Abstract

Recently a spatial spiral phase filter in a Fourier plane of a microscopic imaging setup has been demonstrated to produce edge enhancement and relief-like shadow formation of amplitude and phase samples. Here we demonstrate that a sequence of at least 3 spatially filtered images, which are recorded with different rotational orientations of the spiral phase plate, can be used to obtain a quantitative reconstruction of both, amplitude and phase information of a complex microscopic sample, i.e. an object consisting of mixed absorptive and refractive components. The method is demonstrated using a calibrated phase sample, and an epithelial cheek cell.

© 2006 Optical Society of America

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  1. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Spiral interferogram analysis," to appear in JOSA A (2006).
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Am. A,  18,1862-1870 (2001).
    [CrossRef]
  12. J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, "Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator," J. Opt. Soc. Am. A,  22,2766-2773 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  15. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17,221-223 (1992).
    [CrossRef] [PubMed]
  16. H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
    [CrossRef]
  17. A. Y. M. NG, C. W. See, and M. G. Somekh, "Quantitative optical microscope with enhanced resolution using a pixelated liquid crystal spatial light modulator," J. Microscopy 214,334-340 (2004).
    [CrossRef]
  18. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, "Fourier phase microscopy for investigation of biological structures and dynamics," Opt. Lett. 29,2503-2502 (2004).
    [CrossRef] [PubMed]
  19. K. G. Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 13, 8097-(8121) (2005).
    [CrossRef] [PubMed]
  20. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The new physical optics notebook: Tutorials in Fourier optics (SPIE Optical Engineering Press, Bellingham, Washington, 1989).
    [CrossRef]

2006

2005

2004

2001

2000

1994

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
[CrossRef]

1993

Z. Jaroszewicz and A. Kolodziejczyk, "Zone plates performing generalized Hankel transforms and their metrological applications," Opt. Commun. 102, 391-396 (1993).
[CrossRef]

1992

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17,221-223 (1992).
[CrossRef] [PubMed]

’t Hooft, G. W.

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

Badizadegan, K.

Bernet, S.

Bone, D. J.

Campos, J.

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

Cottrell, D. M.

Crabtree, K.

Dasari, R. R.

Davis, J. A.

De la Rosa, I.

Deflores, L. P.

Eliel, E. R.

Feld, M. S.

Fürhapter, S.

Heckenberg, N. R.

Iwai, H.

Jaroszewicz, Z.

Z. Jaroszewicz and A. Kolodziejczyk, "Zone plates performing generalized Hankel transforms and their metrological applications," Opt. Commun. 102, 391-396 (1993).
[CrossRef]

Jesacher, A.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, "Spiral interferometry," Opt. Lett. 30,1953-1955 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Shadow effects in spiral phase contrast microscopy," Phys. Rev. Lett. 94,233902 (2005).
[CrossRef] [PubMed]

Kadono, H.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
[CrossRef]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

Kloosterboer, J. G.

Kolodziejczyk, A.

Z. Jaroszewicz and A. Kolodziejczyk, "Zone plates performing generalized Hankel transforms and their metrological applications," Opt. Commun. 102, 391-396 (1993).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Am. A,  18,1862-1870 (2001).
[CrossRef]

McDuff, R.

McNamara, D. E.

Miramontes, G.

Moreno, I.

Oemrawsingh, S. S. R.

Ogusu, M.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
[CrossRef]

Oldfield, M. A.

Popescu, G.

Quiroga, J. A.

Ritsch-Marte, M.

Sheppard, C. J. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

Smith, C. P.

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

Swartzlander, G. A.

Toyooka, S.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
[CrossRef]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

van Houwelingen, J. A.W.

Vaughan, J. C.

Verstegen, E. J. K.

Villa, J.

White, A. G.

Woerdman, J. P.

Appl. Opt.

J. Microscopy

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, "Linear phase imaging using differential interference contrast microscopy," J. Microscopy 214,7-12 (2004).
[CrossRef]

A. Y. M. NG, C. W. See, and M. G. Somekh, "Quantitative optical microscope with enhanced resolution using a pixelated liquid crystal spatial light modulator," J. Microscopy 214,334-340 (2004).
[CrossRef]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39,1147-1154 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

H. Kadono, M. Ogusu, and S. Toyooka, "Phase shifting common path interferometer using a liquid-crystal phase modulator," Opt. Commun. 110,391-400 (1994).
[CrossRef]

Z. Jaroszewicz and A. Kolodziejczyk, "Zone plates performing generalized Hankel transforms and their metrological applications," Opt. Commun. 102, 391-396 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Shadow effects in spiral phase contrast microscopy," Phys. Rev. Lett. 94,233902 (2005).
[CrossRef] [PubMed]

Other

A. Jesacher, S. F¨urhapter, S. Bernet, and M. Ritsch-Marte, "Spiral interferogram analysis," to appear in JOSA A (2006).

K. G. Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 13, 8097-(8121) (2005).
[CrossRef] [PubMed]

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The new physical optics notebook: Tutorials in Fourier optics (SPIE Optical Engineering Press, Bellingham, Washington, 1989).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Basic principle of a spiral phase plate spatial Fourier filter. A transmissive input image is illuminated by a plane wave. The illumination beam is scattered into the directions of amplitude or phase gradients within the input image (two directions indicated by red and blue rays). The largest part of the illumination light passes without being scattered (green rays). A first lens (L1) located at a focal distance after the input image creates a Fourier transform of the image in its right focal plane, where the spiral phase plate is located. The design of the spiral phase plate is shown below (grey-values correspond to phase values in a range between 0 and 2π). The undiffracted part of the illumination beam (green) corresponds to the zero-order Fourier component of the image field and focuses in the center of the phase plate. The diffracted parts of the input field (red and blue) focus at different positions at the spiral phase plate (indicated below), which are determined by their propagation directions in front of L1, and thus by the gradient directions within the input image. The spiral phase plate adds a phase offset to each off-axis beam. A second lens L2 placed at a focal distance behind the spiral phase plate performs a reverse Fourier transform and creates the output image in its right focal plane. There, the zero-order component of the incident light field (green) is again a plane wave, superposing coherently with the remaining light field. This remaining light field now carries a spatially dependent phase-offset with respect to the input image, which corresponds to the geometrical angle into which the (amplitude- or phase) gradient of the input image is directed.

Fig. 2.
Fig. 2.

Sketch of the experimental setup: The sample is illuminated with a collimated white-light beam. The transmitted light passes the objective (NA 0.95, 63x), then a first folding mirror M1, and a set of two lenses L1 and L2, which project the Fourier transform of the image at the upper part of a reflective SLM. There, a spiral phase creating hologram with a typical fork-like dislocation in its center is displayed (as sketched in the upper part of the SLM image). If the zero-order Fourier component of the incident light field coincides with the central grating dislocation, the first order diffracted light field is the desired spiral phase filtered image, however, with an undesired dispersion due to the bandwidth of the illumination light (indicated as red/green/blue rays in the figure). In order to compensate for the dispersion, the diffracted light field passes through a further Fourier-transforming lens L3, which creates a real image in its focal plane where a mirror M2 is located. The mirror is adjusted such that the back-reflected light passes again through the Fourier-transforming lens L3 and focuses at another position on the SLM. There, a “normal” grating with the same spatial frequency as that of the spiral phase hologram is displayed (lower image at the right side), from where another first-order diffraction process compensates the dispersion induced by the first one. Finally, the diffracted light field is reflected by a further folding mirror M3 to a camera objective lens L4, which projects the spatially filtered image at a CCD chip.

Fig. 3.
Fig. 3.

Imaging of a Richardson phase pattern. The total length of the two scale bars at the right and lower parts of the image are 80 μm, each divided into 8 major intervals with a length of 10 μm. All images are displayed as negatives (i.e. dark areas correspond to bright structures in the real images) for better image contrast. (A), (B), and (C) are three shadow-effect images recorded at spiral phase plate angles of 0, 2π/3 and 4π/3, respectively. For comparison, (D) is a brightfield image recorded with our setup by substituting the spiral phase hologram at the SLM by a “normal” grating. (E) and (F) are the corresponding intensity and phase images, respectively, obtained by numerical processing of the shadow-images (A)–(C) according to the method described in the text.

Fig. 4.
Fig. 4.

Comparison of the spiral phase contrast method with data obtained from an atomic force microscope (AFM). (A) shows a section from the sample displayed in Figure 3(F), which corresponds to the section (B) scanned with the AFM. In (C), the phase topography of the selected section as measured with the spiral phase method is displayed as a surface plot, with the calculated depth of the etched pattern scaled in absolute units. It turns out that the pattern depth measured with the spiral phase method seems to be (150 ± 20) nm as compared to the AFM reference measurement, where a depth of (240 ± 10) nm is obtained.

Fig. 5.
Fig. 5.

Spiral phase imaging of a cheek cell. (A) is a bright-field image of the cell. (B–D) are three shadow-effect images with apparent illumination directions of 0, 2π/3 and 4π/3, respectively. (E) and (F) are numerically processed intensity transmission and phase profile images of the sample. (G) is a surface plot of the phase profile, displaying the absolute calculated phase shift (without calibration correction) in radians.

Equations (12)

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

I out 1,2,3 = ( E in E in 0 ) Φ exp ( i α 1,2,3 ) + E in 0 2
I out 1,2,3 = ( E in E in 0 ) Φ 2 + E in 0 2
+ [ ( E in E in 0 ) Φ ] E in 0 * exp ( i α 1,2,3 )
+ [ ( E in E in 0 ) Φ ] * E in 0 exp ( i α 1,2,3 )
I C = 1 3 [ I out 1 exp ( i α 1 ) + I out 2 exp ( i α 2 ) + I out 3 exp ( i α 3 ) ]
I C = [ ( E in E in 0 ) Φ ] E in 0 *
( E in E in 0 ) E in 0 * = I C Φ 1
E in ( x , y ) exp [ i ( θ in ( x , y ) θ in 0 ) ] = ( I C Φ 1 + E in 0 2 ) E in 0
I Av = 1 3 ( I out 1 + I out 2 + I out 3 )
I Av = ( E in E in 0 ) Φ 2 + E in 0 2
E in 0 4 I Av E in 0 2 + I C 2 = 0 ,
E in 0 2 = 1 2 I Av ± 1 2 I Av 2 4 I C 2

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