1. Introduction

Digital holographic microscopy (DHM) is one of the effective methods for quantitative microscopic imaging, surface inspection, and microstructure measurement with its non-contact and nondestructive properties [1–8]. In DHM, the spatial resolution is a critical issue because it determines the smallest structures that can be resolved [9]. However, due to the influence of numerical aperture (NA) of microscopes and pixel parameters of an image recording sensor, the spatial resolution of traditional DHM cannot exceed the optical diffraction limit. According to the resolution criteria of coherent imaging, various resolution enhancement techniques of DHM have been reported, which can be classified into three types. The use of a shorter wavelength to enhance the resolution of DHM is one way of them [10]. The second type of methods is to increase the illumination NA by oblique illumination [11–17], structured illumination (SI) [18–24], speckle illumination [25–28], or to enlarge the NA of the recording system by hologram extrapolation [29,30], hologram synthesis [31,32] and pixel super-resolution [33,34]. Another type of techniques is the use of deep learning to retrieve the high-resolution image without any prior knowledge about the imaging model [35]. In recent years, research on the structured illumination in DHM mainly focuses on two aspects to improve its application in high-resolution imaging of transparent object. For the algorithm aspect of artifact-free super-resolution images, the speed and accuracy of calculating structured illumination parameters have been further enhanced by developing different algorithms [36,37]. In the aspect of reconstruction ways, a phase-shifting-free reconstruction of structured illumination in DHM is investigated according to the polarization characteristics of the structured illumination [38], and a DL-SI-DHM method with deep-learning is proposed, which can directly obtain high-resolution phase and amplitude images from wide-field images without demands of phase correction and frequency synthesis [23]. In the phase-shifting-free DHM under structured illumination, a special filter is required, while the extensive training is needed in the DL-SI-DHM method to obtain a well-trained network.

Dual-wavelength digital holography is an effective technique for measurement of the surface shapes and thickness of transparent objects and biological cells when their maximum thickness difference is over one wavelength [39–42]. In dual-wavelength imaging reconstruction, the unwrapped phase map under the synthesized wavelength can be obtained by directly subtracting the two phase maps reconstructed from two single-wavelength holograms. Because the synthesized wavelength is longer than either of the two single wavelengths, the dual-wavelength reconstruction greatly expands the optical measurement range. In recent years, some real-time dual-wavelength digital holographic systems applicable for living-cell or moving-object imaging have been reported [43–47], by which two sets of interference fringes under the single wavelengths can be record into one hologram simultaneously. In the imaging reconstruction, it should be indicated that the spatial resolution of the reconstructed phase maps under two recording wavelengths is different, which will affect the resolution of the synthesized-wavelength phase map. The resolution of dual-wavelength-reconstructed phase map is actually equal to that by the longer one of two wavelengths, because it is lower in the two wavelengths. Therefore, increasing the resolution of the phase map under the longer wavelength is a feasible way for improvement of the dual-wavelength reconstructed result [48].

In this paper, we present a dual-wavelength resolution matching digital holographic microscopy using one path structured-illumination, to improve the resolution of phase reconstruction in dual-wavelength digital holographic imaging. The single-shot dual-wavelength digital holographic microscopy combined with the structured illumination are designed in the optical configuration, to capture the dual-wavelength interferograms at one shot for the shorter wavelength with a plane-wave illumination (PI) and the longer wavelength with a structured illumination.

2. Methods

2.1 Phase shift processing and resolution features of structured-illumination DHM

The spatial resolution is one of the important performance parameters of an optical imaging system. A DHM with structured illumination can shift the phase of an object wave by illuminating the sample with a fringe-like structured light, to make the high spatial-frequency components of the sample detectable. The typical cosine pattern of structured illumination with a certain orientation and initial phase shift can be generated by a spatial light modulator (SLM) or a digital micro-mirror device (DMD). The structured illumination with the ${x}$-orientation can be expressed as:

Next, before the reconstruction imaging by inverse Fourier transform on the signal spectrum, it is required to decompose and superimpose the three terms of the zero-order, ${{+1}^{\rm st}}$-order and the ${{-1}^{\rm st}}$-order diffraction spectrums of the signal spectrum under structured illumination. Herein, we use the three-step phase shift method for the spectrum decomposing, i.e. to separate ${\tilde A_{-1}}$, ${\tilde A_{0}}$ and ${\tilde A_{+1}}$. If the three holograms are recorded under structured illumination with the initial phases ${\varphi _n}$ set as 0, 2${\mathrm{\pi} }$/3 and 4${\mathrm{\pi} }$/3 typically, where the subscript ${n}$=1, 2, 3 represents three cases of different initial phases, ${\tilde A_{-1}}$, ${\tilde A_{0}}$ and ${\tilde A_{+1}}$ can be calculated from the three ${\tilde O'_n}$ with the above-mentioned initial phases, according to the relationship below:

After superimposing the three-order diffraction spectrums together and shifting to the center of hologram’s Fourier spectrum domain, the reconstruction with structured illumination can be completed by acting an inverse FT on the superimposed spectrum.

The lateral resolution of a DHM can be expressed as:

If the structured illumination is used in a DHM, the increase of the ${NA_{\mathrm {illum}}}$ enhances the resolution of the imaging system. The numerical aperture of structured illumination system is determined by the illumination angles of its ${{\pm 1}^{\rm st}}$ diffraction orders, which can be designed by the modulation frequency of the structured light. The centers of the ${{+1}^{\rm st}}$-order and ${{-1}^{\rm st}}$-order diffraction orders are dependent on the modulation frequency ${f_0}$ of the structured illumination. The ${NA_{\mathrm {illum}}}$ of structured illumination can be written as:

2.2 Dual-wavelength DHM with structured illuminations

For a dual-wavelength DHM system, the ${NA_{\mathrm {imag}}}$ under two different wavelengths are identical, but their imaging resolutions are not equal. Such difference of the imaging resolution makes the resolution of phase reconstruction with the synthesized wavelength taking the low value of two resolutions, since the dual-wavelength phase reconstruction is obtained by subtracting the two single-wavelength phase maps. In other words, due to the fact that only the phase information resolved from two single-wavelength phase maps can also be resolved from the synthesized wavelength phase map, the resolution of the synthesized wavelength phase map in dual-wavelength reconstruction depends on the result of the longer wavelength phase map with lower resolution. According to Eq. (4), by enlarging the numerical aperture of the illumination system at the longer of the two wavelengths in a dual-wavelength DHM, the total numerical aperture corresponding to the longer wavelength can be increased, to reach to the same value as that of the shorter wavelength without special illumination. For this aim, if the numerical aperture of the dual-wavelength imaging system is ${NA_{\mathrm {imag}}}$, by using Eq. (4) and Eq. (5) where ${i=1, 2}$ indicating the cases of two different wavelengths, we can calculate the best-matching modulation frequency of structured illumination as:

In addition, for a transmission-type sample, the wrapped phase map reconstructed with respect to ${\lambda _i}$ can be expressed as:

The dual-wavelength phase unwrapping can effectively identify abrupt phases and be good at the reconstruction of the real phase of the object.

3. Optical configuation and reconstruction with structured illumination

A dual-wavelength DHM recording system with structured illumination is shown in Fig. 1, in which the mode of the structured illumination each time loaded can be as the ${x}$-orientation fringe and the ${y}$-orientation fringe. Two lasers with the wavelengths ${{\lambda _1}=532\mathrm {nm}}$ and ${{\lambda _2}=457\mathrm {nm}}$ are used as the light sources in dual-wavelength holographic recording, of which the longer wavelength beam is adjusted as a linear polarization of 45$^{\circ }$ orientation by the half-wave plate ${\mathrm {HWP_1}}$ and the shorter wavelength is adjusted to a ${p}$-polarized by the half-wave plates ${\mathrm {HWP_2}}$. By using this optical setup, the structured light of wavelength 532${\mathrm {nm}}$ can be used in various modulation frequencies and the modes to illuminate the sample, respectively, to generate a structured-illumination object wave. After the 532${\mathrm {nm}}$ beam is reflected on a spatial light modulator (SLM, manufactured by Hamamatsu, X10468) by a non-polarized beam splitter ${\mathrm {BS_2}}$, its ${p}$-polarized part is modulated into the fringe of structured illumination. Then, after adjusting the structured-illumination portion of this beam into the ${s}$-polarized and the non-structured-illumination portion into the ${p}$-polarized by using half-wave plate ${\mathrm {HWP_3}}$, the ${s}$-polarized structured-illumination as an object beam transmits through the lenses ${\mathrm {L_1}}$ and ${\mathrm {L_2}}$ to illuminate on a sample, and the non-structured-illumination beam is also adjusted into the ${s}$-polarized as a reference beam by a ${\mathrm {HWP_4}}$ behind the ${\mathrm {PBS}}$. The hologram under structured-illumination at the wavelength 532${\mathrm {nm}}$ can be recorded on a CCD by the interference of the above ${s}$-polarized object and reference beams. The 457${\mathrm {nm}}$ beam is not modulated with structured illumination, which is adjusted into the ${p}$-polarized by the ${\mathrm {HWP_2}}$ and divided into an object beam and a reference beam by the non-polarized beam splitter ${\mathrm {BS_1}}$. After combined by using the beam splitter ${\mathrm {BS_4}}$ the object beam via the lenses ${\mathrm {L_1}}$ and ${\mathrm {L_2}}$ can interfere optically on the CCD with the reference beam via the lenses ${\mathrm {L_5}}$ and ${\mathrm {L_6}}$, to record the hologram at the wavelength 457${\mathrm {nm}}$. In the presented optical configuration, two object beams at wavelengths 532${\mathrm {nm}}$ and 457${\mathrm {nm}}$ are multiplexed with the orthogonal linear polarization at the same one object path by using the ${\mathrm {PBS}}$, which makes the two holograms respect to the two wavelengths can be recorded at one shot.

 

Fig. 1. Optical configuration of a dual-wavelength digital holographic system with longer wavelength structured illumination in one shot recording; ${\mathrm {HWP}}$, half-wave plate; ${\mathrm {BS}}$, broadband nonpolarizing beam splitter; ${\mathrm {PBS}}$, broadband polarizing beam splitter; ${\mathrm {L}}$, optical lens; ${\mathrm {M}}$, mirror; ${\mathrm {MO}}$, $10\times$ microscope objectives, and ${\mathrm {A}}$, aperture.

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In the above optical configuration of the double-combined Mach-Zehnder interference, the object waves at two wavelengths share the same one object arm, while their reference arms are separated. The two reference arms are adjustable separately via a non-polarized beam splitter ${\mathrm {BS_3}}$ and a mirror ${\mathrm {M_3}}$. The orientation angles of wave vector and the off-axis interference angles for two reference beams of different wavelengths can be flexibly adjusted by tilting the ${\mathrm {BS_3}}$ and ${\mathrm {M_3}}$, respectively. Thus, it is available to record a dual-wavelength off-axis hologram in one shot, which is composed of two sets of interference fringes with different carry frequencies corresponding to two wavelengths. In order to reduce the effect of secondary phase distortion, the lenses ${\mathrm {L_1}}$, ${\mathrm {L_2}}$ and the microscope objective ${\mathrm {MO_1}}$ in one object path are all identical to the lenses and the microscope objectives in two reference paths. The focal lengths of Lenses ${\mathrm {L_1}}$, ${\mathrm {L_3}}$ and ${\mathrm {L_5}}$ are of 200${\mathrm {mm}}$, while the focal lengths of lenses ${\mathrm {L_2}}$, ${\mathrm {L_4}}$ and ${\mathrm {L_6}}$ are of 40${\mathrm {mm}}$. The three microscopic objectives are the same type, with ${\mathrm {NA}}$ of 0.25 and amplification of $10\times$. In addition, to reduce the influence of background noise and distortion, the phase reconstruction can be numerically compensated via recording an additional object-free hologram by using two-step exposure method [50]. A quantitative phase microscopy target (QPMT, Benchmark Technologies) of the USAF target pattern is used as an object for calibration of experimental phase imaging resolution. The nominal height of the line-pairs in the target is of 380${\mathrm {nm}}$, and the refractive index of medium is ${n}$=1.52. The monochrome CCD camera with $1600 \times 1200$ pixels and $3.45 \times 3.45$ µm$^2{\rm / {pixel}}$ is placed at the same focal plane of ${\mathrm {MO_1}}$, ${\mathrm {MO_2}}$, and ${\mathrm {MO_3}}$ to record the hologram including the two sets of wavelength-dependent interference fringes.

As seen in Fig. 1, the two interference beams of the wavelength 532${\rm nm}$ are ${s}$-polarized, and the two interference beams of the wavelength 457${\rm nm}$ are ${p}$-polarized. By using this optical configuration, the two sets of interference fringes respective to the wavelengths 532${\rm nm}$ and 457${\rm nm}$ are recorded in a single dual-wavelength hologram, and their individual Fourier spectrums can be adjusted to the different positions by controlling the reference arms. In the experiment, the object beam with the longer wavelength 532${\rm nm}$ only is modulated with structured illumination. Figure 2 shows such a dual-wavelength hologram and its spatial-frequency distribution in the Fourier spectrum domains. As seen in Fig. 2(b), the spatial-frequency spectrum of the signal term at 532${\rm nm}$ contains the three parts of the ${0^{\rm th}}$-order, ${+1^{\rm st}}$-order and ${-1^{\rm st}}$-order diffractions generated by structured illumination, where each order is carried with the signal spectrum. Thus, in this case with structured illumination, the conventional reconstruction process is unable directly in use. The spatial-frequency distribution of the signal term with structured illumination should be intercepted, as shown in the solid framed area of Fig. 2(b), and then is placed in the center of the hologram’s Fourier spectrum. Next, before the reconstruction by using the spatial-frequency spectrum corresponding to wavelength 532${\rm nm}$ in the hologram, it is required to perform spectrum decomposing, shifting and adding for the ${0^{\rm th}}$-order, ${+1^{\rm st}}$-order and ${-1^{\rm st}}$-order diffraction spectrums. In use of three-step phase shifting method for the decomposing, three holograms with the structured illumination patterns of different initial phases have to be recorded. Then, all the three orders of the diffraction spectrums can be separated by using three sets of the diffraction spectrums of three holograms according to Eq. (3). Figures 2(c1) to 2(c3) show the ${-1^{\rm st}}$-order, ${0^{\rm th}}$-order and ${+1^{\rm st}}$-order spectrums after decomposed, and Fig. 2(c4) shows their sum distribution of the three decomposed spectrums overlapped in aligning the center of the ${0^{\rm th}}$-order spectrum. Further, the complex amplitude of object wave can be retrieved by an inverse Fourier transform on this sum spectrum. Its reconstructed phase map is shown in Fig. 2(d). On the other hand, the spatial-frequency spectrum of the signal term at 457${\rm nm}$ is a conventional distribution due to its plane-wave illumination, as shown in the up-left framed area of Fig. 2(b), so its complex amplitude distribution of the object wave can be reconstructed by conventional digital holographic reconstruction. The phase map reconstructed from the spatial-frequency spectrum at 457${\rm nm}$ is shown in Fig. 2(e). For comparison, the phase map with the plane-wave illumination of 532${\rm nm}$ is shown in Fig. 2(f).

 

Fig. 2. (a) Dual-wavelength hologram including the two sets of interference fringes respective to the 532${\rm nm}$ structured-illumination and 457${\rm nm}$ plane-wave illumination, where the inset is the zoom of a selected area; (b) Fourier spectrum distribution of the hologram in (a), where the spatial-frequency spectrum of the signal term with the wavelength 532${\rm nm}$ contains the three parts of the ${0^{\rm th}}$-order, ${+1^{\rm st}}$-order and ${-1^{\rm st}}$-order diffractions generated by structured illumination, respectively; (c1-c3) The ${-1^{\rm st}}$-order, ${0^{\rm th}}$-order and ${+1^{\rm st}}$-order diffraction spectrums after decomposing the spatial-frequency spectrum, and (c4) sum distribution of the three decomposed spectrums in c1 to c3, by aligning the ${+1^{\rm st}}$-order and ${-1^{\rm st}}$-order centers to that of the ${0^{\rm th}}$-order spectrum. Reconstructed phase maps of QPMT: (d) at 532${\rm nm}$ with structured illumination, (e) at 457${\rm nm}$ with plane-wave illumination, (f) at 532${\rm nm}$ with plane-wave illumination.

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By comparing in Figs. 2(d) to 2(f), the resolution of the phase map with plane-wave illumination at 532${\rm nm}$ is the lowest among the three cases. With the similar plane-wave illumination mode, the resolution of the phase map at the shorter wavelength of 457${\rm nm}$ is slightly higher about one line-pair element than that of the phase map at 532${\rm nm}$. The difference between the resolutions at two wavelengths may make the imaging resolution by dual-wavelength reconstruction near the lower one of two resolutions, since the synthesized phase map in dual-wavelength reconstruction is obtained by subtracting the two single-wavelength phase maps. With the structured-illumination for the 532${\rm nm}$ object wave, the resolution of the 532${\rm nm}$ phase map increases at least up to the lever of the resolution with 457${\rm nm}$ plane-wave illumination. By setting the structured illumination on the object wave with the longer wavelength in a dual-wavelength holographic recording, the imaging resolution of dual-wavelength reconstruction can be increased, while the advantages of dual-wavelength DHM in the measurement range is in effect.

4. Experiment and results

The resolution improvement of phase maps reconstructed at the synthesized wavelength in dual-wavelength DHM is investigated in experiment via the dual-wavelength holographic recording by using a 532${\rm nm}$ object wave under structured illumination and a 457${\rm nm}$ object wave under plane-wave illumination. According to Eq. (6), when an object beam at the longer wavelength 532${\rm nm}$ is modulated with the structured illumination of spatial-frequency 63.24${\rm mm^{-1}}$, the phase map from the hologram recorded in this case can reach the same resolution as that recorded by a 457${\rm nm}$ plane-wave illumination. In the experiment, according to the specifications of SLM and by considering as close to the ideal modulation frequency as possible, the modulation frequency for the 532${\rm nm}$ structured illumination is taken as ${f_0}$=65.31${\rm mm^{- 1}}$ in the dual-wavelength DHM system. In the reconstruction, after performing the separation of the ${0^{\rm th}}$-order, ${+1^{\rm st}}$-order and ${-1^{\rm st}}$-order diffraction spectrums with the three-step-phase-shifting and then superimposing together as the previous described, the superimposed spectrum of the three diffractions is intercepted for filtering reconstruction. Figure 3 shows the curves of spectrum intensity along the ${f_x}$ and ${f_y}$ directions under three illumination cases, which are obtained via filtering interception in hologram’s Fourier spectrum domain. As seeing the local curves at the two sides in Figs. 3(a) and 3(b), the intercepted spectrum under the 532${\rm nm}$ structured illumination are extended in the transverse frequency ${f_x}$ and longitudinal frequency ${f_y}$, compared to the case under 532${\rm nm}$ plane-wave illumination. Moreover, the normalized intensity of the intercepted spatial-frequency spectrum along the ${f_x}$ and ${f_y}$ directions with 532${\rm nm}$ structured illumination in the region of the frequencies lower than 120${\rm mm^{-1}}$ is basically similar as that with 457${\rm nm}$ plane-wave illumination. In the high-frequency region, the normalized intensity under 532${\rm nm}$ structured illumination is slightly higher than that under 457${\rm nm}$ plane-wave illumination. Thus, the reconstruction resolution in the dual-wavelength holographic imaging can be optimized by equivalently extracting the spatial-frequency components for the two wavelengths.

 

Fig. 3. Normalized spectrum intensity under three illumination cases of object waves: (a) along the ${f_x}$ axis, and (b) along the ${f_y}$ axis , where the insets show the local curves in the framed areas.

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Figure 4 shows the single-wavelength-reconstructed phase maps of QPMT under three illumination cases and the sectional curves of phase at the selected line-pair elements. As shown in Fig. 4(a) to 4(c), the three bars of the 7-6 line-pair elements in phase maps with the 532${\rm nm}$ structured-illumination and with the 457${\rm nm}$ plane-wave illumination are clearly distinguishable, while the phase map of line-pair element with the 532${\rm nm}$ plane-wave illumination is inferior. On the other hand, not all distinguishable line-pairs in the phase map have the correct phase. According to the refractive index 1.52 and the nominal height 380${\rm nm}$ of the QPMT, its nominal phase value can be calculated as 2.72${\rm rad}$ with 457${\rm nm}$ and 2.33${\rm rad}$ with 532${\rm nm}$. The mean phase curves in Figs. 4(d) to 4(f) exhibit the phase distributions of the line-pairs elements 7-1 and 7-2 in the wide-bar areas marked in Figs. 4(a) to 4(c), with the phase at the QPMT substrate position as the zero-reference value. The phase values of 40-column pixels on 7-1 and 7-2 line-pairs elements marked with the wide bars in Fig. 4(a)-4(c) are taken to calculate the mean value and the uncertainty, respectively. The 40 phase values of each row are averaged and their standard deviation are calculated. It can be seen that the phase of the line-pair element 7-1 with 532${\rm nm}$ structured illumination reaches the nominal value in average, similar as the result in the phase map with 457${\rm nm}$ plane-wave illumination. But, the phase of the line-pair elements 7-1 and 7-2, distinguishable in the phase map with 532${\rm nm}$ plane-wave illumination, are not retrieved to the true value, i.e. obvious deviation from the nominal value of QPMT in the uncertainty range. Accordingly, from the perspective of phase quantization, the phase resolutions with 532${\rm nm}$ structured-illumination and 457${\rm nm}$ plane-wave illumination both are up to the line-pair element 7-1, while the phase map with 532${\rm nm}$ plane-wave illumination has obviously lower resolution than the former two cases. This result demonstrates that the reconstructed phase map with 532${\rm nm}$ structured-illumination well matches the reconstructed phase map with 457${\rm nm}$ plane-wave illumination in the imaging resolution. Thus, a high-resolution synthetic wavelength phase map that reflects the true thickness of an object can be further obtained by subtraction of the two single-wavelength phase maps having correct reconstruction phases. It should be indicated that in evaluating the resolution of phase maps, it is necessary to consider whether the reconstructed phase map conforms to the actual phase value of an object.

 

Fig. 4. Reconstructed single-wavelength phase maps of QPMT (a) with 532${\rm nm}$ structured illumination when ${f_0}$=65.31${\rm mm^{-1}}$; (b) with 457${\rm nm}$ plane-wave illumination; (c) with 532${\rm nm}$ plane-wave illumination. (d)-(f) Phase curves at the marked areas of the line-pairs elements 7-1 and 7-2 in (a) to (c), respectively.

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Figure 5 shows the reconstructed phase maps of QPMT under the synthesized wavelength, i.e. obtained by direct subtraction of two single-wavelength phase maps, and the phase curves along the lines in the maps. The resolution of phase map reconstructed by dual-wavelength DHM with 532${\rm nm}$ structured illumination is obviously higher than that with 532${\rm nm}$ plane-wave illumination, as shown in Fig. 5(a) and 5(b). Moreover, the mean phase values of line-pair elements 7-1 and 7-2 in the phase map under the 532${\rm nm}$ structured illumination mode are closer to the nominal value, by compared to those under 532${\rm nm}$ plane-wave illumination mode, as shown in Fig. 5(c) and 5(d). Particularly, by removing its two-edge abrupt phase values from the phase values corresponding to 11 pixels of each bright line and averaging the other phase values of all the three bright lines, the mean phase and the uncertainty of the line-pairs element 7-1 can be obtained as 0.39${\pm }$0.05${\rm rad}$. The corresponding thickness of the line-pair is calculated as 385.75${\pm }$49.58${\rm nm}$ according to the phase value, which is quite close to the nominal thickness 380${\rm nm}$, as shown in Fig. 5(e).

 

Fig. 5. Reconstructed phase map of QPMT under the synthesized wavelength: (a) with 532${\rm nm}$ structured-illumination and 457${\rm nm}$ plane-wave illumination, (b) with 532${\rm nm}$ and 457${\rm nm}$ plane-wave illuminations; (c)-(d) Phase curves of the line-pairs elements 7-1 and 7-2 at the wide-bar areas marked in (a) and (b), respectively; (e)-(f) Thickness curves of the line-pairs elements 7-1 and 7-2 calculated according to (c) and (d).

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Further, the phase imaging for a paramecium specimen by dual-wavelength DHM under 532${\rm nm}$ structured illumination is performed in the presented optical configuration. Figure 6 shows the dual-wavelength hologram and reconstructed phase results of the paramecia by using dual-wavelength DHM, with 532${\rm nm}$ structured illumination and 532${\rm nm}$ plane-wave illumination, respectively. The phase maps reconstructed at the synthetic wavelength 3.24µm under 532${\rm nm}$ structured illumination and under 532${\rm nm}$ plane-wave illumination are shown in Figs. 6(c) and 6(d), respectively, on which the partially wrapped phase can be seen therein. Compared to the phase of the macronucleus in Fig. 6(d), there occur more wrapped phases of the macronucleus in Fig. 6(c). This indicates that the synthetic-wavelength-reconstructed phase map under 532${\rm nm}$ structured illumination contains more fine structure of the macronucleus. The unwrapped phase maps of paramecia are further achieved by using the least-square phase unwrapping algorithm for unwrapping the above partial-wrapped phase maps. By comparing the unwrapped phase maps in Fig. 6(e) and 6(f), the phase contrast of the macronucleus and the food vacuole under 532${\rm nm}$ structured illumination is better than that under 532${\rm nm}$ plane-wave illumination.

 

Fig. 6. Phase imaging of the paramecia by dual-wavelength DHM. (a) Dual-wavelength hologram under 532${\rm nm}$ structured illumination when ${f_0}$=65.31${\rm mm^{- 1}}$ and ${\varphi _1}$=0; (b) Dual-wavelength hologram under 532${\rm nm}$ plane-wave illumination; Phase maps reconstructed at the synthetic wavelength 3.24µm: (c) under 532${\rm nm}$ structured illumination, and (d) under 532${\rm nm}$ plane-wave illumination; (e) Unwrapped phase map obtained from (c), and (e-1) zoomed-in phase map of the framed area in (e); (f) Unwrapped phase map obtained from (d), and (f-1) zoomed-in phase map of the framed area in (f).

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Figure 7 shows the cross-sectional phase distributions across the boundary of food vacuoles in paramecium cells under two kinds of 532${\rm nm}$ illumination modes. As seen the phase curves at the lines in Figs. 6(e-1) and 6(f-1), obviously exhibit that the phase contrast at the tissue boundary with 532${\rm nm}$ structured illumination is higher than that with 532${\rm nm}$ plane-wave illumination.

 

Fig. 7. Phase curves of the food vacuole of a paramecium under 532${\rm nm}$ structured illumination and 532${\rm nm}$ plane-wave illumination, along the solid line in Fig. 6(e-1) and dash line in Fig. 6(f-1).

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5. Conclusion

A dual-wavelength resolution matching digital holographic microscopy using one path structured-illumination is presented. In this configuration, the longer wavelength DHM adopts the structured illumination mode to modulate object beam, while the shorter wavelength DHM is an interference configuration with plane-wave illumination. So, as the dual-wavelength hologram with two different illumination modes is recorded at one shot, the imaging resolutions respective to the two single wavelengths can reach equivalence by setting the modulation frequency of structure illumination. We give the expression about the relationship among the modulation frequency of a structured illumination with the two wavelengths and the numerical aperture of the imaging system. Particularly, by setting an optimal fringe frequency of structured illumination, the longer-wavelength imaging resolution can be improved to the same as the shorter-wavelength imaging resolution, which results in the resolution improvement of the synthetic-wavelength phase map. In the experiment, the thickness of the QPMT target measured from the unwrapped synthetic-wavelength phase map is quite close to its nominal thickness, which demonstrates the validity of the optical configuration and resolution-matching reconstruction approach. Moreover, the reconstructed phase map for a paramecium specimen is obtained, which exhibits the internal structure of the cell, including the macronucleus, food vacuole and cilia. This dual-wavelength digital holographic microscopy with structured illumination provides a feasible means for imaging biological cells and quantitative phase measurement of movable objects.