- Email: [email protected]
Controllable tomography phase microscopy
Optics and Lasers in Engineering 66 (2015) 301–306
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Controllable tomography phase microscopy Peng Xiu a, Xin Zhou a, Cuifang Kuang a,n, Yingke Xu b, Xu Liu a a b
State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China Key Laboratory of Biomedical Engineering of Ministry of Education, Department of Biomedical Engineering Hangzhou 310027, China
art ic l e i nf o
a b s t r a c t
Article history: Received 29 May 2014 Received in revised form 28 September 2014 Accepted 2 October 2014
Tomography phase microscopy (TPM) is a new microscopic method that can quantitatively yield the volumetric 3D distribution of a sample's refractive index (RI), which is significant for cell biology research. In this paper, a controllable TPM system is introduced. In this system a circulatory phaseshifting method and piezoelectric ceramic are used which enable the TPM system to record the 3D RI distribution at a more controllable speed, from 1 to 40 fps, than in the other TPM systems reported. The resolution of the RI distribution obtained by this controllable TPM is much better than that in images recorded by phase contrast microscopy and interference tomography microscopy. The realization of controllable TPM not only allows for the application of TPM to the measurement of kinds of RI sample, but also contributes to academic and technological support for the practical use of TPM. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Tomographic Refractive index image Cell structure Microscopy
1. Introduction The refractive index (RI) distributions in cells are various and changeable. They reflect the active states of cells and cannot be shown directly from intensity information, a fact that has long drawn the attention of researchers. For example carcinogenesis increases the cell's RI [1], and Plasmodium falciparum infection can change the internal structure and RI of red blood cells [2]. Phase contrast microscopy [3] and differential interference microscopy [4] are traditional techniques that enable RI information to be presented in the form of intensity information, giving rise to their wide application in biological research. In recent years more advanced phase microscopy techniques have been developed to record quantitative phase images induced by specimens [5–9], but most of them obtain just the average or approximate distribution of the RI [10–12], which cannot quantitatively reflect the 3D RI changes in samples. To solve this problem we image 3D RI information using tomography phase microscopy (TPM), which allows the RI to be imaged more accurately. In most microscopies that merely focus on intensity imaging the microscopic image can be regarded, in theory, as the convolution of the sample and the point spread function of the system [13], and the imaging quality depends on the intensity contrast of the specimen and the sharpness of the system's point spread function. To enhance the imaging quality, various dyes are typically used to make specimens scatter or absorb more light [14].
n
Corresponding author. E-mail address: [email protected] (C. Kuang).
http://dx.doi.org/10.1016/j.optlaseng.2014.10.001 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
The use of specific fluorescence labeling to obtain the expected fluorescence from the samples is another common approach [15– 17]. However, these traditional methods do not apply to imaging the RI. That is, unlike the case in intensity imaging, the distribution of the RI itself is not directly involved in imaging, which mainly modulates the light path of transmitted beams [7]; this modulation can be accumulated along a certain light path, which means it has linear integral characteristics. Thus, in analogy to the use of integral characteristics for X-ray absorption of samples in the computed tomography technique, TPM [18] reconstructs the 3D distribution of the RI of a sample by obtaining the phase information in different projective directions and using algorithms to render the image. Nevertheless, TPM is a phase microscopic method based on large data calculations that needs to record numerous interference images and use phase-shift algorithms to quantitatively analyze the phase information under different projective angles at a tremendous speed. This implies that the speed of phase shifting and the rate of image collection and processing are both constraints in the development of the TPM system. In existing research, acousto-optic modulator phase shifting is a common method [18] that can shift the phase at a speed of 5000 times/s; when it is combined with certain imaging rates, 3D phase information can be collected at a speed of 10 fps. Although acousto–optic modulator phase shifting can shift the phase quite rapidly, its phase shifting rate is fixed, so the speed of imaging in the system is not adjustable; this makes it difficult to observe specimens of different active statuses and also puts strict requirements to the camera. In this paper, we present a controllable TPM using a piezoelectric ceramic (lead zirconium titanate, PZT), instead of acousto-optic modulators, to perform phase shifting. Because PZT has high controllability and
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P. Xiu et al. / Optics and Lasers in Engineering 66 (2015) 301–306
M1
λ/2 PBS1 GM L3
BE
PZT L1 BF C S
M2 L4
OL L2
Camera
Laser
P PBS2
M3
Fig. 1. Controllable TPM system. a) Principal system: beam expander (BE); reflecting mirrors (M1–M3); polarized beam splitters (PBS1 and PBS2); galvanometer scanning mirror (GM); lenses L1–L4 (f1 ¼250 mm, f2¼ 200 mm, f3¼50 mm, f4 ¼150 mm); back focal plane of condenser lens (BF); condenser lens (C); sample stage (S); objective lens (OL); polarizer (P). b) Photograph of experimental system.
position keeping ability it can adjust the phase shifting speed for different samples, allowing for the entire system more controllability and adjustability. Additionally our system can collect 3D phase data at speeds of up to 40 fps during continuous shooting, greatly improving the performance of TPM and offering theoretical and technical support to biological research.
Camera control signal
U 1 0
1
2
3
Our controllable TPM system is based on the Mach–Zehnder interference microscope structure, as shown in Fig. 1. A 633 nm He–Ne laser beam is expanded and then divided into reference and sample light paths by a polarization dispersion prism (PBS1 in Fig. 1). The light intensity distribution of each light path is modulated by rotating the half-wave plate (λ/2) in front of PBS1. The sample light goes through four lenses: scanning lens L1, convergent lens C (Olympus, NA ¼1.4), objective lens OL (Olympus, UApo N, 100 , NA ¼1.49), and field lens L2; any two continuous lenses can form a 4f system. The scanning galvanometer, sample, and camera (CMOS, MotionBLTZs EoSens Cube7) are located at the three conjugate planes of the consecutive 4f systems. When the galvanometer is scanning, parallel laser beams pass through samples in different directions, from angles of 501 to 501, forming images on the camera. In the reference path, the laser beam is expanded by two lenses (L3, L4) and then phase shifted by a PZT element. The sample path and reference path combine at the second polarization dispersion prism (PBS2), with uniform polarization achieved through the polarizer, and finally interfere on the imaging surface of the camera. As a special and important part of our system, the PZT (P-885.11, PI) element can respond to the input voltage in tens of microseconds and achieve phase shifts at speeds greater than 5000 times/s. However, because of the mechanical structure and voltage instability, the PZT element oscillates randomly after responding to the input voltage. This process will last from 400 to 600 ms, introducing a large amount of noise to the interference images and restricting the application of PZT in the TPM. We present a control method of cyclical scanning (“cyclical scanning control method” hereafter) to solve this problem and improve the controllability of the system. The process of the cyclical scanning control method is shown in Fig. 2. Fig. 2 shows the details of the cyclical scanning method, including the camera control signal, PZT control signal, galvanometer scanning mirror (GM) control signal, and sample package method that renders the 3D information of the RI. Though the
t
PZT control signal
U
2. System and control
4
V4 V3 V2 V1
0
1
2
4
3
t
GM control signal
U Va
0
1
Vb
2
3
t
4
Sample P1
0
P2
1
P3
2
P4
3
P5
4
t
Fig. 2. Cyclical scanning control method. a) Camera control signal; the frequency is set in accordance with the active status of samples. b) PZT control signal; V1–V4 are corrected voltages corresponding to the four-step frequency-shifted method, which changes the reference arm's optical path by one-quarter wavelength each time. c) Galvanometer scanning mirror control signal. As the signal voltage changes from Vb to Va, the sample beam illuminates the sample at angles from 501 to 501. d) Sample package method; the images recorded in four continuous scanning processes form an information package describing the 3D RI. e) PZT control signal (blue) and galvanometer scanning mirror control signal (green) tested by an oscilloscope in practice. (For interpretation of the reference to color in this figure, the reader is referred to the web version of this article.)
P. Xiu et al. / Optics and Lasers in Engineering 66 (2015) 301–306
position shift of PZT is proportional to the voltage variation in general, the hysteresis and nonlinearity of the PZT may affect the accuracy of phase shifting. In order to control the system accurately, the voltage corresponding to certain position shift should be set depending on PZT's characteristics, experimental conditions and the way voltages changes. Thus, we calibrate the working voltages of PZT in advance; in each scanning circle, V1, V2, V3, and V4 are the incremental post-calibration voltages driving the PZT to change the light path in reference arm by one-quarter wavelength (λ/4) each time. The angle of the GM has a linear relationship with the input voltage; when the input voltage varies from Vb to Va, the direction of the laser beam that goes through the sample varies from 501 to 501. The traditional control method sets the GM first and then obtains phase information through phase-shifting. That is, when the GM is set at a certain direction angle, the voltage of the PZT changes four times, resulting in a phase shift; meanwhile, the camera records the corresponding four images to obtain the phase information. As the direction angle varies from 501 to 501 by the rotation of the GM, data collection for a 3D RI distribution is completed. In the traditional method, the response oscillation caused by the structure of the PZT and the step rotation of the GM can both introduce noise into the data collection process and reduce the data collection speed. In our cyclical scanning method we set the status of the PZT first and then rotate the GM, with the camera recording the images synchronously, to achieve interference images under certain phase differences through direction angles from 501 to 501. Next, we use the PZT to alter the optical path length of the reference light by λ=4 and then repeat the process mentioned above; the images recorded during four continuous voltage changes can form a data package describing the 3D RI distribution. During the collection of interference images the exposure time of the camera is tens of microseconds, which is negligible compared with the scanning period of the GM. In the cyclical scanning control method the response oscillation of the PZT and GM no longer affects the collection of interference information, and the speed of the entire collection process can be adjusted according to the imaging speed of the camera and variable characteristics of the samples. The phase information at each illuminating angle is calculated by interference images obtained in four cycles of the GM. The vibration or displacement of GM may also bring noise to the phase calculation process. Driving the GM linearly and coordinating the camera imaging rate work well to reduce this effect. Additionally, the four-phase-shifting method is periodic; thus, information recorded from four arbitrary continuous phase shifts can form a data package describing the 3D RI distribution. Theoretically, we can obtain data during the dynamic process of imaging four times faster than by the traditional control method.
3. Main theory of TPM TPM can image the 3D position-dependent RI of the sample. The process has two parts; the first is the collection of phase information by varying the direction of the illuminating beam, and the second is the reconstruction of the 3D distribution of the RI. We use the four-phase-shifting method [19] to acquire the quantitative phase information, in which the interference images of the sample and reference light fields can be described as Iðx; y; θ; NÞ:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Nπ km sin θ þ ϕθ ðx; y; θÞ þ x I x; y; θ ; N ¼ I R þ I S x; y; θ þ 2 I R I S x; y; θ cos 2 M
ð1Þ Here, θ is the angle of illumination of the sample beam with respect to the optical axis, nm is the RI of the medium, and km ¼ 2πnm =λ is the wavenumber of the light in the medium. I R
303
and I S ðx; y; θÞ are the intensities of the reference and sample fields, respectively, at the illumination angle θ. ϕθ ðx; y; θÞ is the phase change induced by the sample, with transverse coordinates ðx; yÞ. M¼110 is the magnification of the system. N is the number of times the PZT signal changes, and with each change the phase is shifted by π/2. km sin θ =M is the ramp induced by tilt illumination. I 1 ¼ Iðx; y; θ; NÞ, I 2 ¼ Iðx; y; θ; N þ1Þ, I 3 ¼ Iðx; y; θ; N þ 2Þ, and I 4 ¼ Iðx; y; θ; N þ 3Þ are the interference images at each of the four phase-shift times. In the first part of the process, the phase information of the sample field can be calculated by the equation. ψ N x; y; θ ¼ angle½ðI4 I2 Þ þ iðI3 I1 Þ h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i ð2Þ ¼ angle 4 I R I S ðx; yÞexpðiϕθ ðx; y; θÞ þ i km sin θ x=M Here, angleðÞ denotes the function used to calculate the phase angle of a complex number. Then, a phase-unwrapping algorithm is used to resolve the 2π-phase ambiguities [20]. In order to eliminate the phase ramp aberration induced by tilt illumination and background noise we also record thebackground phase image with a blank sample and then extract ϕθ x; y; θ by calculating the difference between the phase of sample and background, which theoretically removes the ramp along the beam tilting direction. In our experiment we repeated the above and obtained a procedures set of quantitative phase images, ϕθ x; y; θ , at different illumination angles θ. The algorithm used to reconstruct the 3D distribution of the RI image is the reverse Radon transformation. The Radon transformation [21] is a method of recording the sample's 3D information by collecting and analyzing its linear projection information in different directions. Analogously, when the GM rotates, parallel light illuminates the sample at different angles in x–z plane. Each projection can be regarded as the linear integral of the RI distribution in a certain direction, as described by the following equation: pðs; ys ; θÞ ¼ ∬ ðnðxs ; ys ; zs Þ nm Þkm δ xs cos ðθÞ þ zs sin ðθÞ s dxs dzs ð3Þ In the equation, pðs; ys ; θÞ is a phase image obtained by the linear integral of the RI in the direction described by the angle of illumination of the sample beam with respect to the optical axis, θ, and s is the distance between the integral line and the center of the x–z plane; nðxs ; ys ; zs Þ is the RI distribution of the sample with coordinates ðxs ; ys ; zs Þ. Further, the reverse transformation of Eq. (3) is nðxs ; ys ; zs Þ ¼ ∬
∂pðs; ys ; θÞ 1 ds dθ þnm ∂s 2π 2 xs cos ðθÞ þ zs sin ðθÞ s ð4Þ
Using Eq. (4), the tomographic images of the sample can be calculated as nðxs ; ys ; zs Þ. Eqs. (3) and (4) represent the separate collection and reconstruction of images for a section (in a certain direction), and the image of the 3D distribution is a superposition of all the sections. We can calculate pðs; ys ; θÞ from the phase image ϕθ ðx; y; θÞ by the equation pðs; ys ; θÞ ¼ ϕθ ðsM cos ðθÞ; Mys ; θÞ
ð5Þ
Eq. (5) acts as a link combining two part of the TPM method to finish the entire process, from the acquisition of phase information at a certain illumination angle to the reconstruction of the RI distribution.
4. Results and analysis
for
Silica samples have a fixed and uniform RI distribution (n ¼ 1.47 λ ¼ 633 nm), which is helpful for testing the tomographic
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Fig. 3. Results for silica samples immersed in oil (n¼ 1.518) by controllable TPM system. a) Upper left: model of 10 μm silica ball; Roman numerals indicate slices along which 3D tomographic RI images I–V (right and bottom) of single sample are taken. b) Images of 5 μm silica sticks: (i) intensity image; (ii) view of 3D RI image along z axis; and (iii) 3D tomographic RI image.
Fig. 4. Results for 3 μm silica balls (on two levels): a) Distribution model of silica balls; b) intensity image under one projection; c) phase image under the same projection as in 4 (b); d), e) sections (different z values) of the sample labeled I and II, respectively, in (a); f) distribution of the intensity along the lines in (b)–(d), in which A denotes the intensity image, P denotes the phase image, and I is the RI image in the focal plane.
capability of TPM. First, we observed a single silica ball (diameter, 10 mm) immersed in oil (n ¼1.518 for λ ¼ 633 nm; hereafter, the oil we used has the same RI). Because the ball's RI is isotropic and disturbances in its attitude scarcely affect its phase images, we can set the camera imaging rate to 800 fps, galvanometer scanning frequency to 8 Hz, and scanning angle from 501 to 501. We calculate the scale and RI of the sample using the interference images, and the results are in very good agreement with the parameters of the sample (10 mm silica ball). Therefore, the phase images used to calculate the tomogram images are quantitative and credible. Then we observed silica sticks (diameter, 5 mm) immersed in oil. The sticks remain suspended, and their relative spatial locations are various and changeable. We set the camera imaging rate to 4000 fps, the galvanometer scanning frequency to 40 Hz, and the scanning angle from 501 to 501. Fig. 3a demonstrates that the controllable TPM can image the 3D RI distribution map of the sample, but the signal-to-noise ratio decreases in the sections far from the focal plane. This phenomenon, caused by projection approximation, is common in all types
of TPM, and a propagation algorithm has been proposed to reduce this effect [22]. In Fig. 3b (i) shows the intensity image at one projection, whereas (ii) and (iii) show the RI tomographic map of two silica sticks from different perspectives so that we can clearly determine their location and attitude. The results shown in Fig. 3 demonstrate the tomographic capacity of the controllable TPM system. An outstanding feature of this system is that the imaging speed can be changed according to the sample. Fig. 4 shows the imaging results for 3 μm silica balls which are also suspended in oil. We can see only the rough profile of the sample in Fig. 4b and c, but cannot distinguish the number of spheres or how they are distributed. However, the 3D RI tomogram images obtained by our controllable TPM system (camera rate 4000 Hz, galvanometer scanning frequency 40 Hz and scanning angle 501 to 501) clearly reveal that the sample consists of five balls on the top level and two on the bottom. More importantly, from the contrast image shown in Fig. 4f, we can conclude that the sections of our reconstructed 3D RI distribution map have higher lateral resolution than the intensity and phase images.
P. Xiu et al. / Optics and Lasers in Engineering 66 (2015) 301–306
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Fig. 5. RI tomogram of 3T3 mouse cells (immersed in water). a) 3D tomographic RI map; b) interference image under 01 projection; c) view along z axis of tomographic RI image; i)–iv) RI images at different sections (marked in (a) along the z axis; the RI bar indicates that the sample's RI varies from 1.3 (water) to 1.4. (For interpretation of the reference to color in this figure, the reader is referred to the web version of this article.)
Mouse 3T3 cell lines, originally extracted from the mouse fetus, have long been used for in vitro experiments in cancer research, for example, for cancers induced by tumor viruses and carcinogenic agents [23]. The 3T3 cell sample used in our experiment was first soaked in formalin and then immersed in water. Fig. 5b shows one interference image of the ecptomas of one cell; from the image we can easily define the outline of the ecptomas but cannot obtain further internal information. The 3D RI tomogram in Fig. 5a shows that the cellular material is concentrated on one side, and the other side is filled with water; because the cytomembrane is destroyed by formalin, the water can penetrate freely. Fig. 5i–iv shows slices of the tomogram at the different heights indicated in Fig. 5a. The yellow dashed line marks the outline of the ecptomas. The RI of the cell material is nearly 1.36 (λ ¼633 nm), and its distribution reflects the 3D structural change in the ecptomas after cell death. This proves the potential of this system in providing strong support to related biomedical research.
5. Conclusion In this paper we propose a new systematic control method, the cyclical scanning control method, and a controllable TPM system. This system inherits the principle and advantages of TPM and makes the imaging speed more controllable; moreover, a high speed camera is no more a necessity for TPM, which will promote the development of this novelty microscopy. We imaged silica balls, silica sticks, and mouse cells in our experiments, the results of which demonstrated the excellent performance. Compared to traditional TPM systems, our system has a more controllable speed, more stable performance, and stronger operability with a lower building cost, all of which provide significant contributions to the development and application of TPM.
Acknowledgments This work was financially supported by grants from the National Basic Research Program of China (973 Program) (No. 2015CB352003)
and the National Natural Science Foundation of China (Nos. 61377013, 61427818, 61205160, 61378051 , 61335003 and 31301176).
References [1] Choi WJ, Jeon DI, Ahn S-G, Yoon J-H, Kim S, Lee BH. Full-field optical coherence microscopy for identifying live cancer cells by quantitative measurement of refractive index distribution. Opt Express 2010;18:23285–95. [2] Park Y, Diez-Silva M, Popescu G, Lykotrafitis G, Choi W, Feld MS, et al. Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum. Proc Natl Acad Sci 2008;105:13730–5. [3] Zernike F. Phase contrast, a new method for the microscopic observation of transparent objects. Physica 1942;9:686–98. [4] Nomarski G. Microinterféromètre différentiel à ondes polarisées. J Phys Radium 1955;16:S9–13. [5] Popescu G, Park Y, Badizadegan K, Dasari RR, Feld MS. Diffraction phase and fluorescence microscopy. In: Proceedings of the Frontiers in Optics, Optical Society of America, 2006. [6] Popescu G, Ikeda T, Dasari RR, Feld MS. Diffraction phase microscopy for quantifying cell structure and dynamics. Opt Lett 2006;31:775–7. [7] Barty A, Nugent KA, Paganin D, Roberts A. Quantitative optical phase microscopy. Opt Lett 1998;23:817–9. [8] Fang-Yen C, Oh S, Park Y, Choi W, Song S, Seung HS, et al. Imaging voltagedependent cell motions with heterodyne Mach–Zehnder phase microscopy. Opt Lett 2007;32:1572–4. [9] Marquet P, Rappaz B, Magistretti PJ, Cuche E, Emery Y, Colomb T, et al. Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy. Opt Lett 2005;30:468–70. [10] Popescu G, Ikeda T, Goda K, Best-Popescu CA, Laposata M, Manley S, et al. Optical measurement of cell membrane tension. Phys Rev Lett 2006;97:218101. [11] Rappaz B, Marquet P, Cuche E, Emery Y, Depeursinge C, Magistretti P. Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy. Opt Express 2005;13:9361–73. [12] Lue N, Popescu G, Ikeda T, Dasari RR, Badizadegan K, Feld MS. Live cell refractometry using microfluidic devices. Opt Lett 2006;31:2759–61. [13] Park SK, Schowengerdt R, Kaczynski M-A. Modulation-transfer-function analysis for sampled image systems. Appl Opt 1984;23:2572–82. [14] Ruifrok AC, Johnston DA. Quantification of histochemical staining by color deconvolution. Anal Quant Cytol Histol/Int Acad Cytol Am Soc Cytol 2001;23:291–9. [15] Hell SW, Wichmann J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt Lett 1994;19:780–2. [16] Shroff H, Galbraith CG, Galbraith JA, Betzig E. Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics. Nat Methods 2008;5:417–23.
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[17] Shotton DM. Confocal scanning optical microscopy and its applications for biological specimens. J Cell Sci 1989;94:175–206. [18] Choi W, Fang-Yen C, Badizadegan K, Oh S, Lue N, Dasari RR, et al. Tomographic phase microscopy. Nat Methods 2007;4:717–9. [19] K. Creath Phase-shifting speckle interferometry. In: Proceedings of the 29th annual technical symposium, International Society for Optics and Photonics, 1985. p. 337–46. [20] Goldstein RM, Zebker HA, Werner CL. Satellite radar interferometry: two‐ dimensional phase unwrapping. Radio Sci 1988;23:713–20.
[21] Fiddy MA. The Radon transform and some of its applications. Journal of Modern Optics 1985;32:3–4. [22] Choi W, Fang-Yen C, Badizadegan K, Dasari RR, Feld MS. Extended depth of focus in tomographic phase microscopy using a propagation algorithm. Opt Lett 2008;33:171–3. [23] Greenberg ME, Ziff EB. Stimulation of 3T3 cells induces transcription of the c-fos proto-oncogene. Nature 1983;311:433–8.
Contents lists available at ScienceDirect
Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Controllable tomography phase microscopy Peng Xiu a, Xin Zhou a, Cuifang Kuang a,n, Yingke Xu b, Xu Liu a a b
State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China Key Laboratory of Biomedical Engineering of Ministry of Education, Department of Biomedical Engineering Hangzhou 310027, China
art ic l e i nf o
a b s t r a c t
Article history: Received 29 May 2014 Received in revised form 28 September 2014 Accepted 2 October 2014
Tomography phase microscopy (TPM) is a new microscopic method that can quantitatively yield the volumetric 3D distribution of a sample's refractive index (RI), which is significant for cell biology research. In this paper, a controllable TPM system is introduced. In this system a circulatory phaseshifting method and piezoelectric ceramic are used which enable the TPM system to record the 3D RI distribution at a more controllable speed, from 1 to 40 fps, than in the other TPM systems reported. The resolution of the RI distribution obtained by this controllable TPM is much better than that in images recorded by phase contrast microscopy and interference tomography microscopy. The realization of controllable TPM not only allows for the application of TPM to the measurement of kinds of RI sample, but also contributes to academic and technological support for the practical use of TPM. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Tomographic Refractive index image Cell structure Microscopy
1. Introduction The refractive index (RI) distributions in cells are various and changeable. They reflect the active states of cells and cannot be shown directly from intensity information, a fact that has long drawn the attention of researchers. For example carcinogenesis increases the cell's RI [1], and Plasmodium falciparum infection can change the internal structure and RI of red blood cells [2]. Phase contrast microscopy [3] and differential interference microscopy [4] are traditional techniques that enable RI information to be presented in the form of intensity information, giving rise to their wide application in biological research. In recent years more advanced phase microscopy techniques have been developed to record quantitative phase images induced by specimens [5–9], but most of them obtain just the average or approximate distribution of the RI [10–12], which cannot quantitatively reflect the 3D RI changes in samples. To solve this problem we image 3D RI information using tomography phase microscopy (TPM), which allows the RI to be imaged more accurately. In most microscopies that merely focus on intensity imaging the microscopic image can be regarded, in theory, as the convolution of the sample and the point spread function of the system [13], and the imaging quality depends on the intensity contrast of the specimen and the sharpness of the system's point spread function. To enhance the imaging quality, various dyes are typically used to make specimens scatter or absorb more light [14].
n
Corresponding author. E-mail address: [email protected] (C. Kuang).
http://dx.doi.org/10.1016/j.optlaseng.2014.10.001 0143-8166/& 2014 Elsevier Ltd. All rights reserved.
The use of specific fluorescence labeling to obtain the expected fluorescence from the samples is another common approach [15– 17]. However, these traditional methods do not apply to imaging the RI. That is, unlike the case in intensity imaging, the distribution of the RI itself is not directly involved in imaging, which mainly modulates the light path of transmitted beams [7]; this modulation can be accumulated along a certain light path, which means it has linear integral characteristics. Thus, in analogy to the use of integral characteristics for X-ray absorption of samples in the computed tomography technique, TPM [18] reconstructs the 3D distribution of the RI of a sample by obtaining the phase information in different projective directions and using algorithms to render the image. Nevertheless, TPM is a phase microscopic method based on large data calculations that needs to record numerous interference images and use phase-shift algorithms to quantitatively analyze the phase information under different projective angles at a tremendous speed. This implies that the speed of phase shifting and the rate of image collection and processing are both constraints in the development of the TPM system. In existing research, acousto-optic modulator phase shifting is a common method [18] that can shift the phase at a speed of 5000 times/s; when it is combined with certain imaging rates, 3D phase information can be collected at a speed of 10 fps. Although acousto–optic modulator phase shifting can shift the phase quite rapidly, its phase shifting rate is fixed, so the speed of imaging in the system is not adjustable; this makes it difficult to observe specimens of different active statuses and also puts strict requirements to the camera. In this paper, we present a controllable TPM using a piezoelectric ceramic (lead zirconium titanate, PZT), instead of acousto-optic modulators, to perform phase shifting. Because PZT has high controllability and
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P. Xiu et al. / Optics and Lasers in Engineering 66 (2015) 301–306
M1
λ/2 PBS1 GM L3
BE
PZT L1 BF C S
M2 L4
OL L2
Camera
Laser
P PBS2
M3
Fig. 1. Controllable TPM system. a) Principal system: beam expander (BE); reflecting mirrors (M1–M3); polarized beam splitters (PBS1 and PBS2); galvanometer scanning mirror (GM); lenses L1–L4 (f1 ¼250 mm, f2¼ 200 mm, f3¼50 mm, f4 ¼150 mm); back focal plane of condenser lens (BF); condenser lens (C); sample stage (S); objective lens (OL); polarizer (P). b) Photograph of experimental system.
position keeping ability it can adjust the phase shifting speed for different samples, allowing for the entire system more controllability and adjustability. Additionally our system can collect 3D phase data at speeds of up to 40 fps during continuous shooting, greatly improving the performance of TPM and offering theoretical and technical support to biological research.
Camera control signal
U 1 0
1
2
3
Our controllable TPM system is based on the Mach–Zehnder interference microscope structure, as shown in Fig. 1. A 633 nm He–Ne laser beam is expanded and then divided into reference and sample light paths by a polarization dispersion prism (PBS1 in Fig. 1). The light intensity distribution of each light path is modulated by rotating the half-wave plate (λ/2) in front of PBS1. The sample light goes through four lenses: scanning lens L1, convergent lens C (Olympus, NA ¼1.4), objective lens OL (Olympus, UApo N, 100 , NA ¼1.49), and field lens L2; any two continuous lenses can form a 4f system. The scanning galvanometer, sample, and camera (CMOS, MotionBLTZs EoSens Cube7) are located at the three conjugate planes of the consecutive 4f systems. When the galvanometer is scanning, parallel laser beams pass through samples in different directions, from angles of 501 to 501, forming images on the camera. In the reference path, the laser beam is expanded by two lenses (L3, L4) and then phase shifted by a PZT element. The sample path and reference path combine at the second polarization dispersion prism (PBS2), with uniform polarization achieved through the polarizer, and finally interfere on the imaging surface of the camera. As a special and important part of our system, the PZT (P-885.11, PI) element can respond to the input voltage in tens of microseconds and achieve phase shifts at speeds greater than 5000 times/s. However, because of the mechanical structure and voltage instability, the PZT element oscillates randomly after responding to the input voltage. This process will last from 400 to 600 ms, introducing a large amount of noise to the interference images and restricting the application of PZT in the TPM. We present a control method of cyclical scanning (“cyclical scanning control method” hereafter) to solve this problem and improve the controllability of the system. The process of the cyclical scanning control method is shown in Fig. 2. Fig. 2 shows the details of the cyclical scanning method, including the camera control signal, PZT control signal, galvanometer scanning mirror (GM) control signal, and sample package method that renders the 3D information of the RI. Though the
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Fig. 2. Cyclical scanning control method. a) Camera control signal; the frequency is set in accordance with the active status of samples. b) PZT control signal; V1–V4 are corrected voltages corresponding to the four-step frequency-shifted method, which changes the reference arm's optical path by one-quarter wavelength each time. c) Galvanometer scanning mirror control signal. As the signal voltage changes from Vb to Va, the sample beam illuminates the sample at angles from 501 to 501. d) Sample package method; the images recorded in four continuous scanning processes form an information package describing the 3D RI. e) PZT control signal (blue) and galvanometer scanning mirror control signal (green) tested by an oscilloscope in practice. (For interpretation of the reference to color in this figure, the reader is referred to the web version of this article.)
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position shift of PZT is proportional to the voltage variation in general, the hysteresis and nonlinearity of the PZT may affect the accuracy of phase shifting. In order to control the system accurately, the voltage corresponding to certain position shift should be set depending on PZT's characteristics, experimental conditions and the way voltages changes. Thus, we calibrate the working voltages of PZT in advance; in each scanning circle, V1, V2, V3, and V4 are the incremental post-calibration voltages driving the PZT to change the light path in reference arm by one-quarter wavelength (λ/4) each time. The angle of the GM has a linear relationship with the input voltage; when the input voltage varies from Vb to Va, the direction of the laser beam that goes through the sample varies from 501 to 501. The traditional control method sets the GM first and then obtains phase information through phase-shifting. That is, when the GM is set at a certain direction angle, the voltage of the PZT changes four times, resulting in a phase shift; meanwhile, the camera records the corresponding four images to obtain the phase information. As the direction angle varies from 501 to 501 by the rotation of the GM, data collection for a 3D RI distribution is completed. In the traditional method, the response oscillation caused by the structure of the PZT and the step rotation of the GM can both introduce noise into the data collection process and reduce the data collection speed. In our cyclical scanning method we set the status of the PZT first and then rotate the GM, with the camera recording the images synchronously, to achieve interference images under certain phase differences through direction angles from 501 to 501. Next, we use the PZT to alter the optical path length of the reference light by λ=4 and then repeat the process mentioned above; the images recorded during four continuous voltage changes can form a data package describing the 3D RI distribution. During the collection of interference images the exposure time of the camera is tens of microseconds, which is negligible compared with the scanning period of the GM. In the cyclical scanning control method the response oscillation of the PZT and GM no longer affects the collection of interference information, and the speed of the entire collection process can be adjusted according to the imaging speed of the camera and variable characteristics of the samples. The phase information at each illuminating angle is calculated by interference images obtained in four cycles of the GM. The vibration or displacement of GM may also bring noise to the phase calculation process. Driving the GM linearly and coordinating the camera imaging rate work well to reduce this effect. Additionally, the four-phase-shifting method is periodic; thus, information recorded from four arbitrary continuous phase shifts can form a data package describing the 3D RI distribution. Theoretically, we can obtain data during the dynamic process of imaging four times faster than by the traditional control method.
3. Main theory of TPM TPM can image the 3D position-dependent RI of the sample. The process has two parts; the first is the collection of phase information by varying the direction of the illuminating beam, and the second is the reconstruction of the 3D distribution of the RI. We use the four-phase-shifting method [19] to acquire the quantitative phase information, in which the interference images of the sample and reference light fields can be described as Iðx; y; θ; NÞ:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Nπ km sin θ þ ϕθ ðx; y; θÞ þ x I x; y; θ ; N ¼ I R þ I S x; y; θ þ 2 I R I S x; y; θ cos 2 M
ð1Þ Here, θ is the angle of illumination of the sample beam with respect to the optical axis, nm is the RI of the medium, and km ¼ 2πnm =λ is the wavenumber of the light in the medium. I R
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and I S ðx; y; θÞ are the intensities of the reference and sample fields, respectively, at the illumination angle θ. ϕθ ðx; y; θÞ is the phase change induced by the sample, with transverse coordinates ðx; yÞ. M¼110 is the magnification of the system. N is the number of times the PZT signal changes, and with each change the phase is shifted by π/2. km sin θ =M is the ramp induced by tilt illumination. I 1 ¼ Iðx; y; θ; NÞ, I 2 ¼ Iðx; y; θ; N þ1Þ, I 3 ¼ Iðx; y; θ; N þ 2Þ, and I 4 ¼ Iðx; y; θ; N þ 3Þ are the interference images at each of the four phase-shift times. In the first part of the process, the phase information of the sample field can be calculated by the equation. ψ N x; y; θ ¼ angle½ðI4 I2 Þ þ iðI3 I1 Þ h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i ð2Þ ¼ angle 4 I R I S ðx; yÞexpðiϕθ ðx; y; θÞ þ i km sin θ x=M Here, angleðÞ denotes the function used to calculate the phase angle of a complex number. Then, a phase-unwrapping algorithm is used to resolve the 2π-phase ambiguities [20]. In order to eliminate the phase ramp aberration induced by tilt illumination and background noise we also record thebackground phase image with a blank sample and then extract ϕθ x; y; θ by calculating the difference between the phase of sample and background, which theoretically removes the ramp along the beam tilting direction. In our experiment we repeated the above and obtained a procedures set of quantitative phase images, ϕθ x; y; θ , at different illumination angles θ. The algorithm used to reconstruct the 3D distribution of the RI image is the reverse Radon transformation. The Radon transformation [21] is a method of recording the sample's 3D information by collecting and analyzing its linear projection information in different directions. Analogously, when the GM rotates, parallel light illuminates the sample at different angles in x–z plane. Each projection can be regarded as the linear integral of the RI distribution in a certain direction, as described by the following equation: pðs; ys ; θÞ ¼ ∬ ðnðxs ; ys ; zs Þ nm Þkm δ xs cos ðθÞ þ zs sin ðθÞ s dxs dzs ð3Þ In the equation, pðs; ys ; θÞ is a phase image obtained by the linear integral of the RI in the direction described by the angle of illumination of the sample beam with respect to the optical axis, θ, and s is the distance between the integral line and the center of the x–z plane; nðxs ; ys ; zs Þ is the RI distribution of the sample with coordinates ðxs ; ys ; zs Þ. Further, the reverse transformation of Eq. (3) is nðxs ; ys ; zs Þ ¼ ∬
∂pðs; ys ; θÞ 1 ds dθ þnm ∂s 2π 2 xs cos ðθÞ þ zs sin ðθÞ s ð4Þ
Using Eq. (4), the tomographic images of the sample can be calculated as nðxs ; ys ; zs Þ. Eqs. (3) and (4) represent the separate collection and reconstruction of images for a section (in a certain direction), and the image of the 3D distribution is a superposition of all the sections. We can calculate pðs; ys ; θÞ from the phase image ϕθ ðx; y; θÞ by the equation pðs; ys ; θÞ ¼ ϕθ ðsM cos ðθÞ; Mys ; θÞ
ð5Þ
Eq. (5) acts as a link combining two part of the TPM method to finish the entire process, from the acquisition of phase information at a certain illumination angle to the reconstruction of the RI distribution.
4. Results and analysis
for
Silica samples have a fixed and uniform RI distribution (n ¼ 1.47 λ ¼ 633 nm), which is helpful for testing the tomographic
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Fig. 3. Results for silica samples immersed in oil (n¼ 1.518) by controllable TPM system. a) Upper left: model of 10 μm silica ball; Roman numerals indicate slices along which 3D tomographic RI images I–V (right and bottom) of single sample are taken. b) Images of 5 μm silica sticks: (i) intensity image; (ii) view of 3D RI image along z axis; and (iii) 3D tomographic RI image.
Fig. 4. Results for 3 μm silica balls (on two levels): a) Distribution model of silica balls; b) intensity image under one projection; c) phase image under the same projection as in 4 (b); d), e) sections (different z values) of the sample labeled I and II, respectively, in (a); f) distribution of the intensity along the lines in (b)–(d), in which A denotes the intensity image, P denotes the phase image, and I is the RI image in the focal plane.
capability of TPM. First, we observed a single silica ball (diameter, 10 mm) immersed in oil (n ¼1.518 for λ ¼ 633 nm; hereafter, the oil we used has the same RI). Because the ball's RI is isotropic and disturbances in its attitude scarcely affect its phase images, we can set the camera imaging rate to 800 fps, galvanometer scanning frequency to 8 Hz, and scanning angle from 501 to 501. We calculate the scale and RI of the sample using the interference images, and the results are in very good agreement with the parameters of the sample (10 mm silica ball). Therefore, the phase images used to calculate the tomogram images are quantitative and credible. Then we observed silica sticks (diameter, 5 mm) immersed in oil. The sticks remain suspended, and their relative spatial locations are various and changeable. We set the camera imaging rate to 4000 fps, the galvanometer scanning frequency to 40 Hz, and the scanning angle from 501 to 501. Fig. 3a demonstrates that the controllable TPM can image the 3D RI distribution map of the sample, but the signal-to-noise ratio decreases in the sections far from the focal plane. This phenomenon, caused by projection approximation, is common in all types
of TPM, and a propagation algorithm has been proposed to reduce this effect [22]. In Fig. 3b (i) shows the intensity image at one projection, whereas (ii) and (iii) show the RI tomographic map of two silica sticks from different perspectives so that we can clearly determine their location and attitude. The results shown in Fig. 3 demonstrate the tomographic capacity of the controllable TPM system. An outstanding feature of this system is that the imaging speed can be changed according to the sample. Fig. 4 shows the imaging results for 3 μm silica balls which are also suspended in oil. We can see only the rough profile of the sample in Fig. 4b and c, but cannot distinguish the number of spheres or how they are distributed. However, the 3D RI tomogram images obtained by our controllable TPM system (camera rate 4000 Hz, galvanometer scanning frequency 40 Hz and scanning angle 501 to 501) clearly reveal that the sample consists of five balls on the top level and two on the bottom. More importantly, from the contrast image shown in Fig. 4f, we can conclude that the sections of our reconstructed 3D RI distribution map have higher lateral resolution than the intensity and phase images.
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Fig. 5. RI tomogram of 3T3 mouse cells (immersed in water). a) 3D tomographic RI map; b) interference image under 01 projection; c) view along z axis of tomographic RI image; i)–iv) RI images at different sections (marked in (a) along the z axis; the RI bar indicates that the sample's RI varies from 1.3 (water) to 1.4. (For interpretation of the reference to color in this figure, the reader is referred to the web version of this article.)
Mouse 3T3 cell lines, originally extracted from the mouse fetus, have long been used for in vitro experiments in cancer research, for example, for cancers induced by tumor viruses and carcinogenic agents [23]. The 3T3 cell sample used in our experiment was first soaked in formalin and then immersed in water. Fig. 5b shows one interference image of the ecptomas of one cell; from the image we can easily define the outline of the ecptomas but cannot obtain further internal information. The 3D RI tomogram in Fig. 5a shows that the cellular material is concentrated on one side, and the other side is filled with water; because the cytomembrane is destroyed by formalin, the water can penetrate freely. Fig. 5i–iv shows slices of the tomogram at the different heights indicated in Fig. 5a. The yellow dashed line marks the outline of the ecptomas. The RI of the cell material is nearly 1.36 (λ ¼633 nm), and its distribution reflects the 3D structural change in the ecptomas after cell death. This proves the potential of this system in providing strong support to related biomedical research.
5. Conclusion In this paper we propose a new systematic control method, the cyclical scanning control method, and a controllable TPM system. This system inherits the principle and advantages of TPM and makes the imaging speed more controllable; moreover, a high speed camera is no more a necessity for TPM, which will promote the development of this novelty microscopy. We imaged silica balls, silica sticks, and mouse cells in our experiments, the results of which demonstrated the excellent performance. Compared to traditional TPM systems, our system has a more controllable speed, more stable performance, and stronger operability with a lower building cost, all of which provide significant contributions to the development and application of TPM.
Acknowledgments This work was financially supported by grants from the National Basic Research Program of China (973 Program) (No. 2015CB352003)
and the National Natural Science Foundation of China (Nos. 61377013, 61427818, 61205160, 61378051 , 61335003 and 31301176).
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