## Coherence-controlled holographic microscope |

Optics Express, Vol. 18, Issue 21, pp. 21990-22003 (2010)

http://dx.doi.org/10.1364/OE.18.021990

Acrobat PDF (1164 KB)

### Abstract

Transmitted-light coherence-controlled holographic microscope (CCHM) based on an off-axis achromatic interferometer allows us to use light sources of arbitrary degree of temporal and spatial coherence. Besides the conventional DHM modes such as quantitative phase contrast imaging and numerical 3D holographic reconstruction it provides high quality (speckle-free) imaging, improved lateral resolution and optical sectioning by coherence gating. Optical setup parameters and their limits for a technical realization are derived and described in detail. To demonstrate the optical sectioning property of the microscope a model sample uncovered and then covered with a diffuser was observed using a low-coherence light source.

© 2010 OSA

## 1. Introduction

*ex post*numerical refocusing.

2. F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. **38**(34), 7085–7094 (1999). [CrossRef]

5. F. Dubois, C. Yourassowsky, N. Callens, C. Minetti, and P. Queeckers, “Applications of digital holographic microscopes with partially spatial coherence sources,” J. Phys. Conference Series **139**, 012027 (2008). [CrossRef]

6. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. **24**(5), 291–293 (1999). [CrossRef]

7. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**(34), 6994–7001 (1999). [CrossRef]

8. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A **3**(6), 847–855 (1986). [CrossRef]

5. F. Dubois, C. Yourassowsky, N. Callens, C. Minetti, and P. Queeckers, “Applications of digital holographic microscopes with partially spatial coherence sources,” J. Phys. Conference Series **139**, 012027 (2008). [CrossRef]

9. P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. **44**(10), 1806–1812 (2005). [CrossRef] [PubMed]

6. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. **24**(5), 291–293 (1999). [CrossRef]

*z-*axis [11

11. J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. **19**(7), 074007 (2008). [CrossRef]

9. P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. **44**(10), 1806–1812 (2005). [CrossRef] [PubMed]

12. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. **30**(10), 1165–1167 (2005). [CrossRef] [PubMed]

13. D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. **43**(36), 6536–6544 (2004). [CrossRef]

15. B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. **11**(3), 34005 (2006). [CrossRef] [PubMed]

16. E. N. Leith and J. Upatnieks, “Holography with Achromatic-Fringe Systems,” J. Opt. Soc. Am. **57**(8), 975–980 (1967). [CrossRef]

18. E. N. Leith and G. J. Swanson, “Recording of phase-amplitude images,” Appl. Opt. **20**(17), 3081–3084 (1981). [CrossRef] [PubMed]

19. E. N. Leith and B. J. Chang, “Space-invariant holography with quasi-coherent light,” Appl. Opt. **12**(8), 1957–1963 (1973). [CrossRef] [PubMed]

20. E. N. Leith, W. C. Chien, K. D. Mills, B. D. Athey, and D. S. Dilworth, “Optical sectioning by holographic coherence imaging: a generalized analysis,” J. Opt. Soc. Am. A **20**(2), 380–387 (2003). [CrossRef]

21. R. Chmelík and Z. Harna, “Parallel-mode confocal microscope,” Opt. Eng. **38**(10), 1635–1639 (1999). [CrossRef]

21. R. Chmelík and Z. Harna, “Parallel-mode confocal microscope,” Opt. Eng. **38**(10), 1635–1639 (1999). [CrossRef]

22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE **4356**, 118–123 (2000). [CrossRef]

23. R. Chmelík and Z. Harna, “Surface profilometry by a parallel–mode confocal microscope,” Opt. Eng. **41**(4), 744–745 (2002). [CrossRef]

22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE **4356**, 118–123 (2000). [CrossRef]

24. R. ChmelÍk, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. **53**(18), 2673–2689 (2006). [CrossRef]

## 2. Optical setup and principles of operation

### 2.1 Basic setup parameters, origin of achromatic fringes

16. E. N. Leith and J. Upatnieks, “Holography with Achromatic-Fringe Systems,” J. Opt. Soc. Am. **57**(8), 975–980 (1967). [CrossRef]

*f*

_{G}and trace the axial ray coming out from the source (S) and passing through the relay lens (L). This ray traverses the grating and is split into two beams, each deflected by an angle

*ϑ*from the interferometer axis:where

*λ*is a wavelength of light. Interferometer arms are deflected by an angle

*ϑ*

_{0}corresponding to the central wavelength

*λ*

_{0}= 650 nm (see sec. 2.3).

*λ*=

*λ*

_{0}while for

*λ*≠

*λ*

_{0}it is laterally shifted. According to Eq. (1) the longer is

*λ*the bigger is

*ϑ*, so the primary images of the light source are shifted for longer

*λ*further from the interferometer axis and from each other.

*λ*the closer are the secondary images to the interferometer axis and to each other. So, if the beams emitted from the secondary images of the source were propagated directly to the output plane (OP), it would give rise to interference fringes of a different spatial frequency for a different wavelength

*λ*. Longer wavelength light beams would recombine being deflected by a smaller angle, thus producing interference fringes of lower spatial frequency and vice versa. For this reason the reference and the object interferometer arms has to be crossed, e.g. using mirrors (M) in the sense that the light beam coming from the upper objective lens (see Fig. 1) enters the output plane from bellow and vice versa. The arms can be crossed on the objectives side or on the condenser side of the interferometer, but not both.

*λ*, because the interferometer is achromatic. If an object is observed, an image plane off-axis hologram with the spatial carrier

*f*

_{OP}is formed in the output plane. Formation of the achromatic interference fringes is analysed in subsection 2.5.

### 2.2 Image processing

8. T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A **3**(6), 847–855 (1986). [CrossRef]

*f*

_{OP}; size of the window corresponds to the maximum image frequency

*f*

_{OM}. The frequency origin is then translated to the centre of the window and the windowed image spectrum is multiplied by the Hann window function in the form 0.5(1 – cos π

*ρ*), where

*ρ*is the normalized distance from the centre of the window with

*ρ*= 1 on the edge of the window. Finally, the image complex amplitude is computed using the two-dimensional inverse FFT and the image amplitude and phase are computed from the complex amplitude.

### 2.3 Spatial frequency of the diffraction grating

*λ*≠

*λ*

_{0}has generally non-zero intensity that cannot be neglected and has to be separated out from the pupils of condensers. It might decrease the contrast of interference fringes in the worst case if arrived at the output plane. Let us suppose the pupil of condenser to be identical with its mechanical aperture of a diameter

*d*, and to be placed in a distance

*l*from the grating, measured along the optical axis of the condenser, and the primary image of the light source to be imaged in the aperture plane and to be also

*d*in diameter. The distance from the centre of the zero order primary image to the centre of the aperture can be expressed approximately according to Eq. (1) as

*l*sin

*ϑ*

_{0}=

*lf*

_{G}

*λ*

_{0}. To ensure the zero order image be formed out of the condenser aperture, the distance

*lf*

_{G}

*λ*

_{0}has to be greater or equal to

*d*, and this gives the first condition for the spatial frequency:A positive value of the overlapindicates intersection of the zero order image with the condenser aperture (see Table 1 ).

*f*

_{OP}has to meet the holographic condition [24

24. R. ChmelÍk, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. **53**(18), 2673–2689 (2006). [CrossRef]

*f*

_{OM}is the maximum spatial frequency of the image complex amplitude limited by the objective lens with a numerical aperture NA and a magnification

*m*:

25. N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. **48**(34), H186–H195 (2009). [CrossRef] [PubMed]

*f*

_{G}is given by Eq. (1) and by the condition |sin

*ϑ*| ≤ 1 which gives

*f*

_{G}≤ 1/

*λ*. The greater is

*f*

_{G}, the finer is the interference structure in the output plane and the larger magnification is needed to resolve the fringes by a detector and thus the smaller is the field of view. Therefore it is convenient to keep

*f*

_{G}as low as possible.

*f*

_{G}= 71 mm

^{−1}which meets both the conditions given by Eq. (3) and Eq. (7) for most of wavelengths from a spectral transmittance interval of the microscope. At the same time it allows for a reasonable field of view width. The central wavelength was set to be

*λ*

_{0}= 650 nm with respect to application of the microscope in biology. Equation (1) then gives the deflection of the interferometer arms

*ϑ*

_{0}≈2.7°. The microscope employs four identical pieces of planachromatic microobjective lenses of 160 mm tube length and

*l*≈150 mm. Aperture diameters for some of the lenses used are specified in Table 1 together with the corresponding overlap Δ

*d*that indicates fulfilment of the first condition represented by Eq. (3) and the lower limit of

*λ*meeting the second condition given by Eq. (7). The last two columns of Table 1 specify the spectral transmittance intervals of the microscope for each of the microobjectives.

### 2.4 Output lens and the field of view

*m*

_{OL}of the output lens (OL) is dependent on the highest spatial frequency present in hologram at the output plane that has to be resolved and recorded digitally. Maximum spatial frequency equals to

*f*

_{OP}+

*f*

_{OM}, sum of the carrier frequency and the maximum image frequency [24

24. R. ChmelÍk, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. **53**(18), 2673–2689 (2006). [CrossRef]

*f*

_{D}(pixel density) of a detector:which in terms of Eq. (2) and Eq. (5) gives:

*f*

_{D}= 155 mm

^{−1}and Eq. (9) for

*f*

_{G}= 71 mm

^{−1}gives

*m*

_{OL}≥ 2.8. OL used in the microscope is a standard 4 × /0.12 microobjective lens, 160/–, i.e.

*m*

_{OL}= 4 and the condition by Eq. (9) is thus fulfilled. Field of view with this lens is 2.2 mm × 1.7 mm (2.8 mm diagonal), measured in OP.

_{OL}of OL is the second parameter that should be found. All the light passing through OP has to pass also through OL in order to form a hologram in the image plane of OL where a detector is placed. Maximum angle of a beam entering OL is given by sum of

*ϑ*

_{0}and α’, where α’ = arcsin(NA/

*m*) ≈1.5° is the aperture angle of the objective lenses in the image space (see Fig. 3b for illustration). The condition can be expressed as follows: NA

_{OL}≥ sin(

*ϑ*

_{0}+ α’) ≈sin

*ϑ*

_{0}+ sinα’. After substitution from Eq. (1) we get:

_{OL}≥ 0.071. Numerical aperture of the output lens used in our microscope is NA

_{OL}= 0.12 which is in agreement with (10).

*f*

_{OP}= 3

*f*

_{OM}, then the highest spatial frequency present at the output plane is

*f*

_{OP}+

*f*

_{OM}= 4

*f*

_{OM}. Maximum output spatial frequency in case of conventional incoherent imaging process is 2

*f*

_{OM}. Therefore CCHM requires the magnification

*m*

_{OL}of an output lens two times (at least) higher than the conventional microscope and the field of view size is thus two times (at least) smaller.

### 2.5 Spectral transmissivity of the microscope

*d*, a limitation in the spectral transmittance of the microscope has to be considered.

*λ*=

*λ*

_{0}coincide with the pupil centre. Then its displacement

*p*for

*λ*≠

*λ*

_{0}due to the dispersive power of the diffraction grating can be derived by differentiation of Eq. (1) and after approximations: cos

*ϑ*≈1 and Δ

*ϑ*≈

*p/l*for small angle

*ϑ*, it gives:

*λ*=

*λ*

_{0}, both the pupils are fully filled by the same section of the broad-source (see Fig. 2a ). For

*λ*≠

*λ*

_{0}, both the broad-source images are displaced from the pupil centre by distance

*p*, but in opposite directions (see Fig. 2b) and thus slightly different sections of the source appear in each pupil.

*λ*) to the imaging process (see the out-of-area points Z, Z’ in Fig. 2b, c). This is a consequence of spatial incoherence of the broad-source. The effective area is of a lenticular shape,

*d –*2

*p*width. The interference structure is formed only if

*|p*| ≤

*d/*2. Spectral transmittance interval of the microscope is given by this condition substituted to Eq. (11):

*|λ – λ*

_{0}| ≤

*d*/2

*lf*

_{G}. Spectral function of the microscope is a function of the effective area dependent on

*λ*. This function is represented by autocorrelation of a constant function, non-zero on a circular area and it corresponds (quite formally) to the optical transfer function for a purely incoherent system (for the course of the function see e.g [27].). It is an even function, taking its maximum for zero argument and a half of the maximum is taken approximately for 2/5 of the limit of argument. Hence the spectral function of the microscope takes a half of its maximum for |

*p*| ≈(2/5)(

*d*/2) =

*d*/5. If substituted into Eq. (11) it gives Δ

*λ*and double of this value is the full width in a half maximum (FWHM), see Table 1:

### 2.6 Broad-source diameter and interference fringes contrast

*λ*=

*λ*

_{0}, fully filling the condenser pupils (see Fig. 2a). The axial point of the source is imaged in both arms to the centre of condenser’s pupil and further to the centre of objective’s pupil (points A, A’ in Fig. 3a), thus creating a pair of mutually coherent quasi-point secondary sources forming a 3D interference structure with maxima represented by circular hyperboloids of foci in points A and A’.

*f*

_{OP}= 142 mm

^{−1}, field of view width is about 3 mm), the central fringe is linear and a curvature of the marginal fringes is up to 1% of the fringe width, difference of the fringe width between the marginal and the central fringe is 0.01%, so this interference structure in the output plane can be approximated (with respect to the system arrangement) by linear equidistant interference fringes of spatial frequency

*f*

_{OP}.

*l*≈150 mm (see Fig. 3b).

*α*’ (see Fig. 3b, c) that corresponds to the aperture angle (in the image space) of the objective lenses. Rotation introduces a difference in spatial frequency

*f*

_{OP}of the interference pattern being a cross-section of the rotated structure with the output plane. The spatial frequency is lower (wider fringes) compared to the structure from points A, A’. Figure 3c shows the difference

*δ*of the fringe patterns formed by points A, A’ and points B, B’ at a distance

*x*from the centre Q of the output plane. The relation is:

*δ*=

*x*(1/cos

*α*’ – 1) and its maximum occurs at the margin of the field of view (

*x*≈1.5 mm). Maximum aperture angle for the objective lenses in use is

*α*’ ≈1.5° and we get

*δ*

_{max}≈500 nm, i.e. about 7% of the fringe width.

## 3. Experiment

### 3.1 Optical sections

### 3.2 Quantitative phase contrast

*φ*acquired from the CCHM phase images as cross-sections along the white lines shown in Fig. 4 (from the upper left to the lower right; the same place of the specimen in both the phase images) were unwrapped first and then both the profiles were transformed by subtraction of a linear function

*y*=

*ax*+

*b*. Coefficients

*a*and

*b*were different for both the profiles and were chosen to compensate for a tilt and to get the best alignment between the two profiles. Thereafter, the height profile

*h*was calculated from the transformed phase profiles

*φ*:

*h*=

*φ*/

*k*(

*n*–

*n*

_{0}), where

*k*= 2

*π*/

*λ*

_{0},

*λ*

_{0}= 650 nm,

*n*≈1.520 is the refractive index of Cellocate (

*n*= 1.525 for

*λ*= 546 nm) and

*n*

_{0}≈1 is the value for air. The result is shown in Fig. 5 .

## 4. Discussion

### 4.1 Numerical refocusing

*ex-post*numerical refocusing up and down within the specimen [2

2. F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. **38**(34), 7085–7094 (1999). [CrossRef]

3. F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. **11**(5), 054032 (2006). [CrossRef] [PubMed]

4. F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. **45**(5), 864–871 (2006). [CrossRef] [PubMed]

2. F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. **38**(34), 7085–7094 (1999). [CrossRef]

### 4.2 Low-coherence illumination consequences – noise reduction

**38**(34), 7085–7094 (1999). [CrossRef]

5. F. Dubois, C. Yourassowsky, N. Callens, C. Minetti, and P. Queeckers, “Applications of digital holographic microscopes with partially spatial coherence sources,” J. Phys. Conference Series **139**, 012027 (2008). [CrossRef]

29. F. Dubois, M. L. Requena, C. Minetti, O. Monnom, and E. Istasse, “Partial spatial coherence effects in digital holographic microscopy with a laser source,” Appl. Opt. **43**(5), 1131–1139 (2004). [CrossRef] [PubMed]

18. E. N. Leith and G. J. Swanson, “Recording of phase-amplitude images,” Appl. Opt. **20**(17), 3081–3084 (1981). [CrossRef] [PubMed]

30. E. N. Leith and J. A. Roth, “Noise performance of an achromatic coherent optical system,” Appl. Opt. **18**(16), 2803–2811 (1979). [CrossRef] [PubMed]

### 4.3 Low-coherence illumination consequences – optical sectioning and related phenomena

3. F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. **11**(5), 054032 (2006). [CrossRef] [PubMed]

**139**, 012027 (2008). [CrossRef]

22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE **4356**, 118–123 (2000). [CrossRef]

**53**(18), 2673–2689 (2006). [CrossRef]

23. R. Chmelík and Z. Harna, “Surface profilometry by a parallel–mode confocal microscope,” Opt. Eng. **41**(4), 744–745 (2002). [CrossRef]

32. P. C. Sun and E. N. Leith, “Broad source image-plane holography as a confocal imaging process,” Appl. Opt. **33**(4), 597–602 (1994). [CrossRef] [PubMed]

21. R. Chmelík and Z. Harna, “Parallel-mode confocal microscope,” Opt. Eng. **38**(10), 1635–1639 (1999). [CrossRef]

3. F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. **11**(5), 054032 (2006). [CrossRef] [PubMed]

**139**, 012027 (2008). [CrossRef]

22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE **4356**, 118–123 (2000). [CrossRef]

23. R. Chmelík and Z. Harna, “Surface profilometry by a parallel–mode confocal microscope,” Opt. Eng. **41**(4), 744–745 (2002). [CrossRef]

33. H. J. Caulfield, “Holographic imaging through scatterers,” J. Opt. Soc. Am. **58**(2), 150–152 (1968). [CrossRef]

34. E. N. Leith, C. Chen, H. Chen, Y. Chen, J. Lopez, P. C. Sun, and D. Dilworth, “Imaging through scattering media using spatial incoherence techniques,” Opt. Lett. **16**(23), 1820–1822 (1991). [CrossRef] [PubMed]

35. E. N. Leith, C. Chen, H. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. C. Sun, J. Valdmanis, and G. Vossler, “Imaging through scattering media with holography,” J. Opt. Soc. Am. A **9**(7), 1148–1153 (1992). [CrossRef]

36. G. Indebetouw and P. Klysubun, “Optical sectioning with low coherence spatio-temporal holography,” Opt. Commun. **172**(1-6), 25–29 (1999). [CrossRef]

38. G. Indebetouw and P. Klysubun, “Spatiotemporal digital microholography,” J. Opt. Soc. Am. A **18**(2), 319–325 (2001). [CrossRef]

### 4.4 Low-coherence illumination consequences – signal to noise ratio

39. M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A **13**(1), 46–52 (1996). [CrossRef]

### 4.5 Remarkable features of incoherent off-axis holography

20. E. N. Leith, W. C. Chien, K. D. Mills, B. D. Athey, and D. S. Dilworth, “Optical sectioning by holographic coherence imaging: a generalized analysis,” J. Opt. Soc. Am. A **20**(2), 380–387 (2003). [CrossRef]

20. E. N. Leith, W. C. Chien, K. D. Mills, B. D. Athey, and D. S. Dilworth, “Optical sectioning by holographic coherence imaging: a generalized analysis,” J. Opt. Soc. Am. A **20**(2), 380–387 (2003). [CrossRef]

- • Spectrally broad source itself is to give optical sectioning effect through the process of ranging and it enhances the effect of optical sectioning accomplished by either the confocal tandem scanning or the holographic low-spatial-coherence process [22,24
22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE

**4356**, 118–123 (2000). [CrossRef]**53**(18), 2673–2689 (2006). [CrossRef]

- • Low temporal coherence is second order effect for the optical sectioning, while the spatial incoherence is the prime cause; and a diffraction grating achromatic interferometer based low-coherence image plane holography (off-axis):
- • Diffraction grating transforms the temporal incoherence into the spatial incoherence. Spectrally broad point source is converted by the dispersive power of the grating into an linearly extended spatially incoherent source. Broad-spectrum source thus causes a similar effect of optical sectioning as a spatially incoherent monochromatic source.
- • In the case when the source is both spectrally and spatially broad (extended) the sectioning is finer than would be expected from the summation of the two broadening processes – those of broad source and those of broad spectrum and than it is in case of non-grating achromatic interferometers. This statement is valid also for the reflected-light systems.

**20**(2), 380–387 (2003). [CrossRef]

**53**(18), 2673–2689 (2006). [CrossRef]

**53**(18), 2673–2689 (2006). [CrossRef]

### 4.6 Applications

40. H. Janečková, P. Veselý, and R. Chmelík, “Proving tumour cells by acute nutritional/energy deprivation as a survival threat: a task for microscopy,” Anticancer Res. **29**(6), 2339–2345 (2009). [PubMed]

**41**(4), 744–745 (2002). [CrossRef]

41. L. Lovicar, J. Komrska, and R. Chmelík, “Quantitative-phase-contrast imaging of two-level surface described as 2D linear filtering process,” Opt. Express **18**(20), 20585–20594 (2010). [CrossRef] [PubMed]

## 5. Conclusion

- • We have built a transmitted-light holographic microscope that employs an achromatic and space-invariant interferometer for off-axis image plane holography which allows to use extended light sources with substantially reduced spatial and temporal coherence (CCHM) and we described its technical parameters and imaging properties in this paper.
- • CCHM allows for quantitative phase-contrast imaging.
- • CCHM is capable to image structures hidden behind a dispersive layer. This property arises from low-coherence of illumination. It is obvious from the experiment that the light multiply scattered outside the plane being imaged does not affect the imaging process.
- • Coherence degree of the light source in CCHM can be adapted according to the object and to the required image properties. Closer to coherent illumination allows for wider range of numerical refocusing, while closer to incoherent light makes the optical sectioning stronger, i.e. finer optical section [22–24
22. R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE

**4356**, 118–123 (2000). [CrossRef]**53**(18), 2673–2689 (2006). [CrossRef] - • Optical sectioning of the holographic imaging process is primarily a consequence of spatial incoherence. Low temporal coherence added reduces significantly thickness of the optical section in reflected light. It can also achieve optical sectioning in itself in the reflected light and in the special case of transmitted-light setup – that with the diffraction grating achromatic interferometer [20
**20**(2), 380–387 (2003). [CrossRef] - • Coherent noise originating from out-of-plane scatterers is substantially reduced by combining both the low temporal and low spatial coherence [18].
**20**(17), 3081–3084 (1981). [CrossRef] [PubMed] - • Lateral resolution limit corresponds to incoherent imaging process [24
**53**(18), 2673–2689 (2006). [CrossRef]

## Acknowledgments

## References and links

1. | G. A. Dunn, “Transmitted-light interference microscopy: a technique born before its time,” Proc. Royal Microscopical Soc.. |

2. | F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. |

3. | F. Dubois, C. Yourassowsky, O. Monnom, J. C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. |

4. | F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis,” Appl. Opt. |

5. | F. Dubois, C. Yourassowsky, N. Callens, C. Minetti, and P. Queeckers, “Applications of digital holographic microscopes with partially spatial coherence sources,” J. Phys. Conference Series |

6. | E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. |

7. | E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. |

8. | T. Kreis, “Digital holographic interference-phase measurement using the Fourier-transform method,” J. Opt. Soc. Am. A |

9. | P. Massatsch, F. Charrière, E. Cuche, P. Marquet, and C. D. Depeursinge, “Time-domain optical coherence tomography with digital holographic microscopy,” Appl. Opt. |

10. | Y. Emery, E. Cuche, F. Marquet, N. Aspert, P. Marquet, J. Kühn, M. Botkine, T. Colomb, F. Montfort, F. Charrière, C. Depeursinge, P. Debergh, and R. Conde, “Digital Holographic Microscopy (DHM) for metrology and dynamic characterization of MEMS and MOEMS,” Proc. SPIE |

11. | J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. |

12. | T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. |

13. | D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. |

14. | P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. |

15. | B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. |

16. | E. N. Leith and J. Upatnieks, “Holography with Achromatic-Fringe Systems,” J. Opt. Soc. Am. |

17. | E. N. Leith and G. J. Swanson, “Achromatic interferometers for white light optical processing and holography,” Appl. Opt. |

18. | E. N. Leith and G. J. Swanson, “Recording of phase-amplitude images,” Appl. Opt. |

19. | E. N. Leith and B. J. Chang, “Space-invariant holography with quasi-coherent light,” Appl. Opt. |

20. | E. N. Leith, W. C. Chien, K. D. Mills, B. D. Athey, and D. S. Dilworth, “Optical sectioning by holographic coherence imaging: a generalized analysis,” J. Opt. Soc. Am. A |

21. | R. Chmelík and Z. Harna, “Parallel-mode confocal microscope,” Opt. Eng. |

22. | R. Chmelík, “Holographic confocal microscopy,” Proc. SPIE |

23. | R. Chmelík and Z. Harna, “Surface profilometry by a parallel–mode confocal microscope,” Opt. Eng. |

24. | R. ChmelÍk, “Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes,” J. Mod. Opt. |

25. | N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. |

26. | J. B. Pawley, |

27. | M. Born, and E. Wolf, |

28. | H. Uhlířová, |

29. | F. Dubois, M. L. Requena, C. Minetti, O. Monnom, and E. Istasse, “Partial spatial coherence effects in digital holographic microscopy with a laser source,” Appl. Opt. |

30. | E. N. Leith and J. A. Roth, “Noise performance of an achromatic coherent optical system,” Appl. Opt. |

31. | C. J. R. Sheppard, and M. Roy, “Low-Coherence Interference Microscopy,” in |

32. | P. C. Sun and E. N. Leith, “Broad source image-plane holography as a confocal imaging process,” Appl. Opt. |

33. | H. J. Caulfield, “Holographic imaging through scatterers,” J. Opt. Soc. Am. |

34. | E. N. Leith, C. Chen, H. Chen, Y. Chen, J. Lopez, P. C. Sun, and D. Dilworth, “Imaging through scattering media using spatial incoherence techniques,” Opt. Lett. |

35. | E. N. Leith, C. Chen, H. Chen, Y. Chen, D. Dilworth, J. Lopez, J. Rudd, P. C. Sun, J. Valdmanis, and G. Vossler, “Imaging through scattering media with holography,” J. Opt. Soc. Am. A |

36. | G. Indebetouw and P. Klysubun, “Optical sectioning with low coherence spatio-temporal holography,” Opt. Commun. |

37. | G. Indebetouw and P. Klysubun, “Imaging through scattering media with depth resolution by use of low-coherence gating in spatiotemporal digital holography,” Opt. Lett. |

38. | G. Indebetouw and P. Klysubun, “Spatiotemporal digital microholography,” J. Opt. Soc. Am. A |

39. | M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A |

40. | H. Janečková, P. Veselý, and R. Chmelík, “Proving tumour cells by acute nutritional/energy deprivation as a survival threat: a task for microscopy,” Anticancer Res. |

41. | L. Lovicar, J. Komrska, and R. Chmelík, “Quantitative-phase-contrast imaging of two-level surface described as 2D linear filtering process,” Opt. Express |

**OCIS Codes**

(090.0090) Holography : Holography

(110.4980) Imaging systems : Partial coherence in imaging

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(170.1790) Medical optics and biotechnology : Confocal microscopy

(180.3170) Microscopy : Interference microscopy

(110.0113) Imaging systems : Imaging through turbid media

**ToC Category:**

Microscopy

**History**

Original Manuscript: July 21, 2010

Revised Manuscript: September 13, 2010

Manuscript Accepted: September 16, 2010

Published: October 1, 2010

**Virtual Issues**

Vol. 5, Iss. 14 *Virtual Journal for Biomedical Optics*

**Citation**

Pavel Kolman and Radim Chmelík, "Coherence-controlled holographic microscope," Opt. Express **18**, 21990-22003 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-21-21990

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### References

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