1. Introduction

Phase contrast microscopy (PCM) can convert the phase distribution of a transparent object into intensity modulation, and is thus widely used in studies of transparent objects, especially biological structures [1–10]. Central phase contrast method, which adopts an on-axis plane wave for illumination and a point-like phase-shifter for phase retardation on the undiffracted component, is one kind of PCM for quantitative phase measurement [11–15]. Kadono [11], Popescu [12, 13], Glueckstad [14], and Wolfling [15] implemented the central phase contrast microscopy by using liquid crystal spatial light modulator (SLM) as phase-shifting modulator. Besides, Samsheerali [16] performed central phase contrast imaging by using a phase grating displayed on a SLM as phase-shifter. The phase shifted interferograms were recorded by shifting the grating within a selected area corresponding to the dc spot in the Fourier transform plane.

Compared with the two-beam interferometry method, the phase contrast method has two disadvantages. At first, the reconstruction method of the phase contrast imaging method is more complicated than that of two-beam interferometry, since it requires burdensome reconstruction of the undiffracted component through, for example, the global polynomial fitting method [15]. Secondly, the fringe contrast of the interferogram depends on tested specimens, and cannot be freely adjusted. However, the fringe contrast of interferogram is an important factor in interferometry, since it directly influences accuracy and robustness of measurement. Palima and Glückstad [17] proposed and improved the phase contrast of generalized phase contrast imaging by coding object wave with diffractive grating patterns.

In this paper, we present a new phase contrast method by using a grating-based phase-shifter displayed on SLM to eliminate the above-mentioned disadvantages of conventional phase contrast method. By configuring the grating-based phase-shifter digitally, the undiffracted and diffracted components of object wave can be measured independently, and the fringe contrast of the interferogram can be freely adjusted.

2. Experimental setup

The experimental setup of the proposed phase contrast microscopy is shown in Fig. 1 . A He-Ne laser with wavelength 632.8nm is used as light source, and its polarization is set by a linear polarizer P to horizontally-linear polarization. The output beam is expanded by the beam expander BE, and then illuminate the specimen placed in the front focal plane of the microscopic objective MO. The object wave is magnified by the MO and collimated by the lens L₁, and thus becomes a plane wave. After passing through the beamsplitter BS, the object wave is Fourier transformed by the lens L₂, and its frequency spectrum appears in the back focal plane of the lens L₂. In this plane, a grating-based phase-shifter is displayed on a SLM, which is comprised of a central grating and a surrounding grating, to modulate the phases of the undiffracted and diffracted components of object wave, respectively. The two gratings diffract the frequency spectrum of object wave into different diffraction orders. The + 1st order is transformed by the lens L₂, and goes to the CCD camera after reflected by the cube beamsplitter BS. The CCD camera has the pixel number 1024x768 and pixel size 6.45μmx6.45μm.

 

Fig. 1 Phase contrast microscopy with grating-based phase-shifter on a SLM; P, polarizer; BE, beam expander; MO, microscopic objective; L₁ and L₂, achromatic lenses with focal lengths f₁ = 200mm and f₂ = 300mm; SLM, spatial light modulator. (a)~(e) grating-based phase-shifter loaded on the SLM: (a) surrounding grating, (b) central grating, (c)-(d) phase-shifters to generate the phase-shifting interferograms with phase shifts of 0, π/2 and π between diffracted and undiffracted components, respectively.

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In the proposed method, the grating-based phase-shifter displayed on SLM is used to perform the phase contrast imaging. On the phase-shifter, there is a central grating located in the centre of the phase-shifter, and a surrounding grating located outside the central grating. The two gratings cover the undiffracted and diffracted components, respectively. Different from the method in Ref [16]. where sinusoidal phase gratings were used, in our experimentwe use binary phase gratings for both the central grating and the surrounding grating. The advantage to do so is that the grating has the shortest period (two pixels), thus we can make best use of the spatial resolution of the SLM. The modulation depth of the central grating is fixed to π, and that of the surrounding grating is configurable to adjust the diffraction efficiency of the surrounding grating. Thus, the fringe contrast of the phase contrast interferogram can be adjusted. Besides, when the surrounding grating and the central grating are displayed on the SLM separately, as shown in Fig. 1(a) and 1(b), the intensity distributions of the diffracted component and undiffracted component can be measured, respectively. Furthermore, when the phase-shifters with phase shifts of 0, π/2 and π between the central grating and surrounding grating are loaded on the SLM respectively, as shown in Fig. 1(c)-1(e), the quadrant phase-shifting interferograms can be obtained. Note that, to get the interferogram with phase shift of π, the central grating is shifted for a half period with respect to the surrounding grating, as is seen in Fig. 1(e). In this case, the limited phase-modulation capability of the SLM will only influence the contrast of the interferogram, but not the accuracy of the phase shift between diffracted and undiffracted components [16].

To prove the fringe contrast of the interferogram to be adjustable, the simulation has been conducted. The period of the central grating and the surrounding grating are both 16μm. The diameter of the circular area for the central grating is 56μm. As the first case, the central grating and the surrounding grating have the same phase modulation depth of π and phase shift of π/2. The resultant interferogram for a simulated object along the + 1st diffraction order of these gratings is given in the first row in Fig. 2(a) . Besides, the obtained diffracted and undiffracted components of the object wave are obtained and shown in the second and third rows of Fig. 2(a), respectively, when the surrounding grating and central grating are separately used. Since the diameter of the circular area for the central grating is quite small, the intensity of the undiffracted component is much lower than that of the diffracted component. As a result, the contrast of the interferogram is quite low. For the second case, the phase modulation depth of the surrounding grating is set to 0.3π, and that of the central grating keep unchanged. The counterpart intensity distributions are obtained and shown in Fig. 2(b). In this case, the low modulation depth of the surrounding grating leads to low diffraction efficiency into the + 1st order, thus the intensity of the diffracted component on the + 1st order becomes lower and gets close to that of undiffracted component. As a result, the contrast of the interferogram is improved somehow. This is a new feature for the proposed method when compared with the method in Ref [16].

 

Fig. 2 Fringe contrast adjustment for the proposed phase contrast method; (a) when the phase modulation depth of the surrounding grating is π; and (b) when the phase modulation depth of the surrounding grating is 0.3π. |O_d|² and |O₀|² denote the intensity of diffracted and undiffracted components; I₂ denotes the interferogram between O_d and O₀ with phase shift π/2.

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When the phase-shifters shown in Fig. 1(c)-1(e) are displayed on the SLM, the intensity distributions of the phase-shifting interferograms (I₁-I₃) and the undiffracted component (I₀) can be obtained, and they can be expressed with the following equations:

The reconstruction method of the proposed method is different with that of the conventional phase contrast method. It is known from Eq. (3) that I₀ = |O₀(x, y)|² is obligatory to reconstruct the complex amplitude of object wave. For the conventional method, I₀ is usually solved out from the first three equations in Eqs. (1), which form a quadratic equation. There are always two solutions for the equation in arbitrary point (x, y), which correspond to the value of |O₀(x, y)|² and that of |O_d(x, y)|², respectively. A global smoothness argument is necessary to choose one of the two local solutions to form a low-pass function for |O₀(x, y)|², considering the |O₀(x, y)|² should be a low-pass function in the field stop [15]. Alternatively, Wolfling [15] utilized a global polynomial fitting method to solve the |O₀(x, y)|² from the three phase-shifting interferograms. These methods works well to retrieve |O₀(x, y)|², but all of them require burdensome computation task. For the proposed method, |O₀(x, y)|² is directly measured when the central grating is loaded on the SLM, thus the computation task is released.

Note that, in the proposed method, although the spatial variation on the amplitude of O₀(x, y) has been measured and compensated, the spatial variation on the phase of O₀(x,y) is still ignored. For the high accuracy measurement, the spatially-varied phase of O₀(x,y) can also be measured and compensated in the reconstruction [18]. Besides, the circular area for the central grating should not be too small, otherwise the boundary effect will come into being, which will make the undiffracted component intensity |O₀(x, y)|² change with different phase shifts in the central grating, and will in turn influence the accuracy of phase measurement. This gives a limitation of the proposed method that the pixel size of SLM should be much smaller than the size of the phase-filter for the undiffracted component. We found that if the circular area for undiffracted component contains at least two periods of the gratings, the boundary effect can be ignored.

3. Experimental result and discussion

To demonstrate the feasibility of the proposed method, the following experiments have been carried out. As the first experiment, a rectangular phase-step (70μm × 20μm) was used as specimen. The phase-step was etched in silica glass plate, and the thickness corresponds to optical path length (OPD) 95nm (0.15λ_633nm). When the phase-shifters shown in Fig. 1(a)-1(e) were loaded on the SLM, the intensity patterns of |O_d(x, y)|² and |O₀(x, y)|², and the interferograms with phase shifts of 0, π/2 and π in-between were obtained and shown in Fig. 3(a) -3(e), respectively. By using Eqs. (1)-(3), the phase distribution of the tested phase-step was retrieved and shown in Fig. 4(a) . To check the accuracy of the measurement, a cut line across the phase-step is extracted, and its phase distribution is shown in Fig. 4(b). It is known that optical path length of the phase-step reaches approximately its factual value 0.15λ_633nm, which implies that the proposed method can be used for quantitative measurement with high accuracy.

 

Fig. 3 Phase contrast measurement on a rectangular phase-step; (a)-(b) intensity distributions of diffracted and undiffracted components; (c)-(e) phase contrast interferograms with phase shifts of 0, π/2 and π between the undiffracted and diffracted components, respectively.

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Fig. 4 Reconstructed phase distribution of the tested rectangular phase-step. (a) 2D reconstructed phase map; (b) the phase distribution along the cutline in (a).

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To demonstrate that the fringe contrast of the interferogram can be adjusted, the experiment on a vortex phase plate has been carried out. At first, the surrounding grating and the central grating are set with the same modulation depth of π and with the phase shift of π/2 in-between. In this case, the interferogram with phase shift of π/2 between the undiffracted component and diffracted component was obtained and shown in Fig. 5(a) . Since the intensity of |O_d(x, y)|² is much higher than that of |O₀(x, y)|², the contrast of the interferogram is quite low. For comparison, the modulation depth of the surrounding grating was changed to 0.7π, and that of the central grating kept unchanged. The interferogram was obtained and shown in Fig. 5(b). It can be seen that the contrast of the interferograms was enhanced obviously. This is because that the intensity of |O_d(x, y)|² becomes lower and gets close to that of |O₀(x, y)|². Finally, when the phase-shifters shown in Fig. 1(a)-1(e) were loaded on the SLM subsequently, the corresponding intensity patterns were obtained. By using the proposed method, the phase distribution of the vortex phase plate was obtained and given in Fig. 5(c).

 

Fig. 5 Fringe contrast adjustment of interferograms through changing the phase modulation depth of the surrounding grating. (a) the modulation depth of the surrounding grating is π; (b) the modulation depth of the surrounding grating is 0.7π; (c) reconstructed phase distribution of the tested vortex phase plate.

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4. Summary

A phase contrast microscopy with fringe contrast adjustable is proposed, where the undiffracted and diffracted components of object wave can be adjusted comparatively and measured independently. This is done by introducing a grating-based phase-shifter comprised of a central grating and a surrounding grating, which modulate the phases of the undiffracted and diffracted components in the Fourier plane, respectively. This method has two advantages: at first, the contrast of the phase contrast interferogram can be adjusted by changing the phase modulation depth of the two gratings. Secondly, the undiffracted and diffracted components can be measured independently by loading the central and surrounding gratings respectively on the SLM, thus the reconstruction process of the phase contrast microscopy is simplified greatly.