Dynamic beam shaping with programmable diffractive optics

Transcription

1 Dynamic beam shaping with programmable diffractive optics Bosanta R. Boruah Dept. of Physics, GU Page 1

2 Outline of the talk Introduction Holography Programmable diffractive optics Laser scanning confocal microscopy (LSCM) Aberration correction in LSCM Programmable reference phase stepping interferometry Conclusion Page 2

3 The principle of holography Reference plane wave Resulting interference pattern Crest Object beam Trough Page 3

4 The principle of holography transmittance=1 transmittance=0 f diffracted beams f Incident coherent beam (reference) hologram lens diffraction pattern Reconstructed object beam (Fourier plane of the hologram) Conjugate beam Page 4

5 Phase only hologram phase delay=π phase delay=0 f f Phase hologram lens diffraction pattern Page 5

6 Binary phase only hologram phase delay=π phase delay=0 f f Binary phase hologram lens diffraction pattern Page 6

7 Liquid crystal spatial light modulator (LCSLM) SLM panel ~10 µm glass plates alignment layers 4 4 pixels (can go upto 2Kx1K) transparent electrodes liquid crystal V Page 7

8 Nematic LC pixel E max glass plate mirror glass plate mirror NLC molecules alignment layer Analog phase modulation Response time of the molecules :~ms Frame rate :60Hz Light efficiency :50% alignment layer Page 8 (a) (b)

9 Ferroelectric LC pixel E + E - Director axis : (view along z) on off d z PBS p s /p FLC cell Binary amplitude or phase (0 or π) modulation Response time of the molecules :~10µs Frame rate :1440 Hz Light efficiency (amplitude modulation) : 70% Page 9

10 Binary Hologram Design for phase and amplitude modulation Complex amplitude over the pupil plane (x,y) = a(x,y) e iφ(x,y) =u(x,y)+iv(x,y) a(x,y) = normalised amplitude= φ(x,y) = desired phase+overall tilt= S(mx, my)=phase delay at (mx, my) 2 2 u + v tan 1 u v [u(x,y),v(x,y)] Binary phase mapping (mx, my) (m=magnification factor) F (ferroelectric) LCSLM plane Pupil plane Page 10

11 Binary phase mapping algorithm Complex amplitude desired = [u(x,y), v(x,y)] v Binary phase map φ(x, y) S(mx,my) π 0 u Desired amplitude profile In the pupil plane Off-axis hologram on FLCSLM amplitude =1 amplitude =0 Page 11

12 Binary phase mapping algorithm Complex amplitude over the pupil plane (x,y) = e iφ(x,y) such that a(x,y)=1 S(mx, my) =0 if cos(φ(x,y))>0 =π if cos(φ(x,y))<0 Desired amplitude profile In the pupil plane Off-axis hologram on FLCSLM Phase delay QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. Page 12

13 Generation of arbitrary complex amplitude profile FLCSLM Laser beam Iris diaphragm Hologram Desired complex amplitude in the pupil plane Page 13

14 Wide field microscope Reflected light image Detection lens object Diffraction limited illumination volume Point source Beam splitter Illumination Lens (L1) Collimated beam of wavelength λ is focused by L1 to a diffraction limited volume The illumination volume depends on λ, focal length and diameter of the illumination lens A point object is imaged into a diffraction limited volume in the image space Resulting image has poor axial resolution Page 14

15 Optical sectioning in a confocal microscope detector pin hole detector pin hole detection lens Sample plane Focal point Sample plane Laser beam Laser beam Illumination lens Confocal arrangement of focal point and pinhole blocks light from out of focus planes or points away from the optic axis The detector receives light mostly from the focal point Image, free of out of focus blur, of a point object located at the focal point Page 15

16 Optical sectioning in a confocal microscope detector PC BS scan Wide field image Confocal image (Source : Either the sample holding stage or the illumination spot is scanned Scanning is controlled by a PC For each object point at the illumination spot, the detector signal is stored in the PC Results in an optically sectioned image (image corresponds to a sharply defined object plane, devoid of out of focus blur) of the sample Much better axial and marginally better lateral resolutions than a conventional (wide field) microscope Page 16

17 Effects of aberrations Entrance pupil Point spread function (PSF) W(x, y) Lens Unaberrated wavefront Aberrated wavefront PSF for an unaberrated Beam, Airy disc Zernike Modes PSFs Presence of aberrations in the illumination beam effects the performance of the confocal microscope Need for aberration compensation Page 17

18 Modal wavefront sensor 50/50 beam splitter Positive bias plate Incident aberrated beam I 1 (0) I 2 (0) I 1 (0) Detector pin hole mirror I 2 (0) Sensor signal=i 2 (0)-I 1 (0) Negative bias plate Positive and the negative bias plates adds and subtracts a certain of a zernike mode aberration LCSLM assembly can be used to detect and correct aberrations in terms of various zernike modes Page 18

19 Modal wavefront sensor (results) biased orders (Z 4 ) before correction after correction biased orders (Z 6 ) PSF Peak intensity improves by a factor of three Page 19

20 Aberration sensitivity and correction using a helical beam Helical phase profile across the pupil 2π 0 Sensor circle Helical type beams are highly sensitive to azimuthally dependent aberrations! Low NA aberrated PSFs to 0.8 Strehl ratio in normal beam (normally considered well corrected) d7 d6 d8 d9 d5 d4 d10 d11 d3 d12 d2 d1 Normal beam Helical beam Z 5 Z 6 Z 7 Z 8 Z 9 Z 10 Z 11 Z 14 Z 15 Page 20

21 (a) Low NA aberration correction demonstration PSF (helical beam) PSF (normal beam) Drop due to slide reflectivity (b) (a) (b) Iteration (a) With aberrated test slide (b) With initial offset aberration (1.4 radian RMS) Page 21

22 Phase stepping interferometry Test Mirror L 1 L 2 BS Reference motion Laser L 3 Reference mirror with PZT L 4 CCD Reference mirror stepped n times with a step size λ/(2n) CCD records n interference patterns, where n>2 Intensity at a CCD pixel as a function of step index is a sine wave Surface profile of the test mirror manifests as phase delay Not effected by the inhomogenity in the beam intensity profile No fringe centering required Does not depend on the number of fringes Page 22

23 Programmable reference PSI Test Mirror L 1 L 2 λ/2 λ/4 control unit Laser FLCSLM BS polariser L 3 L 4 iris diaphragm CCD Accurate and repeatable phase stepping Reference wavefront can be programmed to match the test surface Accuracy in phase measurements are effected by aliasing Page 23

24 Aliasing Profile to be sampled After sampling φ (x) N*2π phase S(x) In disguise as low frequency square wave, if no of pixels for N square waves <2N N square waves Page 24

25 Random binarisation to remove aliased orders v S(x, y)=[cos(φ(x, y)<rand(x,y)] π QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. u Fourier plane of a binarised hologram Fourier plane of a randomly Binarised hologram QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture Page 25

26 Phase profile using 24 bit random binarization Blue red yellow green blue Phase: 0 2π Normal binarization 24 bit random binarization Page 26

27 Conclusion Generation of arbitrary wavefront using an LCSLM accurate, fast and with excellent repeatability LCSLM can be used both for detection and correction of optical aberrations Can used in a phase stepping interferometer to generate the reference beam Poor light efficiency May effect its applicability to other areas Page 27

28 Thank You Page 28