Abstract

A hybrid imaging system combines a modified optical imaging module and a digital postprocessing step. We define what to our knowledge is a new metric to quantify the blurring of a defocused image that is more suitable than the defocus parameter for describing defocused hybrid imaging systems. We use this metric to design a pupil phase grating to reduce the depth of field, thereby increasing the axial resolution, of an incoherent hybrid imaging system using quasi-monochromatic illumination. By introducing this grating at the exit pupil and digitally processing the output of the detector, we reduce the depth of field by more than a factor of 2. Finally, we examine the effect of using a CCD optical detector, instead of an ideal optical detector, on the reduction of the depth of field.

© 2002 Optical Society of America

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References

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1999

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

1998

1997

1995

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

1994

1988

1985

1984

Agard, D. A.

J. R. Swedlow, J. W. Sedat, D. A. Agard, “Deconvolution in optical microscopy,” in Deconvolution of Images and Spectra, 2nd ed., P. A. Janssen, ed. (Academic, San Diego, Calif., 1997), pp. 284–309.

Andres, P.

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Beveridge, G. S.

G. S. Beveridge, R. S. Schechter, Optimization: Theory and Practice (McGraw-Hill, New York, 1970), Chap. 8, pp. 355–507.

Bille, J.

Cathey, W. T.

Conchello, J. A.

Erhardt, A.

Franks, L. E.

L. E. Franks, Signal Theory, revised ed. (Dowden & Culver, Stroudsburg, Pa., 1981).

Frieden, B. R.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5, pp. 157–236.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6, pp. 126–171.

Greivenkamp, J. E.

Hegedus, Z. S.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 8, pp. 267–341.

Juskaitis, R.

Komitowski, D.

Kowalczyk, M.

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Lowman, A. E.

Martinez-Corral, M.

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Morris, G. M.

T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
[CrossRef]

Neil, M.

Ojeda-Casteñada, J.

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Rhodes, W. T.

Rushford, C. K.

Saavedra, G.

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Sales, T. R. M.

T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
[CrossRef]

Schechter, R. S.

G. S. Beveridge, R. S. Schechter, Optimization: Theory and Practice (McGraw-Hill, New York, 1970), Chap. 8, pp. 355–507.

Sedat, J. W.

J. R. Swedlow, J. W. Sedat, D. A. Agard, “Deconvolution in optical microscopy,” in Deconvolution of Images and Spectra, 2nd ed., P. A. Janssen, ed. (Academic, San Diego, Calif., 1997), pp. 284–309.

Sheppard, C. J.

Sherif, S. S.

S. S. Sherif, “Depth of field control in incoherent hybrid imaging systems,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 2002).

Swedlow, J. R.

J. R. Swedlow, J. W. Sedat, D. A. Agard, “Deconvolution in optical microscopy,” in Deconvolution of Images and Spectra, 2nd ed., P. A. Janssen, ed. (Academic, San Diego, Calif., 1997), pp. 284–309.

Wilson, T.

Zapata-Rodriguez, C.

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

Zinser, G.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

M. Martinez-Corral, P. Andres, J. Ojeda-Casteñada, G. Saavedra, “Tunable axial superresolution by annular binary filters. Applications to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

M. Martinez-Corral, P. Andres, C. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

T. R. M. Sales, G. M. Morris, “Axial superresolution with phase-only pupil filters,” Opt. Commun. 156, 227–230 (1998).
[CrossRef]

Opt. Lett.

Other

J. R. Swedlow, J. W. Sedat, D. A. Agard, “Deconvolution in optical microscopy,” in Deconvolution of Images and Spectra, 2nd ed., P. A. Janssen, ed. (Academic, San Diego, Calif., 1997), pp. 284–309.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6, pp. 126–171.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 8, pp. 267–341.

S. S. Sherif, “Depth of field control in incoherent hybrid imaging systems,” Ph.D. dissertation (University of Colorado, Boulder, Colo., 2002).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5, pp. 157–236.

L. E. Franks, Signal Theory, revised ed. (Dowden & Culver, Stroudsburg, Pa., 1981).

G. S. Beveridge, R. S. Schechter, Optimization: Theory and Practice (McGraw-Hill, New York, 1970), Chap. 8, pp. 355–507.

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Figures (11)

Fig. 1
Fig. 1

Defocused imaging system.

Fig. 2
Fig. 2

Hybrid imaging system.

Fig. 3
Fig. 3

Profile of a rectangular RDF phase grating.

Fig. 4
Fig. 4

Defocused diffraction-limited PSF with a rectangular RDF phase grating.

Fig. 5
Fig. 5

Defocused diffraction-limited PSF with a clear rectangular aperture.

Fig. 6
Fig. 6

Diffraction-limited Hilbert space angles with a clear aperture and a rectangular RDF phase grating.

Fig. 7
Fig. 7

Magnitude of a defocused diffraction-limited OTF with a rectangular RDF phase grating.

Fig. 8
Fig. 8

Phase angle of a defocused diffraction-limited OTF with a rectangular RDF phase grating.

Fig. 9
Fig. 9

Defocused diffraction-limited OTF with a clear aperture.

Fig. 10
Fig. 10

Computer-simulated images of a defocused spoke target with a clear rectangular aperture and a rectangular RDF phase grating.

Fig. 11
Fig. 11

Diffraction-limited and CCD-limited Hilbert space angles with a clear aperture and a rectangular RDF phase grating.

Tables (2)

Tables Icon

Table 1 Optimal Values of θ Corresponding to Different Number of Coefficients bn

Tables Icon

Table 2 Rectangular RDF Phase Grating Optimal Parameters

Equations (30)

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wx=121za-1zixmax2,
wy=121za-1ziymax2,
ψx=kwx,
ψy=kwy,
ψx=πλδzzazixmax2,
ψy=πλδzzaziymax2,
ψx=πλNAx2δz,
ψy=πλNAy2δz,
HInversefx, fy=HClear-aperturefx, fyHPhase-platefx, fyHPhase-platefx, fy0,=0HPhase-platefx, fy=0,
lc=cΔν,
Δνν= Δλλ,
lc= cλνΔλ,
lc= λ2Δλ.
λ2Δλ>OPDmax.
cos θψ= hu, 02, hu, ψ2hu, 02hu, ψ2,
hu, 02, hu, ψ2=-hu, 02hu, ψ2du,
hu, 02= -hu, 02hu, 02du1/2,
hu, ψ2= -hu, ψ2hu, ψ2du1/2.
hu, ν, ψx, ψy2= κ -11-11expjψxx2+ψxy2-jkuxmaxxzi+ νymaxyzidxdy2,
hu, ψx2= -11expjψxx2-jk fx+ uxmaxxzidx2.
minfhu, 02, hu, ψx2hu, 02hu, ψx2,
fx12n=-NN cn expjπnx,
cn=12-11 fxexp-jπnxdx.
fxn=0N an cos2πnϑx+n=1N bn sin2πnϑx.
fx=n=1N bn sin2πnϑx.
bk+1= bk-μcos θ k,
cos θk= cos θϑk cos θb1k   cos θbNkT,
fx, y=n=15 bn sin2πnϑx+n=15 bn sin2πnϑy.
λ2Δλ>OPDmax.
hu, ψx2CCD-limited=hu, ψx2Diffraction-limited* rectuacombuus,

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