Abstract

We describe the design of a microscope combining rotational shear interferometer (RSI)-based coherence imaging with an objective lens to simultaneously obtain high numerical aperture and high depth of field imaging. We present experimental results showing the operation of this instrument.

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References

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  1. Daniel L. Marks, Ronald A. Stack, David J. Brady, David C. Munson and Rachael B. Brady, "Visible Cone-Beam tomography with a lensless interferometric camera," Science 284, 2164-2166 (1999).
    [CrossRef] [PubMed]
  2. Daniel L. Marks, Ronald A. Stack and David J. Brady "Three-dimensional coherence imaging in the Fresnel domain" Appl. Opt. 8, 1332-1342 (1999).
    [CrossRef]
  3. Sara Bradburn, Thomas W. Cathey and Edward R. Dowski, Jr. "Realizations of focus invariance in optical-digital systems with wave-front coding" Appl. Opt. 35, 9157-9166 (1997).
    [CrossRef]
  4. Sara C. Tucker, Thomas W. Cathey and Edward R. Dowski, Jr. "Extended depth of field and aberration control for inexpensive digital microscope systems," Opt. Express 4, 467-474 (1999), http://www.opticsexpress.org/oearchive/source/9522.htm.
    [CrossRef]
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, Cambridge, UK, 1995).
  6. J.D. Armitage and A.Lohmann, "Rotary shearing interferometry," Opt. Acta 12, 185-192 (1965).
    [CrossRef]
  7. F. Roddier, "Interferometric imaging in optical astronomy," Phys. Rep. 170, 97-166 (1988).
    [CrossRef]
  8. K. Itoh and Y. Ohtsuka, "Fourier-transform spectral imaging: retrieval of source information from three-dimensional spatial coherence," J. Opt. Soc. Am. A 3, 94-100 (1986).
    [CrossRef]
  9. K. Itoh, T. Inoue, and Y. Ichioka, "Interferometric spectral imaging and optical three-dimensional Fourier transformation," J. Appl. Phys 29, L1561-L1564 (1990).
  10. Zeiss Microscopes, http://www.zeiss.com.
  11. E. Hecht, Optics, (Addison and Wesley Inc., New York, 1998).

Other (11)

Daniel L. Marks, Ronald A. Stack, David J. Brady, David C. Munson and Rachael B. Brady, "Visible Cone-Beam tomography with a lensless interferometric camera," Science 284, 2164-2166 (1999).
[CrossRef] [PubMed]

Daniel L. Marks, Ronald A. Stack and David J. Brady "Three-dimensional coherence imaging in the Fresnel domain" Appl. Opt. 8, 1332-1342 (1999).
[CrossRef]

Sara Bradburn, Thomas W. Cathey and Edward R. Dowski, Jr. "Realizations of focus invariance in optical-digital systems with wave-front coding" Appl. Opt. 35, 9157-9166 (1997).
[CrossRef]

Sara C. Tucker, Thomas W. Cathey and Edward R. Dowski, Jr. "Extended depth of field and aberration control for inexpensive digital microscope systems," Opt. Express 4, 467-474 (1999), http://www.opticsexpress.org/oearchive/source/9522.htm.
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, Cambridge, UK, 1995).

J.D. Armitage and A.Lohmann, "Rotary shearing interferometry," Opt. Acta 12, 185-192 (1965).
[CrossRef]

F. Roddier, "Interferometric imaging in optical astronomy," Phys. Rep. 170, 97-166 (1988).
[CrossRef]

K. Itoh and Y. Ohtsuka, "Fourier-transform spectral imaging: retrieval of source information from three-dimensional spatial coherence," J. Opt. Soc. Am. A 3, 94-100 (1986).
[CrossRef]

K. Itoh, T. Inoue, and Y. Ichioka, "Interferometric spectral imaging and optical three-dimensional Fourier transformation," J. Appl. Phys 29, L1561-L1564 (1990).

Zeiss Microscopes, http://www.zeiss.com.

E. Hecht, Optics, (Addison and Wesley Inc., New York, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of a Rotational Shear Interferometer: RSI is a Michelson interferometer with folding mirrors. The folding axes of the mirrors lie in the transverse plane at angles of θ/2 and -θ/2 with respect to the x-axis. The translation stage dithers by a few microns during each image capture.

Fig. 2.
Fig. 2.

Schematic diagram of an mRSI

Fig. 3.
Fig. 3.

Images of a diffraction mask obtained from the mRSI: The mask was placed at a distance of (a) 4mm, (b) 6mm, (c) 13mm and (d) 30mm from the objective. The DC component of the Fourier transform has been blocked.

Fig. 4.
Fig. 4.

Images of two combined diffraction masks obtained from a light microscope and video camera

Fig. 5.
Fig. 5.

Images of the two diffraction masks obtained from the mRSI: (a) The masks are placed close to each other, (b) the masks are separated by an air gap of around 10mm. The angular scale of the images is 10°. Note that the two masks have different spatial scales in (b).

Equations (11)

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J ( Δ x , Δ y ) = I s ( r s ) z s 2 exp [ j 2 π λ z s ( x s Δ x + y s Δ y ) ] d 3 r s
S ( u , υ ) = J ( Δ x , Δ y ) exp [ j 2 π ( u Δ x + υ Δ y ) ] d Δ x Δ y
= I s ( r s ) z s 2 δ ( u x s λ z s , υ y s λ z s ) d 3 r s
I ( x f , y f , x g , y g ) = I 1 + I 2 + 2 Re { J ( Δ x , Δ y , q , Δ z ) }
Δ x ( x f , y f ) = 2 y f sin 2 θ
Δ y ( x f , y f ) = 2 x f sin 2 θ and
q ( x f , y f , x g , y g ) = ( y f x g x f y g ) sin ( 2 θ )
N . A . = λ Δ sin θ
Δ θ = Aperture diameter 0.15 m
Δ Ω = λ N Δ sin θ
I ( x f , y f ) = I 1 + I 2 + 2 Re { J ( Δ x , Δ y ) exp ( 2 πil / λ ) }

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