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Single-path single-shot phase-shifting quantitative phase microscopy with annular bright-field illumination

Wu You, Yuheng Jiao, Jingyi Wang, Changchun Chai, Wenlong Lu, and Xiaojun Liu

Open Access Open Access

Abstract

We propose single-path single-shot phase-shifting quantitative phase microscopy (SSP-QPM) with annular illumination, oil top lens, and wide-field objectives. We analyze the difference between bright-field SSP-QPM, phase-contrast SSP-QPM, and the proposed microscopy by resolution, contrast, and noise. The proposed microscopy enhances the lateral resolution by promoting the numerical-aperture of illumination, improves the image contrast by suppressing multiple-scattering, and reduces dynamic noise by decreasing exposure time. Experiments validate the characters of the proposed microscopy by quantitative phase imaging of oocyte cells, intestinal tissues, and polystyrene microspheres. Besides, we demonstrate the simultaneous recording of fluorescence and quantitative phase images.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

In microscopy, bright-field imaging and phase-contrast imaging [1,2] are fundamental applications. Bright-field microscopy adopts full-aperture illumination and wide-fielding objectives, while phase-contrast microscopy adopts annular aperture illumination and phase-contrast objectives. Quantitative phase microscopy (QPM) utilizes these basic configurations and develops holographic applications [3–5]. In QPM, single-path interferometry is highlighted by its high stability in dynamic measurement [6]. Fourier phase microscopy (FPM) [7,8], diffraction phase microscopy (DPM) [9,10], and spatial light interference microscopy (SLIM) [11,12] are representative methods in this field. FPM and DPM adopt bright-field imaging, while SLIM utilizes Zernike phase-contrast imaging. Recently, single-path single-shot phase-shifting quantitative phase microscopy (SSP-QPM) [13–15] is proposed by combining parallel phase-shifting (PPS) interferometry [16–18] with FPM and SLIM. For clarity, we show the evolution process of SSP-QPM in Fig. 1.

 figure: Fig. 1.

Fig. 1. The evolution process of SSP-QPM.

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However, bright-field SSP-QPM (bSSP-QPM) [14,15] presents some disadvantages. (1) Bright-field imaging is obliged to adopt low illumination NA to show enough contrast, which limits the lateral resolution of the system. (2) Bright-field imaging is strongly affected by multi-scattering from defocusing planes, which dramatically limits the imaging contrast of thick samples. (3) The reconstruction quality is affected by the angular-spectrum distribution of the specimen. On the other hand, phase-contrast SSP-QPM (pSSP-QPM) [13] presents the following disadvantages. (1) The dark imaging field of pSSP-QPM causes heavy noise, which limits the exposure time in single-shot imaging. (2) pSSP-QPM is hard to be simultaneously recorded with fluorescence, which limits its application in biomedical analysis.

In this article, we propose single-path single-shot phase-shifting quantitative phase microscopy with annular illumination and wide-field objectives (aSSP-QPM). To the best of our knowledge, it is the first time that annular illumination, oil top lens, and wide-field objectives are integrated into SSP-QPM. Notice that phase-contrast objectives are incompatible with oil top lens, because the phase plates at the back focus plane limit the illumination NA. The effective illumination NA of state-of-the-art phase-contrast objectives is limited by 0.9, while that of bright-field is ∼1.4. By introducing oil top lens and wide-field objectives, aSSP-QPM obtains more high-frequency information than other SLIM techniques.

As shown in Table 1, the proposed microscopy presents the following advantages. (1) Annular illumination and oil top lens enhance the maximum illumination NA. (2) The light field of aSSP-QPM is brighter than that of pSSP-QPM, reducing the exposure time. (3) Annular low-coherence illumination enables high contrast imaging by suppressing multiple-scattering from defocusing planes [19]. (4) Quantitative phase images and fluorescence images are simultaneously recorded. (5) The reconstruction process is sample-independent.

Tables Icon

Table 1. Comparisons of different SSP-QPM

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In Section 2, we introduce the principle of the proposed microscopy. In Section 3, experiments demonstrate quantitative phase imaging of oocyte cells, intestinal tissues, and polystyrene microspheres. Sub-cellular structures of oocyte cells are visualized, such as chromosomes (800nm in width), membranes (400nm in width), and nutrition bubbles (1µm in diameter). Besides, we show the simultaneous recording of fluorescence and quantitative phase images.

2. Principle

Figure 2 shows the schematic of SSP-QPM with annular illumination, oil top lens, and wide-field objectives. The proposed microscopy adopts the following configurations: (I) a commonly used bright-field microscope with annular illumination, (II) a 4F-system consisting of Fourier transform lens L1-L2 and a non-polarizing beam splitter (NPBS), (III) a reflective twisted nematic liquid-crystal spatial light modulator (TN-SLM), and (IV) a CCD with a pixelated micro-polarizer array. The difference between bSSP-QPM and aSSP-QPM locates in the configuration of illumination and the method of interferometry. Besides, the proposed microscopy selects different imaging wavelengths by introducing different modulation masks, as shown in Fig. 2(c).

 figure: Fig. 2.

Fig. 2. The principle of annular bright-field SSP-QPM.

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If we denote the reference light field as ${U_0}$ and the object light field as ${U_1}$, the wave modulated by the TN-SLM can be expressed as:

$${U_1} = |{{U_1}} |\textrm{exp} (i{\varphi _1})\left[ \begin{array}{l} 1\\ 0 \end{array} \right],$$
$${U_0} = |{{U_0}} |\textrm{exp} (i{\varphi _0})\left[ \begin{array}{l} \cos \theta \\ \sin \theta \end{array} \right].$$

The Jones matrix of the QWP is:

$$Q = \sqrt 2 /2\left[ {\begin{array}{cc} 1&i\\ i&1 \end{array}} \right].$$

The Jones matrix of the pixelated-polarizer is:

$$P = \left[ {\begin{array}{cc} {\cos \beta \cos \beta }&{\sin \beta \cos \beta }\\ {\sin \beta \cos \beta }&{\sin \beta \sin \beta } \end{array}} \right].$$

The wave passing through the pixelated-polarizer can be expressed as:

$${U_1}^{\prime} = P \cdot Q \cdot {U_1} = \frac{{\sqrt 2 }}{2}|{{U_1}} |\textrm{exp} [{i({\varphi_1} + \beta )} ]\left[ \begin{array}{l} \cos \beta \\ \sin \beta \end{array} \right],$$
$$\begin{aligned} {U_0}^{\prime} &= P \cdot Q \cdot {U_0}\\ &= \frac{{\sqrt 2 }}{2}|{{U_0}} |\left\{ {\sin \theta \textrm{exp} \left[ {i({\varphi_0} + \frac{\pi }{2} - \beta )} \right] + \cos \theta \textrm{exp} [{i({\varphi_0} + \beta )} ]} \right\}\left[ \begin{array}{l} \cos \beta \\ \sin \beta \end{array} \right]. \end{aligned}$$

The intensity of the hologram on the CCD is:

$$\begin{aligned} I &= \frac{1}{2}{|{{U_0}} |^2} + \frac{1}{2}{|{{U_1}} |^2} + {|{{U_0}} |^2}\left[ {\sin\theta \cos \theta \cos (\frac{\pi }{2} - 2\beta )} \right]\\ &+ |{{U_0}} ||{{U_1}} |\left[ {\sin\theta \cos \left( {{\varphi_1} - {\varphi_0} + \frac{\pi }{2} - 2\beta } \right) + \cos \theta \cos ({{\varphi_1} - {\varphi_0}} )} \right]. \end{aligned}$$

If we define:

$$\left\{ \begin{array}{l} {P_0} = \frac{{{{|{{U_0}} |}^2}}}{2} + \frac{{{{|{{U_1}} |}^2}}}{2}\\ {P_1} = {|{{U_0}} |^2}\sin\theta \cos \theta \\ {P_2} = |{{U_0}} ||{{U_1}} |\sin\theta \\ {P_3} = |{{U_0}} ||{{U_1}} |\cos \theta \\ \gamma = \frac{\pi }{2} - 2\beta \\ \Delta \varphi = {\varphi_1} - {\varphi_0} \end{array} \right.,$$

Equation (7) can be expressed as:

$$I = {P_0} + {P_1}\cos \gamma + {P_2}\cos (\Delta \varphi + \gamma ) + {P_3}\cos \Delta \varphi .$$

For any four localized pixels shown in Fig. 2(b), we define ${\alpha _\lambda }$ as the wavelength-dependent bias constant and $\Delta \alpha$ as the fixed-step increment of the phase-shifts:

$$\left\{ \begin{array}{l} {\alpha_\lambda } = \pi /2 - 2(\pi /4 - {\theta_\lambda }) + 3\Delta \beta = 2{\theta_\lambda } + 3\Delta \beta \\ \Delta \alpha = 2\Delta \beta \\ {\gamma_{A,\lambda }} = {\alpha_\lambda } - 3\Delta \beta \\ {\gamma_{B,\lambda }} = {\alpha_\lambda } - \Delta \beta \\ {\gamma_{C,\lambda }} = {\alpha_\lambda } + \Delta \beta \\ {\gamma_{D,\lambda }} = {\alpha_\lambda } + 3\Delta \beta \end{array} \right..$$

If the wave passes through the QWP is circularly polarized ($\theta = 0.5\pi$), then:

$${I_\lambda } = {P_0}_{,\lambda } + {P_2}_{,\lambda }\cos (\Delta {\varphi _\lambda } + {\gamma _\lambda }).$$

The intensity of the four localized pixels can be expressed as:

$$\left\{ \begin{array}{l} {I_{A,\lambda }} = {P_0}_{,\lambda } + {P_2}_{,\lambda }\cos (\Delta {\varphi_\lambda } + {\alpha_\lambda } - 3\Delta \beta )\\ {I_{B,\lambda }} = {P_0}_{,\lambda } + {P_2}_{,\lambda }\cos (\Delta {\varphi_\lambda } + {\alpha_\lambda } - \Delta \beta )\\ {I_{C,\lambda }} = {P_0}_{,\lambda } + {P_2}_{,\lambda }\cos (\Delta {\varphi_\lambda } + {\alpha_\lambda } + \Delta \beta )\\ {I_{D,\lambda }} = {P_0}_{,\lambda } + {P_2}_{,\lambda }\cos (\Delta {\varphi_\lambda } + {\alpha_\lambda } + 3\Delta \beta ) \end{array} \right..$$

By Carrie algorithm [20], the phase difference $\Delta {\varphi _\lambda }$ can be obtained as:

$$\Delta {\varphi _\lambda } = \arctan \frac{{\sqrt {[{({I_\textrm{A}}_{,\lambda } - {I_D}_{,\lambda }) + ({I_\textrm{B}}_{,\lambda } - {I_C}_{,\lambda })} ][{3({I_\textrm{B}}_{,\lambda } - {I_C}_{,\lambda }) - ({I_\textrm{A}}_{,\lambda } - {I_D}_{,\lambda })} ]} }}{{({I_\textrm{B}}_{,\lambda } + {I_C}_{,\lambda }) - ({I_\textrm{A}}_{,\lambda } + {I_D}_{,\lambda })}} - {\alpha _\lambda }.$$

After a convolution process of 2×2 pixels in the whole hologram, the quantitative phase image is finally reconstructed.

3. Experiments and discussions

The experiments are carried out by a commercially available inverted optical microscope (IX-73, Olympus). The condenser (U-UCD8) is equipped with a set of annular illumination rings and an oil top lens (U-TLO/1.4NA). The objectives are UPLXAPO40X (40X/0.95NA) and UPLXAPO100XO (100X/1.45NA). The wavelength coverage of the TN-SLM (HDSLM80R, 1920×1200, 8 µm pixel pitch) is 420 nm–1100 nm. The imaging camera (PolarCamV, 640×460, 7.6 µm pixel pitch) is a 12-bit CCD with a pixelated micro-polarizer array. The wavelength coverage of the achromatic Fourier transform lens (GCO-0202M) is 400 nm–700 nm. The wavelength coverage of the achromatic QWP (GCL-0608) is 400 nm–700 nm. For clarity, the cross-validation experiments are shown in Table 2.

Tables Icon

Table 2. Cross-validation experiments of different SSP-QPM

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The effective NA of the microscope results from the illumination NA ($N{A_i}$) and the objective NA ($N{A_{obj}}$) [21]:

$$NA = N{A_i} + N{A_{obj}}.$$

Under low-coherence illumination, the lateral resolution of the system is [22]:

$$\varepsilon = \frac{{1.22\lambda }}{{N{A_i} + N{A_{obj}}}}.$$

By adopting an oil top lens (1.4 NA) and an oil bright-field objective (100X/1.45NA), the system’s maximum effective NA is up to ∼2.85. The lateral resolution is ∼226 nm when the illumination wavelength is ∼530 nm in principle. As shown in Fig. 3, we quantitatively evaluate the lateral resolution of the system by decorrelation analysis [23,24], which is widely adopted by high-resolution microscopy. In Fig. 3(f), each curve shows the cross-correlation of the image with its Fourier-filtered normalized version, and each version is subject to additional high-pass filtering. The local maximum indicates the spatial frequency of the best noise rejection and signal preservation ratio, equivalent to the searching for the frequency at which the transfer function vanishes. The maximum frequency of the local maxima of all the curves is the cut-off frequency, and the decorrelation analysis adopts the cut-off frequency to evaluate the lateral resolution of the image (∼235nm). Sub-cellular structures of an oocyte, such as chromosomes (∼800nm in width), membranes (∼400nm in width), and nutrition bubbles (∼1µm in diameter), are experimentally demonstrated by different SSP-QPM. By the same wide-field objective (100X/1.45NA), aSSP-QPM presents higher resolution and contrast than bSSP-QPM.

 figure: Fig. 3.

Fig. 3. Quantitative phase imaging of an oocyte (100X/1.45NA).

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When imaging one section of thick tissues instead of thin cells, bright field SSP-QPM shows even lower contrast due to multiple scattering of defocusing planes. On the other hand, the annular illumination brings in low spatial coherence, which effectively suppresses multiple-scattering in aSSP-QPM and pSSP-QPM. As shown in Fig. 4, experiments demonstrate quantitative phase imaging of thick tissues by different SSP-QPM. The enhancement of contrast by annular illumination is visualized in aSSP-QPM and pSSP-QPM. Notice that bSSP-QPM does not insert an aperture in Ref. [14]. A small LED enables the production of interference fringes, and the decrease in light intensity is avoided. This configuration improves the imaging quality. However, the ideal spatial coherency of bSSP-QPM is similar to FPM in view of the production of good interference fringes. We adopt the traditional FPM-type imaging for comparison, and the illumination NA can be changed from 0.09 to 0.55.

 figure: Fig. 4.

Fig. 4. Quantitative phase imaging of intestinal tissues (40X/0.95NA).

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Then, quantitative phase imaging of polystyrene microspheres (IMNANO) is demonstrated by pSSP-QPM and aSSP-QPM (100X/1.45NA), as shown in Fig. 5. By the same exposure time (∼0.1ms), aSSP-QPM presents lower noise than pSSP-QPM. In our previous work of pSPP-QPM [13], long exposure time (∼10ms) is obliged to effectively suppress the dynamic noise. In the case of ultra-fast imaging, aSSP-QPM shows better performance than pSSP-QPM.

 figure: Fig. 5.

Fig. 5. Imaging of polystyrene microspheres (100X/1.45NA).

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By utilizing a dichroic mirror [25] at the image plane in Fig. 2(a), fluorescence images are simultaneously recorded in the reflection path. The configurations are as shown in Table 3. By config-A, fluorescence imaging shows high specificity in chromosomes and membranes and low specificity in the area of nutrition bubbles, as shown in Fig. 6. Notice that the sample is also H&E stained as shown in Fig. 6(a). H&E staining brings background light into the fluorescence imaging.

 figure: Fig. 6.

Fig. 6. Synthetic imaging of oocyte (100X/1.45NA).

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Tables Icon

Table 3. Configurations of synthetic imaging

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However, aSSP-QPM is based on polarization-multiplexing. The phase map may not be reconstructed correctly if the sample structures have different polarization characteristics. Polarization-sensitive methods are better at imaging anistropic or birefrigent specimens, such as Jones phase microscopy [26]. Besides, aSSP-QPM is hard to image the whole 3D area of thick samples, and GLIM configurations are more suitable in this case [19,27].

4. Conclusions

In this paper, we propose annular bright-field SSP-QPM. By promoting the numerical-aperture of illumination and suppressing multiple-scattering, aSSP-QPM presents higher lateral resolution and image contrast than bSSP-QPM. By introducing wide-field objectives to reduce the exposure time, aSSP-QPM shows lower dynamic noise than pSSP-QPM. Besides, the simultaneous recording of fluorescence and quantitative phase images is accomplished in aSSP-QPM, which paves the way for high specificity synthetic imaging. Experiments validate the characters of the proposed microscopy by quantitative phase imaging of oocyte cells, intestinal tissues, and polystyrene microspheres. The proposed microscopy will provide new applications in biomedical research at the subcellular scale, such as neuron dynamics, stem-cell culture, and cellular immunology.

Funding

National Natural Science Foundation of China (51475192, 51875227, 51975233).

Acknowledgments

We are grateful to UPOlabs for the calibration of the spatial light modulator.

Disclosures

The authors declare no conflicts of interest.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Figures (6)
Fig. 1.
Fig. 1. The evolution process of SSP-QPM.

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Fig. 2.
Fig. 2. The principle of annular bright-field SSP-QPM.

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Fig. 3.
Fig. 3. Quantitative phase imaging of an oocyte (100X/1.45NA).

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Fig. 4.
Fig. 4. Quantitative phase imaging of intestinal tissues (40X/0.95NA).

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Fig. 5.
Fig. 5. Imaging of polystyrene microspheres (100X/1.45NA).

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Fig. 6.
Fig. 6. Synthetic imaging of oocyte (100X/1.45NA).

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Tables (3)

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Table 1. Comparisons of different SSP-QPM

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Table 2. Cross-validation experiments of different SSP-QPM

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Table 3. Configurations of synthetic imaging

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Equations (15)

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U 1 = | U 1 | exp ( i φ 1 ) [ 1 0 ] ,
U 0 = | U 0 | exp ( i φ 0 ) [ cos ⁡ θ sin ⁡ θ ] .
Q = 2 / 2 [ 1 i i 1 ] .
P = [ cos ⁡ β cos ⁡ β sin ⁡ β cos ⁡ β sin ⁡ β cos ⁡ β sin ⁡ β sin ⁡ β ] .
U 1 ′ = P ⋅ Q ⋅ U 1 = 2 2 | U 1 | exp [ i ( φ 1 + β ) ] [ cos ⁡ β sin ⁡ β ] ,
U 0 ′ = P ⋅ Q ⋅ U 0 = 2 2 | U 0 | { sin ⁡ θ exp [ i ( φ 0 + π 2 − β ) ] + cos ⁡ θ exp [ i ( φ 0 + β ) ] } [ cos ⁡ β sin ⁡ β ] .
I = 1 2 | U 0 | 2 + 1 2 | U 1 | 2 + | U 0 | 2 [ sin ⁡ θ cos ⁡ θ cos ⁡ ( π 2 − 2 β ) ] + | U 0 | | U 1 | [ sin ⁡ θ cos ⁡ ( φ 1 − φ 0 + π 2 − 2 β ) + cos ⁡ θ cos ⁡ ( φ 1 − φ 0 ) ] .
{ P 0 = | U 0 | 2 2 + | U 1 | 2 2 P 1 = | U 0 | 2 sin ⁡ θ cos ⁡ θ P 2 = | U 0 | | U 1 | sin ⁡ θ P 3 = | U 0 | | U 1 | cos ⁡ θ γ = π 2 − 2 β Δ φ = φ 1 − φ 0 ,
I = P 0 + P 1 cos ⁡ γ + P 2 cos ⁡ ( Δ φ + γ ) + P 3 cos ⁡ Δ φ .
{ α λ = π / 2 − 2 ( π / 4 − θ λ ) + 3 Δ β = 2 θ λ + 3 Δ β Δ α = 2 Δ β γ A , λ = α λ − 3 Δ β γ B , λ = α λ − Δ β γ C , λ = α λ + Δ β γ D , λ = α λ + 3 Δ β .
I λ = P 0 , λ + P 2 , λ cos ⁡ ( Δ φ λ + γ λ ) .
{ I A , λ = P 0 , λ + P 2 , λ cos ⁡ ( Δ φ λ + α λ − 3 Δ β ) I B , λ = P 0 , λ + P 2 , λ cos ⁡ ( Δ φ λ + α λ − Δ β ) I C , λ = P 0 , λ + P 2 , λ cos ⁡ ( Δ φ λ + α λ + Δ β ) I D , λ = P 0 , λ + P 2 , λ cos ⁡ ( Δ φ λ + α λ + 3 Δ β ) .
Δ φ λ = arctan ⁡ [ ( I A , λ − I D , λ ) + ( I B , λ − I C , λ ) ] [ 3 ( I B , λ − I C , λ ) − ( I A , λ − I D , λ ) ] ( I B , λ + I C , λ ) − ( I A , λ + I D , λ ) − α λ .
N A = N A i + N A o b j .
ε = 1.22 λ N A i + N A o b j .
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