We studied quantitative phase imaging (QPI) using coherent laser illumination coupled with static and moving optical diffusers. The spatial coherence of a continuous-wave laser was controlled by tuning the particle size and the diffusion angle of optical diffusers for speckle-reduced 3D phase imaging of transparent objects. We used a common-path QPI configuration to investigate the coherent phase mapping of polystyrene micro-beads and breast cancer cells (MCF-7) under different degrees of coherent speckles. The proposed speckle reduction method could provide an avenue for enhancing lateral resolution and suppressing coherent artifacts of the phase images from QPI.
© 2017 Optical Society of America
Quantitative phase imaging (QPI) is an emerging research field receiving high attention over the past decades because of the fact that the phase of an image provides more information than the amplitude . In QPI, the optical path length (OPL) maps of transparent target specimens are recorded and translated into relevant biomedical information. The main figures of merit in QPI are high data acquisition rate, high lateral resolution, and high phase sensitivity . The fastest acquisition rates are allowed with off-axis QPI configurations providing a spatial carrier frequency for Fourier-domain phase analysis with a single image [2,3]. The diffraction limited lateral resolution is preserved in phase shifting methods; the lateral resolution is lower in the off-axis configuration by an order of magnitude [4–6]. The temporal phase stability gets better in common-path configurations because of their low sensitivity to environmental disturbances [7–9]. Lastly, higher spatial phase stability can be attained in the absence of coherent artifacts, such as coherent speckles [10–12].
The QPI configuration, satisfying both off-axis and common-path geometry, can provide both benefits of a high data acquisition rate and a high phase stability in the time domain; these features have been demonstrated in biological cellular studies [8,13–18]. As an example, Lee et al. demonstrated an off-axis common-path QPI unit for coherent continuous-wave (cw) lasers using a Wollaston prism acting as the beam shearing element, which provides a simple and cost-effective way realizing QPI . However, due to the highly coherent cw illumination, QPI have been suffered from coherent artifacts (e.g. speckle), which degraded the transverse resolution of QPI so that subcellular structural studies have not been easy to implement. To overcome this limitation, a few QPI methods have been developed using partial coherence illumination [19,20], low-coherence white light illumination, such as spatial light interference microscopy (SLIM) , white-light QPI , and speckle illumination [22,23]. In SLIM, multiple interferograms need to be acquired for each phase image. In white light diffraction phase microscopy (wDPM), a single shot imaging can be realized with high spatial and temporal sensitivities but the system configuration is relatively complex due to the inclusion of diffractive optical elements, a spatial light modulator, and OPL matching optics . One critical advantage of the speckle-field interferometry over a white-light interferometry is that the former can provide full-field and single-shot hologram while the latter cannot. For this aim, the speckle-field illumination was also introduced to the QPI by Park et al., so the image quality and spatial resolution of the intracellular studies was far improved ; however, the requirements for multiple image recordings of the background and sample speckle fields have limited its application in dynamic studies. This issue was revisited by Choi et al. with dynamic speckle-field illumination with rather complicated diffractive and delay-matching optical elements .
In this study, we propose to use coherent cw laser illumination coupled with static and moving diffusers for high-speed speckle-field illumination to suppress the coherent speckles in QPI. Our speckle reduction method was applied to off-axis common-path QPI  for fast data acquisition, higher brightness, high system stability, reliability, and simplicity. We used an electroactive polymer as the mechanical-vibration-free rotating mechanism having a large number of sub-micrometer scattering elements on it for high-speed rotation of the diffused optical fields (at 300 Hz), which suppresses the background coherent speckle noises across the full field-of-view. The proposed method successfully suppressed the background speckle noise from −7.94 dB to −9.30 dB and narrowed down the linewidth of the spatial carrier frequency from 5.36 mm−1 to 4.65 mm−1 in the Fourier domain with the aid of a moving optical diffuser having a 12° diffusion angle (DA). Based on this method, the optical phase of the transparent target samples can be measured with a high lateral resolution at a high measurement speed over a large field-of-view (FOV), which will enable detailed studies on cellular morphology changes, cell growth dynamics, and motile behaviors.
2. System configuration for coherent speckle reduction
The overall QPI setup is composed of three parts: (1) illumination, (2) microscope, and (3) QPI parts. In the illumination part, a coherent monochromatic continuous-wave laser provides a high photon density (for enhanced light-specimen interaction) and high spatial coherence (for larger field-of-view (FOV)). When it comes to full-field QPI imaging, the high spatial coherence of the laser limits its applications; it is due to the coherent artifacts such as speckle, diffraction, and the formation of intensity overshoots on the edges. In order to suppress the coherent speckle effect, we introduced an electroactive polymer based rotational static and moving optical diffusers (SD/MD), which enables us to control the spatial coherence, to the laser illumination part. Figure 1(a) shows the conceptual diagram of the speckle suppression using an optical diffuser and an example QPI interferogram showing the effect on a polystyrene micro-bead. Because the diffuser rotates and scatters the impinging collimated laser beam (λ1, k1), any point on the sample experiences a changing phase of the illumination (λ1, k1∼kN). For any given point in the image plane, therefore, the region of the sample contributing to the formation of a specific image point will experience almost random walk of time varying field amplitudes and phases. As a consequence, the speckle intensity at a point on the image plane changes with time; then, the image sensor (i.e. CCD) captures the integrated intensity over its exposure time. Therefore, when the optical phase is modulated at a much higher frequency than the exposure time, coherent speckle effects can be averaged out in the captured image.
Figure 1(b) shows the experimental system layout for speckle suppression in QPI. The output beam from a continuous-wave 638 nm laser diode was focused onto an optical diffuser; the resulting beam was collected and collimated by a plano-convex lens. Three different diffusers were used in our study; (1) diffuser-1: DA = 1°, (2) diffuser-2: DA = 6°, and (3) diffuser-3: DA = 12° (Refer the detailed specification in Table 1). The diffuser is regarded as an infinite number of small point sources, each with NA of the diffusion angle. We placed the diffuser at the focal point of L1 and L2. Smaller particle makes relatively independent point sources which in turn makes more uncorrelated speckle patterns. This results in the reduction of speckle noise. Thus, based on the beam size on the diffuser, the number of point sources (N) per unit area contributing to the sample illumination is determined. N-point sources (i.e. N uncorrelated speckle patterns) results in the reduction of the speckle contrast by a factor of .The reduction degree can be improved by the including additional diffusers; the double-diffuser configuration was used here by installing one SD and one MD. Then, the collimated beam was illuminated to the sample positioned on the inverted microscope; an objective lens (NA = 0.7, M = 60) was used for the imaging. QPI part is composed of three optical components: a half-waveplate, a Wollaston prism, and a linear polarizer. The vertically polarized beam passes through the half-wave plate, resulting in the polarization rotation by 45°. Then, the Wollaston prism splits the beam into two beams having propagation angles. The linear polarizer located after the Wollaston prism is aligned to 45° with respect to two split beams. This makes the two beams to interfere with each other at the image plane, where a CCD camera records the interferogram. The half-wave plate can be rotated for balancing the intensities at the two polarization states, which results in high visibility of the interferogram.
3. Quantitative phase imaging: experimental results
For the initial test, a polystyrene micro-bead (D = 10 μm, n = 1.59@514 nm) immersed in oil (IMMOIL-F30CC, n = 1.518) was used as the sample; the oil was used for the refractive index matching. The resulting QPI interferogram is shown in Fig. 2(a). Phase reconstruction was performed based on fast Fourier transform (FFT) analysis [25,26] and a quantitative topographic phase map of the sample was reconstructed, the result is shown in Fig. 2(b). This process includes four functional modules: (1) 2D FFT module, (2) cropping, shifting, and zero-padding, (3) 2D inverse FFT (IFFT), and (4) Goldstein's phase unwrapping, slope subtraction, and phase map reconstruction module, as shown in Figs. 2(b-1)-2(b-4). To evaluate the effect of the optical diffuser on the QPI in a quantitative manner, a FFT power spectrum was extracted following the line across three frequency peaks (one DC and two AC peaks) and analyzed in detail, as shown in Figs. 2(c-1)-2(c-3). To analyze the linewidth and signal-to-noise ratio (SNR) of the QPI carrier peak with the suppressed background noise, the 1st QPI harmonic peak was rotationally averaged in the Fourier domain.
A 10-μm diameter polystyrene bead was firstly measured without SD/MD (See Fig. 3(a-1)) and its FFT spectrum was analyzed (See Fig. 3(b-1)). The phase map of the bead was retrieved from a single CCD image via FFT and phase unwrapping process (based on Goldstein algorithm) as shown in Fig. 3(c-1).To suppress the coherent speckle effects, different optical diffusers were installed in the illumination path; then, their contribution to speckle reduction was quantified by analyzing the interferograms (See Figs. 3(a-2)-3(a-4)), their FFT spectrum (See Figs. 3(b-2)-3(b-4)), and topographic phase maps (See Figs. 3(c-1)-3(c-3)). As the DA of the diffuser increases, the interferogram becomes cleaner (meaning the successful suppression of the coherent speckle) compared to the results without the diffuser (See Fig. 3(a)). The background noise suppression is quantified by calculating the standard deviation of the phase images in the background region (it is shown as white rectangle in Fig. 3(c). It was suppressed from 0.20 (without SD/MD) to 0.04 (with SD/MD, DA = 12°) by 0.16 by increasing the DA (See Figs. 3(c-1) and 3(c-4)). In the Fourier domain, higher order harmonic peaks (which were hidden in the background speckle in Fig. 3(b-1)) began to appear in the cases using optical diffusers due to the efficient background speckle noise suppression, (See Figs. 3(b-2)-3(b-4)). In addition, the diameters of the DC and AC peaks in the Fourier domain got smaller as the DA of the diffuser increased, which will be quantitatively analyzed in the later section. The reconstructed phase maps with the diffusers showed smoother phase profiles without high-frequency speckle noise over the full field-of-view; sectioned 2D phase profiles in Fig. 3(d) shows this trend in more detail. Even with the speckle suppression, the measured heights of the polystyrene beads with different diffusers remained the same within 3.4%, which confirms that the phase measurement accuracy was not degraded during the proposed speckle reduction. With a higher DA, the phase line gets smoother at the outer side and sharper at the periphery of the bead.
4. Performance evaluation and discussion
For the detailed analysis of the diffuser effects in the k-space, three critical spectral features were selected in the FFT domain: (1) the background speckle noise, (2) the linewidth of the carrier frequency, and (3) the SNR (See Fig. 4(a)). The FFT line profiles of QPI images under different diffusers are shown in Fig. 4(b). The spatial frequency from 60 to 93 mm−1 was used for the background speckle analysis and the spatial frequency from 35 to 60 mm−1 around the QPI carrier frequency was used for the linewidth and SNR analysis. First, the background noise was suppressed from −7.94 dB (without SD/MD) to −9.30 dB (with SD/MD, DA = 12°) by 1.36 dB by increasing the DA (See Figs. 4(b) and 4(f)). This trend in the FFT domain agrees well with the trends in the raw QPI images as shown in Figs. 3(a-1) and 3(a-4); as DA increases, the background image gets cleaner with suppressed speckle level. Second, the linewidth of the broad pedestal decreased from 5.36 mm−1(for no SD/MD) to 4.65 mm−1 (for SD/MD, DA = 12°) (See Figs. 4(c), 4(d), and 4(g)) and the linewidth of narrow coherent peak decreased from 0.349 mm−1(for no SD/MD) to 0.320 mm−1 (for SD/MD, DA = 12°) (See Figs. 4(c), 4(e), and 4(h)). This linewidth of the QPI carrier mode determines the attainable lateral resolution. In QPI, the DC peak (centered at zero frequency), dominated by intensity profile, should not overlap with the QPI carrier frequency mode in the FFT domain; this constraint determines the effective crop size for the phase map reconstruction (See Fig. 2(b)). Since a narrower carrier linewidth enables a larger crop size around the QPI carrier, a higher spatial resolution can be realized in the reconstructed QPI phase map in the case of using a narrow carrier linewidth. The narrow linewidth partially attributes to the background speckle noise decrease. Third, the SNR was maintained within 2.1% of its original value (7) without a significant change under different DAs (See Fig. 4(i)). This implies that the optical diffuser provides cleaner raw images and higher lateral resolution with negligible SNR variation to QPI. The fringe visibility also remained in a range effective for the phase reconstruction.
For more quantitative evaluation of the background speckle level, QPI interferograms were recorded without a sample under various illuminations as shown in Figs. 5(a-1)-5(a-4). As the DA increases, the interferogram gets cleaner with suppressed speckle noise. 2D FFT also shows the cleaner background level over all the frequency regimes except for the QPI carrier peaks (See Figs. 5(b-1)-5(b-4)). The standard deviation of the spatial phase noise decreases from 0.12 rad (≈170 nm) (for no SD/MD) to 0.05 rad (≈70 nm) (for SD/MD, DA = 12°), as shown in Fig. 5(c). In QPI, the phase reconstruction algorithms have been designed not much sensitive to the background speckle noise by cropping out the spectral range around the carrier frequency. The results in Fig. 4 show that our approach suppressed the background speckle further by 2.4 times, with a simple addition of an optical diffuser in the light illumination path.
A human breast cancer cell (MCF7) was measured as an example of biological samples with and without the optical diffuser. For the purpose, MCF7 cells were cultured in Dulbecco's Modified Eagle Medium (DMEM, from Hyclone Laboratories, Carlsbad, CA) containing 10% fetal bovine serum (FBS) and 1% Penicillin-Streptomycin antibiotics (10,000 U/mL, from Carlsbad, CA) and were maintained in a 37 °C, 5% CO2 humidified incubator. The cells were passaged by trypsinization twice a week. For the experiment, 2.5 × 104 cells were seeded into a petri dish based on Iwaki glass, covered with a 12-mm-diameter coverslip, and were grown for 72 hours in the incubator until the cells reached 70-80% confluence. The cells adhered to the coverslip were used for the imaging. Figs 6(a-1) to 6(a-4) show the interferograms of the MCF7 cell without and with diffusers. When the optical diffuser of higher DA was used, the edge of the cell becomes clearer and sharper and small granular objects inside the cell can be clearly visualized. This shows the improved visibility of the cell images as an evidence of the background speckle noise suppression. Reconstructed QPI phase maps are shown in Figs. 6(b-1)-6(b-4); the cell edges get sharper and high-frequency speckle noise gets lower as the DA increases, as shown in the magnified phase map in Figs. 6(c-1)-6(c-4). This suggests the potential application of the proposed speckle reduction system in revealing various aspects of cellular morphology changes, cell growth dynamics, and motile behaviors.
We demonstrated the speckle suppression in QPI by using an electroactive rotational optical diffuser under the coherent illumination. The spatial coherence of the laser was controlled by tuning the particle size and the diffusion angle of the optical diffuser. Background speckle noise suppression and linewidth reduction of the spatial carrier were well confirmed in the Fourier domain analysis; the background noise was suppressed by 1.36 dB and the linewidth of the QPI carrier frequency was narrowed down to 0.029 mm−1 (to 0.71 mm−1 for the broad pedestal). As the result, our method can provide speckle-free clean raw QPI image even before than the Fourier domain analysis; it also improves the lateral resolution of the QPI while maintaining its measurement accuracy. Quantitative phase reconstruction of polystyrene micro-beads and the cancer cells were performed as examples. This method will pave a way to implement QPI to various industrial and life science applications where coherent imaging without speckle noise matters.
Singapore National Research Foundation (NRF-NRFF2015-02); Ministry of Education - Singapore (MOE) Tier 1 Grant (RG180/16).
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