Abstract

Several different performance criteria have been proposed for assessing the quality of visual afocal sights. Earlier research by one of the authors (Haig) has shown that a high degree of correlation exists between a subjective assessment of performance and the Strehl intensity ratio of the optical system. We discuss some of the problems in choosing an objective performance criterion for visual sights and describe equipment that has been developed for measuring the line Strehl ratio of binoculars, both on and off axes. The equipment can be modified for testing other types of visual sight. It can also be used for measuring several additional performance parameters such as the modulation transfer function, transmission, and field curvature.

© 1995 Optical Society of America

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References

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  1. R. Home, J. Poole, “Measurement of the preferred binocular dioptric settings at a high and low light level.” Opt. Acta 24, 97–98 (1977).
    [CrossRef]
  2. M. A. Bouman, F. L. van Nes, “Spatial modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 401–406 (1967).
    [CrossRef]
  3. Troxler (1804), quoted in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 2, Chap. 10, p. 197.
  4. G. J. Burton, N. D. Haig, “Criteria for the testing of afocal visual instruments,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 191–201 (1981).
  5. G. J. Burton, N. D. Haig, “Effects of the Seidel aberrations on visual target discrimination,” J. Opt. Soc. Am. A 1, 373–385 (1984).
    [CrossRef] [PubMed]
  6. N. D. Haig, G. J. Burton, “Effects of wavefront aberration on visual instrument performance and a consequential test technique,” Appl. Opt. 26, 492–500 (1987).
    [CrossRef] [PubMed]
  7. N. D. Haig, “The interferograms and spread functions of the sixth order aberrations,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 21–36 (1981).
  8. A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–279 (1947).
  9. H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
    [CrossRef]
  10. H. H. Hopkins, B. Zalar, “Aberration tolerances based on the line spread function,” J. Mod. Opt. 34, 371–406 (1987).
    [CrossRef]
  11. G. Kuwabara, “Studies on the image formed by lenses. 1. On the characteristics of an image and their quantitative representation,” J. Opt. Soc. Am 45, 309–319 (1955).
    [CrossRef]
  12. P. Mouroulis, H. Zhang, “Visual instrument quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
    [CrossRef] [PubMed]
  13. G. M. Bryam, “The physical and photochemical basis of visual resolving power. Part 1. The distribution of illumination in the retinal images,” J. Opt. Soc. Am. 34, 571–591 (1944).
    [CrossRef]
  14. T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
    [CrossRef]

1992

P. Mouroulis, H. Zhang, “Visual instrument quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
[CrossRef] [PubMed]

1987

1984

1978

T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
[CrossRef]

1977

R. Home, J. Poole, “Measurement of the preferred binocular dioptric settings at a high and low light level.” Opt. Acta 24, 97–98 (1977).
[CrossRef]

1967

1957

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

1955

G. Kuwabara, “Studies on the image formed by lenses. 1. On the characteristics of an image and their quantitative representation,” J. Opt. Soc. Am 45, 309–319 (1955).
[CrossRef]

1947

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–279 (1947).

1944

Barton, N. P.

T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
[CrossRef]

Bouman, M. A.

Bryam, G. M.

Burton, G. J.

Haig, N. D.

N. D. Haig, G. J. Burton, “Effects of wavefront aberration on visual instrument performance and a consequential test technique,” Appl. Opt. 26, 492–500 (1987).
[CrossRef] [PubMed]

G. J. Burton, N. D. Haig, “Effects of the Seidel aberrations on visual target discrimination,” J. Opt. Soc. Am. A 1, 373–385 (1984).
[CrossRef] [PubMed]

G. J. Burton, N. D. Haig, “Criteria for the testing of afocal visual instruments,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 191–201 (1981).

N. D. Haig, “The interferograms and spread functions of the sixth order aberrations,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 21–36 (1981).

Home, R.

R. Home, J. Poole, “Measurement of the preferred binocular dioptric settings at a high and low light level.” Opt. Acta 24, 97–98 (1977).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, B. Zalar, “Aberration tolerances based on the line spread function,” J. Mod. Opt. 34, 371–406 (1987).
[CrossRef]

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

Kuwabara, G.

G. Kuwabara, “Studies on the image formed by lenses. 1. On the characteristics of an image and their quantitative representation,” J. Opt. Soc. Am 45, 309–319 (1955).
[CrossRef]

Marechal, A.

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–279 (1947).

Mouroulis, P.

P. Mouroulis, H. Zhang, “Visual instrument quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
[CrossRef] [PubMed]

Nunn, M. L.

T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
[CrossRef]

Poole, J.

R. Home, J. Poole, “Measurement of the preferred binocular dioptric settings at a high and low light level.” Opt. Acta 24, 97–98 (1977).
[CrossRef]

Troxler,

Troxler (1804), quoted in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 2, Chap. 10, p. 197.

van Nes, F. L.

Williams, T. L.

T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
[CrossRef]

Zalar, B.

H. H. Hopkins, B. Zalar, “Aberration tolerances based on the line spread function,” J. Mod. Opt. 34, 371–406 (1987).
[CrossRef]

Zhang, H.

P. Mouroulis, H. Zhang, “Visual instrument quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
[CrossRef] [PubMed]

Appl. Opt.

J. Mod. Opt.

H. H. Hopkins, B. Zalar, “Aberration tolerances based on the line spread function,” J. Mod. Opt. 34, 371–406 (1987).
[CrossRef]

J. Opt. Soc. Am

G. Kuwabara, “Studies on the image formed by lenses. 1. On the characteristics of an image and their quantitative representation,” J. Opt. Soc. Am 45, 309–319 (1955).
[CrossRef]

J. Opt. Soc. Am. A

P. Mouroulis, H. Zhang, “Visual instrument quality metrics and the effects of coma and astigmatism,” J. Opt. Soc. Am. A 9, 34–42 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

R. Home, J. Poole, “Measurement of the preferred binocular dioptric settings at a high and low light level.” Opt. Acta 24, 97–98 (1977).
[CrossRef]

Opt. Acta

T. L. Williams, M. L. Nunn, N. P. Barton, “An afocal-system OTF test standard,” Opt. Acta 25, 1097–1111 (1978).
[CrossRef]

Proc. Phys. Soc. London Sect. B

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. London Sect. B 70, 449–470 (1957).
[CrossRef]

Rev. Opt. Theor. Instrum.

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum. 26, 257–279 (1947).

Other

N. D. Haig, “The interferograms and spread functions of the sixth order aberrations,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 21–36 (1981).

Troxler (1804), quoted in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 2, Chap. 10, p. 197.

G. J. Burton, N. D. Haig, “Criteria for the testing of afocal visual instruments,” in Assessment of Imaging Systems II, T. L. Williams, ed., Proc. Soc. Photo-Opt. Instrum. Eng.274, 191–201 (1981).

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Figures (16)

Fig. 1
Fig. 1

Typical human contrast-sensitivity-function responses adopted from Bouman and van Nes.2

Fig. 2
Fig. 2

Correlation of subjective/objective thresholds at 22.6 cycles/deg adopted from Burton and Haig.4

Fig. 3
Fig. 3

Diagram of the basic arrangement for measuring the Strehl ratio.

Fig. 4
Fig. 4

Block diagram of the control and signal-processing system.

Fig. 5
Fig. 5

Lens arrangement used for evaluating the Strehl measurement technique.

Fig. 6
Fig. 6

Comparison of the measured and theoretical through-focus LSR for the lens illustrated in Fig. 5.

Fig. 7
Fig. 7

Facility for measuring the LSR etc. of binoculars.

Fig. 8
Fig. 8

Method of changing between oculars.

Fig. 9
Fig. 9

Method of off-axis testing.

Fig. 10
Fig. 10

LSR as a function of the entrance-pupil diameter for a pair of 10 × 50 binoculars: (a) on axis, (b) ±5-deg off axis, (c) ±10-deg off axis. R and T refer to measurements in the radial (sagittal) and tangential azimuths, respectively.

Fig. 11
Fig. 11

LSR as a function of the image angle for a pair of 10 × 50 binoculars (entrance-pupil diameter, 30 mm).

Fig. 12
Fig. 12

Position of best focus as a function of the image angle for the measurements plotted in Fig. 11.

Fig. 13
Fig. 13

Through-focus LSR for different entrance-pupil diameters for a pair of 7 × 50 binoculars.

Fig. 14
Fig. 14

Comparison of the theoretical values of the PSR and the product of the radial and tangential LSR’s for a 10 × 60 telescope.

Fig. 15
Fig. 15

Through-focus values of the product of the radial and tangential LSR’s for the curves plotted in Fig. 13.

Fig. 16
Fig. 16

Through-focus values of the product of the radial and tangential LSR’s for both oculars of a set of six similar 7 × 50 binoculars. The numbers in the legend box refer to the serial numbers of the binoculars with L and R denoting the left and right oculars, respectively.

Equations (10)

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

I = 4 I b γ ( z o ) / π 2 ,
z o = π NA w / λ ,
γ ( z o ) = [ ( 1 ) n 2 ( 2 n + 1 ) z o ( 2 n + 1 ) / 1 2 3 2 ( 2 n 1 ) 2 ( 2 n + 1 ) 3 ( 2 n + 3 ) ] ,
LSR = I m / I = I m π 2 / 4 I b γ ( z o ) .
LSR c = LSR m × C .
LSR m = MTFtp ( s ) MTFd t ( s ) [ sin ( π w s ) / ( π w s ) ] d s / MTFdif ( s ) [ sin ( π w s ) / ( π w s ) ] d s ,
LSR c = MTFtp ( s ) [ sin ( π w s ) / ( π w s ) ] d s / MTFdif ( s ) [ sin ( π w s ) / ( π w s ) ] d s ,
C = MTFtp ( s ) [ sin ( π w s ) / s ] d s ] / MTFtp ( s ) MTFd t ( s ) [ sin ( π w s ) / s ] d s .
MTFtp ( s ) = { 2 arccos ( s / 2 ) sin [ 2 arccos ( s / 2 ) ] } / π ,
s = s ( λ / NA ) .

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