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  1. Y. Ukita, J. Tsujiuchi, “Interferometric study of microscope objectives,” Optica. Acta 5, 39 (1958); J. Tsujiuchi, “Influence de l’aberration du condenseur sur l’image formee dans un microscope,” Rev. opt. 38, 57 (1959); “Un filtre ameriorant les images aberrantes et son utilisation comme filtre a deux ou trois foyers,” Rev. opt. 37, 1 (1958); “Restitution des images aberrantes par le filtrage des frequences spatiales,” Optica Acta 7, 243, 385 (1960); ibid. 8, 161 (1961).
    [Crossref]
  2. K. Sayanagi, “Information volume of photographic lens (I)–(V),” Φyōbutsuri 25, 189, 193, 443, 449 (1956); ibid. 26, 425 (1957); “Optical noise filter,” Φyōbutsuri 27, 623 (1958); “Response function of the photographic adjacency effect,” Φyōbutsuri 29, 155 (1960).
  3. H. Kubota, H. Ohzu, “Method of measurement of response function by means of random chart,”J. Opt. Soc. Am. 47, 666 (1957).
    [Crossref]
  4. N. Joichi, “The effect of ground glass on the coherency of transmitted or reflected light,” Φyōbutsuri 27, 634 (1958).
  5. K. Kinoshita, S. Tatsuoka, “Distortion of a lens in spatial frequency domain,” Φyōbutsuri 29, 195 (1960); “The distortion factor of a photographic lens,” Φyōbutsuri 29, 679 (1960); M. Tamura, “Influence of Photo-negative graininess upon the resolving power of photographic lenses,” Φyōbutsuri 25, 199 (1956).
  6. S. Ooue, “Response function of the eye,” Φyōbutsuri 28, 531 (1959); “Graininess and granularity of photographic materials (I) (II) (III),” Φyōbutsuri 29, 169, 528, 685 (1960); S. Ooue, I. Hatanaka, “Determination of grain size distribution of silver halide by autocorrelation function,” Φyōbutsuri 30, 180 (1961).
  7. A. Hattori, “Measurement of response function of focussing screen,” Φyōbutsuri 27, 144 (1958).
  8. H. Gamo, “Intensity matrix and degree of coherence,”J. Opt. Soc. Am. 47, 976 (1957); “Transformation of Intensity matrix by the transmission of a pupil,”J. Opt. Soc. Am. 48, 136 (1958).
    [Crossref]
  9. H. Ito, “Asymptotic behaviour of the response function of an optical system with the primary spherical aberration,”J. Phys. Soc. Japan 13, 639 (1958).
    [Crossref]
  10. I. Ogura, “Asymptotic behaviour of the response function of optical systems,”J. Opt. Soc. Am. 48, 579 (1958).
    [Crossref]
  11. K. Miyamoto, “On a comparison between wave optics and geometrical optics by using Fourier analysis I, II, III,”J. Opt. Soc. Am. 48, 57, 567 (1958); ibid. 49, 35 (1959); H. Kubota, K. Miyamoto, K. Murata,” Einige Untersuchungen uber die Ubertragungsfunktion,” Optik 17, 143 (1960).
    [Crossref]
  12. H. Kubota, H. Saito, “Further study on the diffraction images in the polarizing microscope,”J. Opt. Soc. Am. 50, 1020 (1960); H. Saito, “The study on diffraction anomaly in optical systems,” Repts. Inst. Ind. Sci., Univ. of Tokyo 9, No. 3 (1960).
    [Crossref]
  13. E. L. O’Neill, T. Asakura, “Optical image formation in terms of entropy transformations,”J. Phys. Soc. Japan 16, 301 (1961); T. Asakura, R. Barakat, “Annular and annulus apertures with spherical aberration and defocussing,” Φyōbutsuri 30, 728 (1961).
    [Crossref]
  14. K. Kinoshita; to be published.
  15. K. Murata, “Measurement of response function of optical systems,” Φyōbutsuri 28, 276 (1959); “Ein Apparat zur Messung von Übertragungsfunktionen optischer Systems,” Optik 17, 152 (1960).
  16. T. Ose, “On the measurement of response function from the contrast of chart,” Sci. Light 7, 85 (1958); “Study on the measurements of optical transfer function for photographic lenses,” Repts. Inst. Ind. Sci., Univ. of Tokyo Vol. 11, No. 4 (1961).
  17. T. Suzuki, “Measurement of response function,” Φyōbutsuri 26, 331 (1957).
  18. K. Sayanagi, “Fourier analysis with a monofilter for measurement of response function of optical system,” Φyōbutsuri 27, 636 (1958).
  19. T. Tsuruta, “A new type of shearing interferometer and its application to measurement of transfer functions of microscope objective, Φyōbutsuri 30, 770 (1961).

1961 (2)

E. L. O’Neill, T. Asakura, “Optical image formation in terms of entropy transformations,”J. Phys. Soc. Japan 16, 301 (1961); T. Asakura, R. Barakat, “Annular and annulus apertures with spherical aberration and defocussing,” Φyōbutsuri 30, 728 (1961).
[Crossref]

T. Tsuruta, “A new type of shearing interferometer and its application to measurement of transfer functions of microscope objective, Φyōbutsuri 30, 770 (1961).

1960 (2)

H. Kubota, H. Saito, “Further study on the diffraction images in the polarizing microscope,”J. Opt. Soc. Am. 50, 1020 (1960); H. Saito, “The study on diffraction anomaly in optical systems,” Repts. Inst. Ind. Sci., Univ. of Tokyo 9, No. 3 (1960).
[Crossref]

K. Kinoshita, S. Tatsuoka, “Distortion of a lens in spatial frequency domain,” Φyōbutsuri 29, 195 (1960); “The distortion factor of a photographic lens,” Φyōbutsuri 29, 679 (1960); M. Tamura, “Influence of Photo-negative graininess upon the resolving power of photographic lenses,” Φyōbutsuri 25, 199 (1956).

1959 (2)

S. Ooue, “Response function of the eye,” Φyōbutsuri 28, 531 (1959); “Graininess and granularity of photographic materials (I) (II) (III),” Φyōbutsuri 29, 169, 528, 685 (1960); S. Ooue, I. Hatanaka, “Determination of grain size distribution of silver halide by autocorrelation function,” Φyōbutsuri 30, 180 (1961).

K. Murata, “Measurement of response function of optical systems,” Φyōbutsuri 28, 276 (1959); “Ein Apparat zur Messung von Übertragungsfunktionen optischer Systems,” Optik 17, 152 (1960).

1958 (8)

T. Ose, “On the measurement of response function from the contrast of chart,” Sci. Light 7, 85 (1958); “Study on the measurements of optical transfer function for photographic lenses,” Repts. Inst. Ind. Sci., Univ. of Tokyo Vol. 11, No. 4 (1961).

A. Hattori, “Measurement of response function of focussing screen,” Φyōbutsuri 27, 144 (1958).

Y. Ukita, J. Tsujiuchi, “Interferometric study of microscope objectives,” Optica. Acta 5, 39 (1958); J. Tsujiuchi, “Influence de l’aberration du condenseur sur l’image formee dans un microscope,” Rev. opt. 38, 57 (1959); “Un filtre ameriorant les images aberrantes et son utilisation comme filtre a deux ou trois foyers,” Rev. opt. 37, 1 (1958); “Restitution des images aberrantes par le filtrage des frequences spatiales,” Optica Acta 7, 243, 385 (1960); ibid. 8, 161 (1961).
[Crossref]

K. Sayanagi, “Fourier analysis with a monofilter for measurement of response function of optical system,” Φyōbutsuri 27, 636 (1958).

I. Ogura, “Asymptotic behaviour of the response function of optical systems,”J. Opt. Soc. Am. 48, 579 (1958).
[Crossref]

K. Miyamoto, “On a comparison between wave optics and geometrical optics by using Fourier analysis I, II, III,”J. Opt. Soc. Am. 48, 57, 567 (1958); ibid. 49, 35 (1959); H. Kubota, K. Miyamoto, K. Murata,” Einige Untersuchungen uber die Ubertragungsfunktion,” Optik 17, 143 (1960).
[Crossref]

N. Joichi, “The effect of ground glass on the coherency of transmitted or reflected light,” Φyōbutsuri 27, 634 (1958).

H. Ito, “Asymptotic behaviour of the response function of an optical system with the primary spherical aberration,”J. Phys. Soc. Japan 13, 639 (1958).
[Crossref]

1957 (3)

1956 (1)

K. Sayanagi, “Information volume of photographic lens (I)–(V),” Φyōbutsuri 25, 189, 193, 443, 449 (1956); ibid. 26, 425 (1957); “Optical noise filter,” Φyōbutsuri 27, 623 (1958); “Response function of the photographic adjacency effect,” Φyōbutsuri 29, 155 (1960).

Asakura, T.

E. L. O’Neill, T. Asakura, “Optical image formation in terms of entropy transformations,”J. Phys. Soc. Japan 16, 301 (1961); T. Asakura, R. Barakat, “Annular and annulus apertures with spherical aberration and defocussing,” Φyōbutsuri 30, 728 (1961).
[Crossref]

Gamo, H.

Hattori, A.

A. Hattori, “Measurement of response function of focussing screen,” Φyōbutsuri 27, 144 (1958).

Ito, H.

H. Ito, “Asymptotic behaviour of the response function of an optical system with the primary spherical aberration,”J. Phys. Soc. Japan 13, 639 (1958).
[Crossref]

Joichi, N.

N. Joichi, “The effect of ground glass on the coherency of transmitted or reflected light,” Φyōbutsuri 27, 634 (1958).

Kinoshita, K.

K. Kinoshita, S. Tatsuoka, “Distortion of a lens in spatial frequency domain,” Φyōbutsuri 29, 195 (1960); “The distortion factor of a photographic lens,” Φyōbutsuri 29, 679 (1960); M. Tamura, “Influence of Photo-negative graininess upon the resolving power of photographic lenses,” Φyōbutsuri 25, 199 (1956).

K. Kinoshita; to be published.

Kubota, H.

Miyamoto, K.

K. Miyamoto, “On a comparison between wave optics and geometrical optics by using Fourier analysis I, II, III,”J. Opt. Soc. Am. 48, 57, 567 (1958); ibid. 49, 35 (1959); H. Kubota, K. Miyamoto, K. Murata,” Einige Untersuchungen uber die Ubertragungsfunktion,” Optik 17, 143 (1960).
[Crossref]

Murata, K.

K. Murata, “Measurement of response function of optical systems,” Φyōbutsuri 28, 276 (1959); “Ein Apparat zur Messung von Übertragungsfunktionen optischer Systems,” Optik 17, 152 (1960).

O’Neill, E. L.

E. L. O’Neill, T. Asakura, “Optical image formation in terms of entropy transformations,”J. Phys. Soc. Japan 16, 301 (1961); T. Asakura, R. Barakat, “Annular and annulus apertures with spherical aberration and defocussing,” Φyōbutsuri 30, 728 (1961).
[Crossref]

Ogura, I.

Ohzu, H.

Ooue, S.

S. Ooue, “Response function of the eye,” Φyōbutsuri 28, 531 (1959); “Graininess and granularity of photographic materials (I) (II) (III),” Φyōbutsuri 29, 169, 528, 685 (1960); S. Ooue, I. Hatanaka, “Determination of grain size distribution of silver halide by autocorrelation function,” Φyōbutsuri 30, 180 (1961).

Ose, T.

T. Ose, “On the measurement of response function from the contrast of chart,” Sci. Light 7, 85 (1958); “Study on the measurements of optical transfer function for photographic lenses,” Repts. Inst. Ind. Sci., Univ. of Tokyo Vol. 11, No. 4 (1961).

Saito, H.

Sayanagi, K.

K. Sayanagi, “Fourier analysis with a monofilter for measurement of response function of optical system,” Φyōbutsuri 27, 636 (1958).

K. Sayanagi, “Information volume of photographic lens (I)–(V),” Φyōbutsuri 25, 189, 193, 443, 449 (1956); ibid. 26, 425 (1957); “Optical noise filter,” Φyōbutsuri 27, 623 (1958); “Response function of the photographic adjacency effect,” Φyōbutsuri 29, 155 (1960).

Suzuki, T.

T. Suzuki, “Measurement of response function,” Φyōbutsuri 26, 331 (1957).

Tatsuoka, S.

K. Kinoshita, S. Tatsuoka, “Distortion of a lens in spatial frequency domain,” Φyōbutsuri 29, 195 (1960); “The distortion factor of a photographic lens,” Φyōbutsuri 29, 679 (1960); M. Tamura, “Influence of Photo-negative graininess upon the resolving power of photographic lenses,” Φyōbutsuri 25, 199 (1956).

Tsujiuchi, J.

Y. Ukita, J. Tsujiuchi, “Interferometric study of microscope objectives,” Optica. Acta 5, 39 (1958); J. Tsujiuchi, “Influence de l’aberration du condenseur sur l’image formee dans un microscope,” Rev. opt. 38, 57 (1959); “Un filtre ameriorant les images aberrantes et son utilisation comme filtre a deux ou trois foyers,” Rev. opt. 37, 1 (1958); “Restitution des images aberrantes par le filtrage des frequences spatiales,” Optica Acta 7, 243, 385 (1960); ibid. 8, 161 (1961).
[Crossref]

Tsuruta, T.

T. Tsuruta, “A new type of shearing interferometer and its application to measurement of transfer functions of microscope objective, Φyōbutsuri 30, 770 (1961).

Ukita, Y.

Y. Ukita, J. Tsujiuchi, “Interferometric study of microscope objectives,” Optica. Acta 5, 39 (1958); J. Tsujiuchi, “Influence de l’aberration du condenseur sur l’image formee dans un microscope,” Rev. opt. 38, 57 (1959); “Un filtre ameriorant les images aberrantes et son utilisation comme filtre a deux ou trois foyers,” Rev. opt. 37, 1 (1958); “Restitution des images aberrantes par le filtrage des frequences spatiales,” Optica Acta 7, 243, 385 (1960); ibid. 8, 161 (1961).
[Crossref]

Fyobutsuri (9)

N. Joichi, “The effect of ground glass on the coherency of transmitted or reflected light,” Φyōbutsuri 27, 634 (1958).

K. Kinoshita, S. Tatsuoka, “Distortion of a lens in spatial frequency domain,” Φyōbutsuri 29, 195 (1960); “The distortion factor of a photographic lens,” Φyōbutsuri 29, 679 (1960); M. Tamura, “Influence of Photo-negative graininess upon the resolving power of photographic lenses,” Φyōbutsuri 25, 199 (1956).

S. Ooue, “Response function of the eye,” Φyōbutsuri 28, 531 (1959); “Graininess and granularity of photographic materials (I) (II) (III),” Φyōbutsuri 29, 169, 528, 685 (1960); S. Ooue, I. Hatanaka, “Determination of grain size distribution of silver halide by autocorrelation function,” Φyōbutsuri 30, 180 (1961).

A. Hattori, “Measurement of response function of focussing screen,” Φyōbutsuri 27, 144 (1958).

K. Sayanagi, “Information volume of photographic lens (I)–(V),” Φyōbutsuri 25, 189, 193, 443, 449 (1956); ibid. 26, 425 (1957); “Optical noise filter,” Φyōbutsuri 27, 623 (1958); “Response function of the photographic adjacency effect,” Φyōbutsuri 29, 155 (1960).

K. Murata, “Measurement of response function of optical systems,” Φyōbutsuri 28, 276 (1959); “Ein Apparat zur Messung von Übertragungsfunktionen optischer Systems,” Optik 17, 152 (1960).

T. Suzuki, “Measurement of response function,” Φyōbutsuri 26, 331 (1957).

K. Sayanagi, “Fourier analysis with a monofilter for measurement of response function of optical system,” Φyōbutsuri 27, 636 (1958).

T. Tsuruta, “A new type of shearing interferometer and its application to measurement of transfer functions of microscope objective, Φyōbutsuri 30, 770 (1961).

J. Opt. Soc. Am. (5)

J. Phys. Soc. Japan (2)

E. L. O’Neill, T. Asakura, “Optical image formation in terms of entropy transformations,”J. Phys. Soc. Japan 16, 301 (1961); T. Asakura, R. Barakat, “Annular and annulus apertures with spherical aberration and defocussing,” Φyōbutsuri 30, 728 (1961).
[Crossref]

H. Ito, “Asymptotic behaviour of the response function of an optical system with the primary spherical aberration,”J. Phys. Soc. Japan 13, 639 (1958).
[Crossref]

Optica. Acta (1)

Y. Ukita, J. Tsujiuchi, “Interferometric study of microscope objectives,” Optica. Acta 5, 39 (1958); J. Tsujiuchi, “Influence de l’aberration du condenseur sur l’image formee dans un microscope,” Rev. opt. 38, 57 (1959); “Un filtre ameriorant les images aberrantes et son utilisation comme filtre a deux ou trois foyers,” Rev. opt. 37, 1 (1958); “Restitution des images aberrantes par le filtrage des frequences spatiales,” Optica Acta 7, 243, 385 (1960); ibid. 8, 161 (1961).
[Crossref]

Sci. Light (1)

T. Ose, “On the measurement of response function from the contrast of chart,” Sci. Light 7, 85 (1958); “Study on the measurements of optical transfer function for photographic lenses,” Repts. Inst. Ind. Sci., Univ. of Tokyo Vol. 11, No. 4 (1961).

Other (1)

K. Kinoshita; to be published.

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Figures (12)

Fig. 1
Fig. 1

Phase noise filter “Contimat.” (a) a plane view of the filter, (b) a sectional view of the filter, (c) a diagram of pupil function combined with the filter, (d) removal of moiré pattern by the filtering effect.

Fig. 2
Fig. 2

Transfer functions, R, of the grain pattern. (Space constant factor S in frequency numbers: the crossed points between the lines parallel to the axis abscissa through the point R = 1.0 and tangential to the end part of the transfer function curves.)

Fig. 3
Fig. 3

Transfer functions R(u) of the human eye, measured with varying luminance of the test field.

Fig. 4
Fig. 4

(a) Transfer function r(q) for the line image perpendicular to the meridional direction [coma ϕ = ωλυ(u2 + υ2)]. (b) θ, phase shift of r(q) = |r(q)| exp [−(q)]. Solid lines and dashed lines are the curves of wave-optical and geometric-optical transfer functions, respectively.

Fig. 5
Fig. 5

(a) Transfer function of the polarizing microscope. (b) Photograph of the Siemens star (dotted lines are loci of zero of the transfer function).

Fig. 6
Fig. 6

Direct-reading chart for the transfer function (Sayanagi). (a) Original chart. (b) Measured chart.

Fig. 7
Fig. 7

(a) General view of the transfer function-measuring instrument at the Technical Research Laboratory of the Japan Broadcasting Corporation (NHK). (b) The console. S—light source, C—chart, L—lens mounting, T, M—Braun tube, R—recorder.

Fig. 8
Fig. 8

Schematic diagram of the instrument for measuring transfer functions. L1, L2—lamp; K1, K2—condenser lens; K—collimator lens; M—diffuse plate; S—slit; O—lens under test; G—scanning chart (Foucault chart); F—interference filter; Z—beam chopper; S.Z.—cylindrical cam; S.G.—spiral wheel; S.M.—synchronous motor; S.S.—triangular chart; P.M.—photomultiplier; P.Z.—photocell; T.P.—view finder; V1, V2—amplifier; I1, I2—pulse former; F.F.—flip-flop; T—gate; S.R.—transfer function recorder.

Fig. 9
Fig. 9

Recordings of transfer function. (a) Amplitude |R(r)|. (b) Phase P(r).

Fig. 10
Fig. 10

(a) Transfer function-measurement instrument constructed by the Olympus Optical Company. (b) Its inner part (a cam to make recordings linear with respect to spatial frequencies).

Fig. 11
Fig. 11

(a) General view of the instrument for measuring transfer functions made by Ose at the Institute of Industrial Science, University of Tokyo. (b) Recording examples.

Fig. 12
Fig. 12

Sheared interferograms of wave fronts: aberration-free system for (a) s = 0.5, (b) s = 1.0, and (c) s = 1.5, and system with primary spherical aberration 2.0λ for (d) s = 0.5 and (e) a = 1.0 where s is the distance between the centers of sheared circles.

Equations (6)

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V = + R ( ν , ω ) d ν d ω
R ( ν , ω ) = 1 [ 1 + 4 π 2 σ 2 ( ν 2 + ω 2 ) ] 3 / 2
H = i ( λ i j λ j ) log 2 ( λ i j λ j ) ,
R w ( s , t ) = a 1 A λ s , λ t exp { 2 π i λ [ ϕ ( u + λ s 2 · υ + λ t 2 ) ϕ ( u λ s 2 · υ λ t 2 ) ] } d u d υ , R g ( s , t ) = a 1 A 0 0 exp { 2 π i ( s ϕ u + t ϕ υ ) } d u d υ , or = a 1 A 0 0 exp { 2 π i ( s x + t y ) } d u d υ ,
R g ( s , t ) = 1 N i = 1 N cos [ 2 π ( s x k + t y k ) ] i 1 N i = 1 N sin [ 2 π ( s x k + t y k ) ]
A ( r , θ ) = sin 2 θ · J 3 ( 2 π a r / λ l ) ( 2 π a r / λ l ) ,

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