Abstract

The polychromatic behavior in defocused planes produced by different types of axial apodizing and hyperresolving filter is studied. The image quality is determined by comparing the illuminance and chromaticity distributions of the aberration free system with different filters and without a filter. The comparison is done in equivalent planes according to the normalized illuminance.

© 1990 Optical Society of America

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References

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  1. P. Jacquinot, B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 31–186 (1964).
  2. C. S. Chung, H. H. Hopkins, “Influence of Non-Uniform Amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
    [CrossRef]
  3. Z. S. Hegedus, V. Sarafis, “Superresolving Filters in Confocally Scanned Imaging Systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  4. M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
    [CrossRef]
  5. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Ambiguity Function as a Design Tool for High Focal Depth,” Appl. Opt. 27, 790–795 (1988).
    [CrossRef] [PubMed]
  6. J. Ojeda-Castaneda, A. Díaz, “High Focal Depth by Quasibifocus,” Appl. Opt. 27, 4163–4165 (1988).
    [CrossRef]
  7. J. Ojeda-Castaneda, P. Andrés, A. Díaz, “Annular Apodizers for Low Sensitivity to Defocus and to Spherical Aberration,” Opt. Lett. 11, 487–489 (1986).
    [CrossRef] [PubMed]
  8. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. L. Montes, “Bessel Annular Apodizers: Imaging Characteristics,” Appl. Opt. 26, 2770–2772 (1987).
    [CrossRef] [PubMed]
  9. C. J. R. Sheppard, Z. S. Hegedus, “Axial Behavior of Pupil-Plane Filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
    [CrossRef]
  10. Z. S. Hegedus, “Pupil Filters in Confocal Imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 1028, 14–17 (1989).
  11. G. Indebetouw, H. X. Bai, “Imaging with Fresnel Zone Pupil Masks: Extended Depth of Field,” Appl. Opt. 23, 4299–4302 (1984).
    [CrossRef] [PubMed]
  12. M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).
  13. M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673–690 (1975).
    [CrossRef]
  14. M. J. Yzuel, F. Calvo, “A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations,” Opt. Acta 26, 1397–1406 (1979).
    [CrossRef]
  15. H. H. Hopkins, “Canonical and Real-Space Coordinates used in the Theory of Image Formation,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, Eds. (Academic, Orlando, FL, 1983), pp. 307–369.
  16. J. Tsujiuchi, “Correction of Optical Images by Compensation of Aberrations and by Spatial Frequency Filtering,” Prog. Opt. 2, 131–180 (1963).
    [CrossRef]

1989 (3)

M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
[CrossRef]

Z. S. Hegedus, “Pupil Filters in Confocal Imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 1028, 14–17 (1989).

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

1988 (4)

1987 (1)

1986 (2)

1984 (1)

1979 (1)

M. J. Yzuel, F. Calvo, “A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

1975 (1)

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673–690 (1975).
[CrossRef]

1964 (1)

P. Jacquinot, B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 31–186 (1964).

1963 (1)

J. Tsujiuchi, “Correction of Optical Images by Compensation of Aberrations and by Spatial Frequency Filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

Andrés, P.

Bai, H. X.

Berriel-Valdos, L. R.

Calvo, F.

M. J. Yzuel, F. Calvo, “A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

Campos, J.

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
[CrossRef]

Cansado, G.

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

Chung, C. S.

C. S. Chung, H. H. Hopkins, “Influence of Non-Uniform Amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[CrossRef]

Díaz, A.

Escalera, J. C.

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
[CrossRef]

Hegedus, Z. S.

Hopkins, H. H.

C. S. Chung, H. H. Hopkins, “Influence of Non-Uniform Amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[CrossRef]

H. H. Hopkins, “Canonical and Real-Space Coordinates used in the Theory of Image Formation,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, Eds. (Academic, Orlando, FL, 1983), pp. 307–369.

Indebetouw, G.

Jacquinot, P.

P. Jacquinot, B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 31–186 (1964).

Montes, E.

Montes, E. L.

Ojeda-Castaneda, J.

Roizen-Dossier, B.

P. Jacquinot, B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 31–186 (1964).

Santamaría, J.

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673–690 (1975).
[CrossRef]

Sarafis, V.

Sheppard, C. J. R.

Tsujiuchi, J.

J. Tsujiuchi, “Correction of Optical Images by Compensation of Aberrations and by Spatial Frequency Filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

Yzuel, M. J.

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
[CrossRef]

M. J. Yzuel, F. Calvo, “A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673–690 (1975).
[CrossRef]

Appl. Opt. (4)

J. Mod. Opt. (2)

C. S. Chung, H. H. Hopkins, “Influence of Non-Uniform Amplitude on PSF,” J. Mod. Opt. 35, 1485–1511 (1988).
[CrossRef]

M. J. Yzuel, J. C. Escalera, J. Campos, “3-D Differences on the Polychromatic Response Between Nonuniform Transmission Filters and Equivalent Pupils,” J. Mod. Opt. 36, 1341–1351 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Acta (2)

M. J. Yzuel, J. Santamaría, “Polychromatic Optical Image. Diffraction Limited System and Influence of the Longitudinal Chromatic Aberration,” Opt. Acta 22, 673–690 (1975).
[CrossRef]

M. J. Yzuel, F. Calvo, “A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations,” Opt. Acta 26, 1397–1406 (1979).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

Z. S. Hegedus, “Pupil Filters in Confocal Imaging,” Proc. Soc. Photo-Opt. Instrum. Eng. 1028, 14–17 (1989).

M. J. Yzuel, J. C. Escalera, G. Cansado, J. Campos, “Illuminance and Chromaticity of the Image of Optical Systems with Nonuniform Transmission Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 1013, 120–127 (1989).

Prog. Opt. (2)

J. Tsujiuchi, “Correction of Optical Images by Compensation of Aberrations and by Spatial Frequency Filtering,” Prog. Opt. 2, 131–180 (1963).
[CrossRef]

P. Jacquinot, B. Roizen-Dossier, “Apodisation,” Prog. Opt. 3, 31–186 (1964).

Other (1)

H. H. Hopkins, “Canonical and Real-Space Coordinates used in the Theory of Image Formation,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, Eds. (Academic, Orlando, FL, 1983), pp. 307–369.

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Figures (30)

Fig. 1
Fig. 1

Aberration free system without a filter: (a) illuminance and (b) chromaticity along the axis.

Fig. 2
Fig. 2

Aberration free system without a filter: (a) illuminance and (b) chromaticity in the δW20 = 0 plane.

Fig. 3
Fig. 3

Aberration free system without a filter: (a) illuminance and (b) chromaticity in the δW20 = 0.14 plane.

Fig. 4
Fig. 4

Aberration free system without a filter: (a) illuminance and (b) chromaticity in the δW20 = 0.24 plane.

Fig. 5
Fig. 5

Effect of the filter τ(r) = r2: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 6
Fig. 6

Effect of the filter τ(r) = 1 − r2: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 7
Fig. 7

Effect of the filter τ(r) = r2 or τ(r) = 1 − r2: (a) illuminance (– – – –, YN; —— YNF) and (b) chromaticity along the axis.

Fig. 8
Fig. 8

Transmission functions of the filters: 1, 1 − 6.75r2 + 13.5r4 − 6.75r6; 2, 1 − 4r2 + 4r4; 3, 6.75r2 − 13.5r4 + 13.5r6; 4, 4r2 − 4r4.

Fig. 9
Fig. 9

Effect of the filter τ(r) = 4r2 − 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity along the axis.

Fig. 10
Fig. 10

Effect of the filter τ(r) = 4r2 − 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 11
Fig. 11

Effect of the filter τ(r) = 4r2 − 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.18 plane.

Fig. 12
Fig. 12

Effect of the filter τ(r) = 4r2 − 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.32 plane.

Fig. 13
Fig. 13

Effect of the filter τ(r) = 4r2 − 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.47 plane.

Fig. 14
Fig. 14

Effect of the filter τ(r) = 6.75r2 − 13.5r4 + 6.75r6: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity along the axis.

Fig. 15
Fig. 15

Effect of the filter τ(r) = 6.75r2 − 13.5r4 + 6.75r6: (a) illuminance (– – – –, YN; ——,YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 16
Fig. 16

Effect of the filter τ(r) = 6.75r2 − 13.5r4 + 6.75r6: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.2 plane.

Fig. 17
Fig. 17

Effect of the filter τ(r) = 6.75r2 − 13.5r4 + 6.75r6: (a) illuminance, (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.36 plane.

Fig. 18
Fig. 18

Effect of the filter τ(r) = 6.75r2 − 13.5r4 + 6.75r6: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.52 plane.

Fig. 19
Fig. 19

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——,YNF) and (b) chromaticity along the axis.

Fig. 20
Fig. 20

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——,YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 21
Fig. 21

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——,YNF) and (b) chromaticity in the δW20 = 0.1 plane.

Fig. 22
Fig. 22

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.18 plane.

Fig. 23
Fig. 23

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.68 plane.

Fig. 24
Fig. 24

Effect of the filter τ(r) = 1 − 4r2 + 4r4: (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.35 plane.

Fig. 25
Fig. 25

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r6: (a) illuminance(– – – –, YN; ——, YNF) and (b) chromaticity along the axis.

Fig. 26
Fig. 26

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r6: (a) illuminance(– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0 plane.

Fig. 27
Fig. 27

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r6: (a) illuminance(– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.12 plane.

Fig. 28
Fig. 28

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r6 : (a) illuminance (– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.21 plane.

Fig. 29
Fig. 29

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r6: (a) illuminance(– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.67 plane.

Fig. 30
Fig. 30

Effect of the filter τ(r) = 1 − 6.75r2 + 13.5r4 − 6.75r 6: (a) illuminance(– – – –, YN; ——, YNF) and (b) chromaticity in the δW20 = 0.39 plane.

Tables (1)

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Table I Some Image Quality Parameters for the Aberration Free System with Different Filters

Equations (7)

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X = λ 1 λ 2 S ( λ ) G λ ( ρ , ψ ) x ¯ λ d λ , Y = λ 1 λ 2 S ( λ ) G λ ( ρ , ψ ) y ¯ λ d λ , Z = λ 1 λ 2 S ( λ ) G λ ( ρ , ψ ) z ¯ λ d λ .
x = X X + Y + Z ,             y = Y X + Y + Z .
G λ ( ρ ) = 1 λ 2 F λ ( ρ ) 2 ,
F λ ( ρ ) = 1 A A f ( r , φ ) exp ( i 2 π ρ r cos φ ) r d r d φ ,
f ( r , φ ) = { τ ( r , φ ) exp [ i 2 π W ( r , φ ) ] within A 0 outside ,
W ( r ) = m W m r m , τ ( r ) = A 00 + A 20 r 2 + A 40 r 4 + .
Y N = λ 1 λ 2 S ( λ ) G λ ( ρ ) y ¯ λ d λ λ 1 λ 2 S ( λ ) 1 λ 2 y ¯ λ d λ , Y N F = λ 1 λ 2 S ( λ ) G λ ( ρ ) y ¯ λ d λ λ 1 λ 2 S ( λ ) G O F λ ( 0 ) y ¯ λ d λ .

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