Alfredo Dubra's PhD thesis - Imperial College London

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2. Lateral shearing interferometer design NPBS 50-50 PBS 1 1 2 0.5 x ARC 0.5 1 2 0.5 x ARC 2 0.5 x TR 0.5 x ARC 0.5 x TR p-polarisation s-polarisation ER x ARC TR ARC TR 0.5 x ARC 0.5 ER Figure 2.4: Relative intensities of reflections from a 50-50 non- polarising beam splitter (NPBS) and a polarising beam splitter (PBS). ARC is the intensity reflection coefficient for the antireflection coating, TR is the reflection coefficient of the tear film, and ER is related to the extinction ratio of the PBS and the polarisation of the incident beam. The laser tube was rotated (and thus the polarization) to maximize the intensity reflected from the PBS towards the eye (s-polarisation). Then, the quarter waveplate was oriented with its axis at 45 o with respect to the s-polarisation, changing the polarisation state of the light transmitted towards the eye to circular, so that the light reflected at the front surface of the tear is fully transmitted through the PBS. As the reflection on the tear surface occurs at normal incidence, the polarization state is not altered except for the change in rotation direction. The minimization of undesired reflections from the beam splitter surfaces is a crucial point in the experimental setup. The intensity of the light reflected from the tear film is about 2 % of the incident light (assuming a tear mean refractive index of 1.337 [81]. With reference to figure 2.4 we can see that if we used a non-polarising beam splitter (NPBS) to combine the illumination and the imaging branches, the relative intensity of the undesired reflections on the NPBS surfaces would be approximately 2×0.5 2 ×ARC where ARC is the intensity reflection coefficient of the anti-reflection coating on the surfaces, which in the best case scenario (laser-line matched) is 0.001. The ratio of the intensities reflected from the eye to the undesired reflections from the NPBS is about 20, which is very poor. If on the other hand we use the combination of a PBS and a quarter waveplate the intensity of the reflections is a bit more complicated to calculate because it depends on both the extinction ratio of the beam-splitting surface and the polarisation of the incident beam, which in figure 2.4 we have represented as 33
2. Lateral shearing interferometer design ER. The experimentally measured value for the ratio of the light reflected from the tear to that reflected from the PBS is about 2400 that represents an improvement of two orders of magnitude in intensity and one in SNR. This ratio of intensities is a good value from the point of view of the detection, because with the camera that we used the contrast of the undesired interference pattern that would result from the light reflected from the eye and the undesired reflections from the PBS, is comparable (a factor of 2 larger) to the readout noise of the camera. Ideally one would make the contrast between the beam of interest and the undesired reflections equal to or smaller than the noise of the camera to record the interferogram. 2.6.4 Focusing lens The final part of the illumination branch of the experimental setup to consider is the positive lens that makes the beam directed towards the eye converging, focusing at the center of curvature of the cornea. The two main issues to consider here are the eye clearance for comfort and the size of the illuminated area. We considered that the minimum clearance between the closest surface of the lens to the cornea should be no less than 15 mm; that is the accepted distance for spectacles. If we bear in mind that the curvature of the wavefront incident on the tear film should match the curvature of the cornea and the beam before the lens is collimated, then we have a condition to be met by the focal length f of the lens, f > 15 mm + R tc (2.17) where R tc = 8 mm is the radius of a typical cornea, and therefore, f > 23 mm. The diameter of the illuminated area D illum for a typical cornea is ( ) D D illum = 2R tc arctan (2.18) 2f where D is the minimum of the lens and incoming beam diameters, and f is the focal length of the lens. This tell us that D illum depends on the F-number of the lens, assuming the diameter of the incident beam is adjusted accordingly. In the end we compromised between illuminating the largest possible area over the pupil and relatively small optics (17 mm clear diameter) in the rest of the experimental setup to keep costs down, choosing to look at the focal length range 30 − 40 mm. Given the low F-number, a doublet is preferable to a singlet to keep aberrations low, although 34
Page 1 and 2: A Shearing Interferometer for the E
Page 3 and 4: Acknowledgements Pursuing the PhD d
Page 5 and 6: Contents Contents 4 List of Figures
Page 7 and 8: CONTENTS 5.1 Prydal type experiment
Page 9 and 10: List of Figures 1.1 Young’s exper
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Page 13 and 14: Chapter 1 Introduction Assessing an
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Page 17 and 18: 1. Introduction was then modified a
Page 19 and 20: 1. Introduction been achieved by us
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Page 25 and 26: Chapter 2 Lateral shearing interfer
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5. Preliminary experiments bb_focus
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5. Preliminary experiments the corr
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6. Tear topography dynamics experim
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Chapter 7 Summary and discussion Th
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7. Summary and discussion The value
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7. Summary and discussion ao2_radia
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A. Preliminary study of feasibility
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B. Laser safety calculations B.1 MP
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Bibliography [1] T. Young. The Bake
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BIBLIOGRAPHY [22] P. Artal, S. Marc
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BIBLIOGRAPHY [44] Austin Roorda and
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BIBLIOGRAPHY [67] W.N. Charman and
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BIBLIOGRAPHY [89] J.P. Craig, P.A.
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BIBLIOGRAPHY [115] Frangois C. Delo
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Alfredo Dubra's PhD thesis - Imperial College London

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