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  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 1 — Jan. 4, 2012
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Dual wavelength full field imaging in low coherence digital holographic microscopy

Zahra Monemhaghdoust, Frédéric Montfort, Yves Emery, Christian Depeursinge, and Christophe Moser  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24005-24022 (2011)
http://dx.doi.org/10.1364/OE.19.024005


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Abstract

A diffractive optical element (DOE) is presented to simultaneously manipulate the coherence plane tilt of a beam containing a plurality of discrete wavelengths. The DOE is inserted into the reference arm of an off-axis dual wavelength low coherence digital holographic microscope (DHM) to provide a coherence plane tilt so that interference with the object beam generates fringes over the full detector area. The DOE maintains the propagation direction of the reference beam and thus it can be inserted in-line in existing DHM set-ups. We demonstrate full field imaging in a reflection commercial DHM with two wavelengths, 685 nm and 794 nm, resulting in an unambiguous range of 2.494 micrometers.

© 2011 OSA

1. Introduction

In digital holographic microscopy [1

1. 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] [PubMed]

5

5. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

], the long coherence length of laser light causes parasitic interferences due to multiple reflections in and by optical components in the optical path of the microscope and thus degrades the image quality [6

6. L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44(19), 3977–3984 (2005). [CrossRef] [PubMed]

]. The parasitic effects are greatly reduced by using a short coherence length light source such as a femtosecond laser or a broadband continuous wave superluminescent laser diode. In addition to reducing the parasitic effects, a short coherence length enables providing optical sectioning in the axial direction, which enables to exclusively sample the signal from the depth of interest [6

6. L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44(19), 3977–3984 (2005). [CrossRef] [PubMed]

].

The main drawback of using a short coherence light source in off-axis DHM [7

7. R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

, 8

8. 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]

] is the reduction of the interference fringe contrast occurring in the field of view because the reference beam interferes with the object beam only in a diamond shaped area smaller than the field of view as Fig. 1
Fig. 1 Interference of two short coherence length light beams.
illustrates.

If two beams interfere with an angle α, the interference occurs over a distance of
L=12sin(α/2)λ2Δλ
(1)
where λandΔλ are the center wavelength and the bandwidth of the source, respectively. For example, if λ=700nm, Δλ=16nm and α=2°, the fringes occur over a distance of L=877μm, which is approximately 1/10th the lateral size of a typical detector.

There have been several attempts to manipulate short coherence length light beams so that off-axis interference occurs over the whole physical overlap area. These techniques rely on manipulating the pulse front tilt of ultrafast pulsed sources [9

9. T. Balčūnas, A. Melninkaitis, A. Vanagas, and V. Sirutkaitis, “Tilted-pulse time-resolved off-axis digital holography,” Opt. Lett. 34(18), 2715–2717 (2009). [CrossRef] [PubMed]

], or equivalently the coherence plane tilt of continuous wave broadband sources [10

10. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26(6), 334–336 (2001). [CrossRef] [PubMed]

]. In the remaining of this paper, we refer to coherence plane tilt, although the results also apply for pulses.

In [11

11. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 (1998). [CrossRef] [PubMed]

], a diffractive beam-splitter and a pair of relaying lenses provide the coherence plane tilt required for full interference overlap. The concept was applied to digital holography [7

7. R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

] by combining grating and lens into one imaging diffractive lens placed after the interferometer. The imaging diffraction lens provides full field interference. A full field reflection off-axis DHM is presented in [12

12. Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express 19(8), 7587–7595 (2011). [CrossRef] [PubMed]

], that uses a transmission diffraction grating in the reference arm to provide full field interference overlap. In Refs [11

11. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 (1998). [CrossRef] [PubMed]

, 12

12. Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express 19(8), 7587–7595 (2011). [CrossRef] [PubMed]

] full field imaging requires an imaging condition between DOE and the camera plane and occurs at a specific wavelength.

In this paper, we present a diffractive optical element placed in the reference arm of the DHM whose unique features are: 1) to maintain the propagation direction of the reference beam, 2) to provide the coherence plane tilt at several wavelengths simultaneously, 3) no imaging condition is required between DOE and camera image plane. The multi-wavelength capability is essential in a DHM to increase the unambiguous axial range. In a single wavelength reflective DHM, the axial unambiguous range is equal to half the wavelength in the medium i.e. 0.35μmin air when using 685 nm light. By using a DHM with two distinct wavelengthsλ1andλ2, the effective synthetic wavelength is equal to λ1λ2/|λ1λ2|. For example, if λ1=685nm andλ2=794nm, the synthetic wavelength is 4.9898μm which results in an unambiguous range of 2.494μm. In this paper, we experimentally demonstrate single-shot full field imaging and dual wavelength operation with two low coherence sources (685nm (FWHM = 8.3 nm) and 794nm (FWHM = 16.7 nm)) in a commercial reflection DHM, by inserting the developed DOE in the reference arm without any modification/adjustment of the instrument.

The proposed DOE is based on transmission volume phase gratings recorded holographically into a thin (17μm) photopolymer. In section 2, we present two DOE designs for single wavelength operation. In the first design, the holographic grating is laminated on the back of a wedge prism and works in the Raman-Nath regime (multiple diffraction orders). In the second design, both facets of the wedge prism are laminated with a holographic grating. Although the second design is more complex to realize, it provides the advantage of higher effective efficiency than the first design because both gratings operate in the Bragg regime. In section 3, we extend the single wavelength operation of the dual grating design to dual wavelength by adding multiplexing. Experimental results in a DHM are presented in section 4 and show unambiguous depth recovery up to 2.494μm over the full field of view.

2. Single wavelength DOE

2. 1. Background: coherence plane tilt

It is well known that any angularly dispersive system introduces a coherence plane tilt [13

13. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996). [CrossRef]

16

16. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986). [CrossRef]

]. Bor introduced a general relation between the tilt angle and the angular dispersion, which is device-independent [14

14. Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985). [CrossRef]

, 15

15. Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993). [CrossRef]

]:
tanγt=λdδdλ,
(2)
Where λ is the wavelength, dδ/dλ is the angular dispersion, and γtis the angle between the coherence plane and the phase front. It is intuitively simpler to visualize the delay experienced by a short pulse in the time domain. Figure 2
Fig. 2 Coherence plane tilt: the phase fronts of the pulse are always perpendicular to the pulse propagation direction. The pulse front (i.e. the plane of the maximum of the pulse envelope) is tilted by an angle γt.with respect to the propagation direction.
illustrates graphically the tilt angle between the phase fronts (propagation direction) and the pulse front in an angularly dispersive system.

Prisms and diffraction gratings are dispersive elements that provide a convenient mean for producing a coherence plane tilt. We propose to use the combination of prisms and volume phase gratings fabricated in a holographic polymer to engineer the functional coherence plane tilt device.

2.2 DOE in Raman-Nath regime

The structure of the device is shown in Fig. 3(a)
Fig. 3 Wedge-phase grating combination to produce a coherence plane tilt (a) collinear device structure. (b) general structure.
. The wedge prism refracts the incident beam and the volume phase grating diffracts the beam so as to orient the first order diffraction to propagate in the same direction as the incident beam. Figure 3(b) illustrates the parameters of the device. The following analysis computes the phase grating parameters i.e. grating period and slant angle to obtain a specific plane tilt angle for a beam output collinear with the input beam (Fig. 3(a)).

From Fig. 3, the deviation of the output beam direction from the input direction is given by:
δ=θ4θ0+ε,
(3)
where ε is the wedge angle and θ0the angle of incidence. The incident beam direction is fixed and independent of wavelength. Derivation of Eq. (3) with respect to wavelength λ gives the angular dispersion of the device:

dδdλ=dθ4dλ
(4)

At each interface, refraction occurs according to Snell’s law:

sinθ0=nwsinθ0
(5)
nwsin(θ0ε)=nwsinθ0
(6)
ngsinθ4=nwsinθ4
(7)

Inside the volume phase grating, the vectorial grating equation is Ki+KG=Kd, which yields the following two relations:

ngcosθ2sinθ4=λΛcosϕ
(8)
ngcosθ2sinθ4=λΛcosϕ
(9)

In Eq. (8) and (9), Λ and ϕ are the grating period and slant angle, respectively. Taking the derivative of Eq. (8) with respect to wavelength, and using Eq. (2), (4) provides the following relation:

cosθ4tanγtλ=cosϕΛsinε1(sinθ0nw)2dnwdλ
(10)

The system of Eqs. (2-9) and the collinearity condition between input and output provide 8 equations for 9 unknowns (θ0,θ0,θ2,θ4,θ4,ε,δ,Λ,ϕ). To remove the underdetermination, the incident angle θ0is set so that the input beam is at normal incidence to the backfacet of the wedge. It implies that θ0 = ε. This choice forces the output angle θ4=0 in order to obtain collinear input and output (the output being in the direction of the first order diffraction). For a coherence plane tilt γt of 4 degrees and using a wavelength of λ=685nmand a wedge angle of ε=7.41°with dispersion dnw/dλ=2.8022×104, the grating period is calculated by summing the square of Eq. (8) and (9) which yields Λ=10.284μm. The slant angle ϕ=1.2778° is obtained from Eq. (10).

The unitless factor ρ=λ2/Δnn(Λ/cosϕ)2 is smaller than unity for the parameters above. This indicates that the grating is operating in the Raman-Nath regime [17

17. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980). [CrossRef]

]. In this regime, there are multiple diffraction orders. The diffraction efficiency in the first order is a Bessel function of the first kind [18

18. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980). [CrossRef]

],
η=J12(2πdΔnλcosθ),
(11)
where d is the grating thickness and θ is the incident angle. According to Eq. (11), the maximum obtainable diffraction efficiency in the first order is 33.85%.

2.3 Holographic phase grating fabrication

The phase grating was recorded on a BAYFOL® HX photopolymer from Bayer MaterialScience AG which was laminated prior to recording on a round BK7 optical wedge. A continuous-wave, single frequency green laser (532 nm Coherent Compass 315M) is coupled to a single mode polarization maintaining fiber. The output of the fiber is collimated and split by a beam splitter to generate a plane wave reference and signal beams with intensity respectively 2mW/cm2 and 1.7mW/cm2. The reference and signal beams interfere on the photopolymer, thereby recording the phase grating. The angle between the reference and signal beam and the slant angle are controlled by rotation stages with 0.2 milli-degree accuracy (Newport Micro-controle stepper motor URS150BPP).

Figure 4
Fig. 4 Diffractive optical element and diffraction orders.
shows a picture of the fabricated phase grating laminated on the wedge prism. The diffraction orders are shown in this figure. The measured efficiency of the first order diffraction (the output of the DOE) is 5%. This value was not optimized further, although higher efficiency close to the maximum is achievable in the photopolymer given that its maximum refractive index change Δn is of the order of 2%.

The DOE device was inserted in the reference arm of the DHM R2101(LynceeTec). No modification or alignment was necessary except a low pass filter (hole in a plate) was used to filter out the unwanted orders.

The optical set-up is a DHM R2101, shown in Fig. 5
Fig. 5 Optical set-up of the digital holographic microscope.
. Two low coherence sources of different wavelengths are combined and split into two beams by a first beam splitter. One beam (reference beam) is split again in its two monochromatic components (reference beam 1 and 2). The other one illuminates the object through a microscope objective. It is reflected from the sample and recombined with the two reference beams on the camera. Two delay lines equalize the optical path difference between the two references and the object paths. The object and reference beams interfere in off-axis geometry, meaning that the object beam is normal to the camera, whereas an angle is introduced for the reference beams. The planes defined by the object beam and reference 1

1. 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] [PubMed]

is orthogonal to the one defined by the object beam and reference 2

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

. This geometry enables the filtering of the frequencies for each wavelength separately and allows real-time measurements. The hologram records the interference at both wavelengths simultaneously.

For this first part, the DHM is used with a single wavelength. The inline DOE is inserted in the 685nm wavelength reference arm only. It generates a 4 degrees tilt angle in the coherence plane of the reference beam. The inset of Fig. 5 illustrates schematically, for one wavelength, that the tilted coherence plane created by the DOE results in interference throughout the CCD plane.

Figure 6(a)
Fig. 6 (a) Interferogram (left panel) and fringe modulation (right panel) without DOE in the reference arm. (b) Interferogram (left panel) and fringe modulation (right panel) after inserting DOE in the reference arm.
left panel shows the interferogram without the DOE in the reference arm. Figure 6(a) right panel shows the corresponding fringe modulation depth as a function of coordinate along the white line shown in left panel. Figure 6(b) shows the interferogram and the corresponding fringe modulation with the DOE incorporated in the reference beam path. Figure 6(b) clearly demonstrates the increase in the usable field of view. The fringe spacing is measured for both graphs and yielded 20.45μm±2μm, which demonstrates that the insertion of the DOE does not alter the propagation direction of the reference beam.

A drawback of this DOE design is the low efficiency in the first order diffraction (max. 33.85%). The spectral bandwidth of the grating at full width half maximum can be calculated according to the approximate relation: Δλλ=Λdcotθcosϕ [19

19. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

]. With the parameters of the fabricated DOE, the spectral bandwidth is equal to 440 nm. This DOE design can be extended to operate in dual wavelength by multiplexing gratings. However it is not practical because the wavelength separation of a dual wavelength DHM is smaller than the bandwidth of the DOE which would lead to a further decrease of the diffraction efficiency due to cross-talk.

2.4 DOE in Bragg regime

A phase grating operating in the Bragg regime has the advantage of producing a single diffraction order which can reach 100% efficiency. The parameter ρintroduced in section 2.2 needs to be greater than unity in order to obtain the Bragg regime. For example, if the ratio between the wavelength and an unslanted (ϕ=0) grating period is equal to unity, the parameter ρ is 66 for a photopolymer with a refractive index change of 1% and index of refraction n=1.5. In this case, the Bragg condition is well fulfilled. However, the coherence plane tilt generated by a phase grating in the Bragg regime is, according the Eq. (2) given by tanγt=λcosϕΛcosθ1, which gives a tilt angle much larger than the 4 degrees required in the DHM. By introducing a second phase grating in series that provides a negative tilt angle of similar magnitude, the difference between the two tilt angles can generate any arbitrary tilt angle while maintaining operation in the Bragg regime.

The structure of the device operating the Bragg regime is shown in Fig. 7
Fig. 7 Grating-wedge-Grating sequence for generating a coherence plan tilt in the Bragg regime.
.

Similar to the analysis in section 2.1, the slant angle and grating period for each grating are determined by solving a set of two grating equations, Snell’s law at four interfaces, the relation between tilt angle and the device dispersion as well as a condition to maintain collinearity between input and output. Details of the calculation are given in the appendix. There are a total of 11 equations and 13 variables.

After taking the derivative of the tilt angle with respect to wavelength, we obtain the following relation:
cosϕ2Λ2=cosϕ1Λ1+12sinε×(nw2(ngnw)2(λcosϕ1Λ1sinθ0)2)1/2×(2nwnw2ng2nw2cosϕ1Λ1(λcosϕ1Λ1sinθ0)+2ngngnw2+2nwnwng2nw4(λcosϕ1Λ1sinθ0)2)+cosθ4tanγtλ
(12)
where nw and ng are respectively wedge and grating refractive index dispersion. For the grating refractive index, we have used the dispersion curve for PMMA. The system of equation is underdetermined (many possible solutions), therefore we set, as in section 2.2, θ0=ε and choose the period of the top phase grating Λ1=1.2μm so that diffraction is in the Bragg regime. After solving the set of equations setting the tilt angle of 4 degrees and illumination wavelengthλ=685nm, we obtain the following grating period and slant angles for the top (subscript 1) and bottom (subscript 2) phase gratings, Λ1=1.2μm, ϕ1=6.0573°,Λ2=1.101μm, ϕ2=12.013°.

Figure 8
Fig. 8 Diffractive optical element and Bragg diffracted order.
shows a picture of the fabricated two phase gratings laminated on each side of the wedge prism. The Bragg diffraction order is shown in the figure.

3. Dual wavelength DOE

By multiplexing gratings in each photopolymer laminated on both sides of the wedge, the tilt angle can be tailored at several distinct wavelengths.

The two wavelength of the DHM areλ1=685nmandλ2=794nm. By repeating the procedure outlined in section 2.4, the period and slant angle for both wavelengths are determined. For the second wavelengthλ=794nm, we obtain Λ1=1.2μm, ϕ1=7.8361°for the top grating andΛ2=1.123μm, ϕ2=13.6772° for the bottom grating. The measured diffraction efficiency of the fabricated DOE resulted in 68.18% efficiency at 685nm and 30.77% at 794nm. The recording wavelength and set-up is the same as described in section 2.3.

Figure 9(a)
Fig. 9 Diffraction efficiency of: (a) top grating; (b) bottom grating; (c) combined top and bottom gratings, in 794nm (solid) and 685nm (dashed), measured efficiency in 685nm (cross)
and Fig. 9(b) show the simulated diffraction efficiency versus wavelength for the top and bottom phase gratings respectively. The simulated and measured diffraction efficiency of the combined top and bottom phase gratings for each wavelength is shown in Fig. 9(c).

At the output of the DOE, there are in total 8 parasitic beams resulting from zero orders and cross-talk diffraction (e.g. top grating period for λ1 diffracting λ2). Figure 10
Fig. 10 Parasitic beams at the output of the DOE.
illustrates the direction of the parasitic beams. In practice, in a commercial DHM it is difficult to spatially filter beams angularly separated by less than 1 degree. Out of the 8 parasitic beams, beam #7 in Fig. 10 makes an angle of 0.97 degrees with the desired output beam. This beam cannot be filtered in the experiment. Beam #4 makes an angle of 2 degrees with the desired output beam and then can be spatially filtered out. The other parasitic beams can also be easily spatially filtered. Figure 11
Fig. 11 Efficiency ratio between the unfiltered cross-talk beam and the desired output beam of the DOE. The dot on the figure shows the measured relative efficiency of the DOE in the experiment.
shows a plot of the diffraction efficiency ratio between the unfiltered cross talk beam #7 and the desired output beam. The effect of the unfiltered parasitic beam on the phase measurement and beam walk-off has not been quantified in this work. Quantitative phase measurement sensitivity due to the cross-talk beam will be performed in a separate study.

4. Experiments on DHM

In this second experiment, the DHM is used with both wavelengths simultaneously (685nm and 794nm). The DOE with multiplexed gratings (685nm and 794nm) operating in the Bragg regime was placed in the 794nm reference arm, and a single wavelength DOE (685nm) was inserted into the 685nm reference arm. The object used in the experiment is a reflective staircase with heights of 10; 100; 1000; 2000 and 4000 nm.

Holograms are taken in one shot (i.e. simultaneously) with both wavelengths turned on. The orientations of the coherence plane tilt in each arm are orthogonal to each to match the off-axis geometry. Since the multiplexed DOE is placed in the 794 nm arm, cross-talk effects with the 685 nm phase grating are present.

Figure 13
Fig. 13 (a) Intensity(685nm) (b) phase(685nm) (c) intensity(794nm) (d) phase(794nm) without the DOEs.
shows the intensity and phase profiles for both wavelengths without the DOEs. Figure 14
Fig. 14 (a) Intensity(685nm) (b) phase(685nm) (c) intensity(794nm) (d) phase(794nm) with the DOEs in the reference arms.
shows the intensity and phase for both wavelengths with the DOEs inserted in the reference arms of the DHM, after subtracting the reference intensity (extracted from the reference hologram taken with a flat mirror) and numerically filtering out the parasitic interference pattern in the Fourier plane. Comparing Fig. 13 and Fig. 14, it is evident that the field of view is severely limited without the DOEs.

From the intensity and phase images at 685 nm and 794 nm in Fig. 14, a height map can be calculated. Figure 15
Fig. 15 (a) 3D perspective; (b) Profile line; of the measured staircase object.
shows the resulting 3D image.

Stair case heights of 10 nm; 100 nm; 1000 nm and 2000 nm can be unambiguously determined. However, the 4000 nm staircase height cannot be unambiguously determined since the maximum unambiguous range is 2.494μm. The staircase image is clearly shown in its entirety demonstrating full field imaging with low coherence illumination and increased axial range up to 2.494μm due to dual wavelength. Although, this image is taken in single shot, the DOE did not require dual wavelength operation because of the availability of two reference arms in the DHM. However, this experiment validates the concept of multiple wavelength operation in a single DOE. The cross-talk effects are present but manageable (digital fourier filtering) and can be further reduced by using thicker holographic substrates (e.g. 50μmvs 17μm), which would decrease the bandwidth and thus the cross-talk.

5. Conclusion

We have designed and experimentally demonstrated a DOE based on a combination of holographic phase gratings for introducing a desired coherence plane tilt, with high throughput transmission (68%) while maintaining the original propagation direction. This DOE enables full field off-axis digital holographic microscopy with a short coherence illumination. In addition to the intrinsic benefits of short coherence illumination which are optical sectioning and reduced parasitic interferences, the demonstrated DOE enables multi-wavelength operation while maintaining full-field imaging.

We have shown single-shot full-field imaging with two low coherence sources (685nm and 794nm) in a digital holographic microscope. The dual wavelength provides an axial (sample depth) unambiguous measuring range of 2.494μm. To our knowledge, it is the first time that full field imaging with a dual low coherence wavelength source has been demonstrated.

Appendix

In this appendix we provide the formulas and detailed derivation of Eq. (12).

Snell’s law at four interfaces in Fig. 7 requires that

sinθ0=nwsinθ0
(A1)
ngsinθ1=nwsinθ1
(A2)
nwsin(θ1+ε)=ngsinθ2
(A3)
ngsinθ4=sinθ4(A4)
(A4)

The phase grating equation, for the top grating is:

sinθ0+ngsinθ1=λΛ1cosϕ1
(A5)
ngcosθ0ngcosθ1=λΛ1sinϕ1
(A6)

And for the bottom phase grating:

ngsinθ2+sinθ4=λΛ2cosϕ2
(A7)
ngcosθ2+ngcosθ2'=λΛ2sinϕ2
(A8)

After taking derivative of Eq. (A8) with respect to wavelength and substituting (A1) and (A6), we obtain:

cosϕ2Λ2=cosϕ1Λ1+12sinε×(nw2(ngnw)2(λcosϕ1Λ1sinθ0)2)1/2×(2nwnw2ng2nw2cosϕ1Λ1(λcosϕ1Λ1sinθ0)+2ngngnw2+2nwnwng2nw4(λcosϕ1Λ1sinθ0)2)+cosθ4tanγtλ
(A9)

References and links

1.

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] [PubMed]

2.

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

3.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–101 (2002). [CrossRef]

4.

T. C. Poon, Digital Holography and Three-Dimensional Display (Springer, 2006).

5.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

6.

L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44(19), 3977–3984 (2005). [CrossRef] [PubMed]

7.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

8.

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]

9.

T. Balčūnas, A. Melninkaitis, A. Vanagas, and V. Sirutkaitis, “Tilted-pulse time-resolved off-axis digital holography,” Opt. Lett. 34(18), 2715–2717 (2009). [CrossRef] [PubMed]

10.

Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett. 26(6), 334–336 (2001). [CrossRef] [PubMed]

11.

A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 (1998). [CrossRef] [PubMed]

12.

Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express 19(8), 7587–7595 (2011). [CrossRef] [PubMed]

13.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996). [CrossRef]

14.

Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985). [CrossRef]

15.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993). [CrossRef]

16.

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986). [CrossRef]

17.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980). [CrossRef]

18.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980). [CrossRef]

19.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(110.0180) Imaging systems : Microscopy
(090.1995) Holography : Digital holography

ToC Category:
Imaging Systems

History
Original Manuscript: August 25, 2011
Revised Manuscript: October 27, 2011
Manuscript Accepted: October 27, 2011
Published: November 10, 2011

Virtual Issues
Vol. 7, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Zahra Monemhaghdoust, Frédéric Montfort, Yves Emery, Christian Depeursinge, and Christophe Moser, "Dual wavelength full field imaging in low coherence digital holographic microscopy," Opt. Express 19, 24005-24022 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-24-24005


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References

  1. 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] [PubMed]
  2. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett.24(5), 291–293 (1999). [CrossRef] [PubMed]
  3. U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol.13(9), R85–101 (2002). [CrossRef]
  4. T. C. Poon, Digital Holography and Three-Dimensional Display (Springer, 2006).
  5. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  6. L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt.44(19), 3977–3984 (2005). [CrossRef] [PubMed]
  7. R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B16, 267–269 (1999).
  8. 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]
  9. T. Balčūnas, A. Melninkaitis, A. Vanagas, and V. Sirutkaitis, “Tilted-pulse time-resolved off-axis digital holography,” Opt. Lett.34(18), 2715–2717 (2009). [CrossRef] [PubMed]
  10. Z. Ansari, Y. Gu, M. Tziraki, R. Jones, P. M. W. French, D. D. Nolte, and M. R. Melloch, “Elimination of beam walk-off in low-coherence off-axis photorefractive holography,” Opt. Lett.26(6), 334–336 (2001). [CrossRef] [PubMed]
  11. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett.23(17), 1378–1380 (1998). [CrossRef] [PubMed]
  12. Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express19(8), 7587–7595 (2011). [CrossRef] [PubMed]
  13. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron.28(12), 1759–1763 (1996). [CrossRef]
  14. Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun.54(3), 165–170 (1985). [CrossRef]
  15. Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng.32(10), 2501–2504 (1993). [CrossRef]
  16. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun.59(3), 229–232 (1986). [CrossRef]
  17. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun.32(1), 14–18 (1980). [CrossRef]
  18. M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun.32(1), 19–23 (1980). [CrossRef]
  19. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J.48, 2909–2947 (1969).

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