systems,part IV: correlation and evaluation of electro-optical characteristics of imaging systems,” RCA Rev. 9, 653–686 (1948).

Other (12)

“Mil-std-150a photographic lenses,” (1959).

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

“Photography–Electronic still picture imaging–Resolution and spatial frequency responses,” (2017).

Imatest, 2017, http://imatest.com .

Mtf Mapper, 2017, https://sourceforge.net/projects/mtfmapper/ .

“Optics and photonics–Optical transfer function–Definitions and mathematical relationships,” .

“Optics and photonics–Optical transfer function–Principles and procedures of measurement,” .

“Optics and optical instruments–accuracy of optical transfer function (OTF) measurement,” .

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

“Meridian production camera test system,” 2017, http://optikos.com .

“Imagemaster pro 9,” 2017, http://trioptics.com .

K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. thesis (University of Arizona, 1980).

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Figures (9)

Fig. 1.
Fig. 1.

MTF FFD generated using the CODE V optical design code.

Fig. 2.
Fig. 2.

Block diagram of the mathematical relationships between various representations of an image. F T represents the Fourier transform.

Fig. 3.
Fig. 3.

Plot of the MTF as a function of spatial frequency for the 81 field points measured. Solid lines tangential, dashed lines sagittal MTF. A legend is omitted, as 81 entries would be unreasonable.

Fig. 4.
Fig. 4.

Each line represents a slice along which the MTF is measured at several points. The angle θ is the clocking angle between rotations. In this example, θ = 45 ° .

Fig. 5.
Fig. 5.

Example of a plot of MTF versus field for each of four azimuths. This type of display is information dense and is neither intuitive nor quick to read.

Fig. 6.
Fig. 6.

Example of the four types of MTF FFDs, from left to right, top to bottom: sagittal, tangential, average (T&S), difference (T&S). This lens is not well aligned, but this type of behavior is (surprisingly) extremely common.

Fig. 7.
Fig. 7.

Example of the four types of MTF FFDs, from left to right, top to bottom: sagittal, tangential, average (T&S), difference (T&S). This lens is well aligned.

Fig. 8.
Fig. 8.

(a) and (b) Nominal rotation of the lens under test, (c) and (d) after 90° rotation. The rotation is performed to measure the MTF for various azimuths of the lens under test. This spot or PSF was taken to lie on the optical axis of the lens, and the coma results from misalignment.

Fig. 9.
Fig. 9.

Set of difference (T&S) MTF FFDs generated based on measurements across four, eight, and 12 azimuths of the lens under test’s full FOV.

Equations (4)

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OTF ( ν x , ν y ) = | H ( ν x , ν y ) | exp ( i ϕ ( ν x , ν y ) ) ,
OTF ( ν x , ν y ) = PSF ( x , y ) exp ( 2 π i ν x ν y x y ) d x d y .
OTF ( ν x ) = LSF ( x ) exp ( 2 π i ν x x ) d x .
LSF ( x ) = d d x ESF ( x ) .

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