Jones Matrix Imaging for Transparent and Anisotropic Sample

Transcription

1 ones Matrix Imaging for Transparent and Anisotropic Sample Theor of ones Matrix: The plane wave components of the optical field can be written as: )) ( exp( ), ( 0 x x x kz t i t z )) ( exp( ), ( 0 kz t i t z x i x x e 0 i e 0 x i o i x x e e 0 According to ones matrix formalism, x = xx x + x = x x + x x x xx x ' ' For example the linear polarizer is characterized b the relation: x x x P ' P ' x x x P P 0 0 ' ' 0 Px, 1 1

2 Applications of ones Matrix To understand the light matter interaction To measure the stress and strain in materials In biolog - for diagnosis of diseases In cosmetic industries To understand the propagation of light through several polarizing elements xperimental techniques to determine ones Matrix ones phase microscop (PM) of transparent and anisotropic sample Polarization Holographic Microscop (PHM) 2

3 ones phase microscop (PM) of transparent and anisotropic sample Basic Principle: The ones matrix of sample is described as: xx x x To retrieve complete ones matrix +45 and -45 linearl polarized input beam is given to sample C 1 45 C Y Y Y Y Y Y C xx x x C1 C2 0 0 C C C C Y Y C 0 0 C 1 C 2 2 xx x x xx x x xperimental setup: Ref.- Zhuo Wang, Larr. Millet, Martha U. Gillette, and Gabriel Popescu, Opt.Lett.33, (2008), 1270 Figure - xperimental setup of ones Phase Microscop [3], P 0, P R and P A polarizer, C 1, C 2 collimating lenses, L1, L2 Fourier lens pair, BS beam splitter, CCD charge coupled device Requires Four Steps Not applicable for dnamic object 3

4 Polarization Holographic Microscop (PHM) for ones Matrix Imaging Figure - xperimental setup for Polarization Holographic Microscop Ref.-Youngchan Kim, oonwoo eong, aeduck ang, Mahn Won Kim, and YongKeun Park, Opt.xp.20, (2012),

5 Advantages: Our Proposed Technique Requires two steps In our proposed experimental technique, triangular Sagnac interferometer provides freedom to adjust carrier frequencies according to sampling law. Basic Principle: Y Y x = xx x + x ' x xx x x = x x + ' x For +45 input beam xx x x xobject xwo.. object object wo.. object xx x x 5

6 Our Proposed Technique (Double Shot) Basic Principle: Similarl for +45 input beam xperimental Setup: Y Y xx x xx x 1 1 x SF 22 xx x x x CCD - GX 2750 with specifications A/D 14-bit, pixels and pixel pitch 4.54 μm. Figure - xperimental Setup of ones matrix imaging; BS - Beam splitter, PBS - polarization beam splitter, M1, M2, M3 mirrors, HWP - half wave plate, SF spatial filter, CCD charge couple device, L1, L2, L3, L4,L5 lenses Ref.: N. K. Soni, A. S. Somkuwar and R. K. Singh," ones matrix imaging for transparent and anisotropic sample", Proc. SPI9654, International Conference on Optics and Photonics 2015, (une 15, 2015); doi: / ; 6

7 xperimental Results: 1) ones matrix for complete transmission (a) (b) (c) (d) Figure - Interferogram recorded for (a) +45 linearl polarized beam without sample (b)+45 linearl polarized beam with sample (c) -45 linearl polarized beam without sample (d) )-45 linearl polarized beam with sample 7

8 Fourier Fringe Analsis Technique F.T. x Amplitude Phase I.F.T. Two orthogonal polarization components are simultaneousl retrieved through Fourier Fringe Analsis 8

9 1) ones matrix for complete transmission (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for complete transmission ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 9

10 2) ones matrix for horizontal polarizer (a) (b) Figure - xperimentall recorded hologram for (a) +45 (b)-45 illumination beam (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for horizontal polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 10

11 3) ones matrix for vertical polarizer (a) (b) Figure - xperimentall recorded hologram for (a) +45 (b)-45 illumination beam (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for vertical polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 11

12 4) ones Matrix for quarter wave plate with fast axis aligned at horizontal i (a) Figure - xperimentall recorded interferogram for (a) +45 (b)-45 illumination beam (b) (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for QWP with fast axis aligned at horizontal ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, 12 ;

13 Single Shot ones Microscop Limitations Of double shot ones matrix imaging: xperimental Setup: M1 M2 Not applicable for dnamic objects Highl Sensitive for vibration and atmospheric air fluctuations Advantages of Single Shot ones Microscop: Requires onl one measurement Applicable for dnamic objects also Y 11 Y 21 Y 12 Y 22 M4 Capable to tune spatial frequencies Fourier spectrum M3 No need of special optical elements like grating Figure-Single Shot ones Microscop 13

14 xperimental Results 1.Vertical polarizer Interferogram Amplitude of Fourier spectrum 14

15 1.Vertical polarizer (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for vertical polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 15

16 2.Horizontal Polarizer Interferogram Amplitude of Fourier spectrum 16

17 2.Horizontal Polarizer (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for horizontal polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 17

18 Interferogram Amplitude of Fourier spectrum 18

19 (a) 396 μm 396 μm (b) 396 μm (c) 396 μm (d) (e) 396 μm 396 μm (f) 396 μm (g) 396 μm (h) Figure - ones matrix components for polarizer at 45; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 19

20 Interferogram Amplitude of Fourier spectrum 20

21 (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for polarizer at -45; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 21

22 5.Half wave Interferogram Amplitude of Fourier spectrum 22

23 5.Half wave (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for half wave plate at 0 degree; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 23

24 6.Half wave Interferogram Amplitude of Fourier spectrum 24

25 6.Half wave (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for half wave plate at 90; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 25

26 7.Half wave Interferogram Amplitude of Fourier spectrum 26

27 7.Half wave (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for half wave plate at 45; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 27

28 Interferogram Amplitude of Fourier spectrum 28

29 i (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for vertical polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 29

30 Interferogram Amplitude of Fourier spectrum 30

31 i (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for quarter wave plate at 90; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 31

32 10.PVA Interferogram Amplitude of Fourier spectrum 32

33 10. Polvinl Alcohol (PVA) (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for vertical polarizer ; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 33

34 11.Human Hair Interferogram Amplitude of Fourier spectrum 34

35 11.Human Hair (a) (b) (c) (d) (e) (f) (g) (h) Figure - ones matrix components for human hair; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 35

36 12.Blood Sample Interferogram Amplitude of Fourier spectrum 36

37 12. ones matrix components for Blood Sample 99 μm 99 μm 99 μm 99 μm 99 μm 99 μm 99 μm 99 μm Figure - ones matrix components for blood sample; (a), (c), (e), (g) amplitude distributions of xx, x, x, ; (b), (d), (f), (h) phase distributions of xx, x, x, ; 37