Laser oblique scanning optical microscopy (LOSOM) for phase relief imaging

Yichen Ding; Hao Xie; Tong Peng; Yiqing Lu; Dayong Jin; Junlin Teng; Qiushi Ren; Peng Xi

doi:10.1364/OE.20.014100

1. Introduction

Although optical microscopy has been applied to the study of biological material since the 17th century, the transparent nature of biological cells makes optical observation difficult. Frits Zernike won the Nobel Prize in Physics in 1953 for rendering the invisible phase alteration to a detectable amplitude modulation. Among the numerous phase sensing microscopy techniques, phase contrast (PhC) microscopy [1,2] and differential interference contrast (DIC) microscopy [3,4] are considered the most applicable to biological material. In particular, phase relief imaging together with fluorescent microscopy has been widely applied to the study of cell cycle monitoring [5,6] and high throughput RNAi screening [7]. Nevertheless, difficulties, such as the non-straightforward illustration of the phase in the PhC microscopy, and the expense of polarized prisms utilized in DIC microscopy, are associated with these techniques [8,9]. Additionally, other phase sensitive methods using distinct perspectives, such as oblique microscopy [10], Hoffman modulation contrast microscopy [11], differential phase contrast microscopy [12–14], Hilbert phase microscopy [15], and digital holographic microscopy [16,17], have demonstrated their potential applications in transparent specimen imaging.

On the other hand, the boom in the use of confocal laser scanning microscopy (CLSM), has resulted in extensive studies of scanning optical microscopy (SOM) [18]. Because the core of an optical fiber can play the role of a coherent detector, highly accurate phase contrast surface images have been demonstrated [19,20]. The contrast is induced by the retro-reflection of a back scattered signal in such systems. The disadvantage of such a mode rests on the fact that phase objects mainly advance or retard the phase of passing light instead of the amplitude, and the phase information of the sample that is transmitted back along the incident path can only be detected with the assistance of interference [21–23]. Although the axial resolution of CLSM is much higher than the wide-field counterparts, it is still rather coarse for phase contour mapping compared with phase contrast methods [8]. In this work, we introduce a novel optical imaging mechanism in which the phase relief contours of transparent biological cells can be obtained with laser oblique scanning optical microscopy (LOSOM). Based on a conventional CLSM, the images obtained with LOSOM are similar to those obtained by DIC [8], yet the method is fundamentally superior to related work aimed at confocal microscopy in conjunction with DIC [21,22] because it has eliminated the Wollaston prism and other components related to polarization. In addition, it completely abandons diverse phase modulated components, such as the phase plate and annular diaphragm in PhC, and eliminates the slit plate and modulator plate in Hoffman modulation contrast microscopy.

2. Methods

In essence, the major hardware of LOSOM is identical to CLSM (Fig. 1 ). However, in LOSOM, the tilted illumination induces an oblique illumination to the specimen with the assistance of a fluorescent medium behind the specimen. The collecting lens is tuned offset for oblique detection, modulating the retro-reflected signal as a window function. As shown in the theoretical analysis below, the collected SOM images can reflect the phase gradient of the specimen.

Fig. 1 (a) Simplified schematic diagram of the LOSOM system. The incident beam and the dichroic of the confocal system are not illustrated. The red beam represents the axial beam pathway of a confocal microscope, and the light blue beam indicates the beam pathway in the LOSOM. (b) Geometrical relationship between a light beam diameter (red circle) and an aperture of the collecting lens (yellow circle). $O$ and $O'$ , are centers of the beam and the aperture, respectively; $r_{1}$ and $r_{2}$ , are radii of the beam and the aperture, respectively; $D$ denotes the distance of $| O O' |$ ; $L$ denotes a common chordal length of the overlapping areas; $S_{1}$ , $S_{2}$ are the areas of the beam and aperture, respectively; $θ$ , $θ_{1}$ , $θ_{2}$ are the angles in the presented triangle. (c) The entire LOSOM system is illustrated, highlighting the telescope composed of the scan lens and the tube lens. The galvo-scanner is tilted to provide the oblique illumination with the aid of a fluorescent medium. DC: dichroic mirror.

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2.1 Theoretical analysis

Figure 1(a) shows a simplified schematic diagram of the LOSOM. First we consider a right angled illumination and the modulation by the sample, $ρ (x_{1}, y_{1})$ , from which the electric field after travelling through a transparent sample can be expressed as $u_{0} (x_{1}, y_{1}) = A ρ (x_{1}, y_{1})$ . At distance $z$ from the objective, the complex electric field can be expressed as [24]

U (ξ, η) = \iint_{X, Y} u_{0} (x_{1}, y_{1}) \exp [i \frac{k}{f_{1}} (x_{1} ξ + y_{1} η)] \exp (i k z) d x_{1} d y_{1},

where

X

and

Y

denote the boundaries of

x_{1}

and

y_{1}

, respectively. Then, at the focal distance

f_{2}

of the collecting lens, the electric field becomes

\begin{matrix} u_{1} (x_{2}, y_{2}) = \iint_{Ξ, Ω} U (ξ, η) \exp [i \frac{k}{f_{2}} (x_{2} ξ + y_{2} η)] d ξ d η \\ = \exp (i k z) \iint_{Ξ, Ω} \iint_{X, Y} u_{0} (x_{1}, y_{1}) \exp {i k [(\frac{x_{1}}{f_{1}} + \frac{x_{2}}{f_{2}}) ξ + (\frac{y_{1}}{f_{1}} + \frac{y_{2}}{f_{2}}) η]} d x_{1} d y_{1} d ξ d η, \end{matrix}

where

Ξ

and

Ω

denote the boundaries of

ξ

and

η

, respectively. Let

M = - f_{2} / f_{1}

, and we can see that for

x_{2} = M x_{1}

,

y_{2} = M y_{1}

, and Eq. (2) becomes

u_{1} (M x_{1}, M y_{1}) = u_{0} (x_{1}, y_{1}) \exp (i k z),

and consequently

I_{1} (M x_{1}, M y_{1}) = I_{0} (x_{1}, y_{1})

which indicates a magnified imaging relationship. Note that for the above analysis, we assume the presence of infinitely large lenses to collect all the diffractive angular spectra.

With an angular illumination of $ϕ$ , the electric field after the sample can be written as $u_{2} (x_{1}, y_{1}) = u_{0} (x_{1}, y_{1}) \exp (i ϕ x_{1})$ . Here for simplicity, we take the azimuth angle on the $x_{1}$ axis. Thus,

U (ξ', η') = \iint_{X, Y} u_{0} (x_{1}, y_{1}) \exp {i k [x_{1} (\frac{ξ'}{f_{1}} + ϕ) + \frac{η'}{f_{1}} y_{1}]} \exp (i k z) d x_{1} d y_{1},

and therefore

U (ξ', η') = U (ξ - ϕ f_{1}, η)

which denotes that the angular spectrum is shifted by

ϕ f_{1}

due to the oblique illumination.

Now we consider the intensity of $I_{0} (0, 0)$ , which is the imaging region of the confocal system. If the aperture diameter of the objective is set to be $a$ , then at distance $z$ , the intensity distribution can be expressed as $I (ξ, η, z) = \frac{4 I_{0}}{π a^{2}} c i r c (0, 0, \frac{a}{2})$ , where the circ function can be defined as:

c i r c (x_{0}, y_{0}, r) = {\begin{matrix} 1, & {(x - x_{0})}^{2} + {(y - y_{0})}^{2} \leq r^{2} \\ 0, & o t h e r w i s e \end{matrix} .

For angular illumination, $I (ξ, η, z) = \frac{4 I_{0}}{π a^{2}} c i r c (ϕ f_{1}, 0, \frac{a}{2})$ . If we define the aperture diameter of the collecting lens to be $W$ , then the collected intensity is modulated by the window function

I' (ξ, η, z) = \frac{4 I_{0}}{π a^{2}} c i r c (ϕ f_{1}, 0, \frac{a}{2}) c i r c (0, 0, \frac{W}{2}) .

This is the intensity detected by the confocal point scanning setup. Now, consider that within the resolution of the confocal system, a phase gradient of

ρ

is present; this will contribute to the illumination angle

ϕ

so the total phase gradient becomes

ϕ + ρ

. In Fig. 1(b), we make

D = (ϕ + ρ) f_{1}

,

r_{1} = a / 2

,

r_{2} = W / 2

and

S = S_{1} + S_{2}

, hence

\frac{d D}{d x} = f_{1} \frac{d ρ}{d x}

. Based on the geometrical relationship, it is obvious that

S_{1} = S_{\sec t o r} - S_{t r i} = r_{2}^{2} \cdot θ_{2} - (r_{2}^{2} \sin 2 θ_{2}) / 2

, therefore,

\frac{d S_{1}}{d D} = 2 r_{2}^{2} \sin^{2} θ_{2} \frac{d θ_{2}}{d D} = \frac{L^{2}}{2} \frac{d θ_{2}}{d D}

, and similarly

\frac{d S_{2}}{d D} = \frac{L^{2}}{2} \frac{d θ_{1}}{d D}

, and then

\frac{d S}{d D} = \frac{d S_{1}}{d D} + \frac{d S_{2}}{d D} = - \frac{L^{2}}{2} \frac{d θ}{d D} ..

According to the Cosine Theorem,

\cos θ = (r_{1}^{2} + r_{2}^{2} - D^{2}) / (2 r_{1} r_{2})

, and the Sine Theorem,

D / \sin θ = r_{2} / \sin θ_{1}

, this finally yields

\frac{d θ}{d D} = \frac{D}{r_{1} r_{2} \sin θ} = \frac{2}{L},

\frac{d S}{d x} = \frac{d S}{d D} \cdot \frac{d D}{d x} = - L \cdot f_{1} \frac{d ρ}{d x} .

The overlapped area

S

represents the collected fluorescent intensity

I

. When omitting all the components that are not changed with

x_{2}

, Eq. (9) becomes

\frac{d I}{d x} = C \frac{d ρ}{d x},

where C denotes a constant. Equation (10) shows that, the intensity of the collected signal is linearly modulated with the phase gradient of the specimen. It is superimposed on top of a uniform background denoted by Eq. (9), when

\frac{d ρ (x_{1})}{d x_{1}} = 0

, i.e. the phase gradient inside the detectable confocal region is zero.

Figure 1(c) illustrates the design of the LOSOM system. The incident laser beam ( $λ = 0.375$ μm in our experiment) was scanned by the galvo-scanner for 2-D imaging. The incidence beam passed through a telescope composed of a scan lens and a tube lens, before entering the objective. A fluorescent medium which can be excited by the illumination laser in the scanning microscope (for example, a piece of Chroma Chromophore plate (Light Blue) in our experiment) is introduced after the sample. As the galvo-scanner is tilted, the excited fluorescence causes an oblique angle illumination to the specimen. Details of the confocal system can be found in Ref [25]. Generally the thickness of the glass slide (distance between the fluorescent medium and the specimen) is $l = 1.2$ mm, while the oblique angle of the incident beam is $ϕ$ . Thus, the laser focuses on the transparent specimen and then propagates $1.2 / cos ϕ$ mm to excite the fluorescent medium, thus forming a fluorescent source with a diameter greater than 600 μm. The rotation angles of both galvanometers range from zero to one degree. It is necessary to keep angle $ϕ$ over 2° in order to ensure that the oblique angle always remains in the same quadrant during scanning. The choice of the oblique angle is related to the sensitivity of the phase-relief contrast, and the detection range of the phase gradient. Maximum signal intensity is obtained when the oblique angle equals the phase gradient. This means that a smaller oblique angle is more sensitive to a local phase gradient than a larger oblique angle situation. In addition, adjusting the oblique angle can lead to distinct phase relief effects. There are nearly three orders of magnitude difference between the size of the focus beam on the specimen and the fluorescent source, thus, the fluorescent source can be approximately treated as a constant oblique illumination. The normalized diameter of the pinhole is ~5 Airy Units in our experiment.

The advantage of LOSOM is that it easily transforms a confocal microscope into a phase relief imaging microscope. Although oblique microscopy can produce similar phase-relief results [10], the LOSOM detection is made more sensitive by taking advantage of the sensitivity of the point detector, such as a photomultiplier (PMT). As a result, the excitation power can be minimized compared to that used with 2-Dimensional oblique microscopy. Note that, with the introduction of the scanning telescope consisting of scan and tube lenses, the back aperture of the objective will always be filled during imaging [26]. Yet, due to the shift of the collecting lens in relation to the center of the retro-reflection, the overall resolution is sacrificed compared to confocal counterparts.

Here, a uniform intensity distribution was assumed when obtaining the analytic solution to Eq. (10), instead of a Gaussian distribution. Thus, a higher order phase contribution has to be taken into account in conjunction with the linear modulation, when quantitative phase analysis is performed with this method.

2.2 Simulation

Figure 2 illustrates a simulated uniform amplitude distribution of an artificial specimen that varies in optical thicknesses. The variation in amplitude intensity reflects the optical path difference (OPD). According to Eq. (10), the more rapid the change in optical thickness, the more acute the intensity change in the image will be. An artificial donut is represented as a transparent object in Fig. 2(a), and along the azimuth axis (dashed red line), its OPD is plotted in Fig. 2(d). The gradients of the specimen can be clearly visualized in Fig. 2(b) and 2(c) due to the oblique illumination, in which the phase features appear as pseudo 3-Dimensional structures owing to a sudden change of OPD. The opposing effect seen between Fig. 2(b) and 2(c) is a result of the contrasting oblique angles of incidence. The respective intensity distributions are shown in Figs. 2(e) and 2(f).

Fig. 2 Simulation of LOSOM in response to variations in the optical path. (a) Object optical path difference (OPD), the grayscale represents the optical phase. (b)-(c) Intensity distributions of the phase relief generated using opposite directions of illumination rays. (d) OPD along the azimuth axis, corresponding to (a). (e)-(f) Amplitude profiles along the azimuth axis, corresponding to (b)-(c), respectively.

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3. Experimental results

Figure 3 illustrates images from the same area of an unstained HeLa cell culture obtained by using different microscopy methods. Figure 3(a) was imaged with a commercial DIC microscope (Axio Observer, Carl Zeiss), and the arrows indicate the nuclei of HeLa cells. In agreement with the simulated images shown in Fig. 2(b) and 2(c), altering the oblique angle of incidence in the device, caused a distinct phase relief to appear, the bright borders in Fig. 3(b) are reversed in Fig. 3(c) (indicated by the arrows). Modification of the oblique angle causes the “hill” in the relief-like appearance to be converted to a “valley” or vice versa. This is the same effect as changing the phase retardation in DIC microscopy by. As can be seen, this method records the same biological optical thickness changes with a phase relief image that is similar, if not superior, to a conventional DIC image (i.e. absolute intensity is related to changes in the optical gradient).

Fig. 3 Comparison of images captured with DIC and LOSOM. The relief appearance of the same HeLa cells can be compared with (a) DIC (Carl Zeiss, NA = 0.4) and (b-c) LOSOM (Nikon, NA = 0.3). Scale bar: 30 μm.

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In addition, LOSOM can be applied to fluorescently labeled samples and used in conjunction with fluorescence microscopy to obtain multi-modality phase-relief/fluorescence images, provided that the contributed signal from the fluorescence medium is strong enough. Compared with conventional confocal fluorescent images (Fig. 4(a) , 4(d)), and LOSOM surface structure images (Fig. 4(b), 4(e)), the merged fluorescence and structure images shown in (c) and (f) represent information from both modalities. The images not only demonstrate the structures of the mouse kidney with their optical thicknesses, but also reveal the locations of the DAPI labeled cell nuclei, which can only be visualized with fluorescence imaging. In Fig. 4, the introduced fluorescence intensity from the fluorescent medium is so strong that a uniform background level four fold that of the maximum sample intensity is presented. Due to its multi-modality imaging capability, LOSOM can extend the applications of a conventional laser scanning optical system when using phase imaging of transparent specimens.

Fig. 4 Pseudo-color images of a mouse kidney section (F-24630, Invitrogen) using LOSOM to reveal DAPI fluorescent staining for nuclear material (a, d). Note that images of oblique fluorescent illumination show a relief-like structure in the tissue sections (b, e) and the combined images (c, f). Images (a-c) are taken with 10x, NA 0.3 objective, and (d-f) are taken with 20x, NA 0.45 objective. Scale bar: 30 μm.

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We have demonstrated that LOSOM can be used with objectives of different NAs. However, because a high-NA objective has a broader incident angle on the fluorescent medium, the phase-relief effect of LOSOM suffers from less illumination.

When using the phase relief imaging capability of LOSOM, the relative optical thicknesses of different domains in the sample can be evaluated even with a low magnification objective. Taking advantage of the phase relief appearance, this modality can optically section biological specimens by focusing on distinct optical planes, which is similar to the results reported in Ref [27]. It should be noted that the axial resolution of an objective with NA = 0.3 is nearly 8 μm for $λ = 0.375$ μm imaging. Figure 5 demonstrates the optical sectioning capability. The arrows in Fig. 5 highlight the variation within different z-axis imaging planes, within a 4 μm depth in the tissue.

Fig. 5 A series of optical sections of the mouse kidney taken at 2 μm intervals using LOSOM with the 10x objective. Scale bar: 30 μm.

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4. Conclusion and discussion

We report a novel method to achieve phase relief images based on a confocal system that places a fluorescent medium behind the sample to act as a passive back-illumination source, and an oblique laser scanning mechanism for image collection. LOSOM is compatible with fluorescently labeled specimens, and can obtain multi-modality fluorescence/structural images using a single system. Images from various depths can be readily resolved owing to its DIC-like phase relief imaging. Furthermore, quantitative phase extraction may be possible with algorithms developed for optical phase analysis [28]. Laser scanning microscopy is widely applied in biological studies, and our method can provide complimentary information to optical phase imaging, especially when studying cell cycle progression or high throughput screening.

Acknowledgment

The authors thank Dr. Thomas FitzGibbon for comments on earlier drafts of the manuscript, Olivia C. Hoy for proofreading, and funding support from the “973” Program of China (2011CB707502, 2010CB933901, 2011CB809101), and the Natural Science Foundation of China (61178076).

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Laser oblique scanning optical microscopy (LOSOM) for phase relief imaging

Abstract

1. Introduction

2. Methods

2.1 Theoretical analysis

2.2 Simulation

3. Experimental results

4. Conclusion and discussion

Acknowledgment

References and links

Cited By

Figures (5)

Equations (10)

Optics Express