Integration of synthetic optical holography in a commercial confocal scanning microscope unit

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(1)Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Monterrey School of Engineering and Sciences. Integration of Synthetic Optical Holography in a Commercial Confocal Scanning Microscope Unit A thesis presented by Arturo Alejandro Canales Benavides. Thesis Submitted to the School of Engineering and Sciences in partial fulfillment of the requirements for the degree of Master of Science in Electronic Engineering Monterrey Nuevo León, May 15th, 2017.

(2) Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Monterrey Escuela de Ingenierı́a y Tecnologı́as de Información Graduate Program The committee members, hereby, certify that have read the thesis presented byArturo Alejandro Canales Benavides and that it is fully adequate in scope and quality as a partial requirement for the degree of Master of Science in Electronic Engineering,. Dr. Raúl I. Hernández Aranada Tecnológico de Monterrey School of Engineering and Sciences Principal Advisor. Dr. P. Scott Carney University of Illinois at Urbana-Champaign Co-advisor. Dr. Dorilian López Mago Tecnológico de Monterrey Co-advisor. Dr. Rubén Morales Menéndez Dean of Graduate Program School of Engineering and Sciences Monterrey Nuevo León, May 15th, 2017. ii.

(3) Declaration of Authorship I, Arturo Alejandro Canales Benavides, declare that this thesis titled, Integration of Synthetic Optical Holography in a Commercial Confocal Scanning Microscope Unit and the work presented in it are my own. I confirm that: • This work was done wholly or mainly while in candidature for a research degree at this University. • Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated. • Where I have consulted the published work of others, this is always clearly attributed. • Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. • I have acknowledged all main sources of help. • Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.. Arturo Alejandro Canales Benavides Monterrey, Nuevo León, May 15th, 2017. @2017 by Arturo Alejandro Canales Benavides All rights reserved.

(4) When pushing the boundaries of knowledge, we call it science, when pushing the boundaries of technology, we call it engineering, but when pushing both, we should call it progress.. To my parents..

(5) Acknowledgements. First and foremost, I would like to thank my parents for all the support and love they have given to me along my entire life. To my mom, Margarita Benavides, who always sacrifice her own time and put a lot of effort to take care of me without asking for nothing in exchange, that person who taught me to never be scared of nothing. To my dad, Arturo Canales, a person who taught me with his own actions the real meaning of hard-work and to never take anything for granted; a person who never complains even in the most tough times. My parents are the motor of my life. Second, I would like to thank Naidú Morales, my girlfriend, someone who has shown me what disinterested love is. The only person who understand my temperament and accept me as I am, without trying to change me. This effort could not have been possible without her love, support and patience. Now, I want to thank two international organizations to whom I am very grateful. To SPIE, which last year awarded me with a generous scholarship to continue with my master studies in optics. Also for the travel grant the SPIE provided me to attend the 2016 Optics and Photonics meeting at San Diego, CA, which was a very enriching and rewarding experience. Many thanks also to the OSA, which two years ago, supported me with a travel grant to attend the prestigious Siegman School on Lasers, held at Amberg, Germany; an experience that for first time made me realize the significant role that optics has in society. Also for the opportunity of attending the Frontiers in Optics (FiO) meeting during the OSA’s Centennial celebrations, at Rochester, NY where I had the opportunity to meet Dr. P. Scott Carney. Both, OSA and SPIE have given me the possibility to expand my networking and without doubt, they have been crucial in my professional and personal development. I want to thank Dr. P. Scott Carney, who invited me to get involved in the Synthetic Optical Holography (SOH) project and who kindly offered me financial support during my stay. The effort made here and this new adventure in my professional career could have not been possible without him. I also want to thank the Optical Science Group (OSG), especially to Martin Schnell, who always tried to direct me in the correct way during the development of this work. To Lang Wang and Yangyundou Wang, who are v.

(6) spectacular partners and their kindness made me feel like in home. Especially thanks to Yue Zhuo, who kindly helped us to prepare the stem cells used for the project. Also, even not being formally part of the OSG, I want to thank Shravan Gupta for all his support and friendship. There are no words to describe how helpful he has been for the development of the project presented here. Finally, I want to say that despite the fact that I have just been here in Champaign for a brief period of time, I consider all of them excellent people and very good friends. I also want to thank the members of the Photonics and Mathematical Optics Group (PMOG) who more than my colleagues, are my friends. To Benjamin Perez, a person who I deeply admire because of his discipline and hardworking and who was always willing to help me when experiments went wrong. To Robin Orejel, a very kind and humble person, the guy with whom I shared moments of happiness and also frustration during my master’s. To Dr. Dorilian López Mago, a very enthusiastic and committed person with his job, with whom I spent hours of conversation about interesting ideas and new projects, and with whom I have been very glad to work. Finally, there are no words to express my gratitude to Dr. Raúl Hernández, whom more than my advisor, become a friend to me. A person who challenged me since the very beginning when I started my master’s, who believed in my capacity and skills and with whom I spent hours of discussion. With his actions, Raul showed me that, being an advisor is more than sharing knowledge, is about caring about the other. I also want to say that he supported me, financially and emotionally, for many of the international academic experiences I have had during my master’s. So, if someone is behind the efforts made in this work, is him. Many thanks to my alma mater, Tecnológico de Monterrey, for the tuition for my master’s, and to Conacyt for the financial support along this two years of studies. Certainly, there are no words to describe the commitment of both institutions with the development of the education and research in México. Special thanks go to the Carl R. Woese Institute for Genomic Biology group,for giving us the opportunity to work in their facilities. Especially to Dr. Austin Cypersmith and Dr. Mayandi Sivaguru; their help and expertise in microscopy were crucial to finish this project on time. Finally, and most important, I have to thank God, who gave me just what I needed in order to be what I am and to be where I am. I certainly do not believe in fate, but I definitely think he put the correct people in my way.. Arturo Alejandro Canales Benavides vi.

(7) Integration of Synthetic Optical Holography in a Commercial Confocal Scanning Microscope Unit. Arturo Alejandro Canales Benavides, M.S.E. Instituto Tecnológico y de Estudios Superiores de Monterrey, 2017. Thesis advisor: Dr. Raúl I. Hernández Aranada. This thesis is an effort to integrate a relatively new imaging technique called Synthetic Optical Holography (SOH) in commercial confocal scanning microscopes. In this work, we specifically present an integration with a Zeiss 710 confocal microscope. We explored different integration alternatives based on cost, compatibility and functionality. Also, we validated our proof of concept by using the capabilities of this integrated system on biological samples. We successfully retrieved the phase and amplitude of cheek and stem cells. Chapter 1 provides a brief introduction to classical optical holography and its evolution since it was conceived. Subsequently, we present the ideas of Quantitative Phase Imaging (QPI) and its profound relationship with Digital Holographic Microscopy (DHM), which is an imaging technique that has been gaining popularity during the past 20 years. After that, we present the theoretical basis of SOH and its development since it was conceived. Then, we make a brief review about Confocal Microscopy (CM) and its advantages compared to wide-field microscopy. Right away, we present a briefly discussion about the efforts made in the scientific community to combine DHM and CM. Those ideas represent the conceptual frame in which SOH and confocal scanning microscopy converge. Finally, some remarks about the importance of SOH are made. In Chapter 2 we present a characterization tool based on pseudoheterodyne interferometry with the motivation to have a method to characterize the z-stages implemented in non-linear SOH. Also, we propose a Mean Squared Error (MSE) optimization algorithm in order to process the data from the experiment and to be able to estimate the amplitude and drift of the z-stages. We validate the functionality of our approach by.

(8) characterizing a nanopositioning piezo stage from Physik Instrumente (PI) and a ceramic piezo electric from Thorlabs. Finally, we present a discussion and some remarks about this approach. In Chapter 3 we present a successful integration of SOH in a Zeiss 710 confocal microscope. We compare different alternatives of integration in terms of cost and compatibility. Also, we describe the process followed to implement the system, installation of the devices, preparation of the samples, etc. Then, results obtained from using this new integrated system are presented in order to validate the functionality of SOH in the confocal unit. We used SOH in the Zeiss microscope to recover the amplitude and phase of biological samples. Then, we present a discussion about the several factors that should be taken into account when trying to implement SOH in commercial microscopes such as cost, compatibility, and functionality. Finally, we discuss some remarks about this implementation. Finally, in Chapter 4, we present our conclusions about the ideas developed in Chapters 2 and 3. We also discuss the advantages and disadvantages of the SOH modular system implemented and some future work to improve the technique.. viii.

(9) Contents. Acknowledgements. v. Abstract. vii. List of Figures. xi. Chapter 1 Introductory Remarks 1 1.1 Optical Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Quantitative Phase Imaging (QPI) and Digital Holographic Microscopy (DHM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Synthetic Optical Holography (SOH) . . . . . . . . . . . . . . . . . . . 6 1.4 SOH in Confocal Laser-Scanning Microscopy (CLSM) . . . . . . . . . . 8 1.4.1 Optical Sectioning (OS) and Confocal Scanning Microscopy (CSM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4.2 Brief review of Digital Holographic Microscopy in Confocal Scanning Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.3 Advantages of Non-Linear SOH for the integration in CLSM . . 11 1.5 Motivation for integrating SOH in CSM . . . . . . . . . . . . . . . . . 12 Chapter 2 Z-stage characterization based on Pseudoheterodyne Interferometry 2.1 Theoretical basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Optical setup and pseudoheterodyne signal . . . . . . . . . . . . 2.1.2 Spectral content of the signal and estimation of Z . . . . . . . . 2.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Characterization of a closed-loop nanopositioning system . . . . 2.3.2 Characterization of a ceramic piezoelectric chip . . . . . . . . . 2.4 Discussion and Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Analysis for the piezo stages characterized . . . . . . . . . . . .. ix. 13 14 14 15 18 20 20 25 27 27.

(10) 2.4.2. Characterization methodology implemented and implications in non-linear SOH . . . . . . . . . . . . . . . . . . . . . . . . . . .. Chapter 3 Integration of non-linear SOH in a Zeiss 710 Confocal Microscope 3.1 Configuration for the SOH module . . . . . . . . . . . . . . . . . . . . 3.1.1 Microscope Interference Objective (Mirau Objective) . . . . . . 3.1.2 Generating the time-varying reference field . . . . . . . . . . . . 3.2 Quantitative phase imaging of biological cells in Zeiss 710 confocal microscope with SOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Setting up the SOH module . . . . . . . . . . . . . . . . . . . . 3.2.2 Retrieving amplitude and phase from cheek cells . . . . . . . . . 3.2.3 Z-stack imaging for stem cells . . . . . . . . . . . . . . . . . . . 3.3 Discussion and Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Integration factors . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28. 31 32 32 33 36 36 38 43 46 46 47. Chapter 4 Concluding Remarks and Future Work. 50. Bibliography. 52. x.

(11) List of Figures. 1.1. 1.2. 1.3 1.4. 1.5. Optical setup for classical holography. A coherent light beam is collimated by means of lenses L1 and L2. Then, the beam is divided using a beamspliter, BS. Finally, the light from the object interfere with the reference beam and the hologram is recorded with a photographic film. Comparison of the recovered phase-amplitude image of an unstained cheek cell (a) Nomarski DIC image of the cell, (b) recovered phase image with QOPM. (Image taken from [1]). . . . . . . . . . . . . . . . . . . . Two modalities of DHM. (a) Transmission mode and, b) reflection mode. (Image taken from [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical setup for Synthetic Optical Holography (SOH). The coherent light source is divided by means of a beamsplitter, BS. Then, a synthetic reference wave (SRW) is created by using a moving mirror M1 (UR (t)), while the sample US , is scanned pixel by pixel, line by line. Each pixel intensity is recorded with a point detector (PH). In this way, a synthetic hologram is created, Iab . (This image was created based on [3]) . . . . . Diagram of an epi-illumination confocal microscope for fluoresence microscopy. The objective lens (OL) acts as both the condenser and objective lens. Fluorescence light returning from the specimen is transmitted and the excitation light is reflected by means of a dichroic mirror (DM). Finally, out of focus light is rejected by the pinhole (P2). . . . . . . . .. xi. 2. 4 5. 6. 9.

(12) 1.6. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. Widefield fluorescent (top) and single photon confocal scanning laser microscope (CSLM) (bottom) images taken from a 100-mm thick vibratome section of mouse heart that has been stained for f-actin (green) and connexin 43 (red). In the widefield image out-of-focus light that contributes to the formation of the image significantly decreases the resolution and contrast of the image. Use of the pinhole in the confocal image to remove the out-of-focus light results in an image of much higher contrast and resolution as shown by the striated pattern of the myocyte sarcomeres and distinct cell: cell junctions labeled by the connexin 43 antibody. (The image and the legend was taken from [4]). . . . . . . . . Optical setup for the characterization of the amplitude Z of the piezo stage. The beam is divided in two identical copies by the beamsplitter (BS). By means of the mirrors, M1 and M2, both signals return to the beamsplitter they are recombined. Finally, the interference signal is recorded by a photodiode (PD) detector. . . . . . . . . . . . . . . . . Simulation of, a) normalized intensity signal recorded for the detector (blue line) and normalized input signal (orange), b) the Fourier domain of the intensity signal. For the simulation, fg = 15 Hz and V0 = 13.3 mVpp. Besides, G = 10 µm/V. . . . . . . . . . . . . . . . . . . . . . . Logarithm of the Mean Squared Error algorithm. The y-axis is the desired voltage applied to the servo controller and the x-axis is the initial reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The PI P-611.3S nanopositioning system from Physik Instrumente (PI). This model has a gain equal to 10 µm/V and a maximum displacement in closed loop of 100 µm. The resonant frequency in the z-axis for a 30 g load is 230 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results for, a) normalized intensity signal recorded for the detector (blue line) and normalized input signal (orange), b) the Fourier domain of the intensity signal. For the experiment, fg = 15 Hz, V0 = 13.3 mVpp and G = 10 µm/V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithm of the Mean Squared Error algorithm. The y-axis is the desired voltage applied to the servo controller and the x-axis is the initial reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TA0505D024W ceramic piezoelectric chip from Thorlabs. This model has a free stroke (maximum displacement without load) of 2.8 µm ± 15 % and a resonant frequency (without load) of 315 kHz. . . . . . . . . .. xii. 10. 14. 18. 19. 20. 21. 22. 25.

(13) 3.1. 3.2. 3.3 3.4. 3.5. 3.6. 3.7. 3.8. Diagram of an microscope interference objective used to integrate Synthetic Optical Holography (SOH) in commercial confocal scanning microscopes. OL goes for objective lens, M1 is the reference mirror and BS is a beamsplitter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two modalities for the SOH module. a) In the first configuration, a piezo objective scanner is used to move the reference mirror M1 and the sample is kept fixed. b) in the second modality, a microscope z-stage is used to move the reference mirror M2, along with the sample. . . . . . Illustrative image of a Zeiss LSM 700 confocal microscope (previous version of the Zeiss LSM 710). Image taken from Zeiss . . . . . . . . . SOH module implemented in the Zeiss 710 microscope. a) Interference objectives from Nikon (green collar), 20× magnification and 0.4 NA. b) NZ400 microscope z-stage from Prior Scientific. This model has a travel range of 400 µm and a resolution of 1 nm. The resonant frequency of this device is 1 kHz. Images taken from Edmund Optics and Prior Scientific, respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical process followed in SOH in order to recover amplitude and phase of a sample. a) cheek cell interferogram using a Nikon interference objective with a magnification of 20X and NA of 0.4. b) Synthetic hologram created by using the Prior z-stage, oscillating with a amplitude of 0.36 µm and a frequency of 79 Hz. c) Reconstructed normalization amplitude information of the cell. d) Reconstructed wrapped phase of the cheek cell going from 0 to 2π. . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical process followed in SOH in order to recover amplitude and phase of a sample. a) cheek cell interferogram using a Nikon interference objective with a magnification of 20× and NA of 0.4. b) Synthetic hologram created by using the Prior z-stage, oscillating with a amplitude of 0.36 µm and a frequency of 79 Hz. c) Reconstructed normalization amplitude information of the cell. d) Reconstructed wrapped phase of the cheek cell going from 0 to 2π. . . . . . . . . . . . . . . . . . . . . . . . . . . . Input signal applied to the z-stage (blue line), 80 mV and 79 Hz. Sensor output of the servo controller (orange line), 9 mV and 79 Hz. Taking in account the servo controller gain which is 40 µm/V, the amplitude of the z-stage is approximately 0.36 µm. . . . . . . . . . . . . . . . . . . Logarithm of the normalized Fourier spectrum of the synthetic holograms for a) the two-cheek cell image and b) the one-cheek cell image. The red and blue dashed boxes contain the real and imaginary part, respectively, of the field US , used to recover the amplitude and phase. .. xiii. 32. 33 36. 37. 39. 40. 41. 42.

(14) 3.9. Z-stack of a stem cell using SOH, going from 0 µm (reference ) to 5 µm. a) Z-stack for the amplitude. In the red dashed circle is possible to appreciate how internal structures appear when changing z. b) Z-stack for the wrapped phase going from 0 to 2π. . . . . . . . . . . . . . . . . 3.10 Typical process followed in SOH in order to recover amplitude and phase of a sample. a) Stem cell interferogram using a Nikon interference objective with a magnification of 20× and NA of 0.4. b) Synthetic hologram created by using the Prior z-stage, oscillating with a amplitude of 0.36 µm and a frequency of 79 Hz. c) Reconstructed normalization amplitude information of the cell. d) Reconstructed wrapped phase of the stem cell going from 0 to 2π. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Comparison between Fourier spectrums of the cells. a) Cheek cell interferogram and b) associated Fourier spectrum. c) Stem cell interferogram and d) associated Fourier spectrum. . . . . . . . . . . . . . . . . . . . .. xiv. 44. 45. 49.

(15) Chapter 1. Introductory Remarks. Optical Holography and Confocal Scanning Microscopy, both are relatively old and very well established imaging techniques in the scientific community. Optical holography, in one hand, has the inherent capability of encoding the amplitude and phase of a sample of interest. With the development of digital optical holography this technique triggered the subsequent development of digital holographic microscopy, a wide-field imaging technique with exceptional quantitative phase capabilities, [5, 6]. On the other hand, confocal microscopy provides superior contrast and resolution compared to wide-field techniques because of its optical sectioning capabilities. However, it is not possible to use traditional confocal microscopy to recover the phase of a sample. In fact, if one is trying to work with transparent samples, tagging techniques are required. So, the question is, is it possible to have an imaging technique that takes advantage of the quantitative phase capabilities provided by digital holographic microscopy and the optical sectioning capabilities of confocal microscopy? As far as we know, there are different efforts in this direction [7, 8]. However, because of the complexity of such optical setups, the implementation of these techniques in commercial confocal microscope units is complicated. Unlike the existing approaches, Synthetic Optical Holography (SOH), an imaging technique based on digital holography [9], has been proved to be completely compatible with confocal scanning microscopy [10]. However, until now, SOH had not been formally integrated in commercial confocal units. In this work, we are going to show that SOH can be fully integrated in a Zeiss 710 confocal microscope in an easy, non-invasive, relatively low cost, and most important, functional way. 1.

(16) 1.1. Optical Holography. Optical Holography is a classical imaging technique used to encode the amplitude and phase of a scattered optical field from a previously illuminated object, US , by making it interfere with a known reference wave, UR , [11, 12, 13]. The resulting interference pattern, calleda a hologram, may be expressed as, I(r) = |UR + US |2 = |UR |2 + |US |2 + US∗ UR + US UR∗ ,. (1.1). where the hologram I(r) is an intensity measurement and r = xb x + yb y is an spatial coordinate in the transversal plane. As seen in Eq. 1.1, holography is in essence an interference phenomena. Fig. 1.1 shows a basic setup for classic holography.. Figure 1.1: Optical setup for classical holography. A coherent light beam is collimated by means of lenses L1 and L2. Then, the beam is divided using a beamspliter, BS. Finally, the light from the object interfere with the reference beam and the hologram is recorded with a photographic film. Traditionally, the holograms were recorded using photographic films Fig. 1.1 , but with the invention of CCD cameras, recording holograms became an easier task and digital holography appeared, [14, 15]. Because of its speed and real time capabilities, digital holography has driven the subsequent development of DHM, a wide-field technique that has quantitative phase capabilities [16, 17], provides three dimensional information [18, 19, 20] and offers the possibility of numerical refocusing [21, 22]. 2.

(17) 1.2. Quantitative Phase Imaging (QPI) and Digital Holographic Microscopy (DHM). A big issue when working with live cells, for example, is that they do not absorb or scatter significantly amounts of light, i.e. they are transparent objects [23]. There are two phase imaging techniques that have been used for years in order to overcome this problem, Zernike Phase Contrast Mcroscopy (PCM) [24, 25] and Differential Interference Contrast (DIC) [26]. However, although these techniques are effective in making transparent objects visible, the phase-to-amplitude conversion is nonlinear, which means that they do not produce quantitative phase images. Also, the images obtained using those techniques suffer significant artifacts such as the occurrence of halos or disappearance of contrast along the direction perpendicular to shear [27]. QPI refers to a group of techniques that linearly quantify variations in the effective index of refraction of a sample through phase shifts. The obtained image contains quantitative information about both the local thickness and refractive index of the structure [28]. QPI is an emerging field based on the ideas of Abbe [29], Zernike [24, 25] and most important, the preconception of Gabor about holography [11]. Fig. 1.2 shows a comparison of the recovered phase-amplitude image of an unstained cheek cell by using DIC Fig. 1.2a and Quantitative Optical Phase Microscopy (QOPM) Fig. 1.2b. It is possible to note that unlike QOPM (which is a QPI technique), when using DIC the image obtained contain artifacts such halos that make difficult to discriminate the internal structures of the cheek cell. Also, the contrast obtained in QOPM is better than that obtained with DIC.. 3.

(18) (a). (b). Figure 1.2: Comparison of the recovered phase-amplitude image of an unstained cheek cell (a) Nomarski DIC image of the cell, (b) recovered phase image with QOPM. (Image taken from [1]). Digital Holographic Microscopy (DHM) is in essence a QPI technique due to its intrinsic capabilities of codifying the phase of a sample [5, 6, 16, 27]. Because of that, DHM has found great acceptance in areas of non-contact surface profiling and metrology [30, 31, 2]. Also, its quantitative phase capabilities have played an important role in biology [32], in the analysis of refractive index in cells [33, 34, 17, 31] and even in fluorescence microscopy for 3D reconstruction [20, 35]. In Fig. 1.3 two modalties of DHM (transmission mode Fig. 1.3a and reflection mode Fig. 1.3b) are presented,. 4.

(19) (a). (b). Figure 1.3: Two modalities of DHM. (a) Transmission mode and, b) reflection mode. (Image taken from [2]).. 5.

(20) 1.3. Synthetic Optical Holography (SOH). SOH is a quantitative phase imaging technique based on the ideas of DHM [9, 10, 3]. Unlike classical holography, in SOH a synthetic reference wave (SRW) is created [36, 37, 38, 39]. This is done by moving a piezo-actuated mirror (a time-varying reference field UR (t)) while the sample of interest US is being scanned. So, instead of encoding the phase of the whole image using a CCD as in wide-field holography, in SOH the phase at each pixel position of the image is estimated by means of a point detector. In that way, a synthetic hologram of the sample is obtained. Another way of thinking about it, is in terms of a mapping process, from phase varying in time to phase varying in a 2D xy space. The basic optical setup is shown in Fig. 1.4.. Figure 1.4: Optical setup for Synthetic Optical Holography (SOH). The coherent light source is divided by means of a beamsplitter, BS. Then, a synthetic reference wave (SRW) is created by using a moving mirror M1 (UR (t)), while the sample US , is scanned pixel by pixel, line by line. Each pixel intensity is recorded with a point detector (PH). In this way, a synthetic hologram is created, Iab . (This image was created based on [3]). 6.

(21) From Fig. 1.4 it make sense to express SOH is a discrete notation, [3], ∗ ∗ Ia,b = |US,a,b + UR,a,b |2 = |US,a,b |2 + |UR,a,b |2 + US,a,b UR,a,b + US,a,b UR,a,b ,. (1.2). where (a,b) is each pixel index. Therefore, the signal field at each pixel is just, US,a,b = US (xa x b + yb yb) and the reference field at each pixel is UR,a,b = UR (xa x b + yb yb). Also, it is possible to note that SOH is intrinsically a scanning technique, very well suitable for applications like confocal laser-scanning microscopy or near-field microscopy [40, 41, 42, 43]. In fact, their capabilities have already been tested for s-NOM [9] and in confocal microscopy for surface profiling [10]. Initially, the first UR (t) proposed in SOH was a linearly time-varying reference field [9, 10]. In this way a synthetic wave reference, UR,a,b = AR eiφR (ra,b ) , with a linear-phase reference φR was created. In this work, however, we are going to work with non-linear SOH by using a reference field with a sinusoidal-reference wave in the form, Ur (t) = Ar exp(2πiγ sin(2πfg t + 2πϕ) + 2πφ),. (1.3). where γ is the modulation amplitude, fg is the oscillation frequency of the piezo in Hz, ϕ is a phase from the sinusoidal signal and φ is a phase related with the initial point in the interference pattern. It is worth to note that, the reconstruction algorithm needed in order to recover US will depend on the chosen reference UR (t). One of the advantages of using a linear-phase reference is that there exist so much work about digital processing tools to recover US [14, 15]. However, in the case of sinusoidal-phase references, a solution was already provided in [3].. 7.

(22) 1.4. SOH in Confocal Laser-Scanning Microscopy (CLSM). 1.4.1. Optical Sectioning (OS) and Confocal Scanning Microscopy (CSM). Confocal scanning microscopy (CSM) is an imaging technique that has found very god acceptance among the scientific community because of its optical sectioning capabilities [44, 45, 46], which offer major contrast and resolution than wide-field microscopy [47]. The first confocal laser-scanning microscope was conceptualized and patented in 1957 by Minsky, [48, 49]. Nowdays, there are several modalities of confocal microscopy depending on the application and the field, [50]. Fig. 1.5 shows a typical scheme for an epi-illumination confocal microscope in fluorescence microscopy. Also, it is possible to see, as shown in Fig. 1.6, that the lack of a pinhole in conventional wide field fluorescence systems causes all out of focus light to become a component of the final image. CSM is widely used in biology [51, 52] and its optical sectioning capabilities make it suitable for 3D reconstruction [53]. Also, its strong depth-discrimination capabilities, make confocal microscopy attractive for metrology in non-contact surface profiling [54]. For example, in surface inspection [55] or 3D surface reconstruction, [56], or in surface topography for roughness analysis [57, 58]. Also, it can be employed for inspection of microdevices and microelectromechanical systems (MEMS) [59]. More recently, confocal microscopy was implemented in surface topography to measure steep edges and undercuts [60]. Therefore, it can be seen that even though CM is a relatively old technique, it still playing a big role in both, biology and metrology applications because of its sectioning capabilities, that can hardly be equalized by those offered by other optical imaging techniques, in terms of simplicity and effectiveness.. 8.

(23) Figure 1.5: Diagram of an epi-illumination confocal microscope for fluoresence microscopy. The objective lens (OL) acts as both the condenser and objective lens. Fluorescence light returning from the specimen is transmitted and the excitation light is reflected by means of a dichroic mirror (DM). Finally, out of focus light is rejected by the pinhole (P2).. 1.4.2. Brief review of Digital Holographic Microscopy in Confocal Scanning Microscopy. As mentioned in the introduction, the idea of combining digital holography with confocal scanning microscopy are not new. The first efforts started with the novel ideas of Poon when using heterodyne optical scanning as a way to achieve Optical Scanning Holography (OSH) for 3D microscopy [61, 62]. Subsequently, in the same direction, Indebetouw made more studies of OSH [63, 64] to extend the depth of focus [65] and apply this technique in fluorescence microscopy [66]. Finally, efforts were made to provide optical sectioning capabilities to OSH. However, to provide such capabilities, the optical setup needed special optical components like axicon pinholes [64], or Wigner 9.

(24) Figure 1.6: Widefield fluorescent (top) and single photon confocal scanning laser microscope (CSLM) (bottom) images taken from a 100-mm thick vibratome section of mouse heart that has been stained for f-actin (green) and connexin 43 (red). In the widefield image out-of-focus light that contributes to the formation of the image significantly decreases the resolution and contrast of the image. Use of the pinhole in the confocal image to remove the out-of-focus light results in an image of much higher contrast and resolution as shown by the striated pattern of the myocyte sarcomeres and distinct cell: cell junctions labeled by the connexin 43 antibody. (The image and the legend was taken from [4]). . filters [67], but still the optical sectioning capabilities were not even comparable to those of confocal microscopy. At the same time, other groups were dealing with the problem of combining the quantitative phase capabilities of DOH and the optical sectioning capabilities of CSM. The initial efforts were made by McLeod, with the proposition of Confocal Holography (CH) [7], a technique that showed good quantitative phase capabilities, but the necessity of optical components like Fresnel biprisms made the optical setup complex. Subsequently, he developed the idea of Confocal Scanning Laser Holography [7, 68]. However, the capabilities of this system were just tested for temperature measurements and the optical setup complexity the same as that of CH. Also, based on [69], Chmelik proposed the use of incoherent holography in order to provide depth-discrimination in Holographic Confocal Microscopy (HCM) by using diffuser mirrors [70, 71]. Based on those works, Antosova proved the surface profiling 10.

(25) capabilities of HCM [72]. More recently, Goy demonstrated a confocal scanning microscope based on digital holography [8]. The ideas of Goy are the closest ones to what an actual confocal microscope looks like. However, in his setup, instead of using galvo mirrors to scan the sample like in scanning-laser microscopy, the sample is moved by means of an xy stage. Additionally, the optical sectioning capabilities of this technique are provided by means of a dynamic pinhole. Unlike Indebetow ideas [64, 67], SOH provides better optical sectioning capabilities. In comparison with [7, 68], the optical setup implemented in SOH is more simple, a fact that provides versatility and robustness. Furthermore, the depth-discrimination in SOH do not depend on dynamic pinholes like reference [8]. As mentioned before, SOH is intrinsically a scanning laser technique, and unlike the imaging techniques already mentioned, it is suitable for integration in commercial confocal microscopes. In fact, the capabilities of SOH have already been tested for confocal microscopy in surface profiling [10]. However, the integration of SOH to a commercially confocal microscope and its potential for quantitative phase imaging in biology had not been explored until now. Nevertheless, there are some previous important steps in this direction we are going to discuss below [3].. 1.4.3. Advantages of Non-Linear SOH for the integration in CLSM. As mentioned before, initially the reference field used in SOH was a linearly varying in time reference field [9, 10]. However, there exist some technical limitations in this approach. The most important one is related to the limited travel range of the piezo stages. The larger the sample that is being scanned, the bigger the travel range required for the piezo to effectively create a synthetic hologram. In order to overcome this problem, a sinusoidal-reference wave was proposed (Eq. 1.3). It is worth mentioning that the interference pattern obtained is related to pseudoheterodyne interferometry, [73]. In fact, sinusoidal mirror motion was recently used in wide-field holography, [74, 75, 76]. Another advantage of using a sinusoidal-phase reference is that a closed loop is not necessary anymore, [3], this is due to the fact that. 11.

(26) the piezo stage is oscillating, therefore there is no need to get feedback to determine its exact position. Most important, we are going to show that in order to integrate SOH in a confocal microscope either the sample or the microscope objective need to be displaced in relation to each other, in order to generate the varying in time reference field. This implies that the plane of interest within the sample will eventually be out of focus with respect to the microscope objective. Therefore, the use of a sinusoidal motion partially alleviates this problem because the induced displacement is dramatically smaller in comparison with the linear motion enhancing in this way the possibilities of integrating SOH in commercial confocal microscopes. Finally, as mentioned before, one thing to take into account is that due to the nature of the sinusoidal SWR, the reconstruction algorithm for US is no longer the same as in the linear-phase reference approach, this can be readily seen from the fact that the Fourier spectrums are completely different between each other. In this case, the reconstruction algorithm provided in reference [3] can be followed.. 1.5. Motivation for integrating SOH in CSM. This introduction serves to justify the importance of providing an imaging technique with the quantitative phase imaging capabilities of Digital Holographic Microscopy and with the discrimination capabilities provided by Confocal Microscopy. Again, SOH is an imaging technique that, when combined with confocal microscopy, reunites those characteristics and unlike the actual approaches in the literature, it offers the potential to be integrated in any commercial confocal microscope. This last idea opens the possibility of performing fluorescence and phase imaging experiments at the same time, by means of a commercial confocal microscope. Furthermore, this offers the potential of combining metrology and biological applications. As far as we know, there is no actual system in the market with this added value.. 12.

(27) Chapter 2. Z-stage characterization based on Pseudoheterodyne Interferometry. The amplitude displacement of the sinusoidally z-stage, Z, described by γ and the phase reference φ, dependent of Z0 , both found in Eq. 1.3, are critical parameters in Synthetic Optical Holography. Those parameters have a direct impact in the reconstruction of the amplitude and phase of the sample analyzed. Therefore, a tool which provides quantitative information of the variations (errors) associated to those parameters is essential for understanding the limitations of the used devices and how they will impact in the performance of SOH. Because the SWR used in the SOH in order to integrate it with a confocal microscope is sinusoidal, it makes sense to characterize the amplitude of the z-stage using a sinusoidal oscillation too. In order to have a characterization tool for Z, a Michelson Interferometer was implemented based on the ideas of pseudoheterodyne interferometry [73]. The purpose of this chapter is to present the proposed experimental setup and how the idea behind pseudoheterodyne interferometry is used. Then, a way of estimating Z and φ trough a Mean Squared Error (MSE) algorithm is reviewed. We present some simulations to validate this idea. Then, some experimental results using this approach with a nanopositioning system from Physik Instrumente (PI) and with a ceramic piezoelectric chip from Thorlabs are presented. Finally, we discuss the advantages and disadvantages of this method when estimating Z < λ/2 and some conclusions from the results obtained.. 13.

(28) 2.1 2.1.1. Theoretical basis Optical setup and pseudoheterodyne signal. In non-linear SOH a sinusoidal synthetic wave reference is created by using a z-stage. In order to characterize the amplitude of the oscillation we implemented a Michelson interferometer, the optical setup is shown in Fig. 2.1.. Figure 2.1: Optical setup for the characterization of the amplitude Z of the piezo stage. The beam is divided in two identical copies by the beamsplitter (BS). By means of the mirrors, M1 and M2, both signals return to the beamsplitter they are recombined. Finally, the interference signal is recorded by a photodiode (PD) detector. We are going to show that, the amplitude Z induced in the Piezo Stage and other important parameters are altogether, encoded in the interference signal. The values of these parameters are estimated by a MSE numerical approach. This strategy helps us to determine how the variations in the piezo devices affect the performance of SOH. Consider the setup shown in Fig. 2.1, in which we observe the interference of two perfectly collinear plane waves traveling in the same direction, and whose relative 14.

(29) phase difference is varied by introducing a sinusoidal motion to one of the mirrors. The resulting interference signal can be modeled as (see Appendix), I=. 1 [1 + cos {2πγ(Z) sin(2πfg t + 2πϕ) + 2πφ (Z0 )}] , 2. (2.1). where γ = 2Z/λ, taking into account that, the on-axis displacement of any mirror (M1 or M2) in the Michelson interferometer makes light to experience an effective displacement of 2Z, where Z is the amplitude. Here, Z = GVo where G is the servo controller gain in µm/V, Vo is the voltage applied in Volts and fg is the function generator frequency in Hz. Finally, ϕ is a phase associated to the function generator and φ (z0 ) = z0 /λ is the phase reference of the synthetic hologram in SOH, and it is associated to the initial position of the piezo when starting the oscillation. The devices used for the experiment are: • Function Generator (Keysight 33500B Series) • Osciloscope (PC PicoScope) • Servo Controller (PI E-664 LVPZT) • Piezo Stage (PI P-611.3SF NanoCube) • Photodiode Potentiometer (Thorlabs Biased GaP Detector DET36A). 2.1.2. Spectral content of the signal and estimation of Z. In order to estimate Z, the spectral content of the signal was used, i.e., we obtained the discrete Fourier transform of Eq. 2.1. The resulting equation, (see Apendix) is, o 1 ne e e e D + cos(2πφ)E + sin(2πφ)O , I= 2. (2.2). e is the DC term and E e and O e are the even and odd terms of the spectrum where, D and can be written as,. 15.

(30) e = [1 + cos(2πφ)J0 (2πγ)] δ(f ), D ∞ X e E= J2n (2πγ) e−2πi2nϕ δ(f + 2nfg ) + e2πi2nϕ δ(f − 2nfg ) , n=1 ∞ X. e =i O. J2n−1 (2πγ) e−2πi(2n−1)ϕ δ(f + (2n − 1)fg ) + e2πi(2n−1)ϕ δ(f − (2n − 1)fg ) ,. n=1. where, Jn (x) is the Bessel function of n-th order. Again, φ depends on Z0 , however, this is an unknown parameter and as seen in Eq. 4.3 itis critical in the occurrence of the peaks in the Fourier domain. We do not have direct access to φ, therefore we proposed to determine Z and Z0 trough an optimization problem. Such strategy consists on finding the values of V0 and φ for which the Mean Squared Error (MSE) is minimized. The proposed fit function is, min(M SE) = min(Err1 + Err2 + Err3 ),. (2.3). where, Err1 = (P0 − p0 )2 M 1 X Err2 = (P2n − p2n )2 N n. M 1 X (P2n−1 − p2n−1 )2 Err3 = N n. where p0 , p2n , p2n−1 are the experimental peaks obtained with the FFT of the data and P0 , P2n , P2n−1 are obtained through,. P0 =. 1 [1 + cos(2πφ)J0 (2πγ)] , 2 M. P2n. |cos(2πφ)| X J2n (2πγ), = 2 n=1 16.

(31) M. P2n−1. |sin(2πφ)| X = J2n−1 (2πγ), 2 n=1. where again, Jn (x) is the Bessel function of n-th order and M is the number of elements in the series.. 17.

(32) 2.2. Simulation. In order to determine what to expect in the experiment, a simulation was implemented. Fig. 2.2a shows a typial signal from the function generator (orange line) and and a corresponding typical response for the intensity detector (blue line). Besides, Fig. 2.2b is the Fourier domain of the detector signal. In this simulation we used fg = 15 Hz and V0 = 13.3 mVpp. Furthermore, G = 10 µm/V, which is the same value for the servo controller’s gain, and λ = 532 nm is determined by our light source. Pseudoheterodyne − FourierDomain. Pseudoheterodyne 1 1 0.9 0.8 0.8 0.6 0.7. I/Io [W/m2 ]. I/Io , V/Vo. 0.4 0.2 0 -0.2 -0.4. 0.6 0.5 0.4 X: 15 Y: 0.2004. 0.3. -0.6. 0.2. Interference Function Gen. Signal. -0.8. 0.1. -1 -0.05. -0.04. -0.03. -0.02. -0.01. 0. 0.01. 0.02. 0.03. 0.04. 0 -100. 0.05. -80. -60. -40. -20. 0. 20. 40. 60. 80. 100. f [Hz]. t[s]. (a). (b). Figure 2.2: Simulation of, a) normalized intensity signal recorded for the detector (blue line) and normalized input signal (orange), b) the Fourier domain of the intensity signal. For the simulation, fg = 15 Hz and V0 = 13.3 mVpp. Besides, G = 10 µm/V. In order to fulfill the Nyquist criteria, we chose N = 220 and in order to provide 0.2 Hz in frequency resolution we used T = 5 s. We choose an arbitrary value for φ of 0.125, which for these parameters give a value of Z = GV0 = 133 nm. A test for the optimization code was run. For an ideal fit, where the MSE = 0, the log(M SE) graph looks like Fig. 2.3. Again, V0 = 13.3 mVpp, fg = 15 Hz and T = 5 s. Additionally we set M = 10 and the size of the matrix to be N 2 where N = 1024. It is possible to see in Fig. 2.3 that there exist multiple values for φ that satisfy these conditions. Each value represents a different shift in the signal, however the spectral content of the signal does not change. That is why these values give the same output for the voltage, which is V0 /2. 18.

(33) V[mV]. Log(MSE) 0. 0. 2. -2. 4. -4. -6. 6. -8. 8 -10. 10 -12. 12 -14. 0. 0.2. 0.4. 0.6. 0.8. 1. φ[1/rad]. Figure 2.3: Logarithm of the Mean Squared Error algorithm. The y-axis is the desired voltage applied to the servo controller and the x-axis is the initial reference.. 19.

(34) 2.3 2.3.1. Results Characterization of a closed-loop nanopositioning system. In order to determine the functionality of our optical setup we estimated Z for a nanopositioning system from Physik Instrumente (PI), relying on the fact that it is possible to use this device in closed loop mode, which is supposed to offer major accuracy than the open loop mode. For the model used, the PI P-611.3Sf NanoCube shown in Fig. 2.4, the gain is 10 µm/V and the maximum displacement in closed loop is 100 µm. Also, when using a 30 g load, the resonant frequency in the z-axis is 230 Hz.. Figure 2.4: The PI P-611.3S nanopositioning system from Physik Instrumente (PI). This model has a gain equal to 10 µm/V and a maximum displacement in closed loop of 100 µm. The resonant frequency in the z-axis for a 30 g load is 230 Hz.. As an example, for fg = 15 Hz, V0 = 13.3 mVpp and G = 10 µm/V, which is determined by the servo controller, the curves in Fig. 2.5a and 2.5b were obtained. Fig. 2.5a shows the input signal (orange line) generated with the Keysight 33500B Series function generator, and the signal response (blue line) measured with the Thorlabs DET36A photodiode potentiometer. Finally, Fig. 2.5b shows the Fourier domain associated to the potentiometer signal.. 20.

(35) Pseudoheterodyne − FourierDomain 1. 0.8. 0.9. 0.6. 0.8. 0.4. 0.7. I/Io [W/m2 ]. I/Io , V/Vo. Pseudoheterodyne 1. 0.2 0 -0.2. 0.5 0.4 0.3. -0.4 -0.6. -0.04. -0.03. -0.02. -0.01. 0. 0.01. 0.02. 0.03. 0.04. X: 15 Y: 0.1849. 0.2. Interference Function Gen. Signal. -0.8 -1 -0.05. 0.6. 0.1 0 -100. 0.05. -80. -60. -40. -20. 0. 20. 40. 60. 80. 100. f [Hz]. t[s]. (a). (b). Figure 2.5: Results for, a) normalized intensity signal recorded for the detector (blue line) and normalized input signal (orange), b) the Fourier domain of the intensity signal. For the experiment, fg = 15 Hz, V0 = 13.3 mVpp and G = 10 µm/V. As stated before, the wavelength employed is 532nm, which is determined by our light source. In order to provide 0.2 Hz in frequency resolution we set T = 5. With those parameters, the MSE algorithm gave an estimation that Z = 11.83 nm Fig.2.6. The percentage error associated to this estimation is 19.57 %. For the estimation, we choose M = 10. The size of the matrix was N 2 , where N = 1024. In order to characterize the piezo stage, we estimated different displacements Z, for different frequencies, Table 2.1, and we calculated its percentage error based on Eq. 2.4, |ZT he − ZExp | , (2.4) ZT he is the required theoretical displacement and ZExp is the displacement ob%ErrZ =. where ZT he. tained through the MSE estimation. In Table 2.1, ZT he = Z2 , which is the theoretical displacement based on the real voltage delivered by the function generator V . We made 5 measurements for each experiment, for example, 5 measurements for V0 = 5 mVpp and fg = 15 Hz were taken and averaged. Then, the displacement was estimated by using the MSE algorithm proposed. The period of sampling was T = 5 s. The number of peaks used for the estimation was M = 10. We ran 5 measurements for each experiment. Also, in order to determine 21.

(36) Log(MSE) 0. 0. -1. 2 -2. 4. V[mV]. -3. 6 -4. 8. -5. 10. -6. -7. 12 -8. 0. 0.2. 0.4. 0.6. 0.8. 1. φ[1/rad]. Figure 2.6: Logarithm of the Mean Squared Error algorithm. The y-axis is the desired voltage applied to the servo controller and the x-axis is the initial reference the precision of the nanopositioning system, we calculated its standard deviation, Table 2.2, based on Eq. 2.5, s SZ =. PN. Zi − Z N −1. 2. i=1. where Zi represent each observed value and Z is the average of those values,. 22. (2.5).

(37) Table 2.1: Percentage error in the estimation of Z for the P-611.3S nanopositioning system from PI. The MSE algorithm was employed for the estimation of each experiment. 5 measurements were taken for each experiment. The last column represent the average for each row. The last row represent the average for each column. fg [Hz] V0. Z1. V. Z2. 1. 5. 10. 15. 30. 2.0. 20. 2.9. 28.7. 5.8%. 5.3%. 7.7%. 11.2%. 21.3%. 10.2%. 5.3. λ/10. 6.1. 60.7. 6.7%. 9.7%. 13.2%. 14.8%. 38.4%. 16.6%. 6.7. λ/8. 7.4. 74.0. 8.7%. 10.5%. 19.0%. 19.2%. 41.8%. 19.8%. 13.3. λ/4. 13.9. 138.8. 1.4%. 4.1%. 5.6%. 24.2%. 52.1%. 17.5%. 53.2. λ. 53.4. 533.8. 2.4%. 3.0%. 9.7%. 21.5%. 43.2%. 16.0%. 106.4. 2λ. 106.2. 1062.3. 1.6%. 4.2%. 10.1%. 18.3%. 43.0%. 15.5%. 4.4%. 6.1%. 10.9%. 18.2%. 40.0%. V0 is the requested input voltage in [mVpp]. Z1 is the theoretical displacement in [nm]. V is the real voltage delivered by the function generator in [mVpp]. Z2 is the new theoretical displacement in [nm], based on V .. 23.

(38) Table 2.2: Standard deviation in the estimation of Z for the P-611.3S nanopositioning system from PI. fg [Hz] V0. Z1. V. Z2. 1. 5. 10. 15. 30. 2.0. 20.0. 2.9. 28.7. 1.4nm. 0.8nm. 1.4nm. 1.8nm. 2.4nm. 1.6nm. 5.3. λ/10. 6.1. 60.7. 2.4nm. 3.5nm. 1.6nm. 2.2nm. 1.6nm. 2.3nm. 6.7. λ/8. 7.4. 74.0. 2.3nm. 1.8nm. 2.7nm. 1.9nm. 3.5nm. 2.5nm. 13.3. λ/4. 13.9. 138.8. 1.3nm. 4.1nm. 4.7nm. 10.2nm. 2.1nm. 4.5nm. 53.2. λ. 53.4. 533.8. 3.0nm. 1.1nm. 2.3nm. 1.9nm. 0.4nm. 1.7nm. 106.4. 2λ. 106.2. 1062.3. 5.1nm. 1.7nm. 1.9nm. 1.2nm. 0.6nm. 2.1nm. 2.6nm. 2.2nm. 2.4nm. 3.2nm. 1.8nm. V0 is the requested input voltage in [mVpp]. Z1 is the theoretical displacement in [nm]. V is the real voltage delivered by the function generator in [mVpp]. Z2 is the new theoretical displacement in [nm], based on V .. 24.

(39) 2.3.2. Characterization of a ceramic piezoelectric chip. We characterized the amplitude displacement Z for the TA0505D024W piezoelectric chip from Thorlabs, Fig. 2.7. This piezoelectric chip is an open loop device made from ceramic and this particular model has a free stroke, (maximum displacement without load) of 2.8 µm ± 15 % for 70 V and a resonant frequency (without load) of 315 kHz.. Figure 2.7: TA0505D024W ceramic piezoelectric chip from Thorlabs. This model has a free stroke (maximum displacement without load) of 2.8 µm ± 15 % and a resonant frequency (without load) of 315 kHz. In order to perform the experiments, we mounted a mirror in the piezoelectric chip. For such a load (∼ 25 g), the resonant frequency of the piezo is around 25 kHz, which is far from the frequency used for our purposes, which is less than 100 Hz. Then, the device was mounted in the interferometer, Fig. 2.1. Finally, we applied the desired voltage and frequency with the function generator. For our purposes, we characterize the piezo for low voltages and low frequencies (the values applied are displayed in Table 2.3). We made 5 measurements for each experiment, for example, 5 measurements for V0 = 5 Vpp and fg = 10 Hz were taken and averaged. Then, the displacement was estimated by using the MSE algorithm proposed. It is worth mentioning that Thorlabs does not provide characterization curves for the approach followed here, i.e., driving the piezo with an oscillating signal to a specific frequency and estimating the amplitude.. 25.

(40) Table 2.3: Estimation of the amplitude displacement Z, for the TA0505D024W piezoelectric chip from Thorlabs. The values shown in the table refer to the average of the displacement estimated Z. 5 measurements were taken for each experiment. fg [Hz] V0 [Vpp]. 1. 10. 25. 50. 0.5. 18.20 nm. 25.17 nm. 26.39 nm. 26.31 nm. 1. 50.53 nm. 43.79 nm. 48.15 nm. 34.90 nm. 5. 101.12 nm. 95.32 nm. 120.98 nm. 141.56 nm. 10. 240.05 nm. 219.36 nm. 230.48 nm. 229.86 nm. The precision of the piezo was estimated by calculating the standard deviation of the MSE using Eq. 2.5. The calculated values are reported in Table 2.4. Table 2.4: Estimation of standard deviation for the TA0505D024W piezoelectric chip from Thorlabs. fg [Hz] V0 [Vpp]. 1. 10. 25. 50. 0.5. 10.95 nm. 1.45 nm 4.04 nm. 1. 2.08 nm. 4.18 nm. 4.18 nm 4.49 nm. 5. 3.66 nm. 1.88 nm. 4.63 nm 3.05 nm. 10. 1.20 nm. 1.06 nm. 1.80 nm 0.69 nm. 1.52 nm. Finally, we calculated the ratio between the average and the standard deviation, (SZ /Z)100%, Table 2.5,. 26.

(41) Table 2.5: Estimation of the ratio between the standard deviation and the average (SZ /Z)100%. fg [Hz]. 2.4 2.4.1. V0 [Vpp]. 1. 10. 25. 50. 0.5. 60.1%. 5.8%. 15.3%. 5.8%. 1. 4.1%. 9.6%. 8.7%. 12.9%. 5. 3.6%. 2.0%. 3.8%. 2.2%. 10. 0.5%. 0.5%. 0.8%. 0.3%. Discussion and Remarks Analysis for the piezo stages characterized. There are some aspects to discuss in relation to the PI nanopositioning system characterized. First, when working with such small displacements, the output sensor of the piezo does not work properly, which means that, the only reference we had to estimate the error was the signal of the function generator, V . The most important aspect is that, according to the results in Table 2.1, the higher the frequency used, the bigger the error obtained. This is a typical behavior in low resonance frequency systems that we do not intend to review in detail, but essentially there exists a specific cutoff frequency for which the amplitude decreases, i.e., there are losses. On the other side, we can see that the behavior of the error does not show a defined tendency in relation with the voltage V0 which suggests that there is no systematic error in the measurements for this parameter. However, in order to validate that a more robust statistic analysis should be made. In regards to the standard deviation results presented in Table 2.2, which are more important for our analysis, we notice that the averages of the standard deviation with respect to the frequency applied show a non-defined behavior, i.e., it seems to be a statistical error related to the device, which suggests that our approach for estimating the error works properly. Again, in order to validate that, a better statistical analysis is required. On the other hand, when working with a device like the 0505D024W piezoelectric chip it is complicated to have a reference for comparison. Typically there is no gain 27.

(42) information provided by the manufacturer for those chips because of their poor linearity. Also, there is no servo controller to measure its output response. Therefore, in this case we decide to completely rely on the average, the standard deviation and the ratio between both parameters in order to provide a analysis for the variations of this piezo.. It is possible to see that the standard deviation for this piezo tends to decrease when applying higher voltages, but also the ratio between the standard deviation and the average for this particular device tends to decrease for larger amplitudes. This fact is of particular importance in SOH, because roughly speaking, the lower the ratio between the standard deviation and the amplitude of oscillation, the lower the error in the reconstruction of the sample. Also, we see in Table 2.3 that, contrary to the PI nanopositioning system, the amplitude of the 0505D024W piezoelectric chip does not decrease significantly when increasing the frequency.This can probably be explained due to the fact that we are working with low frequencies compared to the resonant frequency of this piezo, which is on the order of kHz, contrary to the 230 Hz exhibited by the PI piezo. This suggests that the cutoff frequency for the 0505D024W piezo is relatively large for our purposes and therefore, there is no significant attenuation in amplitude.. 2.4.2. Characterization methodology implemented and implications in non-linear SOH. Given the nature of Fourier expression in Eq. 4.3, it is possible to note that the Z value is not associated to a frequency, but to the Bessel function weights. This means we are relying in the amplitude of the Fourier peaks to determine Z. It is also worth noting that φ(Z0 ) is crucial for the existence of the odd and even terms of the Fourier domain.This fact makes the estimation of Z more complicated because we do not know φ(Z0 ) a priori. It is true that Z0 can be controlled by adjusting the second mirror in the Michelson Interferometer. In fact, in this experiment it is enough to adjust the voltage in the servo controller to change the reference, but this does not provide a meaningful insight about the value of Z0 . The task of estimating Z get more complicated because the experimental results suggest that both, Z and Z0 are not fixed, i.e., they slightly change during the experi28.

(43) ment. In fact, we suspect that this specific behavior of Z and Z0 depend on the nature of the piezo being analyzed. However, in the end, when estimating Z and Z0 , those variations are averaged and counted as a global error in the MSE algorithm. The latter helps us understand why a MSE algorithm was proposed to estimate Z. Up to this point we have not specified how Z0 and Z impact in non-linear SOH. In the case of Z0 , it is related with the amplitude ratio between the even and odd peaks in the Fourier spectrum. In fact, in the next chapter we show that the even and odd peaks are related with the real and imaginary part of Us . Consequently, the variations of this parameter affect both, the phase φS and amplitude AS . The value of Z, on the other hand, is related to the absolute amplitude of the peaks in the Fourier domain, that is the reason why this parameter also affect both φS and AS . If the changes or variations in Z and Z0 are relatively slow in comparison with the scanning sample time, then, the error when reconstructing the sample will be minimum. That is why the period of characterization of the z-stage T , i.e. the time for recording the signal, is intimately connected with the sample scanning time used in the confocal unit. On the other hand, also the changes in magnitude affect the reconstruction of the image. If the variations in amplitude of Z and Z0 are comparable with λ, the error when recovering AS will be considerable. It is possible to note that both parameters are independent from each other, which means that also the variations and, therefore, the errors associated to each one are independent. With this setup implemented and the MSE algorithm proposed is possible to track each error because we are relying in a optimization problem. Also, it is important to understand that for the purpose of this work, we focus more on the variations in Z and Z0 than in their absolute value, because when reconstructing the sample US the former is more complicated to fix numerically. Furthermore, another advantage in this approach is that the answer obtained for Z is unvalued, and even the one obtained for Z0 is not unique, it provides the variation associated to the parameter.. It is worth noting that the higher the value of V0 , i.e., the higher the amplitude Z, in consequence, the higher the bandwidth of the signal. It is possible to understand this effect with the Bessel coefficients appearing in the Fourier domain, Eq. 4.3. This is important because when trying to estimate Z trough this MSE algorithm proposed, high values for V0 demand more terms M for the estimation of Z and 0 , what implies 29.

(44) more computational power. Therefore, this approach present more advantage for values of Z in the order of λ. Finally, the most important value for this chapter is not the results obtained for the particular piezo systems analyzed but the procedure by which those results were obtained. This methodology is intended to be a criteria in order to decide whether or not a piezo system is appropriate to be implemented in non-linear SOH. However, in the future those analysis should be made by using more robust statistic techniques. Also, an error in terms of the standard deviation and the wavelength used should be provided in relation to the specific imaging application the piezo stage is intended to be used.. 30.

(45) Chapter 3. Integration of non-linear SOH in a Zeiss 710 Confocal Microscope. For a new technique to get acceptance between the scientific community, must provide, among other things, an added value with respect to the already established techniques in the field. In this case, we are confident that the SOH added value consist in providing quantitative phase capabilities to confocal laser-scanning microscopes in a relatively easy way, without compromising the functionality of the system The objective of this chapter is to demonstrate that there is a relatively easy way to integrate Synthetic Optical Holography in a Zeiss 710 Confocal Microscope. To do this, the initial optical setup Fig. 1.4, was changed. We are going to show that for achieve the full integration of SOH just an interference objective and a microscope z-stage are required. This represent a relatively low cost and, most important, a non-invasive implementation of holographic microscopy in a commercial laser-scanning confocal microscope. We also present some experimental results obtained in the Zeiss 710 by using SOH that prove the functionality of this technique. We first encoded the amplitude and phase of biological cells by means of a synthetic hologram and, then, the information was retrieved using a reconstruction algorithm proposed in [3].. 31.

(46) 3.1 3.1.1. Configuration for the SOH module Microscope Interference Objective (Mirau Objective). In order to fully integrate SOH in commercial confocal microscopes, the basic optical setup was changed. Because of SOH was implemented using a Michelson Interferometer, Fig. 1.4, there exist multiple compatibility disadvantages when trying to adapt this technique to exiting commercial microscope systems. The first suggestion was to replace the Michelson Interferometer by a Mirau objective, [10], Fig. 3.1.. Figure 3.1: Diagram of an microscope interference objective used to integrate Synthetic Optical Holography (SOH) in commercial confocal scanning microscopes. OL goes for objective lens, M1 is the reference mirror and BS is a beamsplitter. We see in Fig. 3.1 that the light entering to the objective is divided by means of a beamsplitter located at the tip of the device, BS. The transmitted light is used to illuminate the sample and the scattered light (Us ) is collected using a second mirror, M2. Then, the scattered light is recombined with the reference beam (reflected light) by means of a mirror located inside of the interference objective, M1. In this way, an interference hologram can be created.. 32.

(47) 3.1.2. Generating the time-varying reference field. Finally, in order to generate the reference field, UR (t) there are two possible options, Fig. 3.2. The first one is by mounting the microscope interference objective in a piezo scanner (piezo objective scanner or scanning system for microscope objectives, the name can change depending on the company), Fig. 3.2a. In this modality, the microscope objective is moved in a sinusoidal way when scanning the sample. In the other hand, it is possible to use a microscope z-stage Fig. 3.2b, and instead of moving the objective, the sample is put to oscillate.. (a) Objective scanner configuration. (b) Z-stage configuration.. Figure 3.2: Two modalities for the SOH module. a) In the first configuration, a piezo objective scanner is used to move the reference mirror M1 and the sample is kept fixed. b) in the second modality, a microscope z-stage is used to move the reference mirror M2, along with the sample. There are too many options when dealing with nanopositioning systems. Here, we present some of the possible system that can be used for the implementation of SOH. Table 3.1 contain different models for objective scanners and Table 3.2 present some models for microscope z-stages. 33.

(48) The most important parameters we need to take in account when choosing a nanopositioning system are the travel range and the step resolution. Typically, in SOH a couple of microns are required for the travel range. In regards to the resolution, this depend on the specific application and the wavelength λ used for the experiment. For example, if using a z-stage with a step resolution of 10 nm combined with a HeNe laser of 633 nm, then the variation for the phase reconstruction is around 1.58 %, which seem to be a low error. However, if the application require a discrimination of structures smaller than 10 nm, then there is no possibility to make such discrimination. Also, even not included in the tables, the resonant frequency of the system should be taken in account. Normally, less than 100 Hz are required when oscillating the systems. The systems presented here widely full fill those requirements. Table 3.1: Comparative table between different microscope objective scanners. Manufacturer. OLTR. CLTR. OPR. CLR. Price∗. ThorLabs. 600 um. 450 um. 1 nm. 3 nm. $9,210. P-721.0LQ. PI. 140 um. N/A. 0.5 nm. N/A. $3,258. PD72Z1SAQ. PI. N/A. 100 um. N/A. 5 nm. $5,880. MIPOS 20 SG. Piezosystem. 20 um. 16 um. 0.04 nm. 1 nm. $5,260. MIPOS 20. Piezosystem. 20 um. N/A. 0.04 nm. N/A. $5,179. Nano-OP Series. Mad City Labs. N/A. 30 um. N/A. 0.06 nm. $6,250. Nano-F100. Mad City Labs. N/A. 100 um. N/A. 0.2 nm. $6,050. Product Name Obj. Scanner. OLTR: Open Loop Travel Range, CLTR: Closed Loop Travel Range, OPR: Open Loop Resolution, CLR: Cloosed Loop Resolution. ∗. Price is in USD.. Table developed by the CUBE Consulting group.. 34.

(49) Table 3.2: Comparative table between different microscope z-stages. Product Name. Manufacturer. OLTR. CLTR. OLR. CLR. Nano-LPMW. Mad City Labs. 200 um. N/A. 0.4 nm. N/A. Nano-LPS100. Mad City Labs. 100 um. N/A. 0.2 nm. N/A. P-736.ZR1S. PI. N/A. 100 um. 0.2 nm. 0.4 nm. PD73Z2ROW. PI. N/A. 200 um. N/A. 1 nm. NZ200FCE NanoScanZ. Prior. N/A. 200 um. N/A. 1 nm. NZ400 NanoScanZ. Prior. N/A. 400 um. N/A. 1 nm. OLTR: Open Loop Travel Range, CLTR: Closed Loop Travel Range, OPR: Open Loop Resolution, CLR: Cloosed Loop Resolution.. 35.

(50) 3.2. Quantitative phase imaging of biological cells in Zeiss 710 confocal microscope with SOH. 3.2.1. Setting up the SOH module. To test the capabilities of SOH in the 710 Zeiss confocal microscope and validate our proof of concept, we decided to analyze biological samples. We first analyzed human cheek cells and then, we decided to run a z-stack experiment for stem cells. For both samples, we successfully retrieved the amplitude and phase. As an illustrative way, we show a previous version of the Zeiss 710 (the Zeiss 700) Fig. 3.3 in which the SOH module was implemented.. Figure 3.3: Illustrative image of a Zeiss LSM 700 confocal microscope (previous version of the Zeiss LSM 710). Image taken from Zeiss. For the SOH module, we used an infinity corrected interference objective from Nikon Fig. 3.4a. This device has a magnification of 20× and a numerical aperture (NA) of 0.4. Also, for this microscope objective, the working distance is 4.7 mm and the depth of field is 4.8 µm. Also, in order to generate the synthetic wave reference we used a microscope z-stage from Prior Scientific, the NZ400 Fig. 3.4b. This model has a travel range of 400 µm, a resolution of 1 nm and a resonant frequency of 1 kHz. 36.

(51) Additionally, the servo controller employed for this z-stage has an input range of 0-10 V and a gain of 40 µm/V.. (a). (b). Figure 3.4: SOH module implemented in the Zeiss 710 microscope. a) Interference objectives from Nikon (green collar), 20× magnification and 0.4 NA. b) NZ400 microscope z-stage from Prior Scientific. This model has a travel range of 400 µm and a resolution of 1 nm. The resonant frequency of this device is 1 kHz. Images taken from Edmund Optics and Prior Scientific, respectively The first step when setting up the SOH module is installing the interference objective in the turret. Because of the difference in brands, in this case a ring adapter was used to match the system of measurement between the Zeiss turret and the Nikon objective. After installing the objective, we proceed to install the nanopositioning zstage. For this purpose, a homemade adapter was required to fit the Prior z-stage into the Zeiss 710 microscope xy-stage. Once the SOH module was installed, we proceed to plug the function generator (Keysight 33500B Series) in order to generate the input signal. Besides, we connected the oscilloscope (PC PicoScope) to analyze the input signal and the sensor response. Finally, in regards to the samples preparation, for the cheek cells a sample was diluted with distilled water directly onto an aluminum slide (reflective slide), then, a 37.

(52) cover slip was used to isolate the sample from the environment. In the case of the stem cells, they were first grown directly on cover slips and then, the cover slips were placed onto the aluminum slides.. 3.2.2. Retrieving amplitude and phase from cheek cells. Once the SOH module was installed in the confocal unit, we proceed to run the experiments. Fig. 3.5 and 3.6 show the results obtained when imaging cheek cells. In Fig. 3.5 is possible to appreciate two joined cheek cells whose length is around 100 µm. In the other side, in Fig. 3.6 an isolated cheek cell with a length of approximately 80 µm is observed. In regards to the confocal microscope parameters, for the image size we choose 2048 × 2048 pixels with a total scanning area of 140.4 µm × 140.4 µm for the two-cheek cell image Fig.3.5 and 111.8 µm × 111.8 µm for the one-cheek cell image Fig. 3.6. Also, the total scanning time for both images was 3.87 s and the aperture of the pinhole was set to 34 AU’s (Airy Unit). Finally, we used a 633 nm He-Ne laser for the experiments.. Fig. 3.5a and 3.6a show how the cheek cell interferogram looks like when using a Mirau objective. It is possible to appreciate the change in contrast induced by the variations on the effective index of refraction of the cells.. 38.

(53) (a). (b). (c). (d). Figure 3.5: Typical process followed in SOH in order to recover amplitude and phase of a sample. a) cheek cell interferogram using a Nikon interference objective with a magnification of 20X and NA of 0.4. b) Synthetic hologram created by using the Prior z-stage, oscillating with a amplitude of 0.36 µm and a frequency of 79 Hz. c) Reconstructed normalization amplitude information of the cell. d) Reconstructed wrapped phase of the cheek cell going from 0 to 2π.. 39.

(54) (a). (b). (c). (d). Figure 3.6: Typical process followed in SOH in order to recover amplitude and phase of a sample. a) cheek cell interferogram using a Nikon interference objective with a magnification of 20× and NA of 0.4. b) Synthetic hologram created by using the Prior z-stage, oscillating with a amplitude of 0.36 µm and a frequency of 79 Hz. c) Reconstructed normalization amplitude information of the cell. d) Reconstructed wrapped phase of the cheek cell going from 0 to 2π.. 40.

(55) In order to generate the synthetic holograms Fig. 3.5b and 3.6b, the non-linear SOH approach was followed, i.e., a sinusoidal voltage function was applied to the zstage. For both experiments a signal of 80 mVpp for the amplitude and 79 Hz for the frequency was applied Fig. 3.7 (blue line). As discussed before, because of the low frequency resonance of this kind of z-stages (in comparison with the frequency applied), there is an attenuation in the output amplitude, which in this case gives a value of 9 mV as result Fig. 3.7 (orange line). Therefore, taking in account the gain of the servo controller which is 40 µm/V, the amplitude of the z-stage in length is approximately 0.36 µm. Z − StageOutputSensor. 50. Function Gen. Signal Output Sensor. 40 30. V[mV]. 20 10 0 -10 -20 -30 -40 -50 -0.025. -0.02. -0.015. -0.01. -0.005. 0. 0.005. 0.01. 0.015. 0.02. 0.025. t[s]. Figure 3.7: Input signal applied to the z-stage (blue line), 80 mV and 79 Hz. Sensor output of the servo controller (orange line), 9 mV and 79 Hz. Taking in account the servo controller gain which is 40 µm/V, the amplitude of the z-stage is approximately 0.36 µm.. 41.

(56) Finally, by using the Fourier spectrum of the holograms Fig. 3.8 and 3.8b, and the reconstruction algorithm proposed in [3], we recovered the amplitude Fig. 3.5c and 3.6c, and the phase Fig. 3.5d and 3.6d of the cells. Those are the most important results in this work because it proves the functionality of the SOH integration with the Zeiss 710 confocal microscope.. (a). (b). Figure 3.8: Logarithm of the normalized Fourier spectrum of the synthetic holograms for a) the two-cheek cell image and b) the one-cheek cell image. The red and blue dashed boxes contain the real and imaginary part, respectively, of the field US , used to recover the amplitude and phase.. 42.