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where m is the order of the retarder, and δ denotes the modulo 2π retardance. For these multiple-order retarders, the function ϕ(λ) change very rapidly and the retarder suffers from larger retardance variations with temperature and wavelength. These variations are reduced significantly with zero-order retarders, where the retardance is directly the design value, ϕ = δ, i.e., m = 0, and consequently the function ϕ(λ) changes slowly.
We added two other curves in Fig. 2(c) and (d). Here the two retarders are placed in between the polarizers. In Fig. 2(c) the two retarders are aligned with the fast axis in the same orientation, while in Fig. 2(d) the second one is rotated 90° with respect to the first one. Thus, in Fig. 2(c) the total retardance is the addition ϕ(λ) = ϕ 1(λ) + ϕ 2(λ), while in Fig. 3(d) the total retardance is the subtraction ϕ(λ) = ϕ 1(λ)−ϕ 2(λ). Note that the retardance addition doubles the spectral oscillation. On the contrary, when the retardances are subtracted, a very slow oscillation remains because the two retarders have small thickness difference. A retardance difference of π radians is obtained for the wavelength of 700 nm. Note that this last case mimics a zero-order retarder. And this result shows how the spectral method is a very simple technique to clearly distinguish between multiple-order and zero-order waveplates.
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POST AMERICA DEPRESSIONIn Japan, however, I found myself suffering from Post America Depression or PAD. The environment for researchers in Japan was quite different in many ways from that in the U.S. At the medical school, very few scientists showed interest in the basic biology of mouse ES cells, and there was little thought-provoking discussion with my colleagues. Some of my colleagues advised me to work on something more related to medicine. Furthermore, I could not get enough funding and had to change the cages of the numerous mice by myself every week. What was worse, the Nat1 work was being rejected by many journals. I felt lonely and depressed, and I was about to give up my career as a scientist and return to the path of physician.
Working at the hospital, I found that my surgical skills were not as good as I expected. One time it took me two hours to do a surgical operation which could have been completed in 30 minutes by other surgeons. My supervisors were very tough on new residents like me, and I lost confidence in my ability. In addition, treating many patients with intractable diseases and injuries such as rheumatoid arthritis and spinal cord injury, I realized that there were many diseases that even talented surgeons and physicians cannot cure. Even now, I recall clearly one female patient who had severe rheumatoid arthritis. There was a photograph of a cheerful woman on her bedside cabinet. I though it must be her sister or something. Learning that it was herself only a few years back, I was shocked that the patient looked totally different because of the disease. Painful and unforgettable bedside experiences finally drove me to switch my goal from becoming a surgeon who would help free patients from pain to becoming a basic scientist who would eradicate those intractable diseases by finding out their mechanisms and ultimately a way of curing them.
where subindices “par” and “cros” refer to having the two polarizers parallel or crossed respectively. Here, ϕ denotes the wave-plate retardance. These relations assume ideal retarders and polarizers, where no other polarization phenomena different than linear retardance occurs. This is a reasonable approximation for linear retarders, and no additional polarimetric measurements are required.
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Yeh, P.: Some applications of anisotropic layered media, Ch. 10 in Optical Waves in Layered Media. John Wiley & Sons (2005).
Since the discovery of human iPS cells, I have seen iPS cell technology advancing at an amazing speed. Owing to its simple and reproducible method, numerous laboratories inside and outside Japan are now working on iPS cell research, and protocols have been developed for direct reprogramming, whereby somatic cells are directly converted into mature cells of a different type. My lab developed a method to generate safer iPS cells without integrating viral vectors into the cell genome, which was one of the major safety concerns. Now CiRA is promoting the iPS cell stock project, in which we make clinical-grade iPS cell lines from blood cells donated by healthy HLA-homozygous individuals. The iPS cell lines will be distributed to other institutes so that they can differentiate them into various types of cell for use in transplantation therapy. Scientists at CiRA have succeeded in recapitulating a number of abnormalities in the cells of patients with such diseases as amyotrophic lateral sclerosis (ALS) and chronic infantile neurologic cutaneous and articular (CINCA) syndrome, which I hope will contribute to development of new therapeutic drugs. I have a small laboratory at Gladstone since I was offered a senior investigator position in 2007 and the lab members are also working hard. Working for Gladstone is a great pleasure for me as it means I can make some contribution to the institute where I received excellent training as a young scientist.
Yamanakalab
Sordillo, L.A., Pu, Y., Pratavieira, S., Budansky, Y., Alfano, R.R.: Deep optical imaging of tissue using the second and third near-infrared spectral windows. J. Biomed. Opt. 19, 056004 (2014)
Figure 6 shows our experimental results for the LO filter with two stages (LCR1 and LCR2). In this case, since our LCR devices have (only approximately) the same thickness, we have to play with the applied voltage to reduce the retardance of one of them to become half the retardance of the other. In Fig. 6(a), LCR1 is left without applied voltage (V1 = 0), so its transmission between polarizers is that in Fig. 5(a). The device LCR2 is then tuned to provide half the retardance, i.e., ϕ LCR1 = 2ϕ LCR2. This is achieved by applying a voltage V2 = 2.07 volts, thus yielding a transmission between polarizers as shown in Fig. 6(b). We adjusted the maximum transmittance to be located at the wavelength of 565 nm, the same wavelength where there is a maximum in Fig. 6(a). Therefore, the combination of the two elements in cascade to generate a LO filter provides a single transmission band around 565 nm, as can be seen in Fig. 6(c). Note that the retarder with lower retardance (in this case LCR2) fixes the free spectral range of the filter (wavelength range between consecutive maxima). In this case, since the retardance of LCR2 must be reduced significantly, only one single maximum is observed in the entire wavelength range from 450 to 1600 nm, and the IR has been completely removed. This type of filter might be useful to highly remove the IR content and only transmit the visible range.
With the ability to differentiate into virtually all types of cell and to grow robustly like ES cells, iPS cells have enormous potential for pharmaceutical and clinical applications. Patient-specific iPS cells can be used to produce disease model cells in which the pathological process can be studied. Thousands of chemicals and natural products can be tested on such cells, some of which we hope will become new effective medicines for intractable diseases.
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THANK YOU FOR YOUR SUPPORT!Looking back at my life, I have been very fortunate that I have encountered many talented students and colleagues who have supported and encouraged me on many occasions, including my lab members in the past and the present. In addition to my direct mentors, I also owe much not only to the great scientists who made breakthrough discoveries in biology but also to countless predecessors who have contributed to the development of nuclear reprogramming and stem cell biology. I am deeply thankful to my wife and our two daughters, who have supported my hectic life as a scientist for years. Finally I am grateful to my parents. I was glad that my mother was able to take part in the award ceremony of the 2012 Nobel Prize in Stockholm. My father wanted me to become a physician who helps a lot of patients. Although I gave up my career as a surgeon, I still hope to help people suffering from serious diseases and injuries. With iPS cell technology I will continue to work hard together with my colleagues to achieve this goal as quickly as possible.
CENTER FOR IPS CELL RESEARCH AND APPLICATIONThe Ministry of Education, Sports, Science and Technology of Japan has since supported iPS cell research in cooperation with other government agencies by providing sufficient funding. Encouraged by this support, in January 2008, about two months after we reported the generation of the human iPS cells, Kyoto University founded the Center for iPS Cell Research and Applications (CiRA), the world’s first organization solely focusing on iPS cell technology, under the auspices of the Institute for Integrated Cell-Material Sciences (iCeMS). I was appointed as the Director of CiRA. I had given up my career as a physician, but I had found a powerful tool that could help develop new cures for disease. This center is designed not only to progress with basic research to improve fundamental iPS cell technology but also to use the technology in clinical applications. In April 2010, CiRA became independent of iCeMS as a full-fledged institute in a newly opened research building. At the inauguration ceremony for the new CiRA research building, I publicly pledged to achieve four goals over the first ten years:
Normalized spectral intensity transmission T par (λ) for the LCR without applied voltage; a the LCR plus the Fresnel rhomb; b the LCR alone and c the LCR minus the Fresnel rhomb. d Spectral retardance for the three cases considered
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where k e and k o are the wavenumbers for the extraordinary and ordinary waves, n e and n o are the extraordinary and ordinary indices of refraction respectively, and d denotes the thickness of the plate. In multiple-order retarders, the thickness d is large, and the total retardance for the design wavelength is
As a result we can measure the spectral retardance of different retarders and easily identify the kind of reterder (multiple order, zero-order, achromatic). We show results with tunable liquid-crystal retarders as well, where the technique is applied to determine the spectral retardance as a function of the applied voltage. Finally, the accuracy of the technique is verified by the generation of a birefringent spectral filter.
Nuclear reprogramming was first proved by Sir John Gurdon in 1962, the year I was born. He reported the generation of new frogs by transferring tadpole intestine cell nuclei into enucleated eggs from the African clawed toad, Xenopuslaevis. Then, in 1997, Sir Ian Wilmut’s team unveiled Dolly the sheep, the first cloned mammal created using a nuclear transfer method. These achievements showed that the genome DNA of mature cells theoretically have all the information needed to develop animals. A further advance came in a 2001 report by Takashi Tada of Kyoto University, who demonstrated that thymocytes acquire pluripotency upon electrofusion with mouse ES cells, which indicated that ES cells also contain factors that induce pluripotency in somatic cells. However, I knew that making pluripotent cells from somatic cells would be extremely difficult, and when I started this project with my lab members at NAIST, I was not sure if the goal could be achieved in my lifetime.
Safrani, A., Abdulhalim, I.: Spectropolarimetric method for optic axis, retardation, and birefringence dispersion measurement. Opt. Eng. 48, 053601 (2009)
To cite this section MLA style: Shinya Yamanaka – Biographical. NobelPrize.org. Nobel Prize Outreach AB 2024. Wed. 6 Nov 2024.
Nagib, N.N., Khodier, S.A., Sidki, H.M.: Retardation characteristics and birefringence of a multiple-order crystalline quartz plate. Opt. Laser Technol. 35, 99–103 (2003)
Optical retarders are key elements for the control of the state of polarization of light, and their wavelength dependance is of great importance in a number of applications.
Fortunately, two events rescued me from PAD and from giving up on science. First, James Thomson of the University of Wisconsin-Madison and his colleagues announced that they had succeeded in generating human ES cells in 1998. His success taught me that ES cells have enormous potential in medicine and encouraged me to continue my research. Second, in December 1999, I got a new position as an associate professor with my own laboratory for the first time in my career at the Nara Institute of Science and Technology (NAIST ) in Nara Prefecture. This institute has brilliant investigators in basic and applied sciences, an excellent research environment and competent Ph.D. students. I was fortunate that several talented colleagues and students joined my laboratory.
Six prizes were awarded for achievements that have conferred the greatest benefit to humankind. The 12 laureates' work and discoveries range from proteins' structures and machine learning to fighting for a world free of nuclear weapons.
A technique to measure the spectral retardance of a linear retarder in a wide spectral range is applied to identify different types of retarders, and provide an accurate description of the spectral polarization conversion properties of these elements.
1. Establish basic iPS cell technology and secure intellectual property.2. Create an iPS cell stock for clinical use in regenerative medicine.3. Conduct preclinical and clinical studies on such diseases as Parkinson’s disease, diabetes and blood diseases.4. Contribute to the development of therapeutic drugs using patient-derived iPS cells.
THE DISCOVERY OF IPS CELLSIn 2004, I moved to the Institute of Frontier Medical Sciences at Kyoto University as a professor. The major reason for the change was that I wanted to conduct experiments using human ES cells. NAIST did not have a medical school and a hospital attached, and therefore had no institutional review board to examine a study plan using human ES cells. At that time, Kyoto University was the only institute in Japan that had succeeded in culturing human ES cells. I came to Kyoto with the 24 candidate genes, the Fbxo15-neoR knock-in mice and many members of my lab, including Tomoko and Kazutoshi. I asked Kazutoshi to test the 24 candidates using the Fbxo15 knock-in mice. He was pleased to take over this very risky project and did a remarkable job. When Kazutoshi introduced each candidate into the Fbxo15-neoR reporter fibroblasts using retroviral vectors, no G418-resistant colonies emerged. However, when he introduced the mixture of all 24 genes via retroviral vectors, we observed several drug-resistant colonies in a Petri dish. These cells were similar to ES cells in morphology, proliferation and gene expression. When transplanted into nude mice, they formed teratomas containing a variety of tissues from all three germ layers, showing their pluripotency. Among the myriad combinations of the 24 factors, Kazutoshi found that four transcription factors – Oct3/4, Sox2, Klf4 and c-Myc – are essential.
In 2005, we succeeded in generating ES-like cells with the four factors, and I named the resulting cells “induced pluripotent stem cells or iPS cells.” I was anxious about whether they were really the pluripotent cells that we were looking for because the method used to generate the iPS cells was much simpler than I had expected. In addition, after hearing about a big scandal involving a Korean researcher who falsely reported the successful generation of human ES cells by cloning at around that time, I thought we should repeat our experiments to make sure of the result so that no researcher could cast doubt on our findings. In 2006, we published a paper in Cell on the successful generation of mouse iPS cells using the four factors. Some researchers seemed surprised at the finding that only four genes are needed to reprogram somatic cells into the embryonic state. But in the following months, a few labs at MIT and Harvard demonstrated that they had been able to produce mouse iPS cells using our protocol, and an increasing number of researchers have since started working on the new technology.
All these different types of retarders exhibit very different spectral retardance functions, that can be easily visualized in the spectrometer, as shown next.
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This work received financial support from Ministerio de Economía y Competitividad and FEDER funds (grant ref.: FIS2015-66328-C3-3-R). A. Vargas acknowledges financial support from Fondecyt (grant ref.: 1151290).
We start by using two different quartz quarter-wave plate (QWP) multiple order retarders, designed for wavelengths of 514 nm and 488 nm respectively. We denote them as QWP514 and QWP488 respectively. Figure 2(a) and (b) show the normalized data T par (λ) for these two retarders. Blue and red points denote the data captured with the VIS and NIR spectrometers respectively.
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POSTDOCTORAL FELLOW AT GLADSTONEAt the time, I was astonished by mouse transgenesis and gene targeting, which specifically induce or delete a single gene of interest, because no pharmacological agents could perform such miracles. After finishing my Ph.D. work in 1993, I applied for as many postdoctoral positions as I could in labs doing mouse molecular genetics because I wanted to obtain postdoctoral training and further skills including techniques to make knockout mice. However, it was very natural that a failed surgeon with little experience in molecular biology had a hard time finding a position. A turning point came when I got a fax from Thomas Innerarity at the Gladstone Institute of Cardiovascular Diseases in San Francisco. After a short telephone conversation, Tom was brave enough to give me a postdoctoral position in his lab! Working at Gladstone was one of the best decisions I ever made in my life. Gladstone provided an almost perfect environment for an ambitious new researcher like me thanks to its skillful technicians and the provocative discussions about science I had with enthusiastic colleagues.
My initial hypothesis was that factors that maintain the pluripotency of mouse ES cells might induce pluripotency in somatic cells. With the great help of the initial members of my lab – Tomoko, Yoshimi, and two other students, Kazutoshi Takahashi and Eiko Kaiho, and then Assistant Professor Kaoru Mitsui, my lab identified many factors that either are specifically expressed by or have important roles in mouse ES cells. Among them was the transcription factor Klf4, identified by Yoshimi. By 2004, with our own work and that of other groups, we had collected 24 initial candidate genes that might be able to induce pluripotency in somatic cells. We then needed a simple and sensitive assay system to evaluate these candidates, and the Fbxo15-knockout mice turned out to be such a system. Instead of simply deleting the gene, we knocked the neomycin resistant gene (neoR) into the Fbxo15 locus. Somatic cells derived from these mice do not express neoR and are sensitive to the antibiotic G418. Somatic cells that become ES cell–like pluripotent cells after transfection with some of our candidate genes should express neoR and become resistant to G418.
Here we apply the above mentioned technique of measuring the transmittance spectra between crossed or parallel polarizers to determine the spectral retardance function [6–12], but we use an optical calibration system developed for extending the measurement range to wavelengths from 450 nm to 1600 nm. The system incorporates a thermal broadband light source or a super-continuum laser, two broadband beam-splitter polarizers, and two spectrometers that operate in the VIS and in the NIR band regions respectively. As a result, we can determine the spectral retardance function of different retarders in a very wide spectral range by fitting the measured and the simulated transmission curves. In some cases, a Cauchy-like dispersion relation can be applied, which has been proved to give good approximations far from the absorption bands of anisotropic materials [6, 7, 10, 12].
From The Nobel Prizes 2012. Published on behalf of The Nobel Foundation by Science History Publications/USA, division Watson Publishing International LLC, Sagamore Beach, 2013
In some applications it is of interest to use retarders with a retardance that does not change with wavelength. Achromatic retarders are made by placing together two retarder layers of different materials with opposite dispersion relations [17, 18]. The difference in thickness and refractive index of these two anisotropic layers can be adjusted to provide the same retardance for two separated wavelengths, and ϕ(λ) only shows a very small amount of deviation from this value in between. Alternatively, Fresnel rhombs are retarders with almost perfect wavelength independent retardance [19], since they are not based on a material’s birefringence, but on the difference in phase-shift for the s and p polarized components in a total internal reflection.
Throughout my school years, I was good at mathematics and physics. Thinking about my career, I considered studying basic sciences in college but decided to go to medical school, partly because my father used to advise me to become a physician instead of taking over his business. I don’t know why that was his wish, but he may have thought that I was not cut out for business or may have wanted me to have a job more stable than running a small business that is easily affected by the economic climate. A book also pushed me to become a medical doctor. I was deeply inspired by Torao Tokuda, a physician who founded a hospital group in the 1970s that tried to revolutionize the Japanese medical care system. In 1981, I succeeded in my ambition of being accepted at Kobe University’s School of Medicine. There again, I enjoyed playing judo and rugby, and suffered many broken bones while doing sports. In addition, I often suffered from severe pain in my legs due to over-training. These experiences made me interested in sports medicine and I decided to become an orthopedic surgeon.
Normalized spectral intensity transmission T par (λ) for a the LCR in the off state; b with Vpp = 1.5 V; c with Vpp = 2 V; d with Vpp = 2.5 V; e Spectral retardance for the four cases
RESIDENT AT A HOSPITALAfter receiving an M.D. from Kobe University in 1987, I served as a resident at the Osaka National Hospital for two years. During this period, two major events happened to me. I married Chika, whom I first met as a classmate at junior high school. She became a dermatologist and now runs a clinic in Osaka. The other unforgettable event was my father’s death. He had long suffered from diabetes and also had hepatitis caused by a blood transfusion he had received a few years earlier to treat an injury. During his last two years, as a medical student and resident I gave him injections and administered intravenous drips, and he seemed happy to receive such treatments from his son.
Aharon, O., Abdulhalim, I.: Liquid crystal Lyot tunable filter with extended free spectral range. Opt. Express 17, 11426–11433 (2009)
Vargas, A., Donoso, R., Ramírez, M., Carrión, J., Sánchez-López, M.M., Moreno, I.: Liquid crystal retarder spectral retardance characterization based on a Cauchy dispersion relation and a voltage transfer function. Opt. Rev. 20, 378–384 (2013)
In the results in Fig. 4, the LCR is off. But LCR devices are of interest mainly because the retardance can be controlled via an applied voltage. Normally, in parallel aligned nematic LCR devices, the maximum retardance occurs in the absence of voltage, and the application of voltage reduces the retardance due to the tilt of the liquid-crystal director [7]. Figures 5(a)-(d) show the spectral transmittance and retardance for the LCR without applied voltage, and when a 1.6 KHz square-amplitude signal with polarity inversion is applied, with peak to peak voltages Vpp = 1 V, Vpp = 1.5 V and Vpp = 2 V respectively. The first result that becomes apparent is the shift of the oscillations to the left part of the graphs (lower wavelengths) due to the reduction of the retardance. Because the peak to peak voltage can be tuned continuously, we can follow the shift of the maxima, and therefore identify where integer values of π radians are obtained, as indicated in the figures.
FROM SURGEON TO SCIENTISTAs the first step toward my new goal, I became a Ph.D. student in pharmacology at Osaka City University Graduate School of Medicine in 1989, working in Kenjiro Yamamoto’s laboratory. During the next four years, I learned the essentials about how to design and conduct experiments and analyze data from my direct mentor, Katsuyuki Miura. The first instruction he gave me was to read as many papers as possible to help me think about a research theme. A few months later he assigned me to perform an experiment to study the role of a blood lipid named platelet-activating factor in lowering blood pressure in dogs. Miura’s hypothesis was that administering an inhibitor of another lipid, thromboxane A2, which is activated by platelet-activating factor, would prevent the blood pressure from going down. But my experiment showed a completely opposite result. I was so excited with the unexpected outcome that I became totally fascinated by basic science. Miura was also enthusiastic about the findings even though they were against his hypothesis. This study later became my Ph.D. dissertation, published in Circulation Research in 1993. There was an eye-opening moment when Miura told me that scientists have to compete with researchers around the world. When I was a resident, my rivals were other residents at the same hospital. As a scientist, I could win global recognition in a scientific field, albeit a small one, if my findings were published in high-profile journals. His words made me pay keen attention to research abroad.
A second interesting example involves using retarders with flat spectral retardance functions. We consider here two examples: an achromatic QWP retarder from Thorlabs, model AQWP05M-600, designed for the range 400–800 nm, and a quarter-wave Fresnel rhomb also from Thorlabs, model FR600QM, designed for the range 400–1550 nm. Figure 3 shows the corresponding experimental data for the normalized intensity transmission T par . In these cases, the spectral oscillations present in the previous retarders do not appear, and the normalized transmission is approximately constant at the value T par = 0.5, as expected for a QWP. But for the achromatic retarder, this is approximately true only in the spectral range of design, while the Fresnel rhomb shows a much better flat transmission in the wide spectral range. The VIS spectral region between 450 and 800 nm, where the achromatic QWP retarder operates, has been marked in Fig. 3(a). The two extremes of this regions shows the exact normalized transmission of 50 %, and it shows only a small variation for wavelengths in between. On the contrary, for wavelengths larger than 800 nm, the normalized transmission is slowly but progressively increasing, thus showing the deviation from the quarter-wave retardation at these wavelengths.
Two features are clearly visible in these graphs: 1) A rapid oscillation as a function of wavelength is observed in both cases, and 2) a value T par = 0.5 is obtained at the design wavelengths. The rapid oscillation observed in Fig. 2(a) and (b) indicates that the retardance is experimenting a very rapid change with wavelength, as expected in a multiple-order retarder. The number of complete oscillations for QWP488 is slightly larger than the total oscillation for QWP514, and the total retardance variation is around 36π radians in the covered spectral range for the two retarders. Another interesting aspect to note is that, although the design wavelength is located at the lower extreme of the measured wavelength range, the oscillatory behavior is maintained up to the other extreme at 1600 nm. This denotes that these retarders operate properly in the entire spectral range, although they are normally commercialized for a single specific designed wavelength.
All coauthors contributed to the paper. AM contributed with the realization of the optical system, taking the measurements data, and analyzing them. MMS-L contributed in the design of the experiments, the analysis of the results, and writing the manuscript. PG-M participated in the design of the experiments and in the discussion and analysis of the results. AV participated in the realization of the experimental system, and designed the procedure for taking the experimental data. Finally, IM contributed in the design of the experiments, the analysis of the results, and the preparation of the manuscript. All authors read and approved the final manuscript.
This normalization makes the experimental data directly comparable to Eqs. (1). Again, note that this kind of normalization ignores possible spectral variations in the transmission/extinction of the analyzer, and therefore high quality polarizers must be employed. Our goal here is to measure the spectral retardance function, i.e., the function ϕ(λ) which describes the dependence of the retardance with wavelength λ. For that purpose the function ϕ(λ) that best fits the curves T par (λ) and T cros (λ) must be determined.
Normalized spectral intensity transmission T par (λ) for a An achromatic quarter-wave retarder designed for the indicated spectral range from 450 to 800 nm; b A quarter-wave Fresnel rhomb; c Spectral retardance for these two retarders
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Staromlynska, J., Rees, S.M., Gillyon, M.P.: High-performance tunable filter. Appl. Opt. 37, 1081–1088 (1998). https://www.osapublishing.org/ao/abstract.cfm?uri=ao-37-6-1081.
Right after we generated mouse iPS cells, my team began to work on reprogramming human somatic cells. In November 2007, we reported the generation of human iPS cells from human fibroblasts by introducing the same quartet of genes via viral vectors. On the same day, Thomson’s lab announced in Science that they had also succeeded in making human iPS cells using a different set of four factors – Nanog, Lin28, Oct3/4 and Sox2. I remember that I worked day and night to publish our paper as quickly as possible after I heard a rumor in the summer that a U.S. group had submitted an article on the successful generation of human iPS cells. My lab members continued to improve the induction and selection methods. Keisuke Okita, with the help of Tomoko, succeeded in making iPS cells that are competent for production of adult chimeras and germline transmission. Masato Nakagawa and Michiyo Koyanagi then showed that iPS cells can be generated without c-Myc, an oncogene. Takashi Aoi showed that iPS cells can be generated not only from fibroblasts but also from adult mouse hepatocytes and gastric epithelial cells.
Nevertheless, these experiments can be used to fit the spectral retardance function which can then be adjusted according to a microscopic physical model, as for instance the Cauchy-type series that are usually a good approximation far from the material absorption bands [20]. The experimental curves in Fig. 2(a) and (b) were thus fitted to a numerical simulation of Eq. (1) assuming a spectral dependence of ϕ(λ) as:
One of the interesting uses of the spectral properties of retarders is their application to build birefringent filters [25], i.e., spectral filters based on the variations in the state of polarization for different wavelengths caused by the birefringence dispersion. They have become more interesting with the development of liquid-crystal technology since they can be tuned, and nowadays we can find commercial tunable spectral filters based on this technology [26, 27]. The successful realization of such filters depends critically on the correct characterization of the spectral retardance of the retarders used to compose the filter. Therefore, in order to confirm the validity of the previous results, this last section of the paper shows as an example the classical Lyot-Ohmann (LO) birefringent filter [28] made by combining two LCR retarders.
Usually, linear retarders are designed introducing a specific retardance (typically a half-wave or a quarter-wave) for a given operating wavelength. However, characterization of their spectral retardance properties can be very valuable for several reasons: 1) the retarder can be used at wavelengths different to the original design; 2) the retarder can be applied to build spectral birefringent filters, which are based on the wavelength variation of the retardance [4], 3) it allows the simple identification of the ordinary and extraordinary neutral axes of the retarder [5], and 4) the retardance modulation of tunable LC retarders can be characterized [6, 7]. In addition, the spectral retardance function can provide very useful information about the fabrication characteristics of the retarder, allowing a simple identification of multiple-order, low-order or zero-order retarders, as well as achromatic retarders.
Since we have used two quartz waveplates from the same supplier, purchased at the same time, we can assume exactly the same retardance dispersion for the two retarders, with a simple multiplicative factor. Therefore, we have considered the retardance for QWP514 as ϕ 514(λ) following the relation in Eq. (5), and we have considered the retardance for QWP488 follows a relation ϕ 488(λ) = t ϕ 514(λ), where t is a multiplicative factor that takes into account the small amount of thickness difference between the two plates. Thus, the numerical fit consists in a single search of the A, B, C, and D constants for ϕ514(λ) and the constant t, that simultaneously match for the four curves in Fig. 2. This way we obtain a more confident result than simply fitting the result for a single retarder. Figure 2(a), (b), (c) and (d) show the simulated curves as well, revealing a very good agreement with the experimental data. The corresponding spectral retardance functions are shown in Fig. 2(e). The spectral retardance is very similar for the two waveplates, since the thickness difference parameter is t = 0.9657.
In fact, different types of retarders show very different spectral retardance functions [16]. Therefore, these spectral measurements are of interest to easily identify the kind of retarder. For instance, a simple retarder composed of a single layer of uniaxial plate, the retardance is given by
As a principal investigator, I needed to set a long-term goal for my laboratory. Because of my interest in ES cells, because of the successful generation of human ES cells and because I had to use ES cells anyway in the knockout mouse core facility, I decided to list “ES cells” in the title of my lab website. At the time, most researchers focused on differentiating from ES cells into somatic cells. Human ES cells are associated with two major hurdles – ethical issues regarding the use of human embryos and immune rejection after they are transplanted into a human body. The use of human embryos has been an obstacle to the promotion of ES cell research in many countries, including the U.S. and Japan. To overcome these major hurdles, I decided nuclear reprogramming would be the goal of my lab. More precisely, I set my lab’s goal as being to generate ES cell-like pluripotent cells from somatic cells, without using embryos.
The LO filter is generated by cascading various polarizer – retarder – polarizer subsystems, where the retarder is oriented at 45° relative to the parallel polarizers, and where the retardance in each consecutive subsystem doubles that of the previous subsystem. Each polarizer – retarder – polarizer subsystem generates an oscillatory spectrum, such as those we have presented in the previous sections. A subsystem with double retardance provides a spectrum with doubled oscillations. Therefore, cascading various subsystems generates a maximum transmission only at the wavelengths where all subsystems coincide to have maximum transmission. In order to properly generate the filter, it is important that the retarders are made with the same material, to ensure that all retarders show the same type of retardance dispersion.
Figure 1 shows a scheme of the optical system, including a picture in the inset. We use a quartz tungsten halogen lamp from Oriel, model 66882, with a power that can be adjusted from 10 to 250 watts. It provides white light of continuous broadband spectrum that covers the wavelength range from 400 to 1600 nm. The housing includes a fused silica condenser that can be adjusted to provide a collimated output beam with a diameter of 33 mm.
When I joined Tom’s lab, he had a hypothesis that forced expression in the liver of APOBEC1, the ApoB messenger RNA-editing enzyme, would lower plasma cholesterol levels and thus prevent atherosclerosis. To examine this hypothesis, I generated transgenic mice overexpressing Apobec1 in their livers. To our surprise, however, the transgenic mice developed liver tumors. We learned that Apobec1 is a potent protooncogene. Naturally, Tom was disappointed, but I became very interested in the molecular mechanisms of this totally unexpected result. Tom, despite the finding being against his hypothesis, encouraged me to continue studying the APOBEC1-mediated oncogenesis. Thanks to his support, I identified a novel target of Apobec1, Nat1, which was aberrantly edited in the transgenic mouse livers. I decided to generate Nat1-knockout mice to study the gene’s function. Robert Farese at Gladstone and his research associate Heather Myers kindly taught me how to culture mouse embryonic stem (ES) cells and make chimeras.
Beam Expanders-CASTECH INC. -Lens assemblies for changing the laser beam diameter and divergence.
We apply the developed system to different types of retarders such as multiple-order, zero-order and achromatic retarders. We show how their spectral characteristics allow a very simple identification of these different types of retarder designs. In all cases we determine the spectral retardance function, and we also include some interesting configurations that can be obtained by simply placing two retarders.
Sánchez-López, M.M., Vargas, A., Cofré, A., Moreno, I., Campos, J.: Simple spectral technique to identify the ordinary and extraordinary axes of a liquid crystal retarder. Opt. Commun. 349, 105–111 (2015)
Optical linear retarders are very useful components for any optical application requiring control of the state of polarization [1]. High quality retarders are usually fabricated with anisotropic optical materials such as quartz or calcite. Lower cost retarders are fabricated with birefringent polymers, having additionally the advantage of being produced with much larger areas. Tunable retarders can be fabricated with liquid crystal (LC) materials, where the application of a relative low voltage yields a large variation of the effective retardance, due to the tilt of the liquid-crystal director. Liquid crystal retarders (LCR) can be manufactured in the form of a single retarder element, or in the form of one or two-dimensional arrays, as in the liquid-crystal on silicon (LCOS) displays [2]. Other tunable retarders are fabricated with electro-optic materials, such as lithium niobate (LiNbO3). They require higher voltages and have much smaller areas than LC retarders, but can be switched at much faster rates [3]. Therefore, these tunable retarders are becoming very useful in all kind of applications that require programmable control of the intensity, the phase, or the state of polarization of an input light beam, thus becoming key components in advanced optical instruments for optical microscopy, interferometry, polarimetry or optical communications.
In 1996, my wife Chika and our two daughters, Mika and Miki, who were living in San Francisco with me, returned to Japan to enroll Mika in an elementary school in Osaka. About six months after they left, I went back to Japan as I missed them so much. Back in my home country, I eventually got an assistant professor position in the department of pharmacology at Osaka City University Medical School. Tom kindly let me continue the Nat1 work and shipped three chimeric mice I had made to Japan. The then chairman of the department, Hiroshi Iwao, was very supportive and allowed me to work on Nat1, which seemed to have little value in pharmacology. I found that Nat1 is required for early mouse development. More importantly, I found that Nat1-null embryonic stem (ES) cells proliferate normally but cannot properly differentiate. These surprising findings changed the meaning of mouse ES cells for me from a research tool to a research subject. I became intrigued in how ES cells maintain their differentiation ability while rapidly proliferating.
Gladstone also provided me with the opportunity to acquire presentation skills and to learn a key idea for success as a scientist. One day, Robert Mahley, the then president of Gladstone, gathered about 20 postdocs and said that “VW” was a magic word to make us successful scientists. What he meant was that scientists need to have a clear vision and work hard toward it. I found myself not having a clear vision, although I was confident that I was one of the most hard-working postdocs at Gladstone at the time. I have since set my vision as being “to contribute to the development of new cures for patients through basic research.” I still have the “VW” lesson in mind and often quote it to my students in my lab.
Running CiRA with some 250 staff, I have come to spend less time discussing their data with my colleagues and students, and have been absorbed by my duties as the “chief executive officer” of CiRA, including devising strategies to advance both basic and applied research and to obtain sufficient funding. Anxious about the lack of financial resources for the future to allow us to continue hiring research support staffers, I even ran the full Kyoto Marathon in 2012 to raise online donations from the public. It was hard but helped us raise more than 10 million yen. Now I hope that receiving the Nobel Prize in Physiology or Medicine will consolidate long-term support from the government and the general public for iPS cell research nationwide.
Wang, Z.P., Li, Q.B., Tan, Q., Huang, Z.J., Shi, J.H.: Novel method for measurement of retardance of a quarter-wave plate. Opt. Laser Technol. 36, 285–290 (2004)
These results show an interesting limiting factor. Note how the amplitude of the oscillations is reduced in the low part of the spectrum. This is due to the resolution limit of the spectrometer. As the retardance varies so fast in this region, so does the spectral transmission. Therefore, the limited size of the pixel detector cannot detect this rapid oscillation, and zero and one transmission are not properly detected.
In Fig. 5(b), (c) and (d), the spectral retardance was derived by fitting the experimental data to a function ϕ(V,λ) = g(V)ϕ(V = 0,λ), where ϕ(V = 0,λ) is the LCR spectral retardance without applied voltage (result in Fig. 4(d)), and g(V) is a voltage transfer function that can take values between 1 and 0, and which allows describing the spectral retardance modulation with a single value [7]. For every voltage, the value g(V) that best fits the experimental data is retrieved, obtaining values g(V pp = 1 V) = 0.732, g(V pp = 1.5 V) = 0.467 and g(V pp = 1 V) = 0.294 respectively. Note that all cases again show a very good agreement between the experimental data and the numerically fitted curve. The evolution of the spectral retardance with voltage is given in Fig. 5(e). Note that the retardance in Fig. 5(c) (V pp = 2 V) is slightly less than half of the retardance in Fig. 5(a) (V pp = 0). We will use these results in the next section.
We have provided some useful tricks to be applied in the fitting procedure of the experimental data in order to derive an accurate spectral retardance function. For instance, the combination of two retarders made of the same material (thus having exactly the same spectral birefringence dispersion) helps to obtain additional curves by adding or subtracting retardance, as we showed in Fig. 3. Or the combination of a retarder under evaluation with a Fresnel rhomb retarder that adds/subtracts a constant shift of one quarter oscillation, which is useful to achieve an accurate measurement in all the spectral range (in opposition to a single measurement, which shows less accuracy at the maxima and minima of the spectral transmittance curve). Finally, we have confirmed the accuracy of the spectral measurements by demonstrating the realization of a classical birefringent Lyot-Ohmann filter. As a result of the correct calibration of the spectral retardance of the LCRs involved in the filter, the spectral transmittance was predicted with great accuracy.
There are 1250 calories in 1.68 pounds of Beef Inside Skirt Steak (Lean Only, Trimmed to 1/4" Fat). Get full nutrition facts and other common serving sizes ...
Sell business goods or services, the selling of which requires a technical background equivalent to a baccalaureate degree in engineering. Excludes Engineers ...
Departamento de Física y Arquitectura de Computadores, Instituto de Bioingeniería, Universidad Miguel Hernández, 03202, Elche, Spain
Li, J., Wen, C.H., Gauza, S., Lu, R., Wu, S.T.: Refractive indices of liquid crystals for display applications. J. Displ. Technol. 1, 51–61 (2005)
Vargas, A., Sánchez-López, M.M., García-Martínez, P., Arias, J., Moreno, I.: Highly accurate spectral retardance characterization of a liquid crystal retarder including Fabry-Perot interference effects. J. Appl. Phys. 115, 033101 (2014)
These basic engineering studies may consist of consolidating a process package initiated by an external process licensor. Front End Engineering Design (FEED).
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Figure 4(d) shows the retardance that best simultaneously fits the three curves in Fig. 4(a), (b) and (c). Again, a spectral response given by Eq. (5) is assumed for the LCR spectral retardance ϕ LCR(λ). The Cauchy dispersion relation assumed in this equation for the refractive indices has been shown to be a good approximation for liquid-crystal materials [23, 24]. Figures 4(b) shows the theoretical curve together with the experimental data, and the agreement is excellent. Figure 4(a) and (c) show the theoretical curves derived using Eq. (1) for ϕ LCR(λ) + ϕ FR(λ) and ϕ LCR(λ)-ϕ FR(λ) respectively, again with excellent agreement with the experimental data. The simultaneous fit of the three curves in Fig. 4 thus provides a very reliable procedure to accurately determine the LCR retardance function.
RESEARCH AT NAISTAt NAIST, I was expected to establish a knockout mouse core facility. It was a difficult task, but thanks to an excellent technician, Tomoko Ichisaka, and to funding from NAIST, we were able to establish it within a few years. The first gene that we knocked out was Fbxo15, which we identified as a gene specifically expressed in mouse ES cells. One of my first Ph.D. students, Yoshimi Tokuzawa, with the help of Tomoko, successfully targeted the gene. However, we did not see any phenotypes in mice or ES cells lacking Fbxo15. We were disappointed, but this knockout mouse line turned out later to be useful in the generation of induced pluripotent stem cells or iPS cells.
Specifications. Iris diaphragm; Recommended for controlling depth of field in photography; Close the iris diaphram to increase the depth of field ...
Abdulhalim, I.: Dispersion relations for liquid crystals using the anisotropic Lorentz model with geometrical effects. Liq. Cryst. 33, 1027–1041 (2006)
As linear polarizers (P1 and P2) we use two high-quality calcite Glan-Taylor cube polarizers from Edmund Optics, covering a spectral range from 350 to 2200 nm, with a nominal extinction ratio less than 5 × 10-6. This kind of polarizers is required since common commercial polaroid sheets do not act properly as polarizers in the IR range. They have been mounted on rotatable mounts, so the angle of the transmission axis can be rotated continuously. The retarder to be characterized is placed in between the two polarizers. Then, the transmitted light is divided in two beams by means of a B270 Glass Polka Dot beam-splitter from Thorlabs. Again, this kind of beam-splitter is required since it operates in a wide range of wavelengths from 350 nm to 2.0 μm. These two beams are analyzed with two different spectrometers. The beam reflected by the beam-splitter is captured with a STN-F600-UVVIS-SR optical fiber that is connected to a VIS spectrometer from Stellar-Net, STN-BLK-C-SR model, which measures the spectrum in the range from 200 nm to 1080 nm with a resolution of 2 nm. The second beam is directly sent to another spectrometer from Stellar-Net, model STE-RED-WAVE-NIR-512-25, which measures the spectrum from 900 nm to 1700 nm, with a resolution of 3 nm. In this case we do not use a fiber to avoid absorption bands in the IR region. Finally, in order to avoid second-order contribution from the visible light that enters this IR spectrometer, we include a filter in front of the slit entrance, which filters the visible spectrum.
Abuleil, M.J., Abdulhalim, I.: Birefringence measurement using rotating analyzer approach and quadrature cross points. Appl. Opt. 53, 2097–2104 (2014)
Nobel Prize in Physiology or Medicine
SCHOOL DAYSI remember that when I was a child, I found it very exciting to dismantle clocks and radios into small pieces and then try to assemble them again, though most of the time I ended up breaking them. Maybe I just copied what my father was doing. My childhood dream was to become an engineer like him. Science was one of my favorite classes at school. I liked reading a monthly scientific magazine for elementary school children. This magazine came with various kits for children to do experiments. I remember one time I was doing an experiment with an alcohol lamp that came with the magazine. It dropped onto a kotatsu heater table and the quilt over it caught fire. I was severely scolded by my mother.
Emam-Ismail, M.: Spectral variation of the birefringence, group birefringence and retardance of a gypsum plate measured using the interference of polarized light. Opt. Laser Technol. 41, 615–621 (2009)
We have generated a LO filter by using two LCR devices as that calibrated in Fig. 5. The system is therefore composed of a first polarizer, LCR1, a second polarizer, LCR2 and a third polarizer. The three polarizers are oriented at 45° to the vertical direction, while the LC director of the LCR devices is vertically oriented. The advantage of using LCR devices is that the LO filter can be tuned to different wavelengths [29, 30]. And if combined with other types of filters is able to provide narrowband multispectral tunable filters [31].
I was born on September 4, 1962, in Osaka, Japan. My father, Shozaburo, ran a small factory in the city of Higashi-Osaka manufacturing components for sawing machines, which he took over in his early 20s after my grandfather passed away. Higashi-Osaka is well known for its cluster of highly skilled small and midsize manufacturers. Like other owners of small companies in the area, my father was an engineer who designed new products and made them by himself. My mother, Minako, helped him run the business, raising their two children, me and my older sister, Yumiko. Looking back on my childhood, I can see now that my father exerted a great influence on me. He did not force me to do or be anything, but, by showing diligence in his work, he taught me silently how meaningful it is to create something from the drawing board, and how interesting it is to seek for oneself a better way of achieving a goal.
Velásquez, P., Sánchez-López, M.M., Moreno, I., Puerto, D., Mateos, F.: Interference birefringent filters fabricated with low cost commercial polymers. Am. J. Phys. 73, 357–361 (2005)
This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/ Nobel Lectures/The Nobel Prizes. The information is sometimes updated with an addendum submitted by the Laureate.
Most of the works mentioned above use visible (VIS) light. However, there is an increasing interest in extending the spectral range in the near infra-red (NIR) range, for applications such as optical fiber communications, with its transparency window centered at 1550 nm [14], or biomedical imaging, where the therapeutical windows in the ranges of 650–950 nm (first window) or 1100–1350 nm (second window) are conventionally used for tissue imaging, and deeper IR windows seem to have potential great interest [15].
Several works have demonstrated different techniques for the spectral retardance characterization. A usual technique consists in inserting the retarder in between two linear polarizers, which are oriented at ±45° with respect to the retarder neutral axes. The system is illuminated with a light source with broadband spectrum, and the transmission is analyzed with a spectrometer [6–10]. The transmitted spectrum typically shows an oscillatory dependence with wavelength from which the spectral retardance function can be retrieved. Similar spectral methods sequentially rotate the polarizers to achieve more data [11, 12]. In addition, this kind of spectral measurements provide a simple test to identify whether the retarder presents multiple-reflection Fabry-Perot interferences [13].
However, in order to make a more precise spectral retardance fit, we combined the LCR with the QWP Fresnel rhomb. The reason for this combination is related to the fact that measurements show the maximum accuracy around quarter-wave retardance values (i.e., where the normalized transmission is 50 %) [10, 12]. The QWP Fresnel rhomb introduces an additional π/2 retardance that can be added or substracted to the LCR retardance depending on their relative orientation. In Fig. 4(a) the LCR and the Fresnel rhomb are oriented such that their retardances add, and therefore the oscillations are shifted to lower wavelengths. In Fig. 4(b), the LCR is the only retarder in the system. Finally, in Fig. 4(c) the LCR is rotated by 90°, and therefore the retardances subtract. In this case the oscillations shift to higher wavelengths. In both cases the shift introduced by the Fresnel rhomb transforms the maxima and minima in Fig. 4(b) into points at 50 % transmittance, therefore improving the accuracy at these wavelengths. Note that an equivalent technique has been used to measure the retardance of half-wave retarders with monochromatic light [22].
Normalized spectral intensity transmission for the polarizer – LCR – polarizer system with: a LCR1 without applied voltage b LCR2 tuned to have half retardance than LCR1. c Normalized spectral intensity transmission of the Lyot-Ohmann filter made of the two previous systems showing a maximum transmission 565 nm
Normalized spectral intensity transmission T par (λ) for a Multiple-order QWP for 488 nm; b Multiple-order QWP for 514 nm; c Addition of the two QWPs; d Subtraction of the two QWPs. In all cases the continuous lines correspond to the simulation that best fits the experimental data. e Spectral retardance for the four cases derived after fitting the experimental data
In this work we consider a LCR device from ArcOptix [21]. Figure 4 shows the measurement for this retarder. Again, the oscillatory behavior in the normalized intensity as in Fig. 2 is observed. But the number of oscillations is much lower since the LCR is a low-order retarder. Secondary oscillations are observed in the IR range from 1400 to 1600 nm. This is due to a Fabry-Perot interference effect at the LC layer, as studied in Ref. [13]. For simplicity, we ignore here this secondary effect, and we will consider the retarder simpler approximation. A fit of the experimental data to the spectral retardance function in Eq. (5) was performed. The locations of the maxima and minima indicate the wavelengths for which the retardance is an integer multiple of π radians. These points are indicated in Fig. 4(b), being ϕ = 2π for 1030 nm, ϕ = 3π for 710 nm, and ϕ = 4π for 560 nm.
As a final example we consider a liquid crystal retarder (LCR). These are tunable retarders where the retarder layer is made of nematic liquid crystal, showing maximum retardance when the device is off and the liquid crystal director is aligned to the plane of the retarder. When a voltage is applied to the device electrodes, the liquid-crystal director tilts and the effective retardance is reduced.
In order to normalize the experimental spectral data, the intensity of the transmitted light is measured in two ways: one first measurement with parallel polarizers, I par (λ), and a second with crossed polarizers, I cros (λ). The retarder is inserted in between the polarizers with the principal axis rotated 45° to polarizer P1. Then, data are normalized for each wavelength as:
Messaadi, A., Sánchez-López, M., García-Martínez, P. et al. Optical system for measuring the spectral retardance function in an extended range. J. Eur. Opt. Soc.-Rapid Publ. 12, 21 (2016). https://doi.org/10.1186/s41476-016-0023-7
Figure 3(b) displays the corresponding experimental data for the Fresnel rhomb. In this case a perfect flat normalized transmission T par = 0.5 is obtained in the complete spectral range, showing the superior behavior of this retarder in providing a wavelength-independent quarter-wave retardance. Finally, Fig. 3(c) shows the derived spectral retardances ϕ ACRH(λ) and ϕ FR(λ) for the achromatic retarder and the Fresnel rhomb respectively.
The retarder is inserted between two parallel or crossed linear polarizers, with the principal c-axis oriented with a relative angle of 45° with respect the transmission axes of the polarizers. In this situation, the normalized transmission output is given by [4]:
Zhang, Z., You, Z., Chu, D.: Fundamentals of phase-only liquid crystal on silicon (LCOS) devices. Light: Sci Appl 3, e213 (2014)
In summary, we have applied a classical spectral technique for measuring the retardance of linear retarders, but in a very wide spectral range from 450 to 1600 nm. For that purpose, we developed an optical system that uses two spectrometers, one for the VIS range and another for the NIR range. With this system we measured the spectral retardance function of different types of crystal retarders as well as of LCRs. The measured spectral content allows a very simple identification of the type of retarder according to its order (multiple, low or zero-order retarders). Also, the wavelength shifts of the oscillations observed in the spectral transmittance allows a simple identification of situations where the retardance increases or decreases, that can be useful with fixed retarders, and specially with variable LCRs.
I was educated at the Tennoji Junior High School/High School attached to Osaka Kyoiku University and received an excellent education, with many unique friends and teachers. Entering the junior high in 1975, I joined its judo team as my father recommended me. He thought I was too skinny and should become stronger. I devoted myself to judo and continued practicing it for several years until I quit it due to a serious injury in my second year at college. At the high school, there were some teachers who often told students that we should try to become a superman or superwoman, meaning that we should not only study hard but also try to experience many activities such as sports and activities in the student association. Inspired by them, I formed a folk song band with my classmates, called “Karesansui” (‘Dry Garden Style’), and performed at the school’s student festivals. I played the guitar and was a vocalist. I also committed to the school association as a vice president.
We apply a well-known technique for determinig the spectral retardance by measuring the transmission spectra between crossed or parallel polarizers. But we we develop an optical system to perform this measurement in a wide spectral range covering the visible (VIS) and near infrared (NIR) spectrum in the range from 400 to 1600 nm.
Mawet, D., Hanot, C., Leanerts, C., Riaud, P., Defréfre, D., Vandormael, D., Loicq, J., Fleury, K., Plesseria, J.Y., Surdej, J., Habraken, S.: Fresnel rhombs as achromatic phase shifters for infrared nulling interferometry. Opt. Express 15, 12850–12865 (2007)
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The first three terms correspond to a third order Cauchy approximation for the refractive indices in Eq. (2), while the last term provides good results for quartz in the IR region [10]. A numerical search for the constants A, B, C, and D that minimize the difference between simulation and experimental data was performed for the two retarders. This is done by numerically evaluating the mean absolute error (MAE) between the normalized transmission experimental data and the simulated data, and seeking for the values that minimize this difference. This was programmed in Microsoft Excel and was solved with the SOLVER routine, which employs a generalized reduced gradient algorithm (https://support.microsoft.com/en-us/kb/214115).