Quantitative Phase Contrast Microscopy with Optimized Partially Coherent Illumination

Abstract

This paper presents a partially coherent illumination quantitative phase contrast microscopic (PCI-QPCM) prototype. In the PCI-QPCM prototype, the light scattered by a rotating diffuser is coupled into a multi-mode fiber, and the output light is used as the illumination for PCI-QPCM. The illumination wave has a constrained spectrum with a diameter of tens of micrometers, which can reduce speckle noise and will not broaden the dc term of the object wave. In the Fourier plane of the object wave, grating-masked phase shifters generated by a spatial light modulator (SLM) allow for measuring the intensity of the undiffracted and diffracted components of the object wave, as well as the phase-shifted interference patterns of the two. Quantitative phase images can be reconstructed from the recorded intensity images. The proposed PCI-QPCM was demonstrated with quantitative phase imaging of a transparent waveguide and a phase-step sample.

1. Introduction

Biological samples are often transparent under visible light, and hence their images have low contrast under conventional light microscopy. A number of techniques have been developed for rendering transparent objects with high contrast by using fluorescent labeling or phase contrast concepts. Fluorescence microscopy can provide high-contrast images for specific bio-structures, despite the photo-bleaching and photo-toxicity of the fluorophore troubling long-term imaging of live samples [1]. Quantitative phase microscopy (QPM) is important because it allows determination of the optical thickness or refractive index distribution of a transparent object with sub-wavelength accuracy in a label-free manner [2,3,4,5,6], and therefore it has played very important roles in biomedical study [7] and industrial applications. Among different QPM techniques, digital holographic microscopy (DHM) is a fast, minimally invasive imaging technique, which can provide high-contrast images for transparent samples [8,9,10,11,12]. However, at present, most DHM devices adopt separate object and reference waves, and the disturbance of the external environment will induce different phase fluctuations on object and reference waves, making the hologram extremely vulnerable to environmental disturbance. Common-path QPM can circumvent this drawback by the concept that both the object and reference waves pass through the same paths and suffer from the same environmental disturbances [13]. As one of the representatives of common-path QPM, phase contrast microscopy can convert the phase distribution of a transparent object into intensity modulation delaying the dc term of the object wave in phase, and is thus widely used in studies of transparent objects [14,15,16,17,18,19,20]. Kadono [21] and Popescu [22] implemented phase contrast microscopy by using a liquid crystal SLM for phase modulation. Moreover, Samsheerali [23] performed phase contrast microscopy by using a phase grating masked phase-shifter displayed on a SLM, with which the phase shifting was performed by translating the phase grating within a selected area corresponding to the dc spot in the Fourier transform plane. Quantitative Zernike phase-contrast microscopy (qZ-PCM) was also proposed to obtain high-resolution and high-contrast phase images of weekly scattering samples by using annular illumination and annular phase modulations on the unscattered wave [24,25,26,27]. Recently, condenser-free flat-fielding quantitative Zernike phase-contrast microscopy (FF-QPCM) was recently proposed with an unprecedented spatiotemporal resolution of 230 nm and 250 frames per second (FPS), which can remove the adverse effect of the fuzzy and lumpy overall outline of live cells and avoid the cell contamination caused by the water-immersed condenser objective lens [28]. In general, the nature of the common path interference structure endows phase contrast microscopy with strong immunity to environmental perturbations.

Phase contrast microscopy methods also have disadvantages: First, the fringe contrast of the interferogram depends on tested samples and cannot be adjusted freely since the low-frequency and high-frequency components vary with samples. The fringe contrast of interferograms is an important factor in interferometry, and it affects the accuracy and robustness of the measurement [29]. Second, the reconstruction method of phase contrast microscopy is more complicated than conventional interferometric approaches since the undiffracted and diffracted terms should be decoupled from the interferograms [30]. A new phase contrast method using a grating-based phase-shifter displayed on SLM was proposed to overcome the above-mentioned disadvantages of the conventional phase contrast method [31]. Yet, this method utilized coherent illumination (CI), and hence the signal-to-noise ratio (SNR) of the construction is low. A wide variety of approaches have been proposed to reduce the coherence of illumination, such as using a halogen-lamp [32,33] or light emitting diodes (LEDs) [34], rotating ground glass, and vibrating a multi-mode optical fiber [35].

In this paper, we propose a partially coherent illumination quantitative phase contrast microscopy (PCI-QPCM) prototype, which utilizes a rotating diffuser and a multi-mode fiber to generate partially coherent illumination (PCI) and a SLM for phase modulation. This approach retains the advantages of conventional quantitative phase contrast microscopy [21,22,23,24,25,26,27,28], such as high-speed, high stability, and high accuracy of phase measurement. Meanwhile, this prototype has two additional merits. First, PCI-QPCM has a lower halo effect and lower coherent noise due to the partially coherent illumination with a limited spectrum. Second, PCI-QPCM can directly measure the intensity distributions of non-diffracted and diffracted components, simplifying the reconstruction process.

2. Methods

2.1. Experimental Setup of PCI-QPCM

The schematic diagram of the proposed PCI-QPCM system is shown in Figure 1a. A 532-nm solid-state crystal laser (1875-532L, Laserland, Wuhan, China) is used as the illumination source. The diameter of the laser output is 4 mm. A microscope objective MO₁ (20×/0.4, Nanjing Yingxing Optical Instrument Co., Ltd., Nanjing, China) focuses the light on a rotating glass diffuser (diffusing angle is 15°), and the scattered light is collimated by a lens L₁ (f = 75 mm). The diffuser is fixed on a motor (KN335714, Huatong Electronics, Co., Ltd., CityShenzhen, China), and is rotated at a speed of around 2000 revolutions per second (RPS). Then, the collimated light is refocused by a lens L₂ (f = 75 mm) into a 25 μm-diameter (the core) multi-mode fiber (DH-FMM025-FC-1, Daheng Optics, Beijing, China). At the other end of the fiber, the output light is collimated by a L₃, yielding a versatile partially coherent illumination (PCI) for PCI-QPCM. Compared to the coherent illumination (CI) that has a point-like spectrum (Figure 1b), the partially coherent illumination (PCI) has a slightly extended spectrum, of which each point will generate a plane wave illumination with different directions to illuminate the sample. In essence, these plane waves are generated when the focused light beam is transiently scattered by specific patterns on the diffuser. Resultantly, the speckle noise can be suppressed by superimposing and averaging the time-varying illuminations. The coupling efficiency is maximized when the rotating diffuser is placed at the focal plane of the telescope system MO₁-L₁. In our experiment, we set the distance between the diffuser and the focal plane of MO₁ to ~0.3 mm, compromising the spatial coherence of the illumination and the coupling coefficiency of the MMF.

Under such partially coherent illumination (PCI), a sample is magnified by a telescope system consisting of a microscopic objective MO₂ (10×/0.5, CFI Plan Apochromat, Nikon, Japan) and a lens L₄ (f = 250 mm), and the transmitted light forms the object light. The object wave is Fourier transformed by the lens L₅, and its spectrum appears on a spatial light modulator (SLM) being reflected by a triangle-prism TP. A polarizer P is placed on the object wave before the SLM to optimize the phase modulation efficiency of the SLM. On the SLM, different grating-based phase shifters will be loaded to perform the PCI-QPCM imaging. Specifically, the phase shifters is, in general, composed of a circular area and surrounding area, covering the undiffracted and diffracted components of the object wave, respectively. Both the circular and surrounding areas are filled with blazed grating that changes the propagation direction of the modulated spectrum so that it can enter the microscope. After being modulated by the SLM, the spectrum is reflected by the TP and Fourier transformed by the L₆. The resultant object wave along the +1 order of the blazed grating is imaged on CCD₂. The waves along the other diffraction orders are blocked by a rectangular aperture placed just after the lens L₆. Meanwhile, a telescope system L₆–L₇ images the spectrum of the object wave and the phase patterns loaded on the SLM to the CCD₁ to monitor the coincidence of the two in real-time.

To perform PCI-QPCM imaging, five phase masks shown in Figure 2a–e will be loaded to the SLM in sequence. First, the phase masks with blazed grating distributed only in the circular area (Figure 2a) or the surrounding area (Figure 2b) are loaded, the intensity distribution of the undiffracted term (Figure 2f) and diffracted terms (Figure 2g) can be imaged. Then, three phase masks (Figure 2c–e), where the circular and surrounding areas are filled with blazed grating and have phase shifts of 0, 2π/3 and 4π/3 in between, are loaded, and the phase shifted interferograms I₁, I₂, I₃ between the undiffracted and diffracted terms (Figure 2h–j) can be recorded by CCD₂. The quantitative phase image of a sample can be reconstructed from the five intensity images using the algorithm in Section 2.2. The frame rate of the SLM is 60 FPS, and the maximal frame rate of CCD₂ is 120 FPS. Therefore, limited by the SLM refreshing speed, the time resolution of PCI-QPCM is 83 ms, considering five raw images (I₀, I_d, I₁–I₃) are required.

We also compared CI-QPCM with PCI-QPCM. CI-QPCM was performed by taking the rotating diffuser out of the setup. For both imaging modalities, the spectra of the object waves in the absence of any samples were imaged by the telescope system L₆–L₇ onto the CCD₁. The spectra of CI- and PCI-QPCM are shown in Figure 3a and 3b, respectively. It is found that the spectrum of PCI-QPCM is much larger than that in CI-QPCM. The spectrum in Figure 3a is actually the image of the single-mode fiber (core) for CI-QPCM, and the spectrum in Figure 3b is actually the image of the multi-mode fiber (core) for PCI-QPCM after being imaged to the SLM plane, as depicted in Figure 1b. For a quantitative comparison, the intensity distributions along two lines that pass through the centers of the spectra in Figure 3a, b were extracted and shown in Figure 3c. Gaussian fit of the two curves reveals the full width at half maximum (d_FWHM) is 24.4 ± 0.2 μm (mean ± s.d.) for CI-QPCM and 48.9 ± 0.6 μm for PCI-QPCM, respectively. The spectrum in Figure 3b is close to the diameter of the undiffracted component (the dashed circle) calculated by d_undiffr = 2λ/(ML)f₅ = 53.2 μm. Here L is the width of the field of view (FOV) on the sample plane_, M being the magnification of the telescope system MO₂-L₄, and f₅ being the focal length of the lens L₅. The diameter of the multimode fiber should be chosen such that the spectrum of the illumination (after imaged to the SLM plane) has a diameter no larger than d_undiffr. In this way, the phase modulation on the dashed circle area will not erroneously modulate the diffracted component of the object light, avoiding the halo and shade-off artifacts; on the other hand, the slight extension of the illumination spectrum will reduce the coherent noise and allows better sampling of the undiffracted component with SLM pixels.

2.2. Numerical Reconstruction of PCI-QPCM

Once the phase masks in Figure 2a–e are loaded to the SLM one by one, the intensity distribution of the undiffracted term I₀, diffracted term I_d, and the interference pattern between the two, namely I₁, I₂, I₃ with the phase shifts 0, 2π/3, and 4π/3 can be obtained, as shown in Figure 2f–j. These intensity distributions can be expressed with the following equations:

$$\begin{array}{l}{I}_0=|O_0{|}^2,\\ I_{\mathrm{d}}=|O_d{|}^2,\\ I_1=|O_0{|}^2+|O_d{|}^2+O_0{O}_d{}^{\ast }+O_0{}^{\ast }{O}_d,\\ I_2=|O_0{|}^2+|O_d{|}^2+O_0{O}_d{}^{\ast }\exp \left(i\frac{2\pi }{3}\right)+O_0{}^{\ast }{O}_d\exp \left(-i\frac{2\pi }{3}\right),\\ I_3=|O_0{|}^2+|O_d{|}^2+O_0{O}_d{}^{\ast }\exp \left(i\frac{4\pi }{3}\right)+O_0{}^{\ast }{O}_d\exp \left(-i\frac{4\pi }{3}\right).\end{array}$$

(1)

The following relation can be obtained from Equation (1):

$$O_0{}^{\ast }{O}_d=\frac{1}{3}{I}_1+\frac{\sqrt{3}i-1}{6}{I}_2-\frac{\sqrt{3}i+1}{6}{I}_3$$

(2)

We assume that O₀ has a uniform phase distribution, and this is often the case when the circular area (diameter) is no larger than the diffraction limit of the system, i.e., 2λ/(ML)f₅. Under this assumption, we will have O₀ = $\sqrt{I_0}$ and O_d = (O₀*O_d)/$\sqrt{I_0}$. Consequently, the reconstructed object wave can be obtained with

$$O(x,y)=O_0+O_d=\sqrt{I_0}+\frac{O_0{}^{\ast }{O}_d}{\sqrt{I_0}}$$

(3)

In conventional phase contrast microscopy, only phase-shifted interferograms such as I₁–I₃ are recorded. For quantitative phase reconstruction, the intensity of undiffracted term I₀ = |O₀(x,y)|² should be reconstructed from I₁–I₃. The relation between I₀ and I₁–I₃, in essence, is a quadratic equation. For each pixel on the image, there are always two solutions for I₀, corresponding to the value of |O₀(x,y)|² and that of |O_d(x,y)|², respectively. A global smoothness assumption is necessary to choose one of the two local solutions to form a low-pass function for I₀(x,y) in space. Alternatively, Wolfling utilized a global polynomial fit method to solve I₀(x,y) from the three phase-shifting interferograms [36]. The above-mentioned methods work well to retrieve I₀(x,y), despite they need to carry out burdensome computation. For the proposed method, I₀(x,y) is directly measured when loading the blazed grating solely to the circular area in the phase mask, and therefore the computation task is released. Concerning the diameter of the circular area, if the circular area is too large, it will modulate the diffracted component of the object wave together with the dc term, which will, in turn, induce spatially varied O₀(x, y). On the other side, the circular area filled with blazed 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, and will in turn, influence the accuracy of the phase measurement. We found that the boundary effect can be ignored once the circular area for undiffracted component contains more than five pixels (diameter) along the diagonal direction. A larger focal length of Fourier lens L₆ can be used to satisfy this requirement. We find the proposed PCI is also beneficial to have a slightly extended undiffracted component to be better sampled with the SLM pixels. While a broadly extended illumination source (e.g., having a diameter around hundreds of micrometer) will induce an halo effect due to the spatially mixed undiffracted and diffracted terms, as is in spatial light interference microscopy (SLIM). By contrast, PCI-QPCM has an optimized illumination emitter (~25 μm) that matches the dc term of the object wave, and resultantly, it will have lower halo and shade-off artifacts in phase imaging.

3. Results

3.1. Imaging of Phase-Step Sample Using PCI-QPCM

PCI-QPCM has been applied for phase imaging of a phase-step sample. The phase-step (70 μm × 20 μm) was etched on a silica slide, and the phase of the step against the background is 2.49 rad for the wavelength of 532 nm. The undiffracted term I₀, diffracted term I_d, as well as the interferograms I₁, I₂, I₃ with the phase shifts 0, 2π/3, and 4π/3 were obtained by loading the phase masks in Figure 2f–j. Then, the phase distribution of the phase-step was reconstructed by using Equations (1)–(3), and shown in Figure 4a. For comparison, we also used conventional DHM that has independent object and reference arms to image the same sample. The phase image of the step reconstructed from the recorded off-axis DHM hologram is shown in Figure 4b. It is found that the PCI-QPCM image has much lower speckle noise than the conventional DHM. Furthermore, to quantify the accuracy of PCI-QPCM on phase measurement, two cut lines from the same position of the phase-step in Figure 4a,b were extracted and compared in parallel in Figure 4c. The results of PCI-QPCM (the green curve) and the conventional DHM (the orange curve) turn out that the phase values of the phase-step are 2.49 ± 0.15 rad and 2.49 ± 0.21 rad, respectively. The comparison confirms that two different methods result in similar phase distributions for the phase step, which implies that the proposed method can be used for quantitative measurement with high accuracy.

3.2. Comparison of Speckle Noise between CI-QPCM and PCI-QPCM

In the second experiment, a comparison of the uniformity and the speckle noise level between CI-QPCM and PCI-QPCM was conducted. In this experiment, the sample was imaged by CI-QPCM and PCI-QPCM in sequence. In CI-QPCM imaging, the rotating scatter was taken out of the setup, and the light was delivered to the setup with a single-mode fiber (SMF). In PCI-QPCM imaging, the rotating diffuser was used, and the 25 μm-diameter multi-mode fiber delivered the illumination light. Figure 5a,b are the images obtained by CI-QPCM and PCI-QPCM, respectively. To compare the uniformity of CI-QPCM and PCI-QPCM, the phase distributions along the orange/green lines from the same position in a blank area of the sample in Figure 5a,b, were extracted and compared in parallel in Figure 5c. The comparison confirms that the phase distribution of PCI-QPCM has much lower fluctuation (due to lower speckle noise) than that of CI-QPCM. To further quantify the level of speckle noise, the standard deviation (STD) of the intensities within the orange/green boxes (with 200 × 180 pixels) in Figure 5a,b was calculated. The results turn out that the STD is 0.19 ± 0.24 (mean ± s.d.) for CI-QPCM and 0.11 ± 0.05 for PCI-QPCM. It is meant that PCI-QPCM reduces the speckle noise by five folds. Moreover, the reconstructed phase distributions histograms of the transparent waveguide in Figure 5a,b were calculated and fitted with Gaussian function in Figure 5d,e. The result tells that the full width at half maximum (FWHM) is 0.56 ± 0.021 for the CI-QPCM and 0.20 ± 0.006 for the PCI-QPCM, implying that the PCI-QPCM is more uniform than the CI-QPCM due to the time-averaging of the scattered illumination light.

4. Discussion

In this paper, we proposed a partially coherent illumination quantitative phase contrast microscopy (PCI-QPCM) prototype and demonstrated its quantitative phase imaging capability with a standard sample. A partially coherent illumination (PCI) was generated by combining a rotating diffuser with a multi-mode fiber. The generated PCI has a slightly extended spectrum, which is close to the undiffracted component of object waves. Therefore, such illumination can reduce speckle noise, and avoids the halo and shade-off artifacts at the same time. PCI-QPCM has a common-path configuration, so it has good immunity to environmental disturbances. In the PCI-QPCM device, a SLM is used to perform phase modulation with high reproducibility, and it produces high-accuracy quantitative phase images for samples. In addition, the image contrast of PCI-QPCM can be adjusted by digitally redefining the area of the undiffracted and diffracted components on the SLM. We can envisage that the proposed PCI-QPCM will be widely applied to many different fields.